This book provides an introduction to applied statistical mechanics by considering physically realistic models. It provides a simple and accessible introduction to theories of thermal fluctuations and diffusion, and goes on to apply them in a variety of physical contexts. The first part of the book is devoted to processes in thermal equilibrium, and considers linear systems. Ideas central to the subject, such as the fluctuation dissipation theorem, Fokker-Planck equations and the Kramers-Kroenig relations are introduced during the course of (...) the exposition. The scope is then expanded to include non-equilibrium systems and also illustrates simple nonlinear systems. This book will be of interest to final year undergraduate and graduate students studying statistical mechanics, plasma physics, basic electronics, solid state physics and anyone who wants an accessible introduction to the subject. (shrink)

Fluctuation phenomena are the ''tip of the iceberg'' revealing the existence, behind even the most quiescent appearing macroscopic states, of an underlying world of agitated, ever-changing microscopic processes. While the presence of these fluctuations can be ignored in some cases, e.g. if one is satisfied with purely thermostatic description of systems in equilibrium, they are central to the understanding of other phenomena, e.g. the nucleation of a new phase following the quenching of a system into the co-existence region. This (...) volume, originally published several years ago, has stood the test of time well, as interest in fluctuation phenomena continues to grow. It contains a collection of review articles, some of them updated, written by experts in the field, on the subject of fluctuation phenomena. Some of the articles are of a very general nature discussing the modern mathematical formulation of the problems involved, while other articles deal with specific topics such as kinetics of phase transitions and conductivity in solids. The juxtaposition of the variety of physical situations in which fluctuation phenomena play an important role is novel and should give the reader a comprehensive and deeper insight into this fascinating subject. (shrink)

Fluctuating asymmetry (FA) is small deviations from perfect symmetry in normally bilaterally symmetrical traits. We examined the relationship between FA of five body traits (ear height, length of three digits, and ankle circumference) and self-reported scores of physical and verbal aggression in a sample of 90 boys aged 10 to 15 years. The relationships between FA and scores of aggression (particularly physical aggression) were found to be negative; in other words, the most symmetrical boys showed highest aggression. One trait (ankle (...) circumference) showed the characteristics of “ideal” FA—parametric mean of zero and a normal distribution. Mean asymmetries calculated from six repeated measures of ankle FA in 30 subjects taken over a period of five months showed strong negative associations with scores of physical aggression which were independent of age, height, and weight.It is argued that soft tissue “cyclical” FA (as opposed to “fixed” bony FA) is dependent on the secretion of hormones: for example, cortisol. Causal associations between behavioral traits such as aggresion and hormones will lead to similar correlations between FA and behavior. (shrink)

This volume contains the invited lectures and a selection of the contributed papers and posters of the workshop on "Fluctuations and Sensitivity in Nonequil ibrium Systems", held at the Joe C. Thompson Conference Center, Un i vers ity of Texas at Austin, March 12-16, 1984. The workshop dealt with stochastic phenomena and sensi­ tivity in nonequilibrium systems from a macroscopic point of view. Durin9 the last few years it has been realized that the role of fluctuations is far (...) less trivial in systems far from equilibrium than in systems under thermodynamic equilibrium condi­ tions. It was found that random fluctuations often are a determining factor for the state adopted by macroscopic systems and cannot be regarded as secondary effects of minor importance. Further, nonequilibrium systems are also very sensitive to small systematic changes in their environment. The main aims of the workshop were: i) to provide scientists with an occasion to acquaint themselves with the state of the art in fluctuation theory and sensitivity analysis; ii) to provide a forum for the presentation of recent advances in theory and experiment; iii) to bring toge­ ther theoreticians and experimentalists in order to delineate the major open problems and to formulate strategies to tackle these problems. The organizing committee of the workshop consisted of W. Horsthemke, O. K. Konde­ pudi, G. Dewel, G. Nicolis, I. Prigogine and L. Reichl. (shrink)

This volume contains invited and contributed papers delivered at a symposium on the occasion of Professor Glauber's 60th birthday. The papers, many of which are authored by world leaders in their fields, contain recent research work in quantum optics, statistical mechanics and high energy physics related to the pioneering work of Professor Roy Glauber; most contain original research material that is previously unpublished. The concepts of coherence, cooperativity and fluctuations in systems with many degrees of freedom are a (...) common base for all of Professor Glauber's research initiatives and, in fact, for much of contemporary physics. His role in shaping these cconcepts is reflected and honoured in the papers contained in this book. (shrink)

