scholarly journals DEFORMATION QUANTIZATION AND WIGNER FUNCTIONS

2005 ◽  
Vol 20 (17n18) ◽  
pp. 1371-1385 ◽  
Author(s):  
N. COSTA DIAS ◽  
J. N. PRATA
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Deformation Quantization ◽  
Wigner Distribution ◽  
Sufficient Conditions ◽  
Wigner Functions ◽  
Space Function ◽  
Wigner Spectrum ◽  
Necessary And Sufficient ◽  
Phase Space Function

We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution. Based on this formalism we analize the modifications introduced by the presence of boundaries. Finally, we discuss the concept of environment-induced decoherence in the context of the Weyl-Wigner approach.

Quantum mechanics on phase space: The hydrogen atom and its Wigner functions

2018 ◽  
Vol 390 ◽  
pp. 60-70 ◽  
Author(s):  
P. Campos ◽  
M.G.R. Martins ◽  
M.C.B. Fernandes ◽  
J.D.M. Vianna
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Hydrogen Atom ◽  
Wigner Functions

scholarly journals Modes and Noise Propagation in Phase Space

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
J. S. Ben-Benjamin ◽  
L. Cohen
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Dispersion Relation ◽  
Wigner Distribution ◽  
Hermitian Operator ◽  
Type Equation ◽  
Hamiltonian Operator ◽  
Dispersive Media ◽  
Phase Space Methods ◽  
Complex Dispersion

AbstractWe show that phase space methods developed for quantum mechanics, such as the Wigner distribution, can be effectively used to study the evolution of nonstationary noise in dispersive media. We formulate the issue in terms of modes and show how modes evolve and how they are effected by sources.We show that each mode satisfies a Schrödinger type equation where the “Hamiltonian” may not be Hermitian. The Hamiltonian operator corresponds to dispersion relationwhere thewavenumber is replaced by the wavenumber operator. A complex dispersion relation corresponds to a non Hermitian operator and indicates that we have attenuation. A number of examples are given.

scholarly journals KÄHLER POLARIZATION AND WICK QUANTIZATION OF HAMILTONIAN SYSTEMS SUBJECT TO SECOND-CLASS CONSTRAINTS

2002 ◽  
Vol 17 (02) ◽  
pp. 121-129
Author(s):  
S. L. LYAKHOVICH ◽  
A. A. SHARAPOV
Keyword(s):  
Hamiltonian Systems ◽  
Deformation Quantization ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Class Constraint ◽  
Almost Kähler Manifold ◽  
Almost Kähler ◽  
Dirac Brackets ◽  
Necessary And Sufficient ◽  
Constraint Surface

The necessary and sufficient conditions are established for the second-class constraint surface to be (an almost) Kähler manifold. The deformation quantization for such systems is mentioned resulting in the Wick-type symbols for the respective Dirac brackets.

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

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.

scholarly journals Quantum phase-space function formulation of reactive flux theory

2003 ◽  
Vol 119 (2) ◽  
pp. 680-695 ◽  
Author(s):  
Debashis Barik ◽  
Suman Kumar Banik ◽  
Deb Shankar Ray
Keyword(s):  
Phase Space ◽  
Quantum Phase ◽  
Function Formulation ◽  
Space Function ◽  
Phase Space Function ◽  
Reactive Flux

Wigner's phase space function and the bond in LiH

1983 ◽  
Vol 63 (4) ◽  
pp. 349-356 ◽  
Author(s):  
Michael Springborg
Keyword(s):  
Phase Space ◽  
Space Function ◽  
Phase Space Function
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