Related papers: Quantum simulation of partial differential equatio…
We give the regularization for fractional integral by delta sequence and apply it to obtain existence-uniqueness theorems in Colombeau algebras for nonlinear equations with singularities: nonlinear system of integral equations with polar…
Variational quantum algorithms are a promising tool for solving partial differential equations. The standard approach for its numerical solution are finite difference schemes, which can be reduced to the linear algebra problem. We consider…
By their very nature, field-theoretical Hamiltonians are derived in momentum representation. To solve the corresponding integro-differential equations is more difficult than to solve the simpler differential equations in configuration space…
It is shown how the phase-damping master equation, either in Markovian and nonMarkovian regimes, can be obtained as an averaged random unitary evolution. This, apart from offering a common mathematical setup for both regimes, enables us to…
A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic…
In this paper we will construct the Schrodinger representation for the linearly polarized Gowdy $S^1\times S^2$ and $S^3$ models coupled to massless scalar fields. Here the quantum states belong to a $L^2$-space for a suitable quantum…
We investigate the space time fractional nonlinear Schrodinger equation (FNLSE) incorporating the modified Riemann Liouville derivative introduced by Jumari. The equation is characterized by two parameters: the fractional derivative…
Based on the real-time formalism, especially, on Thermo Field Dynamics, we derive the Schwinger-Dyson gap equation for the fermion propagator in QED and Four-Fermion model at finite-temperature and -density. We discuss some advantage of the…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
We present a new parallel numerical method for solving the non-stationary Schr\"odinger equation with linear nonlocal condition and time-dependent potential which does not commute with the stationary part of the Hamiltonian. The given…
In this letter, by establishing the Schr\"odinger equation of the optimization problem, the optimization problem is transformed into a constrained state quantum problem with the objective function as the potential energy. The mathematical…
The time dependent complex Schr\"odinger equation with cubic nonlinearity is solved by constructing differential quadrature algorithm based on sinc functions. Reduction to a coupled system of real equations enables to approach the space…
This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to…
In this paper, we reformulate the semi-classical Schr\"odinger equation in the presence of electromagnetic field by the Gaussian wave packets transform. With this approach, the highly oscillatory Schr\"odinger equation is equivalently…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
In this work, we obtain the numerical temperature field to a thermally developing fluid flow inside parallel plates problem with a quantum computing method. The physical problem deals with the heat transfer of a steady state,…
In the harmonic oscillator representation, the Schrodinger equation has a form of a set of infinite number of algebraical equations which are labeled by the radial quantum number "n". It is shown that at n>>1 these equations are…
Computing solutions to partial differential equations using the fast Fourier transform can lead to unwanted oscillatory behavior. Due to the periodic nature of the discrete Fourier transform, waves that leave the computational domain on one…
Partial differential equations are fundamental tools in mathematics,sciences and engineering. This book is mainly an exposition of the various algebraic techniques of solving partial differential equations for exact solutions developed by…
In this work, a new relationship is established between the solutions of higher fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As…