We investigate several fluctuation effects in high-energy hadronic and nuclear collisions through the analysis of different observables. To introduce fluctuations in the initial stage of collisions, we use the interacting gluon model (IGM) modified by the inclusion of the impact parameter. The inelasticity and leading-particle distributions follow directly from this model. The fluctuation effects on rapidity distributions are then studied using Landau's hydrodynamic model in one dimension. To investigage further the effects of the multiplicity fluctuation, we use the longitudinal (...) phase-space model, with the multiplicity distribution calculated within the hydrodynamic model, and the initial conditions given by the IGM. Forward-backward correlation is obtained in this way. (shrink)

Proceedings of SPIE present the original research papers presented at SPIE conferences and other high-quality conferences in the broad-ranging fields of optics and photonics. These books provide prompt access to the latest innovations in research and technology in their respective fields. Proceedings of SPIE are among the most cited references in patent literature.

The traditional formalism of quantum mechanics is mainly used to describe ensembles of identical systems (with a density-operator formalism) or single isolated systems, but is not capable of describing single open quantum objects with many degrees of freedom showing pure-state stochastic dynamical behaviour. In particular, stochastic 'line-migration' as in single-molecule spectroscopy of defect molecules in a molecular matrix is not adequately described. Starting with the Bohr scenario of stochastic quantum jumps (between strict energy eigenstates), we try to incorporate more general (...) pure-state stochastic dynamical behaviour into the quantum mechanical formalism.Probability distributions of (approximately) pure states, arising through the stochastic pure-state dynamics for long times, give rise to appropriate decompositions of thermal density operators. These decompositions of density operators into pure states mediate between quantum mechanics for ensembles of molecules and quantum theory for single molecules (or single dressed quantum objects). We suggest that such decompositions should be consistent with infinite limits (e.g. the Born-Oppenheimer limit for infinite nuclear masses) in the sense that quantum fluctuations (around classical behaviour in the infinite limit) die out asymptotically. (shrink)

I now understand why the invitation to contribute an article on “chaos theory” invoked both my excitement and reticience. Let me first explain my excitement in terms of intriguing developments generated by the Cosmic Background Explorer satellite. Since COBE strengthened an “inflationary” Big Bang Theory wherein the structure of the universe was induced by random statistical fluctuations, there are implications inter alia of thermodynamics for chaotic fluctuations in both the structure and biological systems formed from it. I shall (...) then explain my reticence concerning a chaosladen cosmology. Though it seems to call for an epistemological revision of deterministic scientific truth, the cosmology is as likely as one influenced by quantum mechanics to lead to either a pseudo-scientific connection of indeterminism to freedom and purpose or their dogmatic exclusion as possible “realities” by the natural and social sciences. What I will be concerned about are the conflation of physics with metaphysics and the need to metaphysically articulate the continuity between a primordial quantum fluctuation, biological “possibilities,” and human freedom. (shrink)

The distribution function associated with a classical gas at equilibrium is considered. We prove that apart from a factorisable multiplier, the distribution function is fully determined by the correlations among local momenta fluctuations. Using this result we discuss the conditions which enable idealised local observers, who are immersed in the gas and form a part of it, to determine the distribution 'from within'. This analysis sheds light on two views on thermodynamic equilibrium, the 'ergodic' and the 'thermodynamic limit' schools, (...) and the relations between them. It also provides an outline for a new definition of equilibrium that is weaker than full ergodicity. Finally, we briefly discuss the possibility that the distribution can be determined by external observers. (shrink)

A comparison between the standard adiabatic piston dynamics and that of a perfectly conducting (diathermal) piston helps to clarify their different behaviors and, in particular, the anomalously large random displacement of the adiabatic piston as compared to the diathermal one. It is shown to be associated with a situation where the presence of a single massive “particle” (the piston), acting as an internal constraint in a many-particle system, plays a somewhat unexpected relevant role. A significant physical insight accounting for the (...) above difference is gained by means of a simple analysis of the phase space available to our system. (shrink)

We propose a stochastic modification of the Schrödinger–Newton equation which takes into account the effect of extrinsic spacetime fluctuations. We use this equation to demonstrate gravitationally induced decoherence of two gaussian wave-packets, and obtain a decoherence criterion similar to those obtained in the earlier literature in the context of effects of gravity on the Schrödinger equation.

