2 edition of **Wigner function and kinetic theory** found in the catalog.

Wigner function and kinetic theory

Howard Vernon Lauer

- 49 Want to read
- 17 Currently reading

Published
**1966**
.

Written in

- Wigner, Eugene Paul, -- 1902-,
- Kinetic theory of gases

**Edition Notes**

Statement | by Howard Vernon Lauer, Jr |

The Physical Object | |
---|---|

Pagination | 106, [2] leaves : |

Number of Pages | 106 |

ID Numbers | |

Open Library | OL14415983M |

For a dilute and nondegenerate relativistic spin- {1}/{2} system two kinds of Wigner functions are defined: one has sixteen spinor components and the other four spin components. Their relationship is established. Statistical expressions for the current density, the energy-momentum density and the spin density are obtained in terms of both kinds of Wigner by: Application of the Wigner Distribution Function in Optics (M.J. Bastiaans) Introduction. Wigner distribution function as a local frequency spectrum. Examples of Wigner distribution functions. Properties of the Wigner distribution function. Ray spread function of an optical system. Transport equations for the Wigner distribution Edition: 1.

This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat. The Wigner quasiprobability distribution (also called the Wigner function or the Wigner–Ville distribution after Eugene Wigner and Jean-André Ville) is a quasiprobability distribution. It was introduced by Eugene Wigner in to study quantum corrections to classical statistical mechanics. The goal was to link the wavefunction that appears in Schrödinger's equation to a probability distribution in phase space. It is a generating function for all spatial autocorrelation functions .

We calculate the Wigner function for massive spin-1/2 particles in an inhomogeneous electromagnetic field to leading order in the Planck constant ℏ. Going beyond leading order in ℏ we then derive a generalized Boltzmann equation in which the force exerted by an inhomogeneous electromagnetic field on the particle dipole moment arises naturally. It is developed in 3 directions: Landauer-like theory, kinetic theory and Green-Kubo linear response theory. This work generalizes the 2 directions of Landauer-like theory and the kinetic theory. Firstly, NEGF is used to derive phonon-phonon Hedin-like functional derivative equations which generates conserving self energy approximations for phonon-phonon : Paperback.

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Elements of quantum kinetic theory, including the Green's-function formalism and the Wigner-Moyal equation. Relativistic kinetic theory and Lorentz invariants. Kinetic properties of metals and amorphous media. Monte Carlo analysis in kinetic theory.

Kinetic study of shock waves This third revised edition features a new section on constants. "This monograph is devoted to a standard approach of kinetic theory in classical and quantum systems. The book is divided in 7 chapters; each of them is ended by a set of interesting problems of different difficulties.

The presentation is clear. The book includes also tables and figures that make more pleasant its reading. Wigner function and kinetic theory for massive spin-1/2 particles Nora Weickgenannt a, Xin-li Shenga,b, Enrico Speranza, Qun Wangb, Dirk H.

Rischkea,b aInstitute for Theoretical Physics, Goethe University, Max-von-Laue-Str. 1, D Frankfurt am Main, Germany. We calculate the Wigner function for massive spin-1/2 particles in an inhomogeneous electromagnetic field to leading order in the Planck constant $\\hbar$.

Going beyond leading order in $\\hbar$ we then derive a generalized Boltzmann equation in which the force exerted Wigner function and kinetic theory book an inhomogeneous electromagnetic field on the particle dipole moment arises naturally. Furthermore, a kinetic equation. About this book. Introduction.

Kinetic Theory: Classical, Quantum, and Relativistic Descriptions goes beyond the scope of other works in the field with its thorough treatment of. A new definition of the Wigner function for quantum fields coupled to curved space–time and an external Yang–Mills field is studied on the example of scalar and Dirac fields.

The definition uses the formalism of the tangent bundles and is explicitly covariant and gauge by: functions which are generated by the y-integrations. In general combining with the Maxwell equation, the quantum kinetic equation of Wigner function Eq.(4) is equivalent to the QED ﬁeld theory.

In order to connect Eq.(4) with kinetic theory, one needs to obtain explicitly the equations of all elements of the Wigner function, which is a 4 × 4.

Wigner's book (published in ) is an expanded and revised English translation of the book originally published in German in Starting from vectors and matrices the author moves on to the description of abstract group theory and its application to atomic spectra/5(6).

