Condensed Matter Physics

We review the recently proposed universal concept of dynamic complexity and its new mathematics based on the unreduced interaction problem solution. We then consider its progress-bringing applications at various levels of complex world dynamics, including complex-dynamical nanometal physics and living condensed matter, unreduced nanobiosystem dynamics and the integral medicine concept, causally complete management of complex economical and social dynamics, and the ensuing concept of truly sustainable world governance.

In this article we argue that idealizations and limiting cases in models play an exploratory role in science. Four senses of exploration are presented: exploration of the structure and representational capacities of theory; proof-of-principle demonstrations; potential explanations; and exploring the suitability of target systems. We illustrate our claims through three case studies, including the Aharonov-Bohm effect, the emergence of anyons and fractional quantum statistics, and the Hubbard model of the Mott phase transitions. We end by reflecting on how our case (...) studies and claims compare to accounts of idealization in the philosophy of science literature such as Michael Weisberg’s three-fold taxonomy. (shrink)

This book presents fresh insights into analogue quantum simulation. It argues that these simulations are a new instrument of science. They require a bespoke philosophical analysis, sensitive to both the similarities to and the differences with conventional scientific practices such as analogical argument, experimentation, and classical simulation. -/- The analysis situates the various forms of analogue quantum simulation on the methodological map of modern science. In doing so, it clarifies the functions that analogue quantum simulation serves in scientific practice. To (...) this end, the authors introduce a number of important terminological distinctions. They establish that analogue quantum ‘computation' and ‘emulation' are distinct scientific practices and lead to distinct forms of scientific understanding. The authors also demonstrate the normative value of the computation vs. emulation distinction at both an epistemic and a pragmatic level. -/- The volume features a range of detailed case studies focusing on: i) cold atom computation of many-body localisation and the Higgs mode; ii) photonic emulation of quantum effects in biological systems; and iii) emulation of Hawking radiation in dispersive optical media. Overall, readers will discover a normative framework to isolate and support the goals of scientists undertaking analogue quantum simulation and emulation. This framework will prove useful to both working scientists and philosophers of science interested in cutting-edge scientific practice. (shrink)

This chapter argues that the physics of condensed matter, such as crystals, superconductors, magnets, liquids, cannot be fully reduced to the supposedly fundamental quantum mechanical theory for all the atoms of which the system consists. The author holds the view that there are in fact many reasons to reject the idea that the world of physics is causally closed with everything being determined bottom-up by fundamental microscopic laws. A considerable part of the chapter is devoted to showing how condensed-matter theory (...) is done in practice. It is never done by starting with a microscopic theory for the interaction of all the atoms of the system. Instead, approximations, plausible assumptions, intuitive models, and phenomenological theories are used to mathematically describe and explain the properties of systems that consist of a macroscopic number of particles. The author argues that this is not merely a matter of convenience, but that there are fundamental and qualitative differences or even contradictions between the microscopic theory and the theory that is used in practice. These differences are in many cases due to the fact that the world is classical, with spatially localized objects, on the macroscopic scale, while quantum mechanics leads to superpositions of objects being in different locations. Concordantly, the theories used in condensed matter physics contain elements from classical physics as well as from quantum physics.The outline of the chapter is as follows: Introduction: The author tells how she struggled as a physics student trying to understand how the calculations presented in the lectures relate to the supposedly fundamental theory, until she came to see many years later that there are fundamental and interesting issues behind the questions she asked herself as a student.Example systems: Several examples from condensed-matter physics are given to illustrate the types of phenomena addressed in the chapter. A distinction is made between equilibrium systems, which can be separated from their environment without losing their properties, and nonequilibrium systems.Defining reduction and emergence: These concepts are defined with an emphasis on the difference between weak and strong emergence. It is explained that the reductionist method has been extremely successful in physics, but that nevertheless a discussion is needed concerning the quality of this reduction: is it complete, or is it incomplete. The relation to top-down causation is explained.Condensed matter research in practice: By quoting three Nobel laureates, it is shown how condensed-matter research is done in practise. These authors provide good arguments against a reductionist view. These three examples are supplemented by the author’s expertise in statistical physics, showing that the supposed reductionist explanations made in this field import ideas that are foreign to the microscopic theory.Arguments for strong emergence in physics: Based on the information provided so far, the author now gives six reasons for strong emergence, including dependence on the environment, stochasticity, and insensitivity to microscopic details.Answers to objections: The author responds to several objections that she often hears in discussions about reduction and emergence. The main objection is that future progress of physics might yield the missing full microscopic explanations. The author counters that her arguments give generic reasons why a full reduction is not possible in principle. (shrink)