The idea that the mass m of an elementary particle is explained in the semi-classical approximation by quantum-mechanical zero-point vacuum fluctuations has been applied previously to spin-1/2 fermions to yield a real and positive constant value for m, expressed through the spinorial connection Γ i in the curved-space Dirac equation for the wave function ψ due to Fock. This conjecture is extended here to bosonic particles of spin 0 and spin 1, starting from the basic assumption that all fundamental (...) fields must be conformally invariant. As a result, in curved space-time there is an effective scalar mass-squared term $m_{0}^{2}=-R/6=2\varLambda_{\mathrm{b}}/3$ , where R is the Ricci scalar and Λ b is the cosmological constant, corresponding to the bosonic zero-point energy-density, which is positive, implying a real and positive constant value for m 0, through the positive-energy theorem. The Maxwell Lagrangian density $\mathcal{L} =- \sqrt{-g}F_{ij}F^{ij}/4$ for the Abelian vector field F ij ≡A j,i −A i,j is conformally invariant without modification, however, and the equation of motion for the four-vector potential A i contains no mass-like term in curved space. Therefore, according to our hypothesis, the free photon field A i must be massless, in agreement with both terrestrial experiment and the notion of gauge invariance. (shrink)

Fast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically evolving systems one can still define a conserved quantum energy. For the fast variables, the energy levels are far separated, such that one may assume these variables to stay in their ground state. This forces them to be entangled, so that, consequently, the slow variables are entangled as well. The fast variables could be the vacuum (...) fluctuations caused by unknown super heavy particles. The emerging quantum effects in the light particles are expressed by a Hamiltonian that can have almost any form. The entire system is ontological, and yet allows one to generate interference effects in computer models. This seemed to lead to an inexplicable paradox, which is now resolved: exactly what happens in our models if we run a quantum interference experiment in a classical computer is explained. The restriction that very fast variables stay predominantly in their ground state appears to be due to smearing of the physical states in the time direction, preventing their direct detection. Discussions are added of the emergence of quantum mechanics, and the ontology of an EPR/Bell Gedanken experiment. (shrink)

Remembering Fermi MORREL H. COHEN Department of Physics and Astronomy, Rutgers University Frelinghuysen Road. Piscataway, NJ 08854-8019 USA and Department ...

My life as a quantum physicist / M. Nakahara -- A review on operator quantum error correction - Dedicated to Professor Mikio Nakahara on the occasion of his 60th birthday / C.-K. Li, Y.-T. Poon and N.-S. Sze -- Implementing measurement operators in linear optical and solid-state qubits / Y. Ota, S. Ashhab and F. Nori -- Fast and accurate simulation of quantum computing by multi-precision MPS: Recent development / A. Saitoh -- Entanglement properties of a quantum lattice-gas model on (...) square and triangular ladders / S. Tanaka, R. Tamura and H. Katsura -- On signal amplification from weak-value amplification / Y. Shikano -- Topological protection of quantum information / K. Fujii -- Quantum annealing with antiferromagnetic fluctuations for mean-field models / Y. Seki and H. Nishimori -- A method to change phase transition nature - Toward annealing methods / R. Tamura and S. Tanaka -- Computational analysis of the first stage of the photosynthetic system, the light-dependent reaction, by quantum chemical simulation method / M. Tada-Umezaki -- Two-qubit gate operation on selected nearest neighboring qubits in a neutral atom quantum computer / E. Hosseini Lapasar... [et al.] -- A simple operator quantum error correction scheme avoiding fully correlated errors / C. Bagnasco, Y. Kondo and M. Nakahara -- Black hole predictability, classical and quantum / A. Ishibashi -- Classical field simulation of finite-temperature Bose gases / T. Sato -- Atomic quantum simulations of lattice gauge theory: Effect of gauge symmetry breaking / K. Kasamatsu, I. Ichinose and T. Matsui -- Recursive construction of noiseless subsystem for qudits / U. Gungordu... [et al.] -- Composite quantum gates for precise quantum control / M. Bando... [et al.] -- New formulation of statistical mechanics using thermal pure quantum states / S. Sugiura and A. Shimizu -- Thermodynamics in unitary time evolution / T. N. Ikeda -- Second law of thermodynamics with QC-mutual information / T. Sagawa. (shrink)

The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its dissipative behavior. This can be illuminated in particular by an example of Brownian motion in an ohmic environment where the dissipative effect can be accounted for by the first-order time derivative of the position. Here we explore the dynamics of the Brownian particle coupled to a supraohmic environment by (...) considering the motion of a charged particle interacting with the electromagnetic fluctuations at finite temperature. We also derive particle’s equation of motion, the Langevin equation, by minimizing the corresponding stochastic effective action, which is obtained with the method of Feynman-Vernon influence functional. The fluctuation-dissipation theorem is established from first principles. The backreaction on the charge is known in terms of electromagnetic self-force given by a third-order time derivative of the position, leading to the supraohmic dynamics. This self-force can be argued to be insignificant throughout the evolution when the charge barely moves. The stochastic force arising from the supraohmic environment is found to have both positive and negative correlations, and it drives the charge into a fluctuating motion. Although positive force correlations give rise to the growth of the velocity dispersion initially, its growth slows down when correlation turns negative, and finally halts, thus leading to the saturation of the velocity dispersion. The saturation mechanism in a supraohmic environment is found to be distinctly different from that in an ohmic environment. The comparison is discussed. (shrink)