The mathematical theory of non-uniform gases: an account of the kinetic theory of viscosity, thermal conduction, and diffusion in gases Cambridge University Press Sydney Chapman, T. Cowling. Kinetic Theory for Quantum Plasmas M. Bonitz momentum and Wigner representation, have been discussed in detail in the text book [3].

A quantum kinetic equation follows from the ﬁrst hierarchy equation upon use of the cluster expansion, F 12 =F 1F 2 +g 12, where g. Chiral magnetic effect and chiral kinetic theory the kinetic theory for chiral fermions. velocity force. 3-dimensional Chiral kinetic equation 22 velocity • We used Wigner function to obtain the chiral kinetic equation with Berry phase.

velocity force. Recent progress Kinetic theory for massive spin-1/2 particles from the Wigner-function formalism C RC- TR Kinetic theory for massive spin-1/2 particles from the Wigner-function formalism N.

Weickgenannt, X.-l. Sheng, E. Speranza, Q. Wang, and D.H. Rischke, PRD () New development of hydrodynamics and its applications in Heavy-Ion Collisions. Fonction Wigner Kinetic theory of matter Matter, Kinetic theory of Matter, Kinetic thory of Méthode Chapmann-Enskog Relativistic mechanics Science / General Science / Mechanics / Dynamics / General Science / Relativity Théorie cinétique relativité Théorie transport Transport theory: Export Citation: BiBTeX EndNote RefMan.

We calculate the Wigner function for massive spin-1/2 particles in an inhomogeneous electromagnetic field to leading order in the Planck constant $\hbar$. Going beyond leading order in $\hbar$ we then derive a generalized Boltzmann equation in which the force exerted by an inhomogeneous electromagnetic field on the particle dipole moment arises : Nora Weickgenannt, Xin-Li Sheng, Enrico Speranza, Dirk H.

Rischke, Qun Wang. Here we give an introductory account of the wave kinetic theory. Its basic ingredients are the Wigner function and its evolution equation. Historically it started inwhen Wigner proposed his function as a way to represent the quantum state of a particle in its classical phase space [1].Author: J.

Mendonça, Hugo Terças. Equal-time Kinetic Theory 3D distribution 𝑥, Ԧ= 0 (𝑥,)is not equivalent to the 4D distribution (𝑥,). They are equivalent to each other only in on-shell case.

How to obtain a quantum kinetic theory. Covariant Wigner function Advantage: covariant theory. A new definition of the Wigner function for quantum fields coupled to curved space-time and an external Yang-Mills field is studied on the example of scalar and Dirac fields.

The definition uses the formalism of the tangent bundles and is explicitly covariant and gauge invariant. Derivation of collisionless quantum kinetic equations is carried out for both quantum fields by using the first. The function /(x, p, s) is hence a combination of a Wigner function in the phase space variables and the Q-function for the spin.

Equivalence with the density matrix formalism The construction above contains the same information as the density matrix, and the distribution function can be used to calculate the expectation value of any. Wigner's book (published in ) is an expanded and revised English translation of the book originally published in German in Starting from vectors and matrices the author moves on to the description of abstract group theory and its application to atomic spectra/5(7).

We calculate the Wigner function for massive spin-1/2 particles in an inhomogeneous electromagnetic field to leading order in the Planck constant ℏ \hbar beyond leading order in ℏ \hbar ℏ we then derive a generalized Boltzmann equation in which the force exerted by an inhomogeneous electromagnetic field on the particle dipole moment arises naturally.

Recommended Books and Resources This lecture course covers three topics: kinetic theory, stochastic processes and linear response. Most decent books on statistical mechanics will have a section covering non-equilibrium topics in general.

However, if you’re looking for details beyond the basics, you’ll probably need a di↵erent book for.This book is an informative guide for researchers, and the benefits are a result from an integrated view of a very broad area of research, which is limited in previous books about this subject.

The main unifying tool explored in this book is the wave kinetic theory based on Wigner functions.The deﬁnition of the Wigner function The derivation of the Wigner transport equation Properties of the Wigner fucntion Another form of the Wigner function Derivation of the Wigere equation —- (q,k) Reference The derivation of the Wigner transport equation I Taking the derivative of Pw(q,p,t) w.r.t t, we will have such a term A in the Wigner File Size: KB.