scholarly journals Phase Space Formulation of Quantum Mechanics. Insight into the Measurement Problem

2005 ◽  
Vol 72 (4) ◽  
pp. 290-296 ◽  
Author(s):  
D Dragoman
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Measurement Problem ◽  
Space Formulation ◽  
Insight Into

Phase-Space Approach to Berry Phases

2006 ◽  
Vol 13 (01) ◽  
pp. 67-74 ◽  
Author(s):  
Dariusz Chruściński
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Wigner Function ◽  
Berry Phase ◽  
Space Formulation ◽  
Berry Phases ◽  
Classical Phase Space ◽  
New Formula ◽  
Space Approach

We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light onto the correspondence between classical and quantum adiabatic phases — both phases are related with the averaging procedure: Hannay angle with averaging over the classical torus and Berry phase with averaging over the entire classical phase space with respect to the corresponding Wigner function.

Hydrogen atom in the phase-space formulation of quantum mechanics

1984 ◽  
Vol 30 (2) ◽  
pp. 691-697 ◽  
Author(s):  
J. M. Gracia-Bondía
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Hydrogen Atom ◽  
Space Formulation

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 The Phase Space Formulation of Time-Symmetric Quantum Mechanics

Quanta ◽  
2015 ◽  
Vol 4 (1) ◽  
pp. 27 ◽  
Author(s):  
Charlyne De Gosson ◽  
Maurice A. De Gosson
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Symmetric Quantum ◽  
Space Formulation ◽  
Time Symmetric Quantum Mechanics

Advanced Topics in Quantum Mechanics

2021 ◽  
Author(s):  
Marcos Mariño
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Path Integral ◽  
Worked Examples ◽  
Wkb Method ◽  
Path Integral Formulation ◽  
Graduate Courses ◽  
Advanced Students ◽  
Key Concepts ◽  
Space Formulation

Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throughout.

scholarly journals Phase space Heisenberg-limited estimation of the average phase shift in a Mach–Zehnder interferometer

2020 ◽  
Vol 18 (01) ◽  
pp. 1941019
Author(s):  
Dario Gatto ◽  
Paolo Facchi ◽  
Vincenzo Tamma
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Zehnder Interferometer ◽  
Exact Results ◽  
Quantum Metrology ◽  
Squeezed Vacuum ◽  
Arbitrary Phase ◽  
Insight Into ◽  
Limited Sensitivity ◽  
Mach Zehnder Interferometer

We address the problem of distributed quantum metrology with a single squeezed-vacuum source by using the formalism of quantum mechanics in phase space. In particular, we demonstrate Heisenberg-limited sensitivity in the measurement of the average of two arbitrary phase shifts in the arms of a Mach–Zehnder interferometer. We obtain exact results for the measurement probability at the interferometer output for any value of the phases, which give us insight into the emergence of Heisenberg-limited sensitivity for periodical values of the phases.

Some Mathematical Considerations on Solid State Physics in the Framework of the Phase Space Formulation of Quantum Mechanics

2013 ◽  
Vol 53 (10) ◽  
pp. 3546-3574 ◽  
Author(s):  
G. Alì ◽  
R. Beneduci ◽  
G. Mascali ◽  
F. E. Schroeck ◽  
J. J. Sławianowski
Keyword(s):  
State Physics ◽  
Quantum Mechanics ◽  
Solid State ◽  
Phase Space ◽  
Solid State Physics ◽  
Space Formulation
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