We present a framework for analyzing black hole backreaction from the point of view of quantum open systems using influence functional formalism. We focus on the model of a black hole described by a radially perturbed quasi-static metric and Hawking radiation by a conformally coupled massless quantum scalar field. It is shown that the closed-time-path (CTP) effective action yields a non-local dissipation term as well as a stochastic noise term in the equation of motion, the Einstein–Langevin equation. Once the thermal (...) Green's function in a Schwarzschild background becomes available to the required accuracy, the strategy described here can be applied to obtain concrete results on backreaction. We also present an alternative derivation of the CTP effective action in terms of the Bogolyubov coefficients, thus making a connection with the interpretation of the noise term as measuring the difference in particle production in alternative histories. (shrink)

This paper investigates the behavior of conformal fluctuations of space-time geometry that are admissible under the quantized version of Einstein's general relativity. The approach to quantum gravity is via path integrals. It is shown that considerable simplification results when only the conformal degrees of freedom are considered under this scheme, so much so that it is possible to write down a formal kernel in the most general case where the space-time contains arbitrary distributions of particles with no other interaction (...) except gravity. The behavior of this kernel near the classical space-time singularity then shows that quantum fluctuations inevitably diverge near the singularity. It is shown further that the root cause of this divergence lies in the fact that the Green's function for the conformally invariant scalar wave equation diverges at the singularity. The limitations on the validity of classical general relativity near the space-time singularity are discussed and it is argued that the notion of singularity itself needs to be radically modified once the quantum effects are taken into account. (shrink)

We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no dynamical quantum fluctuations. Such fluctuations require either an evolving microstate, or time-dependent histories of out-of-equilibrium recording devices, which we argue are absent in stationary states. For a massive scalar field in a fixed de Sitter background, the cosmic no-hair theorem implies that the state of the patch approaches the vacuum, where there are no fluctuations. We argue that (...) an analogous conclusion holds whenever a patch of de Sitter is embedded in a larger theory with an infinite-dimensional Hilbert space, including semiclassical quantum gravity with false vacua or complementarity in theories with at least one Minkowski vacuum. This reasoning provides an escape from the Boltzmann brain problem in such theories. It also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere while slow-roll inflation occurs, suggesting that eternal inflation is much less common than often supposed. On the other hand, if a de Sitter patch is a closed system with a finite-dimensional Hilbert space, there will be Poincaré recurrences and dynamical Boltzmann fluctuations into lower-entropy states. Our analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation, since reheating naturally generates a high-entropy environment and leads to decoherence, nor does it affect the existence of non-dynamical vacuum fluctuations such as those that give rise to the Casimir effect. (shrink)

There are two types of fluctuations in the quantum vacuum: type 1 vacuum fluctuations are on shell and can interact with matter in specific, limited ways that have observable consequences; type 2 vacuum fluctuations are off shell and cannot interact with matter. A photon will polarize a type 1, bound, charged lepton–antilepton vacuum fluctuation in much the same manner that it would polarize a dielectric, suggesting the method used here for calculating the permittivity $$\epsilon _{0}$$ϵ0 of the (...) vacuum. In a model that retains only leading terms, $$\epsilon _{0} \cong ^{2}= 9.10\times 10^{-12}$$ϵ0≅2=9.10×10-12 C/. The calculated value for $$\epsilon _{0}$$ϵ0 is 2.7% more than the accepted value. The permittivity of the vacuum, in turn, determines the speed c of light in the vacuum. Since the vacuum is at rest with respect to every inertial frame of reference, c is the same in every inertial reference frame. (shrink)

We discuss the intimate connection between the chaotic dynamics of a classical field theory and the instability of the one-loop effective action of the associated quantum field theory. Using the example of massless scalar electrodynamics, we show how the radiatively induced spontaneous symmetry breaking stabilizes the vacuum state against chaos, and we speculate that monopole condensation can have the same effect in non-Abelian gauge theories.

