Related papers: Exact Solutions of the Caldeira-Leggett Master Equ…
In this paper, we consider the following indefinite fully fractional heat equation involving the master operator \begin{equation} (\partial_t -\Delta)^{s} u(x,t) = x_1u^p(x,t)\ \ \mbox{in}\ \R^n\times\R , \end{equation} where $s\in(0,1)$,…
Despite the enormous technological interest in micro and nanolasers, surprisingly, no class-B quantum density-matrix model is available to date, capable of accurately describing coherence and photon correlations within a unified theory. In…
As an alternative to solving of Poisson equation in Particle-in-Cell methods, a new construction of current density exactly satisfying continuity equation in finite differences is developed. This procedure called density decomposition is…
We give two classes of spherically symmetric exact solutions of the couple gravitational and electromagnetic fields with charged source in the tetrad theory of gravitation. The first solution depends on an arbitrary function $H({R},t)$. The…
We study solutions of the Thermodynamic Bethe Ansatz equations for relativistic theories defined by the factorizable $S$-matrix of an integrable QFT deformed by CDD factors. Such $S$-matrices appear under generalized TTbar deformations of…
We point out a rather effective approach for solving the time-dependent harmonic oscillator $\ddot q=-\omega^2 q$ under various regularity assumptions. Where $\omega(t )$ is $C^1$ this is reduced to Hamilton equation for the angle variable…
In this work, we establish a general theory of phase transitions and quantum entanglement in the equilibrium state at arbitrary temperatures. First, we derived a set of universal functional relations between the matrix elements of two-body…
Decoherence can be provided by a dissipative environment as described by the Caldeira-Leggett equation. This equation is foundational to the theory of quantum dissipation. However, no experimental test has been performed that measures for…
We describe a method for obtaining the scattering matrix for nuclear or chemical reactions on a finite lattice. Aside from the preparation of the initial and final states as wave packets, the only other operation required is unitary time…
We study a general quantum system interacting with environment modeled by the bosonic heat bath of Caldeira and Leggett type. General interaction Hamiltonians are considered that commute with the system's Hamiltonian so that there is no…
We introduce a non-equilibrium version of the Caldeira-Leggett model in which a quantum particle is strongly coupled to a set of engineered reservoirs. The reservoirs are composed by collections of squeezed and displaced thermal modes, in…
An expansion method for perturbation of the zero temperature grand canonical density matrix is introduced. The method achieves quadratically convergent recursions that yield the response of the zero temperature density matrix upon variation…
A finite element code for heat conduction, together with an adjoint solver and a suite of optimization tools was applied for the solution of Calderon's problem. One of the questions whose answer was sought was whether the solution to these…
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial…
This paper focuses on the analysis of a free energy functional, that models a dilute suspension of magnetic nanoparticles in a two-dimensional nematic well. The {\it first part} of the article is devoted to the asymptotic analysis of global…
We revisit a classical problem of theoretical electrochemistry: the response of an electric double layer capacitor (EDLC) subject to a small, suddenly applied external potential. We solve the Debye-Falkenhagen equation to obtain exact…
We study in this paper the continuous and discrete Euler-Lagrange equations arising from a quadratic lagrangian. Those equations may be thought as numerical schemes and may be solved through a matrix based framework. When the lagrangian is…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
The density matrix, i.e. the Fourier transform of the momentum distribution, is obtained analytically for all magnetization of the Gutzwiller wave function in one dimension with exclusion of double occupancy per site. The present result…
We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of…