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  1. Generalized Two-Level Quantum Dynamics. II. Non-Hamiltonian State Evolution.William Band & James L. Park - 1978 - Foundations of Physics 8 (1-2):45-58.
    A theorem is derived that enables a systematic enumeration of all the linear superoperators ℒ (associated with a two-level quantum system) that generate, via the law of motion ℒρ= $\dot \rho$ , mappings ρ(0) → ρ(t) restricted to the domain of statistical operators. Such dynamical evolutions include the usual Hamiltonian motion as a special case, but they also encompass more general motions, which are noncyclic and feature a destination state ρ(t → ∞) that is in some cases independent of ρ(0).
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  • On Completely Positive Maps in Generalized Quantum Dynamics.Ralph F. Simmons & James L. Park - 1981 - Foundations of Physics 11 (1-2):47-55.
    Several authors have hypothesized that completely positive maps should provide the means for generalizing quantum dynamics. In a critical analysis of that proposal, we show that such maps are incompatible with the standard phenomenological theory of spin relaxation and that the theoretical argument which has been offered as justification for the hypothesis is fallacious.
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  • The Essential Nonlinearity ofN-Level Quantum Thermodynamics.Ralph F. Simmons & James L. Park - 1981 - Foundations of Physics 11 (3-4):297-305.
    This paper explores the possibility that linear dynamical maps might be used to describe the energy-conserving, entropy-increasing motions which occur in closed thermodynamic systems as they approach canonical thermal equilibrium. ForN-level quantum systems withN>2, we prove that no such maps exist which are independent of the initial state.
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  • Generalized Two-Level Quantum Dynamics. III. Irreversible Conservative Motion.James L. Park & William Band - 1978 - Foundations of Physics 8 (3-4):239-254.
    If the ordinary quantal Liouville equation ℒρ= $\dot \rho $ is generalized by discarding the customary stricture that ℒ be of the standard Hamiltonian commutator form, the new quantum dynamics that emerges has sufficient theoretical fertility to permit description even of a thermodynamically irreversible process in an isolated system, i.e., a motion ρ(t) in which entropy increases but energy is conserved. For a two-level quantum system, the complete family of time-independent linear superoperators ℒ that generate such motions is derived; and (...)
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