It is proposed to consider present-day physics as dealing with a special situation, the situation in which the phenomena of life and consciousness play no role. It is pointed out that physical theory has often dealt, in the past, with similarly special situations. Planetary theory neglects all but gravitational forces, macroscopic physics neglects fluctuations due to the atomic structure of matter, nuclear physics disregards weak and gravitational interactions. In some of these cases, physicists were well aware (...) of dealing with special situations, or limiting cases as they are called in the article; in other cases, they were not. It is pointed out that, even if it were true that present-day physics accurately describes the motion of the physical constituents of living bodies, it would not give the whole story. Arguments are adduced, however, to show that the laws of physics, applicable for inanimate matter, will have to be modified when dealing with the more general situation in which life and consciousness play significant roles. (shrink)

Dr. Vukov analyzing patients with disorders of consciousness, proposed that medical well-regarded policy recommendations cannot be justified by looking solely to patients’ actual levels of consciousness (minimally conscious state – MCS versus vegetative state – VS), but that they can be justified by looking to patients’ potential for consciousness. One objective way to estimate this potential (actual physical possibility) is to consider a neurophysiologically informed strategy. Ideally such strategy would utilize objective brain activity markers of consciousness/unconsciousness. The Operational Architectonics (OA) (...) theory of brain-mind functioning is an example of such a strategy. Besides being mathematically simple, neurophysiologically accurate, and compatible with the cognitive/phenomenal perspectives on consciousness, application of OA strategy to quantitative EEG analysis of patients in VS and MCS revealed that the absence of consciousness in VS is paralleled by impairment of overall EEG operational architecture. Specifically, neuronal assemblies become smaller, their life span shortened, and they became highly unstable and functionally disconnected (desynchronized). At the same time, fluctuating (minimal) awareness in patients in MCS was paralleled by partial restoration of EEG operational architecture (increased size, life span, and stability of neuronal assemblies, together with an increased number and strength of functional connections among them), approaching the level found in healthy fully conscious participants. Moreover OA strategy to EEG analysis allowed predicting the emergence of consciousness in VS patients after six years following the brain trauma. Therefore, the OA methodology could reliably predict which patients may regain consciousness, and thus determine which patients may have the potential for consciousness. (shrink)

We review some of the progress made in the past 27 years in understanding the group theoretic and path integral aspects of the hydrogen atom. The group theoretic development was triggered by A. O. Barut who suggested to me the search for a dynamical group larger than SO(4). In this way he became indirectly responsible also for important recent path integral developments.

The symplectic quantization scheme proposed for matter scalar fields in the companion paper (Gradenigo and Livi, arXiv:2101.02125, 2021) is generalized here to the case of space–time quantum fluctuations. That is, we present a new formalism to frame the quantum gravity problem. Inspired by the stochastic quantization approach to gravity, symplectic quantization considers an explicit dependence of the metric tensor gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} on an additional time variable, named intrinsic time at (...) variance with the coordinate time of relativity, from which it is different. The physical meaning of intrinsic time, which is truly a parameter and not a coordinate, is to label the sequence of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} quantum fluctuations at a given point of the four-dimensional space–time continuum. For this reason symplectic quantization necessarily incorporates a new degree of freedom, the derivative g˙μν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{g}}_{\mu \nu }$$\end{document} of the metric field with respect to intrinsic time, corresponding to the conjugated momentum πμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _{\mu \nu }$$\end{document}. Our proposal is to describe the quantum fluctuations of gravity by means of a symplectic dynamics generated by a generalized action functional A[gμν,πμν]=K[gμν,πμν]-S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}[g_{\mu \nu },\pi _{\mu \nu }] = {\mathcal {K}}[g_{\mu \nu },\pi _{\mu \nu }] - S[g_{\mu \nu }]$$\end{document}, playing formally the role of a Hamilton function, where S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S[g_{\mu \nu }]$$\end{document} is the standard Einstein–Hilbert action while K[gμν,πμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {K}}[g_{\mu \nu },\pi _{\mu \nu }]$$\end{document} is a new term including the kinetic degrees of freedom of the field. Such an action allows us to define an ensemble for the quantum fluctuations of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} analogous to the microcanonical one in statistical mechanics, with the only difference that in the present case one has conservation of the generalized action A[gμν,πμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}[g_{\mu \nu },\pi _{\mu \nu }]$$\end{document} and not of energy. Since the Einstein–Hilbert action S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S[g_{\mu \nu }]$$\end{document} plays the role of a potential term in the new pseudo-Hamiltonian formalism, it can fluctuate along the symplectic action-preserving dynamics. These fluctuations are the quantum fluctuations of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document}. Finally, we show how the standard path-integral approach to gravity can be obtained as an approximation of the symplectic quantization approach. By doing so we explain how the integration over the conjugated momentum field πμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _{\mu \nu }$$\end{document} gives rise to a cosmological constant term in the path-integral approach. (shrink)

