Fermionic stochastic Schrödinger equation and master equation: An open-system model

Stochastic Hybrid System for Chemical Master Equation

Open boundaries for the nonlinear Schrödinger equation

We present a new algorithm, the Time Dependent Phase Space Filter (TDPSF) which is used to solve time dependent Nonlinear Schrodinger Equations (NLS). The algorithm consists of solving the NLS on a box with periodic boundary conditions (by any algorithm). Periodically in time we decompose the solution into a family of coherent states. Coherent states which are outgoing are deleted, while those ...

Master-equation approach to stochastic neurodynamics.

A Master equation approach to the stochastic neurodynamics proposed by Cowan[ in Advances in Neural Information Processing Systems 3, edited by R.P. Lippman, J.E. Moody, and D.S. Touretzky (Morgan Kaufmann, San Mateo, 1991), p.62] is investigated in this paper. We deal with a model neural network which is composed of two-state neurons obeying elementary stochastic transition rates. We show that...

Model Reduction and System Identification for Master Equation Control Systems

A master equation describes the continuous-time evolution of a probability distribution, and is characterized by a simple bilinear structure and an often-high dimension. We develop a model reduction approach in which the number of possible configurations and corresponding dimension is reduced, by removing improbable configurations and grouping similar ones. Error bounds for the reduction are de...

Model order reduction for nonlinear Schrödinger equation

We apply the proper orthogonal decomposition (POD) to the nonlinear Schrödinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving symplectic midpoint rule. A priori error estimates are derived for the POD reduced dynamical system. Numerical results for one and two dimensional NLS equations...