Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThree-dimensional Lorentz model in a magnetic field : exact and Chapman-Enskog solutions
53
0
0.0
(
0
)
Authors
F. Cornu
Ask ChatGPT about the research
No Arabic abstract
We derive the exact solution of the Boltzmann kinetic equation for the three-dimensional Lorentz model in the presence of a constant and uniform magnetic field. The velocity distribution of the electrons reduces exponentially fast to its spherically symmetric component. In the long time hydrodynamic limit there remains only the diffusion process governed by an anisotropic diffusion tensor. The systematic way of building the Chapman-Enskog solutions is described.
rate research
Read More
This work examines the idea of applying the Chapman-Enskog (CE) method for approximating the solution of the Boltzmann equation beyond the realm of physics, using an information theory approach. Equations describing the evolution of averages and their fluctuations in a generalized phase space are established up to first order in the Knudsen parameter, which is defined as the ratio of the time between interactions (mean free time) and a characteristic macroscopic time. Although the general equations here obtained may be applied in a wide range of disciplines, in this paper only a particular case related to the evolution of averages in speculative markets is examined.
We investigate, by means of extensive Monte Carlo simulations, the magnetic critical behavior of the three-dimensional bimodal random-field Ising model at the strong disorder regime. We present results in favor of the two-exponent scaling scenario, $bar{eta}=2eta$, where $eta$ and $bar{eta}$ are the critical exponents describing the power-law decay of the connected and disconnected correlation functions and we illustrate, using various finite-size measures and properly defined noise to signal ratios, the strong violation of self-averaging of the model in the ordered phase.
We find an exact general solution to the three-dimensional (3D) Ising model via an exact self-consistency equation for nearest-neighbors correlations. It is derived by means of an exact solution to the recurrence equations for partial contractions of creation and annihilation operators for constrained spin bosons in a Holstein-Primakoff representation. In particular, we calculate analytically the total irreducible self-energy, the order parameter, the correlation functions, and the joined occupation probabilities of spin bosons. The developed regular microscopic quantum-field-theory method has a potential for a full solution of a long-standing and still open problem of 3D critical phenomena.
We show that for a d-dimensional model in which a quench with a rate tau^{-1} takes the system across a d-m dimensional critical surface, the defect density scales as n sim 1/tau^{m u/(z u +1)}, where u and z are the correlation length and dynamical critical exponents characterizing the critical surface. We explicitly demonstrate that the Kitaev model provides an example of such a scaling with d=2 and m= u=z=1. We also provide the first example of an exact calculation of some multispin correlation functions for a two-dimensional model which can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.
We discuss the exact solution for the properties of the recently introduced ``necklace model for reptation. The solution gives the drift velocity, diffusion constant and renewal time for asymptotically long chains. Its properties are also related to a special case of the Rubinstein-Duke model in one dimension.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
