Approximation Scheme for the Quantum Liouville Equation Using Phase-Space Distribution Functions

1985 ◽  
Vol 55 (8) ◽  
pp. 896-896 ◽  
Author(s):  
M. Ploszajczak ◽  
M. J. Rhoades-Brown
Keyword(s):  
Phase Space ◽  
Liouville Equation ◽  
Approximation Scheme ◽  
Distribution Functions ◽  
Space Distribution ◽  
Phase Space 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.

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

scholarly journals Radially anisotropic systems with forces: equilibrium states

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
Pierfrancesco Di Cintio ◽  
L. Ciotti ◽  
C. Nipoti
Keyword(s):  
Phase Space ◽  
Distribution Functions ◽  
Space Distribution ◽  
Anisotropic Models ◽  
Interparticle Forces ◽  
Phase Space Distribution ◽  
Radial Orbital ◽  
Anisotropic Systems ◽  
Preparatory Work ◽  
Tangential Directions

We continue the study of collisionless systems governed by additive$r^{-{\it\alpha}}$interparticle forces by focusing on the influence of the force exponent${\it\alpha}$on radial orbital anisotropy. In this preparatory work, we construct the radially anisotropic Osipkov–Merritt phase-space distribution functions for self-consistent spherical Hernquist models with$r^{-{\it\alpha}}$forces and$1\leqslant {\it\alpha}<3$. The resulting systems are isotropic at the centre and increasingly dominated by radial orbits at radii larger than the anisotropy radius$r_{a}$. For radially anisotropic models we determine the minimum value of the anisotropy radius$r_{ac}$as a function of${\it\alpha}$for phase-space consistency (such that the phase-space distribution function is nowhere negative for$r_{a}\geqslant r_{ac}$). We find that$r_{ac}$decreases for decreasing${\it\alpha}$, and that the amount of kinetic energy that can be stored in the radial direction relative to that stored in the tangential directions for marginally consistent models increases for decreasing${\it\alpha}$. In particular, we find that isotropic systems are consistent in the explored range of${\it\alpha}$. By means of direct$N$-body simulations, we finally verify that the isotropic systems are also stable.

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