Exponential Integrators for Stochastic Schrödinger Equation

Abstract

We present a class of exponential integrators to compute solutions of the stochastic Schrödinger equation arising from the modeling of open quantum systems. In order to be able to implement the methods within the same framework as the deterministic counterpart, we express the solution using the Kunita's representation. With appropriate truncations, the solution operator can be written as matrix exponentials, which can be efficiently implemented by the Krylov subspace projection. The accuracy is examined in terms of the strong convergence, by comparing trajectories, and the weak convergence, by comparing the density-matrix operator. We show that the local accuracy can be further improved by introducing a third-order commutator in the exponential. The effectiveness of the proposed methods is tested using the example from Di Ventra et al. [Journal of Physics: Condensed Matter, 2004].

References in corpus (7)

• Transport in nanoscale systems: the microcanonical versus grand-canonical picture
• Stochastic Time-Dependent Current-Density-Functional Theory
• Efficient method for simulating quantum electron dynamics under the time dependent Kohn-Sham equation
• A stochastic approach to open quantum systems
• Stochastic time-dependent current-density functional theory: a functional theory of open quantum systems
• Numerical solution of conservative finite-dimensional stochastic Schrodinger equations
• The strong convergence of operator-splitting methods for the Langevin dynamics model

Cited by in corpus (7)

• Testing Generalized Einstein-Cartan-Kibble-Sciama Gravity using Weak Deflection Angle and Shadow Cast
• Simulating Open Quantum Systems Using Hamiltonian Simulations
• Super-entropy bumblebee AdS black holes
• Towards robust variational quantum simulation of Lindblad dynamics via stochastic Magnus expansion
• Deflection of charged massive particles by a four-dimensional charged Einstein-Gauss-Bonnet black hole
• Dynamically Optimal Unraveling Schemes for Simulating Lindblad Equations
• Markovian Embedding Procedures for Non-Markovian Stochastic Schrödinger Equations