The “universality” of critical phenomena is much discussed in philosophy of scientific explanation, idealizations and philosophy of physics. Lange and Reutlinger recently opposed Batterman concerning the role of some deliberate distortions in unifying a large class of phenomena, regardless of microscopic constitution. They argue for an essential explanatory role for “commonalities” rather than that of idealizations. Building on Batterman's insight, this article aims to show that assessing the differences between the universality of critical phenomena and two paradigmatic cases of “commonality (...) strategy”—the ideal gas model and the harmonic oscillator model—is necessary to avoid the objections raised by Lange and Reutlinger. Taking these universal explanations as benchmarks for critical phenomena reveals the importance of the different roles played by analogies underlying the use of the models. A special combination of physical and formal analogies allows one to explain the epistemic autonomy of the universality of critical phenomena through an explicative loop. (shrink)

This is an introduction to renormalization group methods in quantum field theory aimed at philosophers of science. review path integral methods, the relationship between early renormalization theory and renormalization group methods, and conceptual shifts in thinking about quantum field theory spurred by the development of renormalization group methods.

The paper rebuts a currently popular criticism against a certain take on the referential role of discontinuities and singularities in the physics of first-order phase transitions. It also elaborates on a proposal I made previously on how to understand this role within the framework provided by the distinction between data and phenomena.

It has been recently debated whether there exists a so-called “easy road” to nominalism. In this essay, I attempt to fill a lacuna in the debate by making a connection with the literature on infinite and infinitesimal idealization in science through an example from mathematical physics that has been largely ignored by philosophers. Specifically, by appealing to John Norton’s distinction between idealization and approximation, I argue that the phenomena of fractional quantum statistics bears negatively on Mary Leng’s proposed path to (...) easy road nominalism, thereby partially defending Mark Colyvan’s claim that there is no easy road to nominalism. (shrink)

Various claims regarding intertheoretic reduction, weak and strong notions of emergence, and explanatory fictions have been made in the context of first-order thermodynamic phase transitions. By appealing to John Norton’s recent distinction between approximation and idealization, I argue that the case study of anyons and fractional statistics, which has received little attention in the philosophy of science literature, is more hospitable to such claims. In doing so, I also identify three novel roles that explanatory fictions fulfill in science. Furthermore, I (...) scrutinize the claim that anyons, as they are ostensibly manifested in the fractional quantum Hall effect, are emergent entities and urge caution. Consequently, it is suggested that a particular notion of strong emergence signals the need for the development of novel physical–mathematical research programs. (shrink)

Two approaches to understanding the idealizations that arise in the Aharonov–Bohm effect are presented. It is argued that a common topological approach, which takes the non-simply connected electron configuration space to be an essential element in the explanation and understanding of the effect, is flawed. An alternative approach is outlined. Consequently, it is shown that the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have important implications for philosophical issues. Also, the alleged indispensable explanatory role of (...) said idealizations is examined via a minimal model explanatory scheme. Last, the idealizations involved in the AB effect are placed in a wider philosophical context via a short survey of part of the literature on infinite and essential idealizations. (shrink)

It is commonly claimed that the universality of critical phenomena is explained through particular applications of the renormalization group. This article has three aims: to clarify the structure of the explanation of universality, to discuss the physics of such RG explanations, and to examine the extent to which universality is thus explained. The derivation of critical exponents proceeds via a real-space or a field-theoretic approach to the RG. Building on work by Mainwood, this article argues that these approaches ought to (...) be distinguished: while the field-theoretic approach explains universality, the real-space approach fails to provide an adequate explanation. (shrink)

Recent discussions of emergence in physics have focussed on the use of limiting relations, and often particularly on singular or asymptotic limits. We discuss a putative example of emergence that does not fit into this narrative: the case of phonons. These quasi-particles have some claim to be emergent, not least because the way in which they relate to the underlying crystal is almost precisely analogous to the way in which quantum particles relate to the underlying quantum field theory. But there (...) is no need to take a limit when moving from a crystal lattice based description to the phonon description. Not only does this demonstrate that we can have emergence without limits, but also provides a way of understanding cases that do involve limits. (shrink)

