Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userStatistical mechanics of Coulomb gases as quantum theory on Riemann surfaces
133
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Statistical mechanics of 1D multivalent Coulomb gas may be mapped onto non-Hermitian quantum mechanics. We use this example to develop instanton calculus on Riemann surfaces. Borrowing from the formalism developed in the context of Seiberg-Witten duality, we treat momentum and coordinate as complex variables. Constant energy manifolds are given by Riemann surfaces of genus $ggeq 1$. The actions along principal cycles on these surfaces obey ODE in the moduli space of the Riemann surface known as Picard-Fuchs equation. We derive and solve Picard-Fuchs equations for Coulomb gases of various charge content. Analysis of monodromies of these solutions around their singular points yields semiclassical spectra as well as instanton effects such as Bloch bandwidth. Both are shown to be in perfect agreement with numerical simulations.
rate research
Read More
The lectures provide a pedagogical introduction to the methods of CFT as applied to two-dimensional critical behaviour.
An interesting connection between the Regge theory of scattering, the Veneziano amplitude, the Lee-Yang theorems in statistical mechanics and nonextensive Renyi entropy is addressed. In this scheme the standard entropy and the Renyi entropy appear to be different limits of a unique mathematical object. This framework sheds light on the physical origin of nonextensivity. A non trivial application to spin glass theory is shortly outlined.
We review phase space techniques based on the Wigner representation that provide an approximate description of dilute ultra-cold Bose gases. In this approach the quantum field evolution can be represented using equations of motion of a similar form to the Gross-Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation. These techniques provide a practical quantitative description of both equilibrium and dynamical properties of Bose gas systems. We develo
These lectures were prepared for the 2014 PCMI graduate summer school and were designed to be a lightweight introduction to statistical mechanics for mathematicians. The applications feature some of the themes of the summer school: sphere packings and tilings.
We develop a microscopic approach to the consistent construction of the kinetic theory of dilute weakly ionized gases of hydrogen-like atoms. The approach is based on the framework of the second quantization method in the presence of bound states of particles and the method of reduced description of relaxation processes. Within the approach we developed the first-order perturbation theory over the weak interaction for a system of kinetic equations for the Wigner distribution functions of free fermions of both kinds and their bound states, the hydrogen-like atoms. It is shown that the conditions of low-temperature approximation, of the gas non-degeneracy and the approximation of weak interaction are realistic and can be met in a wide range of temperatures and the densities of the studied system. We obtain dispersion equations for determining the frequency and wave attenuation coefficients in dilute weakly ionized gas of hydrogen-like atoms near the described equilibrium state. In the two-level atom approximation it is shown that in the system there are longitudinal waves of matter polarization and transverse waves with the behavior characteristic of plasmon polaritons. The expressions for the dependence of the frequency and the Landau damping coefficients on the wave vector for all branches of the oscillations detected, are obtained. Quantitative estimations of the characteristics of the elementary perturbations in the system on an example of a weakly ionized dilute gas of Na-23 atoms are presented. The possibility of using the results of the theory developed to describe the properties of a Bose condensate of photons in dilute weakly ionized gas of hydrogen-like atoms is noted and the directions of its generalizations are discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