The electronic and muonic hydrogen energy levels are calculated very accurately [1] in Quantum Electrodynamics (QED) by coupling the Dirac Equation four vector (c ,mc2) current covariantly with the external electromagnetic (EM) field four vector in QED’s Interactive Representation (IR). The c -Non Exclusion Principle(c -NEP) states that, if one accepts c as the electron/muon velocity operator because of the very accurate hydrogen energy levels calculated, the one must also accept the resulting electron/muon internal spatial and time coordinate operators (ISaTCO) (...) derived directly from c without any assumptions. This paper does not change any of the accurate QED calculations of hydrogen’s energy levels, given the simplistic model of the proton used in these calculations [1]. The Proton Radius Puzzle [2, 3] may indicate that new physics is necessary beyond the Standard Model (SM), and this paper describes the bizarre, and very different, situation when the electron and muon are located “inside” the spatially extended proton with their Centers of Charge (CoCs) orbiting the proton at the speed of light in S energy states. The electron/muon center of charge (CoC) is a structureless point that vibrates rapidly in its inseparable, non-random vacuum whose geometry and time structure are defined by the electron/muon ISaTCO discrete geometry. The electron/muon self mass becomes finite in a natural way due to the ISaTCOs cutting off high virtual photon energies in the photon propagator. The Dirac-Maxwell-Wilson (DMW) Equations are derived from the ISaTCO for the EM fields of an electron/muon, and the electron/muon “look” like point particles in far field scattering experiments in the same way the electric field from a sphere with evenly distributed charge “e” “looks” like a point with the same charge in the far field (Gauss Law). The electron’s/muon’s three fluctuating CoC internal spatial coordinate operators have eight possible eigenvalues [4, 5, 6] that fall on a spherical shell centered on the electron’s CoM with radius in the rest frame. The electron/muon internal time operator is discrete, describes the rapid virtual electron/positron pair production and annihilation. The ISaTCO together create a current that produce spin and magnetic moment operators, and the electron and muon no longer have “intrinsic” properties since the ISaTCO kinematics define spin and magnetic moment properties. (shrink)

This monograph presents the latest findings from a long-term research project intended to identify the physics behind Quantum Mechanics. A fundamental theory for quantum mechanics is constructed from first physical principles, revealing quantization as an emergent phenomenon arising from a deeper stochastic process. As such, it offers the vibrant community working on the foundations of quantum mechanics an alternative contribution open to discussion. The book starts with a critical summary of the main conceptual problems that still beset quantum mechanics. (...) The basic consideration is then introduced that any material system is an open system in permanent contact with the random zero-point radiation field, with which it may reach a state of equilibrium. Working from this basis, a comprehensive and self-consistent theoretical framework is then developed. The pillars of the quantum-mechanical formalism are derived, as well as the radiative corrections of nonrelativistic QED, while revealing the underlying physical mechanisms. The genesis of some of the central features of quantum theory is elucidated, such as atomic stability, the spin of the electron, quantum fluctuations, quantum nonlocality, and entanglement. The theory developed here reaffirms fundamental scientific principles such as realism, causality, locality and objectivity. (shrink)

This study explores the evolutionary-based hypothesis that facial attractiveness (a guiding force in mate selection) is a cue for physical fitness (presumably an important contributor to mate value in ancestral times). Since fluctuating asymmetry, a measure of developmental stability, is known to be a valid cue for fitness in several biological domains, we scrutinized facial asymmetry as a potential mediator between attractiveness and fitness. In our sample of young women, facial beauty indeed indicated physical fitness. The relationships that pertained to (...) asymmetry were in the expected direction. However, a closer analysis revealed that facial asymmetry did not mediate the relationship between fitness and attractiveness. Unexpected problems regarding the measurement of facial asymmetry are discussed. (shrink)

We describe how a model of effective interactions between quantum fluctuations under certain assumptions can be constructed in a way so that the large-scale limit gives an effective theory that matches general relativity (GR) in vacuum regions. This is an investigation of a possible scenario of spacetime emergence from quantum interactions directly in the spacetime, and of how effective quantum behaviour might provide a useful link between detailed properties of quantum interactions and GR. The quantum fluctuations are assumed (...) to entangle sufficiently for a cohesive spacetime to form, so that their effective properties can be described relative to a D-dimensional reference frame. To obtain the desired features of a smooth metric with a vanishing Ricci tensor, the quantum fluctuations are modelled as Gaussian probability distributions, with a shape set relative to the interactions coming from the surroundings. At small scales, the propagation through the spacetime is modelled by a Gaussian random walk. (shrink)