Solid state physics, the study of the physical properties of solid matter, was the most populous subfield of Cold War American physics. Despite prolific contributions to consumer and medical technology, such as the transistor and magnetic resonance imaging, it garnered less professional prestige and public attention than nuclear and particle physics. Solid State Insurrection argues that solid state physics was essential to securing the vast social, political, and financial capital Cold War physics enjoyed in the twentieth century. Solid state’s technological (...) bent, and its challenge to the “pure science” ideal many physicists cherished, helped physics as a whole respond more readily to Cold War social, political, and economic pressures. Its research kept physics economically and technologically relevant, sustaining its cultural standing and policy influence long after the sheen of the Manhattan Project had faded. (shrink)

O perspectivă contemporană asupra materiei, care ia în considerare toate entităţile ştiinţifice observabile, cu accent pe fenomene. În principiu, definiţia materiei se limitează la astfel de entităţi explorate de fizică. În funcţie de condiţiile termodinamice diferite, cum ar fi temperatura şi presiunea, materia poate exista în diferite “faze”, cele mai familiare fiind cele de solid, lichid, şi gaz. Alte faze pot fi cele de plasmă, superfluid, şi condensat Bose-Einstein. Atunci când materia trece dintr-o fază în alta, este supusă la ceea (...) ce este cunoscut ca tranziţie de fază, un fenomen studiat în termodinamică. -/- CUPRINS: -/- Natura atomică a materiei - Ipoteze atomice - Proprietățile atomilor - - Proprietăți nucleare - - Masa - - Forma și dimensiunea - - Dezintegrarea radioactivă - - Momentul magnetic - - Nivelurile energetice - - Valența și comportamentul legăturilor - - Stări - Imagistica atomică - Structura atomului - - Particule subatomice - - Nucleul - - Norul de electroni - Elemente chimice - - Descriere - - Originea elementelor - - Abundenţa - Tabelul periodic al elementelor - - Prezentare generală - - Metode de grupare - - - Grupe - - - Perioade - - - Blocuri - - - Metale, metaloide și nemetale - Izotopi (Variații, ocurența, aplicații) - - Proprietăți chimice și moleculare - - Proprietăți nucleare și stabilitatea - - Numere de izotopi per element - - Numerele de nucleoni pare și impare - - Existența în natură - - Aplicații ale izotopilor - - - Purificarea izotopilor - - - Utilizarea proprietăților chimice și biologice - - - Utilizarea proprietăților nucleare - Compuși și amestecuri - - Compuși chimici - - - Definiții - - - Legături și forțe - - Amestecuri - - - Caracteristicile amestecului - Molecule - - Legături - - - Covalente - - - Ionice - - Dimensiunea moleculară - - Geometria moleculară - - Spectroscopia moleculară - - Aspecte teoretice - Antimateria - - Definiție formală - - Istoria conceptului - - Notaţie - - Proprietăți - - Origine și asimetrie - Materia întunecată - - Definiție tehnică - - Compoziția materiei întunecate: barionică vs. nonbarionică - - - Materia barionică - - - Materia non-barionică - - - Agregarea materiei întunecate și obiectele dense de materie întunecată Solide - Microscopia cu ioni în câmp - - Introducere - - Design, limitări și aplicații - Structura cristalelor - - Celula unitară - - - Indicii Miller - - - Planuri și direcții - - - - Structuri cubice - Densitatea solidelor - - Istorie - - Măsurarea densității - - - Materiale omogene - - - Materiale heterogene - - - Materiale non-compacte - Elasticitatea - - Prezentare generală - - Elasticitatea liniară - - Aplicații - Rezistența materialelor - - Definiție - - Tipuri de sarcini - - Condiții de stres - - Condiții de rezistență - - Condiții de deformare - - Relațiile stres-deformare Lichide - Aplicații - Presiunea - - Definiție - - Unități - - Presiunea fluidelor - - Presiunea în lichid - - - Direcția presiunii lichidului - Flotabilitatea - Principiul lui Arhimede - - Formula - - Rafinare - Forțe în cazurile scufundării și plutirii - - Model simplificat - Stabilitatea statică - Flotarea - Principiul lui Pascal - - Definiție - - Explicaţie - - Butoiul lui Pascal - - Aplicațiile legii lui Pascal - Tensiunea superficială - - Cauze - - Efectele tensiunii de suprafață - - - Apa - - - Surfactanţi - Capilaritatea - - Fenomenul și fizica acțiunii capilare - - La plante și animale - - Exemple - - Înălțimea unui menisc - - Transportul lichidelor în medii poroase Gaze - Caracteristici fizice - Atmosfera - - Scurgeri de atmosferă - - Teren - - Compoziție - - Structura Pământului - - Circulație - - Importanța - - Presiunea atmosferică - - - Mecanism - - - Atmosfera standard - - - Presiunea medie a nivelului mării - - - Variația altitudinii - - - Variația locală - Barometru - - Tipuri - - - Barometre pe bază de apă - - - Barometre cu mercur - - - Barometru cu ulei de pompă de vid - - - Barometre aneroide - - - Barografe - - - Barometre MEMS - - Aplicații - - Barometre și calcularea presiunii atmosferice - Legea lui Boyle - - Istorie - - Definiție - - Relația cu teoria cinetică și gazele ideale - - Ecuaţia - - Sistemul respirator uman - Flotabilitatea în aer (Aerostate) - - Baloane - - Dirijabile - - Aerostate hibride - - Gaze flotante - - - Aer cald - Principiul lui Bernoulli - - Aplicații - - Efectul Coandă - - - Descoperire - - - Mecanismul efectului Coandă - - - Aplicații Plasma - Definiție - Proprietăți și parametri - - Grad de ionizare - - Temperaturi - - Plasme termice vs. nontermice - - Ionizare completă vs. incompletă - - Potențialul plasmei - - Magnetizare - - Comparația fazelor de plasmă și gaz - Plasma în natură, artificială și aplicații - - Plasmă în astronomie și astrofizică - - Plasma comună Schimbarea de fază - Clasificarea tranzițiilor de fază - - Clasificarea Ehrenfest - - Clasificarea modernă a tranzițiilor de fază - Proprietăți ale tranzițiilor de fază - - Puncte critice - - Simetria - - Exponenți critici și clase de universalitate - Evaporarea - - Teorie - - - Echilibru evaporativ - - Factorii care influențează rata de evaporare - Condensarea - - Inițiere - - Scenarii de reversibilitate - - Cele mai frecvente scenarii - - Cum este măsurată condensarea - - Aplicații ale condensării - - Adaptarea biologică - - Condensarea în construcția de clădiri - Ceaţa - - Definiție - - Formare - Nori - - Formarea și distribuția - - - Cum devine saturat aerul - - - Convergența de-a lungul zonelor cu presiune scăzută - - - Divergența de-a lungul zonelor de înaltă presiune - - Efecte asupra climei și atmosferei - Fierberea - - Tipuri - - - Nucleația - - - Fluxul de căldură critic - - - Tranziția - - - Filmul - - - Distilarea - - Fierberea vs. evaporarea - Înghețarea/Solidificarea - - Cristalizare - - Suprarăcirea - - Exotermicități - - Vitrificarea - - Expansiunea - - Înghețarea organismelor vii - - - Bacterii - - - Plante - - - Animale - - Conservarea alimentelor - Topirea - - Topirea ca o tranziție de fază de prim ordin - - Criteriile de topire - - Suprarăcirea - - Topirea solidelor amorfe (sticle) - Căldura latentă - - Folosire - - - Meteorologie - - Căldură latentă specifică Probleme nerezolvate - Fizica materiei condensate - Fizica plasmei Referințe Despre autor - Nicolae Sfetcu - - De același autor - - Contact Editura - MultiMedia Publishing. 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The rigid recoil of a crystal is the accepted mechanism for the Mössbauer effect. It’s at odds with the special theory of relativity which does not allow perfectly rigid bodies. The standard model of particle physics which includes QED should not allow any signals to be transmitted faster than the speed of light. If perturbation theory can be used, then the X-ray emitted in a Mössbauer decay must come from a single nuclear decay vertex at which the 4-momentum is exactly (...) conserved in a Feynman diagram. Then the 4-momentum of the final state Mössbauer nucleus must be slightly off the mass shell. This off-shell behavior would be followed by subsequent diffusion of momentum throughout the crystal to bring the nucleus back onto the mass shell and the crystal to a final relaxed state in which it moves rigidly with the appropriate recoil velocity. This mechanism explains the Mössbauer effect at the microscopic level and reconciles it with relativity. Because off-mass-shell quantum mechanics is required, the on-mass-shell theories developed originally for the Mössbauer effect are inadequate. Another possibility is that that the recoil response involves a non-perturbative effect in the standard model which could allow for a non-local instantaneous momentum transfer between the crystal and the decay, as proposed for example by Preparata and others in super-radiance theory. The recoil time of the crystal is probably not instantaneous, and if it could be measured, one could distinguish between various theories. An experiment is proposed in this paper to measure this time. The idea is to measure the total energy radiated due to bremsstrahlung from a charged Mössbauer crystal which has experienced a recoil. Using Larmor’s formula, along with corrections to it, allows one to design an experiment. The favored idea is to use many small nano-spheres of Mössbauer-active metals, whose outer surfaces are charged. The energy radiated then varies as the charge squared divided by the recoil time. This can then be measured with the extreme sensitivity available in Mössbauer experiments. If it turns out that experiments prove the need for off-mass-shell theory, then this would have profound implications for all of condensed matter physics. It would mean that an off-mass-shell theory like those considered by Stueckelberg, Horwitz, Piron, Greenberger, and many others are required to describe nature. The inclusion of these would be a major shift in the foundations. It would mean that there are new dynamic variables—the rest masses of particles. The ability to measure the diffusion relaxation time should prove useful also in chemical analysis, and provide a new class of analytical methods for material science. This problem is also interesting because the Mössbauer effect is a phenomenon where the solid-state environment dramatically and indisputably influences the probability of a nuclear process. (shrink)

