Related papers: Which differential equations correspond to the Lin…
We are interested in the simulation of open quantum systems governed by the Lindblad master equation in an infinite-dimensional Hilbert space. To simulate the solution of this equation, the standard approach involves two sequential…
As it has been proven, the determination of general one-dimensional Schr\"odinger Hamiltonians having third-order differential ladder operators requires to solve the Painlev\'e IV equation. In this work, it will be shown that some specific…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
The transformation of the Nth- order linear difference equation into a system of the first order difference equations is presented. The proposed transformation gives possibility to get new forms of the N-dimensional system of the first…
In the framework of the Lindblad theory for open quantum systems the damping of the harmonic oscillator is studied. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master…
A first order differential equation with a periodic operator coefficient acting in a pair of Hilbert spaces is considered. This setting models both elliptic equations with periodic coefficients in a cylinder and parabolic equations with…
In this article, we study about the solutions of second order linear differential equations by considering several conditions on the coefficients of homogenous linear differential equation and its associated non-homogenous linear…
An ordinary differential equation is said to have a superposition formula if its general solution can be expressed as a function of a finite number of particular solution. Nonlinear ODE's with superposition formulas include matrix Riccati…
For multi-level open quantum system, the interaction between different levels could pose challenge to understand the quantum system both analytically and numerically. In this work, we study the approximation of the dynamics of the…
The problem of equivalency for linear differential operators of the first order is discussed.
Admissible point transformations of classes of $r$th order linear ordinary differential equations (in particular, the whole class of such equations and its subclasses of equations in the rational form, the Laguerre-Forsyth form, the first…
The purpose of this paper is to present a class of particular solutions of a C(2,1) conformally invariant nonlinear Klein-Gordon equation by symmetry reduction. Using the subgroups of similitude group reduced ordinary differential equations…
A quantum master equation is obtained for identical fermions by including a relaxation term in addition to the mean-field Hamiltonian. [Huang C F and Huang K N 2004 Chinese J. Phys. ${\bf 42}$ 221; Gebauer R and Car R 2004 Phys. Rev. B…
We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting…
The paper studies the harmonic maps on a direction between a Riemannian space and a generalized Lagrange space. Also, it is proved there that the solutions of C^2 class of certain ODEs or PDEs are harmonic maps, in the sense of this paper.
We are interested by the behaviour of a 1D single heavy particle, interacting with an environment made of very fast particles in a thermal state. Assuming that the interactions are instantaneous, we construct an appropriate quantum jump…
This book encompasses both traditional and modern methods treating partial differential equation (PDE) of first order and second order. There is a balance in making a selfcontained mathematical text and introducing new subjects. The Lie…
We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…
The quantum state for the spatial degrees of freedom of photons propagating through turbulence is analyzed. The turbulent medium is modeled by a single phase screen for weak scintillation conditions and by multiple phase screens for general…
We consider the model of a quantum harmonic oscillator governed by a Lindblad master equation where the typical drive and loss channels are multi-photon processes instead of single-photon ones; this implies a dissipation operator of order…