Regularizations of time-crystal dynamics

We demonstrate that nonconvex Lagrangians, as contemplated in the theory of time crystals, can arise in the effective description of conventional, physically realizable systems. Such embeddings resolve dynamical singularities which arise in the reduced description. Microstructure featuring intervals of fixed velocity interrupted by quick resets—“Sisyphus dynamics”—is a generic consequence. In quantum mechanics, this microstructure can be blurred, leaving entirely regular behavior.

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EMERGENT QUANTUM MECHANICS AS A CLASSICAL, IRREVERSIBLE THERMODYNAMICS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887813500072 ◽

2013 ◽

Vol 10 (04) ◽

pp. 1350007 ◽

Cited By ~ 9

Author(s):

D. ACOSTA ◽

P. FERNÁNDEZ DE CÓRDOBA ◽

J. M. ISIDRO ◽

J. L. G. SANTANDER

Keyword(s):

Quantum Mechanics ◽

Degrees Of Freedom ◽

Probability Distributions ◽

Semiclassical Approximation ◽

Irreversible Thermodynamics ◽

Feynman Path Integral ◽

Fundamental Theory ◽

Feynman Path ◽

Additional Support ◽

Effective Description

We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the semiclassical approximation of quantum mechanics. Quantum-mechanical propagators are mapped into thermodynamical probability distributions. The Feynman path integral also arises naturally in this setup. The fact that quantum mechanics can be translated into thermodynamical language provides additional support for the conjecture that quantum mechanics is not a fundamental theory but rather an emergent phenomenon, i.e. an effective description of some underlying degrees of freedom.

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A no-go theorem for theories that decohere to quantum mechanics

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2017.0732 ◽

2018 ◽

Vol 474 (2214) ◽

pp. 20170732 ◽

Cited By ~ 7

Author(s):

Ciarán M. Lee ◽

John H. Selby

Keyword(s):

Quantum Mechanics ◽

Quantum Theory ◽

Incomplete Information ◽

Experimental Evidence ◽

Fundamental Theory ◽

Classical Physics ◽

Lack Of Information ◽

The World ◽

Physical Principles ◽

Effective Description

To date, there has been no experimental evidence that invalidates quantum theory. Yet it may only be an effective description of the world, in the same way that classical physics is an effective description of the quantum world. We ask whether there exists an operationally defined theory superseding quantum theory, but which reduces to it via a decoherence-like mechanism. We prove that no such post-quantum theory exists if it is demanded that it satisfy two natural physical principles: causality and purification . Causality formalizes the statement that information propagates from present to future, and purification that each state of incomplete information arises in an essentially unique way due to lack of information about an environment. Hence, our result can be viewed either as evidence that the fundamental theory of Nature is quantum or as showing in a rigorous manner that any post-quantum theory must abandon causality, purification or both.

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Fractional Schrödinger equation in gravitational optics

Modern Physics Letters A ◽

10.1142/s0217732321400034 ◽

2021 ◽

pp. 2140003

Author(s):

Alexander Iomin

Keyword(s):

Quantum Mechanics ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Fractional Laplacian ◽

Fractional Quantum ◽

Nonlinear Media ◽

Airy Beam ◽

Newton Equation ◽

Optical Effects ◽

Effective Description

This paper addresses issues surrounding the concept of fractional quantum mechanics, related to lights propagation in inhomogeneous nonlinear media, specifically restricted to a so-called gravitational optics. Besides Schrödinger–Newton equation, we have also concerned with linear and nonlinear Airy beam accelerations in flat and curved spaces and fractal photonics, related to nonlinear Schrödinger equation, where impact of the fractional Laplacian is discussed. Another important feature of the gravitational optics’ implementation is its geometry with the paraxial approximation, when quantum mechanics, in particular, fractional quantum mechanics, is an effective description of optical effects. In this case, fractional-time differentiation reflexes this geometry effect as well.

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