This paper analyses the anti-reductionist argument from renormalisation group explanations of universality, and shows how it can be rebutted if one assumes that the explanation in question is captured by the counterfactual dependence account of explanation.

The Hartree–Fock–Popov theory of interacting Bose particles is generalized to the Cooper-pair system with a screened Coulomb repulsive interaction in high-temperature superconductors. At zero temperature, it is found that the condensate density \\) of Cooper pairs is of the order \\simeq 10^{18}\) cm\, consistently with the fact that a small fraction of the total p holes participate in pairing. We find that the phonon velocity c at zero temperature is of the order \\simeq 10\) km s\. The computation shows that (...) the transition temperature \ is a dome-shaped function of the p hole concentration \, which is consistent with experiments. At finite temperature, we find that the condensate fraction \/n\) decreases continuously from \/n\) to zero as the temperature increases from zero to the transition temperature \. For higher temperatures, we find that the repulsive interaction between Cooper pairs drives more Cooper pairs into the condensate. The computation reveals that the phonon velocity c decreases continuously from c to zero as the temperature increases from zero to the transition temperature \. The Cooper-pair system undergoes a first-order phase transition from the normal state to the BEC state. (shrink)

In this work we review the formalism used in describing the thermodynamics of first-order phase transitions from the point of view of maximum entropy inference. We present the concepts of transition temperature, latent heat and entropy difference between phases as emergent from the more fundamental concept of internal energy, after a statistical inference analysis. We explicitly demonstrate this point of view by making inferences on a simple game, resulting in the same formalism as in thermodynamical phase transitions. We show that (...) analogous quantities will inevitably arise in any problem of inferring the result of a yes/no question, given two different states of knowledge and information in the form of expectation values. This exposition may help to clarify the role of these thermodynamical quantities in the context of different first-order phase transitions such as the case of magnetic Hamiltonians. (shrink)

The paper argues that the phenomenon of first-order phase transitions (e.g., freezing) has features that make it a candidate to be classified as 'emergent'. However, it cannot be described either as 'weakly emergent' or 'strongly emergent'; hence it escapes categorization in terms employed in the current literature on the metaphysics of science.

The paper discuses whether the mathematical singularities characterizing first-order phase transitions are 'fictions'.

