Yin Mei Wong | Searcharxiv

arXiv2011

Optimally chosen Nakajima-Zwanzig master equation for mean field approximation

We define an ensemble of projection operators, each of which has an exact associated Nakajima-Zwanzig master equation for quantum open system evolution. A mean field approximation for the memory kernels is introduced that yields, for an optimally chosen projection operator, a completely determined inhomogeneous master equation. Previous proofs of positivity and equilibration are extended to these new inhomogeneous non-Markovian master equations. We study a nitrogen vacancy center in diamond interacting with 13C impurities to illustrate the method.

quant-ph↗

arXiv2006

Comparison Tests of Variable-Stepsize Algorithms for Stochastic Ordinary Differential Equations of Finance

Since the introduction of the Black-Scholes model stochastic processes have played an increasingly important role in mathematical finance. In many cases prices, volatility and other quantities can be modeled using stochastic ordinary differential equations. Available methods for solving such equations have until recently been markedly inferior to analogous methods for deterministic ordinary differential equations. Recently, a number of methods which employ variable stepsizes to control local error have been developed which appear to offer greatly improved speed and accuracy. Here we conduct a comparative study of the performance of these algorithms for problems taken from the mathematical finance literature.

physics.data-an↗