In this paper I continue the investigation in Viaggiu, Viaggiu concerning my proposal on the nature of the cosmological constant. In particular, I study both mathematically and physically the quantum Planckian context and I provide, in order to depict quantum fluctuations and in absence of a complete quantum gravity theory, a semiclassical solution where an effective inhomogeneous metric at Planckian scales or above is averaged. In such a framework, a generalization of the well known Buchert formalism is obtained with (...) the foliation in terms of the mean value \\) of the time operator \ in a maximally localizing state \ of a quantum spacetime and in a cosmological context. As a result, after introducing a decoherence length scale \ where quantum fluctuations are averaged on, a classical de Sitter universe emerges with a small cosmological constant depending on \ and frozen in a true vacuum state, provided that the kinematical backreaction is negligible at that scale \. Finally, I analyse the case with a non-vanishing initial spatial curvature \ showing that, for a reasonable large class of models, spatial curvature and kinematical backreation \ are suppressed by the dynamical evolution of the spacetime. (shrink)

Tissues are shaped and patterned by mechanical and chemical processes. A key mechanical process is the positioning of the mitotic spindle, which determines the size and location of the daughter cells within the tissue. Recent force and position-fluctuation measurements indicate that pushing forces, mediated by the polymerization of astral microtubules against­ the cell cortex, maintain the mitotic spindle at the cell center in Caenorhabditis elegans embryos. The magnitude of the centering forces suggests that the physical limit on the accuracy and (...) precision of this centering mechanism is determined by the number of pushing microtubules rather than by thermally driven fluctuations. In cells that divide asymmetrically, anti-centering, pulling forces generated by cortically located dyneins, in conjunction with microtubule depolymerization, oppose the pushing forces to drive spindle displacements away from the center. Thus, a balance of centering pushing forces and anti-centering pulling forces localize the mitotic spindles within dividing C. elegans cells. We discuss microtubule-based mechanisms of the mitotic spindle positioning, a key mechanical process that shapes and patterns tissues. The magnitude of the centering forces indicates that the physical limit on the accuracy and precision of centering is set by the number of contributing microtubules rather than by thermally driven fluctuations. (shrink)

Tissues are shaped and patterned by mechanical and chemical processes. A key mechanical process is the positioning of the mitotic spindle, which determines the size and location of the daughter cells within the tissue. Recent force and position-fluctuation measurements indicate that pushing forces, mediated by the polymerization of astral microtubules against­ the cell cortex, maintain the mitotic spindle at the cell center in Caenorhabditis elegans embryos. The magnitude of the centering forces suggests that the physical limit on the accuracy and (...) precision of this centering mechanism is determined by the number of pushing microtubules rather than by thermally driven fluctuations. In cells that divide asymmetrically, anti-centering, pulling forces generated by cortically located dyneins, in conjunction with microtubule depolymerization, oppose the pushing forces to drive spindle displacements away from the center. Thus, a balance of centering pushing forces and anti-centering pulling forces localize the mitotic spindles within dividing C. elegans cells. We discuss microtubule-based mechanisms of the mitotic spindle positioning, a key mechanical process that shapes and patterns tissues. The magnitude of the centering forces indicates that the physical limit on the accuracy and precision of centering is set by the number of contributing microtubules rather than by thermally driven fluctuations. (shrink)

The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we show that equilibrium statistical mechanics for the fictitious gas of particles associated with the parametric motion of levels yields spectral fluctuations of the random-matrix type. Previously known clues to that goal are an appropriate equilibrium ensemble and a certain ergodicity of level dynamics. We here complete the reasoning (...) by establishing a power law for the ħ dependence of the mean parametric separation of avoided level crossings. Due to that law universal spectral fluctuations emerge as average behavior of a family of quantum dynamics drawn from a control parameter interval which becomes vanishingly small in the classical limit; the family thus corresponds to a single classical system. We also argue that classically integrable dynamics cannot produce universal spectral fluctuations since their level dynamics resembles a nearly ideal Pechukas–Yukawa gas. (shrink)

The celebrated Dreimännerarbeit by Born, Heisenberg and Jordan contains a matrix-mechanical derivation by Jordan of Planck’s formula for blackbody fluctuations. Jordan appears to have considered this to be one of his finest contributions to quantum theory, but the status of his derivation is puzzling. In our Dreimenschenarbeit, we show how to understand what Jordan was doing in the double context of a Boltzmannian approach to statistical mechanics and of the early ‘statistical interpretation’ of matrix mechanics.

