Related papers: Algebraic solution of master equations
The dynamics of Markovian open quantum systems are described by Lindblad master equations. For fermionic and bosonic systems that are quasi-free, i.e., with Hamiltonians that are quadratic in the ladder operators and Lindblad operators that…
In this paper we classify the solutions to the geometric Neumann problem for the Liouville equation in the upper half-plane or an upper half-disk, with the energy condition given by finite area. As a result, we classify the conformal…
In contrast to regular ordinary differential equations, the problem of accurately setting initial conditions just emerges in the context of differential-algebraic equations where the dynamic degree of freedom of the system is smaller than…
High-temperature dimensional reduction provides a systematic effective field theory framework for studying finite-temperature thermodynamics and cosmological phase transitions. While the matching of super-renormalizable operators in the…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional…
In this paper, we establish two major classes of Liouville type results for the three-dimensional stationary tropical climate model. The first class is obtained under the assumptions imposed on $u,v,\theta$ whereas the second one relies on…
We develop a Widder-type theory for nonlocal heat equations involving quite general L\'evy operators. Thus, we consider nonnegative solutions and look for conditions on the operator that ensure: (i) uniqueness of nonnegative classical and…
This work introduces a methodology to solve ordinary differential equations using the Schur decomposition of the linear representation of the differential equation. This is done by first transforming the system into an upper triangular…
Recently, an effective Lindblad master equation for quantum systems whose dynamics are coupled to dissipative bosonic modes has been introduced [Phys. Rev. Lett. 129, 063601 (2022)]. In this approach, the bosonic modes are adiabatically…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
This paper is concerned with two properties of positive weak solutions of quasilinear elliptic equations with nonlinear gradient terms. First, we show a Liouville-type theorem for positive weak solutions of the equation involving the…
A numerical method is developed leading to algebraic systems based on generalized Lyapunov-Sylvester operators to approximate the solution of two-dimensional Kuramoto-Sivashinsky equation. It consists of an order reduction method and a…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
This paper proposes and analyzes a new operator splitting method for stochastic Maxwell equations driven by additive noise, which not only decomposes the original multi-dimensional system into some local one-dimensional subsystems, but also…
A method to calculate the adjoint solution for a large class of partial differential equations is discussed. It differs from the known continuous and discrete adjoint, including automatic differentiation. Thus, it represents an alternative,…
In this contribution we extend the Taylor expansion method proposed previously by one of us and establish equivalent partial differential equations of DDH lattice Boltzmann scheme at an arbitrary order of accuracy. We derive formally the…
We present a local Master equation for open system dynamics in two forms: Markovian and non-Markovian. Both have a wider range of validity than the Lindblad equation investigated by Davies. For low temperatures, they do not require coupling…
We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras.…
An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the analysis of thermodynamic vibrational properties of molecules. The local anharmonic effects are described by a Morse-like potential and the…