Remark on a Group-Theoretical Formalism for Quantum Mechanics and the Quantum-to-Classical Transition

Abstract The quantum-classical transition of methyl rotation highlights conflicting assumptions of quantum and classical mechanics, the first assuming that identical fermions are indistinguishable while the second recognises they are distinguishable through their histories. When this is introduced into quantum mechanics, the two are compatible and there is a smooth transition of the methyl rotational spectrum with increasing temperature through the merger of three broadening peaks. The changing character of methyl dynamics through this transition is discussed.

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Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility

Journal of Computational Electronics ◽

10.1007/s10825-021-01804-6 ◽

2021 ◽

Author(s):

Michael te Vrugt ◽

Gyula I. Tóth ◽

Raphael Wittkowski

Keyword(s):

Quantum Mechanics ◽

Phase Space ◽

Measurement Problem ◽

Initial Conditions ◽

Classical Case ◽

Master Equations ◽

Wigner Functions ◽

Thermodynamic Behavior ◽

Thermodynamic Irreversibility ◽

Classical Transition

AbstractWigner functions, allowing for a reformulation of quantum mechanics in phase space, are of central importance for the study of the quantum-classical transition. A full understanding of the quantum-classical transition, however, also requires an explanation for the absence of macroscopic superpositions to solve the quantum measurement problem. Stochastic reformulations of quantum mechanics based on spontaneous collapses of the wavefunction are a popular approach to this issue. In this article, we derive the dynamic equations for the four most important spontaneous collapse models—Ghirardi–Rimini–Weber (GRW) theory, continuous spontaneous localization (CSL) model, Diósi-Penrose model, and dissipative GRW model—in the Wigner framework. The resulting master equations are approximated by Fokker–Planck equations. Moreover, we use the phase-space form of GRW theory to test, via molecular dynamics simulations, David Albert’s suggestion that the stochasticity induced by spontaneous collapses is responsible for the emergence of thermodynamic irreversibility. The simulations show that, for initial conditions leading to anti-thermodynamic behavior in the classical case, GRW-type perturbations do not lead to thermodynamic behavior. Consequently, the GRW-based equilibration mechanism proposed by Albert is not observed.

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Testing the foundation of quantum physics in space via Interferometric and non-interferometric experiments with mesoscopic nanoparticles

Communications Physics ◽

10.1038/s42005-021-00656-7 ◽

2021 ◽

Vol 4 (1) ◽

Author(s):

Giulio Gasbarri ◽

Alessio Belenchia ◽

Matteo Carlesso ◽

Sandro Donadi ◽

Angelo Bassi ◽

...

Keyword(s):

Quantum Mechanics ◽

Ab Initio ◽

Quantum Physics ◽

State Of The Art ◽

Superposition Principle ◽

New Physics ◽

Space Science ◽

Level Of Detail ◽

Space Environment ◽

Classical Transition

AbstractQuantum technologies are opening novel avenues for applied and fundamental science at an impressive pace. In this perspective article, we focus on the promises coming from the combination of quantum technologies and space science to test the very foundations of quantum physics and, possibly, new physics. In particular, we survey the field of mesoscopic superpositions of nanoparticles and the potential of interferometric and non-interferometric experiments in space for the investigation of the superposition principle of quantum mechanics and the quantum-to-classical transition. We delve into the possibilities offered by the state-of-the-art of nanoparticle physics projected in the space environment and discuss the numerous challenges, and the corresponding potential advancements, that the space environment presents. In doing this, we also offer an ab-initio estimate of the potential of space-based interferometry with some of the largest systems ever considered and show that there is room for tests of quantum mechanics at an unprecedented level of detail.

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Schwinger’s picture of quantum mechanics II: Algebras and observables

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887819501366 ◽

2019 ◽

Vol 16 (09) ◽

pp. 1950136 ◽

Cited By ~ 15

Author(s):

F. M. Ciaglia ◽

A. Ibort ◽

G. Marmo

Keyword(s):

Quantum Mechanics ◽

Harmonic Oscillator ◽

Dynamical Evolution ◽

Transition Functions ◽

Classical Transition ◽

Instrumental Role

The kinematical foundations of Schwinger’s algebra of selective measurements were discussed in [F. M. Ciaglia, A. Ibort and G. Marmo, Schwinger’s picture of quantum mechanics I: Groupoids, To appear in IJGMMP (2019)] and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this paper, the dynamical aspects of the theory are analyzed. For that, the algebra generated by the observables, as well as the notion of state, are discussed, and the structure of the transition functions, that plays an instrumental role in Schwinger’s picture, is elucidated. A Hamiltonian picture of dynamical evolution emerges naturally, and the formalism offers a simple way to discuss the quantum-to-classical transition. Some basic examples, the qubit and the harmonic oscillator, are examined, and the relation with the standard Dirac–Schrödinger and Born–Jordan–Heisenberg pictures is discussed.

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Nonrelativistic Quantum Mechanics and the Classical Transition

Series on Knots and Everything - Zero to Infinity ◽

10.1142/9789812709158_0007 ◽

2007 ◽

pp. 168-190

Keyword(s):

Quantum Mechanics ◽

Nonrelativistic Quantum ◽

Classical Transition ◽

Nonrelativistic Quantum Mechanics

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THE QUANTUM-CLASSICAL TRANSITION: THE FATE OF THE COMPLEX STRUCTURE

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887805000508 ◽

2005 ◽

Vol 02 (01) ◽

pp. 127-145 ◽

Cited By ~ 11

Author(s):

G. MARMO ◽

G. SCOLARICI ◽

A. SIMONI ◽

F. VENTRIGLIA

Keyword(s):

Quantum Mechanics ◽

Quantum Theory ◽

Classical Limit ◽

Symplectic Structure ◽

Complex Structure ◽

Classical Mechanics ◽

Geometric Structures ◽

Metric Tensor ◽

Classical Transition ◽

Schrödinger Picture

According to Dirac, fundamental laws of Classical Mechanics should be recovered by means of an "appropriate limit" of Quantum Mechanics. In the same spirit it is reasonable to enquire about the fundamental geometric structures of Classical Mechanics which will survive the appropriate limit of Quantum Mechanics. This is the case for the symplectic structure. On the contrary, such geometric structures as the metric tensor and the complex structure, which are necessary for the formulation of the Quantum theory, may not survive the Classical limit, being not relevant in the Classical theory. Here we discuss the Classical limit of those geometric structures mainly in the Ehrenfest and Heisenberg pictures, i.e. at the level of observables rather than at the level of states. A brief discussion of the fate of the complex structure in the Quantum-Classical transition in the Schrödinger picture is also mentioned.

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