Under the assumption that the so-called space-time fluctuationy(x) in a classical sense, attached to each point of the gravitational field at some microscopic stage, is summarized as the metrical fluctuation in the formg λκ (x)=gλκ (x)·exp2σ(y(x)), some new physical aspects induced by the conformal scalarσ(x) (≡σ(y(x))) are found: By introducing the torsionT κ λμ (x) from a general standpoint, the resulting micro-gravitational field is made to have a conformally non-Riemannian structure, where a special form ofT κ λμ (i.e.,T κ λμ (...) =δ κ λ σμ−δ κ μ σλ(σμ=∂σ/∂x μ)) shows some peculiar features. An averaging process with respect toy is taken into account, by which the spatial structure of the corresponding macro-field is shown, in general, to have a somewhat “non”-Riemannian structure due to the contributions of the torsionT κ λμ. (shrink)

This paper deals with the philosophical issues of the notion of nothingness and pre-inflationary stage of the universe in physical cosmology. We presuppose that, in addition to cosmological limits, there may be both anthropic and computational limits for our ability to understand and replicate the conditions before the Big Bang. That is, the very notion of nothingness and pre-Big Bang state may be conceptually, but not computationally grasped.

Physical vacuum is a special superfluid medium populated by enormous amount of virtual particle-antiparticle pairs. Its motion is described by the modified Navier–Stokes equation: the pressure gradient divided by the mass density is replaced by the gradient from the quantum potential; time-averaged the viscosity vanishes, but its variance is not zero. Vortex structures arising in this medium show infinitely long lifetime owing to zero average viscosity. The nonzero variance is conditioned by exchanging the vortex energy with zero-point vacuum fluctuations. (...) The vortex has a non-zero core where the orbital speed vanishes. The speed reaches a maximal value on the core wall and further it decreases monotonically. The vortex trembles around some average value and possesses by infinite life time. The vortex ball resulting from topological transformation of the vortex ring is considered as a model of a particle with spin. Anomalous magnetic moment of electron is computed. (shrink)

The procedures of validating computer simulations of particle physicsParticle physics events at the LHCLarge Hadron Collider are summarized. Because of the strongly fluctuating particle content of LHC events and detectorDetector interactions, particle-based Monte Carlo methods are an indispensable tool for dataData analysis analysis. Simulation in particle physicsParticle physics is founded on factorizationFactorization and thus its global validation can be realized by validating each individual step in the simulation. This can be accomplished by drawing on results of previousMeasurement measurements, (...) in situ studies, and models. What is particularly important in particle physicsParticle physics is to quantify how well a simulation is validated such that a systematic uncertainty can be assigned to a measurement. The simulation is tested for a wide range of processes and agrees with dataData within the assigned uncertainties. (shrink)

The quasiclassical theory in terms of Feynman path integrals is used to calculate the decay of the Cooperon amplitude caused by transverse gauge field fluctuations in a disordered electron system. It is found that the phase relaxation rate in two dimensions varies linearly with the temperature as in the more common case of electric field fluctuations, but is proportional to the conductance rather than the resistance. A logarithmic correction factor is found in comparison to an earlier qualitative estimate.

Physical vacuum is a special superfluid medium. Its motion is described by the Navier–Stokes equation having two slightly modified terms that relate to internal forces. They are the pressure gradient and the dissipation force because of viscosity. The modifications are as follows: the pressure gradient contains an added term describing the pressure multiplied by the entropy gradient; time-averaged viscosity is zero, but its variance is not zero. Owing to these modifications, the Navier–Stokes equation can be reduced to the Schrödinger equation (...) describing behavior of a particle into the vacuum, which looks like a superfluid medium populated by enormous amount of virtual particle–antiparticle pairs. (shrink)

A re-evaluation of the notion of vacuum in quantum electrodynamics is presented, focusing on the vacuum of the quantized electromagnetic field. In contrast to the ‘nothingness’ associated to the idea of classical vacuum, subtle aspects are found in relation to the vacuum of the quantized electromagnetic field both at theoretical and experimental levels. These are not the usually called vacuum effects. The view defended here is that the so-called vacuum effects are not due to the ground state of the quantized (...) electromagnetic field. Nevertheless it is possible to maintain an empirically demonstrable notion of vacuum state that is consistent with the interpretation of the formalism of the theory. (shrink)