The physics of condensed matter, in contrast to quantum physics or cosmology, is not traditionally associated with deep philosophical questions. However, as science - largely thanks to more powerful computers - becomes capable of analysing and modelling ever more complex many-body systems, basic questions of philosophical relevance arise. Questions about the emergence of structure, the nature of cooperative behaviour, the implications of the second law, the quantum-classical transition and many other issues. This book is a collection of essays by leading (...) physicists and philosophers. Each investigates one or more of these issues, making use of examples from modern condensed matter research. Physicists and philosophers alike will find surprising and stimulating ideas in these pages. (shrink)

The physics of condensed matter, in contrast to quantum physics or cosmology, is not traditionally associated with deep philosophical questions. However, as science - largely thanks to more powerful computers - becomes capable of analysing and modelling ever more complex many-body systems, basic questions of philosophical relevance arise. Questions about the emergence of structure, the nature of cooperative behaviour, the implications of the second law, the quantum-classical transition and many other issues. This book is a collection of essays by leading (...) physicists and philosophers. Each investigates one or more of these issues, making use of examples from modern condensed matter research. Physicists and philosophers alike will find surprising and stimulating ideas in these pages. (shrink)

With the help of syncretiсs as a new philosophical logic, the philosophy of carriers, the theory of similarity and the theory of Infinite Hierarchical Nesting of Matter, the problems of modern physics are analyzed. We consider the classical and relativistic mechanics, the special and general theories of relativity, the theory of electromagnetic and gravitational fields, of weak and strong interactions. The goal is axiomatization of these theories, building models of elementary particles and of their interactions with each other. The main (...) obtained results are: description of the electrokinetic theory of the origin of magnetic fields in cosmic bodies; calculation of metric in the uniformly accelerated reference frame; the axiomatic construction of electrodynamics, Lorentz invariant (LITG) and covariant theories of gravitation (CTG); comparing CTG with the general theory of relativity and with the results of gravitational experiments. Among other results – the analysis of the properties of ether as the medium responsible for transfer of electromagnetic and gravitational waves, and derivation of the formula for entropy in a tensor form. For students and researchers, as well as for those interested in physical and philosophical problems. (shrink)

The present paper focuses on a particular class of models intended to describe and explain the physical behaviour of systems that consist of a large number of interacting particles. Such many-body models are characterized by a specific Hamiltonian (energy operator) and are frequently employed in condensed matter physics in order to account for such phenomena as magnetism, superconductivity, and other phase transitions. Because of the dual role of many-body models as models of physical sys-tems (with specific physical phenomena as their (...) explananda) as well as mathematical structures, they form an important sub-class of scientific models, from which one can expect to draw general conclusions about the function and functioning of models in science, as well as to gain specific insight into the challenge of modelling complex systems of correlated particles in condensed matter physics. In particular, it is argued that many-body models contribute novel elements to the process of inquiry and open up new avenues of cross-model confirmation and model-based understanding. In contradistinction to phenomenological models, which have received comparatively more philosophical attention, many-body models typically gain their strength not from ‘empirical fit’ per se, but from their being the result of a constructive application of mature formalisms, which frees them from the grip of both ‘fundamental theory’ and an overly narrow conception of ‘empirical success’. (shrink)

It is widely hoped that quantum gravity will shed light on the question of the origin of time in physics. The currently dominant approaches to a candidate quantum theory of gravity have naturally evolved from general relativity, on the one hand, and from particle physics, on the other hand. A third important branch of twentieth century ‘fundamental’ physics, condensed-matter physics, also offers an interesting perspective on quantum gravity, and thereby on the problem of time. The bottomline might sound disappointing: to (...) understand the origin of time, much more experimental input is needed than what is available today. Moreover it is far from obvious that we will ever find out the true origin of physical time, even if we become able to directly probe physics at the Planck scale. But we might learn some interesting lessons about time and the structure of our universe in the process. A first lesson is that there are probably several characteristic scales associated with “quantum gravity” effects, rather than the single Planck scale usually considered. These can differ by several orders of magnitude, and thereby conspire to hide certain effects expected from quantum gravity, rendering them undetectable even with Planck-scale experiments. A more tentative conclusion is that the hierarchy between general relativity, special relativity and Newtonian physics, usually taken for granted, might have to be interpreted with caution. (shrink)

