Quantum distribution functions in the phase space of cylindrical coordinates

1975 ◽  
Vol 18 (8) ◽  
pp. 1157-1159
Author(s):  
N. A. Denisova
Keyword(s):  
Phase Space ◽  
Distribution Functions ◽  
Cylindrical Coordinates ◽  
Quantum Distribution

Hamilton-Jacobi Theory

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Bbgky Hierarchy ◽  
Distribution Functions ◽  
Symplectic Integrators ◽  
Partition Functions ◽  
Von Neumann ◽  
Equipartition Theorem ◽  
Recurrence Theorem ◽  
Phase Amplitude ◽  
Canonical Ensembles

This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.

scholarly journals A comment on quantum distribution functions and the OSV conjecture

2006 ◽  
Vol 2006 (12) ◽  
pp. 069-069 ◽  
Author(s):  
César Gómez ◽  
Sergio Montañez
Keyword(s):  
Distribution Functions ◽  
Quantum Distribution

scholarly journals Wigner Distributions of Quark

2016 ◽  
Vol 40 ◽  
pp. 1660055
Author(s):  
Asmita Mukherjee ◽  
Sreeraj Nair ◽  
Vikash Kumar Ojha
Keyword(s):  
Phase Space ◽  
Wigner Distribution ◽  
Distribution Functions ◽  
Space Distribution ◽  
Parton Distributions ◽  
Transverse Momentum Dependent ◽  
Phase Space Distribution ◽  
Generalized Parton Distributions ◽  
Wigner Distributions ◽  
Classical Phase Space

Wigner distribution functions are the quantum analogue of the classical phase space distribution and being quantum implies that they are not genuine phase space distribution and thus lack any probabilistic interpretation. Nevertheless, Wigner distributions are still interesting since they can be related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) under some limit. We study the Wigner distribution of quarks and also the orbital angular momentum (OAM) of quarks in the dressed quark model.

scholarly journals Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Anthony Mezzacappa ◽  
Eirik Endeve ◽  
O. E. Bronson Messer ◽  
Stephen W. Bruenn
Keyword(s):  
Phase Space ◽  
Weak Interactions ◽  
Kinetic Equations ◽  
Distribution Functions ◽  
Core Collapse ◽  
Algebraic Equations ◽  
Stellar Core ◽  
Dimensional Phase Space ◽  
Solution Methods ◽  
Physical Laws

AbstractThe proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than 50 years after the seminal paper by Colgate and White. The modern version of this paradigm, which we owe to Wilson, proposes that the supernova shock wave is powered by neutrino heating, mediated by the absorption of electron-flavor neutrinos and antineutrinos emanating from the proto-neutron star surface, or neutrinosphere. Neutrino weak interactions with the stellar core fluid, the theory of which is still evolving, are flavor and energy dependent. The associated neutrino mean free paths extend over many orders of magnitude and are never always small relative to the stellar core radius. Thus, neutrinos are never always fluid like. Instead, a kinetic description of them in terms of distribution functions that determine the number density of neutrinos in the six-dimensional phase space of position, direction, and energy, for both neutrinos and antineutrinos of each flavor, or in terms of angular moments of these neutrino distributions that instead provide neutrino number densities in the four-dimensional phase-space subspace of position and energy, is needed. In turn, the computational challenge is twofold: (i) to map the kinetic equations governing the evolution of these distributions or moments onto discrete representations that are stable, accurate, and, perhaps most important, respect physical laws such as conservation of lepton number and energy and the Fermi–Dirac nature of neutrinos and (ii) to develop efficient, supercomputer-architecture-aware solution methods for the resultant nonlinear algebraic equations. In this review, we present the current state of the art in attempts to meet this challenge.

Dynamical maps and nonnegative phase-space distribution functions in quantum mechanics

1987 ◽  
Vol 120 (4) ◽  
pp. 161-164 ◽  
Author(s):  
R. Jagannathan ◽  
R. Simon ◽  
E.C.G. Sudarshan ◽  
R. Vasudevan
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Distribution Functions ◽  
Space Distribution ◽  
Phase Space Distribution
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