Two-oscillator mapping modification of the Poisson bracket mapping equation formulation of the quantum–classical Liouville equation

2020 ◽  
Vol 153 (21) ◽  
pp. 214103
Author(s):  
Hyun Woo Kim ◽  
Young Min Rhee
Keyword(s):  
Poisson Bracket ◽  
Liouville Equation ◽  
Equation Formulation ◽  
Mapping Equation

scholarly journals Improving long time behavior of Poisson bracket mapping equation: A mapping variable scaling approach

2014 ◽  
Vol 141 (12) ◽  
pp. 124107 ◽  
Author(s):  
Hyun Woo Kim ◽  
Weon-Gyu Lee ◽  
Young Min Rhee
Keyword(s):  
Poisson Bracket ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Mapping Equation ◽  
Long Time

scholarly journals Improving long time behavior of Poisson bracket mapping equation: A non-Hamiltonian approach

2014 ◽  
Vol 140 (18) ◽  
pp. 184106 ◽  
Author(s):  
Hyun Woo Kim ◽  
Young Min Rhee
Keyword(s):  
Poisson Bracket ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Hamiltonian Approach ◽  
Mapping Equation ◽  
Long Time

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

scholarly journals Estimates for Liouville equation with quantized singularities

2021 ◽  
Vol 380 ◽  
pp. 107606
Author(s):  
Juncheng Wei ◽  
Lei Zhang
Keyword(s):  
Liouville Equation

scholarly journals Five-brane current algebras in type II string theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Machiko Hatsuda ◽  
Shin Sasaki ◽  
Masaya Yata
Keyword(s):  
Poisson Bracket ◽  
Gauge Field ◽  
The Self ◽  
Dirac Bracket ◽  
Type Ii ◽  
Gauge Transformations ◽  
Transition Rules ◽  
Superstring Theories ◽  
Kaluza Klein ◽  
Current Algebras

Abstract We study the current algebras of the NS5-branes, the Kaluza-Klein (KK) five-branes and the exotic $$ {5}_2^2 $$ 5 2 2 -branes in type IIA/IIB superstring theories. Their worldvolume theories are governed by the six-dimensional $$ \mathcal{N} $$ N = (2, 0) tensor and the $$ \mathcal{N} $$ N = (1, 1) vector multiplets. We show that the current algebras are determined through the S- and T-dualities. The algebras of the $$ \mathcal{N} $$ N = (2, 0) theories are characterized by the Dirac bracket caused by the self-dual gauge field in the five-brane worldvolumes, while those of the $$ \mathcal{N} $$ N = (1, 1) theories are given by the Poisson bracket. By the use of these algebras, we examine extended spaces in terms of tensor coordinates which are the representation of ten-dimensional supersymmetry. We also examine the transition rules of the currents in the type IIA/IIB supersymmetry algebras in ten dimensions. Based on the algebras, we write down the section conditions in the extended spaces and gauge transformations of the supergravity fields.

scholarly journals A derivation of the Liouville equation for hard particle dynamics with non-conservative interactions

2020 ◽  
pp. 1-35
Author(s):  
Benjamin D. Goddard ◽  
Tim D. Hurst ◽  
Mark Wilkinson
Keyword(s):  
Liouville Equation ◽  
Particle Dynamics ◽  
Fundamental Importance ◽  
Continuum Models ◽  
Hard Particle ◽  
Interacting Particles ◽  
Weak Formulation ◽  
Physical Systems ◽  
Physical Particle

The Liouville equation is of fundamental importance in the derivation of continuum models for physical systems which are approximated by interacting particles. However, when particles undergo instantaneous interactions such as collisions, the derivation of the Liouville equation must be adapted to exclude non-physical particle positions, and include the effect of instantaneous interactions. We present the weak formulation of the Liouville equation for interacting particles with general particle dynamics and interactions, and discuss the results using two examples.

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