This paper looks at the nature of idealizations and representational structures appealed to in the context of the fractional quantum Hall effect, specifically, with respect to the emergence of anyons and fractional statistics. Drawing on an analogy with the Aharonov–Bohm effect, it is suggested that the standard approach to the effects— the topological approach to fractional statistics—relies essentially on problematic idealizations that need to be revised in order for the theory to be explanatory. An alternative geometric approach is outlined and (...) endorsed. Roles for idealizations in science, as well as consequences for the debate revolving around so-called essential idealizations, are discussed. (shrink)

This paper is devoted to prove the existence of strong solutions for a brittle fracture model of quasi-static crack propagation in the two dimensional antiplane setting. As usual, the time continuous evolution is obtained as the limit of a discrete in time evolution by letting the time step tend to zero. The analysis rests on a density lower bound estimate for quasi-minimizers of Mumford-Shah type functionals, under a homogeneous Dirichlet boundary condition on a part of the boundary. In contrast with (...) the previous results, since boundary cracks may be obtained as limits of interior cracks, such a density lower bound has to be established also on balls centered inside the domain but possibly intersecting the Dirichlet boundary. Thanks to a 2D geometrical argument, the discrete in time crack turns out to satisfy a uniform density lower bound which can pass to the limit, leading to the closedness of the continuous in time crack. We also establish better convergence properties of the discrete in time displacement/crack pair towards its time continuous counterpart. (shrink)

Despite the close connection between the central limit theorem and renormalization group (RG) methods, the latter should be considered fundamentally distinct from the kind of probabilistic framework associated with statistical mechanics, especially the notion of averaging. The mathematics of RG is grounded in dynamical systems theory rather than probability, which raises important issues with respect to the way RG generates explanations of physical phenomena. I explore these differences and show why RG methods should be considered not just calculational tools but (...) the basis for a physical understanding of complex systems in terms of structural properties and relations. (shrink)

The framework of effective field theory is a natural one in which to understand the claim that the spacetime of general relativity is an emergent low-energy phenomenon. I argue for a pragmatic understanding of EFT, given that the appropriate conception of emergence it suggests is necessarily epistemological in a sense. Analogue models of spacetime are examples of the top-down approach to EFT. They offer concrete illustrations of spacetime emergent within an EFT, and lure us toward a strong analogy between condensed (...) matter physics and GR. I argue that we should be wary of this strong analogy, not least because the pragmatic view of EFT places limits on how much we can legitimately draw from it. On the other hand, programs that treat GR as an EFT and calculate quantum corrections are an example of the bottom-up approach and are explicitly pragmatic in character. I explore what we may learn about the nature of emergent spacetime by comparing these two approaches. (shrink)

This paper contrasts and compares strategies of model-building in condensed matter physics and biology, with respect to their alleged unequal susceptibility to trade-offs between different theoretical desiderata. It challenges the view, often expressed in the philosophical literature on trade-offs in population biology, that the existence of systematic trade-offs is a feature that is specific to biological models, since unlike physics, biology studies evolved systems that exhibit considerable natural variability. By contrast, I argue that the development of ever more sophisticated experimental, (...) theoretical, and computational methods in physics is beginning to erode this contrast, since condensed matter physics is now in a position to measure, describe, model, and manipulate sample-specific features of individual systems – for example at the mesoscopic level – in a way that accounts for their contingency and heterogeneity. Model-building in certain areas of physics thus turns out to be more akin to modeling in biology than has been supposed and, indeed, has traditionally been the case. (shrink)

Atomistic metaphysics motivated an explanatory strategy which science has pursued with great success since the scientific revolution. By decomposing matter into its atomic and subatomic parts physics gave us powerful explanations and accurate predictions as well as providing a unifying framework for the rest of science. The success of the decompositional strategy has encouraged a widespread conviction that the physical world forms a compositional hierarchy that physics and other sciences are progressively articulating. But this conviction does not stand up to (...) a closer examination of how physics has treated composition, as a variety of case studies will show. (shrink)

I present a novel approach to the scholarly debate that has arisen with respect to the philosophical import one should infer from scientific accounts of phase transitions by appealing to a distinction between representation understood as denotation, and faithful representation understood as a type of guide to ontology. It is argued that the entire debate is misguided, for it stems from a pseudo-paradox that does not license the type of claims made by scholars and that what is really interesting about (...) phase transitions is the manner by which they force us to rethink issues regarding scientific representation, idealizations, and realism. (shrink)