Related papers: Time Dependent Effective Actions at Finite Tempera…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
We present a comprehensive analysis of effective temperatures based on fluctuation-dissipation relations in a model of an active fluid composed of self-propelled hard disks. We first investigate the relevance of effective temperatures in…
Temperature of a finite-sized system fluctuates due to the thermal fluctuations. However, a systematic mathematical framework for measuring or estimating the temperature is still underdeveloped. Here, we incorporate the estimation theory in…
We present a simple analytical method to solve master equations for finite temperatures and any initial conditions, which consists in the expansion of the density operator into normal modes. These modes and the expansion coefficients are…
The behavior of finite temperature planar electrodynamics is investigated. We calculate the static as well as dynamic characteristic functions using real time formalism. The temperature and density dependence of dielectric and permeability…
Chapter one is devoted to a study of fermions and bosons in two spatial dimensions in external electromagnetic fields. The effectve action is calculated by integrating out the matter fields. In chapter two, I investigate the resummation…
The optimized linear $\delta$-expansion is applied to the $\lambda \phi^4$ theory at high temperature. Using the imaginary time formalism the thermal mass is evaluated perturbatively up to order $\delta^2$. A variational procedure…
We investigate the theoretical foundations of the simulated tempering method and use our findings to design efficient algorithms. Employing a large deviation argument first used for replica exchange molecular dynamics [Plattner et al., J.…
In this thesis we introduce the concept of a guided dynamical system, and exploit this idea to solve various problems in functional equations and PDE's. Our main results are 1) a necessary and sufficient condition for unique-solvability of…
We describe some interesting effects observed during the evolution of nonequilibrium systems, using domain growth and glassy systems as examples. We breafly discuss the analytical tools that have been recently used to study the dynamics of…
In this work, exact solutions are derived for an integer- and fractional-order time-delayed diffusion equation with arbitrary initial conditions. The solutions are obtained using Fourier transform methods in conjunction with the known…
We apply the $\delta$-expansion perturbation scheme to the $\lambda \phi^{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\delta$-expansion the interaction term is written as $\lambda (\phi^{2})^{ 1 +…
In this paper, we summarize the historical development of finite-time thermodynamics and review the current state of research over the past two decades in this field, focusing on fundamental constraints of finite-time thermodynamic cycles,…
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
A method is presented for the computation of the one-loop effective action at finite temperature and density. The method is based on an expansion in the number of spatial covariant derivatives. It applies to general background field…
We consider the problem of the definition of an effective temperature via the long-time limit of the fluctuation-dissipation ratio (FDR) after a quench from the disordered state to the critical point of an O(N) model with dissipative…
This paper considerers the problem of computing the value of a solution of the heat equation at a given point inside a bounded domain after the initial time. It is assumed that the initial value of the solution inside the domain (possibly…
We are used to measure temperature with a thermometer and we know from everyday life that different types of thermometers measure the same temperature. This experience can be based on equilibrium thermodynamics, which explains the…
The process of deriving an interatomic potentials represents an attempt to integrate out the electronic degrees of freedom from the full quantum description of a condensed matter system. In practice it is the derivatives of the interatomic…
A method for determining the leading quantum contributions to the effective action for both zero and finite temperatures is presented. While it is described in the context of a scalar field theory, it can be straight-forwardly extended to…