Related papers: An Approximate Solution of the Jaynes-Cummings Mod…
We study convergence rates for Gibbs measures, with density proportional to $e^{-f(x)/t}$, as $t \rightarrow 0$ where $f : \mathbb{R}^d \rightarrow \mathbb{R}$ admits a unique global minimum at $x^\star$. We focus on the case where the…
In this paper we give a conjectural refinement of the Davenport-Heilbronn theorem on the density of cubic field discriminants. We explain how this refinement is plausible theoretically and agrees very well with computational data.
We propose a density functional to find the ground state energy and density of interacting particles, where both the density and the pair density can adjust in the presence of an inhomogeneous potential. As a proof of principle we formulate…
A system of $N$ spin-1/2 particles interacting with a thermal reservoir is used as a pedagogical example for advanced undergraduate and graduate students. We introduce and illustrate some methods, approximations, and phenomena related to…
We investigate the simplest quintessence dissipative dark matter attractor cosmology characterized by a constant quintessence baryotropic index and a power--law expansion. We show a class of accelerated coincidence--solving attractor…
We describe how density-functional theory, well-known for its many uses in ab initio calculations of electronic structure, can be used to study the ground state of inhomogeneous model Hamiltonians. The basic ideas and concepts are discussed…
In a recent paper we have suggested that the finite temperature density matrix can be computed efficiently by a combination of polynomial expansion and iterative inversion techniques. We present here significant improvements over this…
Exact and nonperturbative quantum master equation can be constructed via the calculus on path integral. It results in hierarchical equations of motion for the reduced density operator. Involved are also a set of well--defined auxiliary…
This paper is concerned with the asymptotic expansions of the amplitude of the solution of the Helmholtz equation. The original expansions were obtained using a pseudo-differential decomposition of the Dirichlet to Neumann operator. This…
Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an…
Reduction operators of generalized Burgers equations are studied. A connection between these equations and potential fast diffusion equations with power nonlinearity -1 via reduction operators is established. Exact solutions of generalized…
A relation between Fick-Jacobs and Schr\"{o}dinger equation is shown. When the diffusion coefficient is constant, exact solutions for Fick-Jacobs equation are obtained. Using a change of variable the general case is studied.
We study a pressureless Euler system with a nonlinear density-dependent alignment term, originating in the Cucker-Smale swarming models. The alignment term is dissipative in the sense that it tends to equilibrate the velocities. Its density…
We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is that it provides quantitative convergence guarantees at a much…
Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and…
A method of exactly solving the master equation is presented in this letter. The explicit form of the solution is determined by the time evolution of a composite system including an auxiliary system and the open system in question. The…
The phenomenological two-level atom is re-analysed using the methods of effective field theory. By presenting the Dicke-Jaynes-Cummings model in real space, an exact diagonalization is accomplished going beyond the rotating wave…
In the present paper, the effects of viscous dark matter are analysed within the $\Lambda$CDM model. Here we consider bulk viscosity through the Israel-Stewart theory approach, leading to an effective pressure term in the continuity…
We compare the equilibrium solution for the condensate obtained in the mean--field approximation to the master equation for sympathetic cooling with the one obtained by Scully for a system in contact with a heat bath with the help of an…
A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a…