From non-Hermitian linear response to dynamical correlations and fluctuation-dissipation relations in quantum many-body systems
KT Geier, P Hauke - PRX Quantum, 2022 - APS
Quantum many-body systems are characterized by their correlations. While equal-time
correlators and unequal-time commutators between operators are standard observables, the …
correlators and unequal-time commutators between operators are standard observables, the …
A class of new Magnus-type methods for semi-linear non-commutative Ito stochastic differential equations
In this paper, a class of new Magnus-type methods is proposed for non-commutative Itô
stochastic differential equations (SDEs) with semi-linear drift term and semi-linear diffusion …
stochastic differential equations (SDEs) with semi-linear drift term and semi-linear diffusion …
[HTML][HTML] Higher strong order methods for linear Itô SDEs on matrix Lie groups
M Muniz, M Ehrhardt, M Günther, R Winkler - BIT Numerical Mathematics, 2022 - Springer
In this paper we present a general procedure for designing higher strong order methods for
linear Itô stochastic differential equations on matrix Lie groups and illustrate this strategy …
linear Itô stochastic differential equations on matrix Lie groups and illustrate this strategy …
Curved schemes for stochastic differential equations on, or near, manifolds
J Armstrong, T King - Proceedings of the Royal Society A, 2022 - royalsocietypublishing.org
Given a stochastic differential equation (SDE) in R n whose solution is constrained to lie in
some manifold M⊂ R n, we identify a class of numerical schemes for the SDE whose …
some manifold M⊂ R n, we identify a class of numerical schemes for the SDE whose …
Unified signature cumulants and generalized Magnus expansions
The signature of a path can be described as its full non-commutative exponential. Following
T. Lyons, we regard its expectation, the expected signature, as a path space analogue of the …
T. Lyons, we regard its expectation, the expected signature, as a path space analogue of the …
[PDF][PDF] Cutoff stability of multivariate geometric Brownian motion
This article quantifies the asymptotic ε-mixing times, as ε tends to 0, of a multivariate
geometric Brownian motion with respect to the Wasserstein-2-distance. We study the cases …
geometric Brownian motion with respect to the Wasserstein-2-distance. We study the cases …
Formulae for mixed moments of wiener processes and a stochastic area integral
This paper deals with the expectation of monomials with respect to the stochastic area
integral and the increments of two Wiener processes,. In a monomial, if the exponent of one …
integral and the increments of two Wiener processes,. In a monomial, if the exponent of one …
On the impact of feeding cost risk in aquaculture valuation and decision making
We study the effect of stochastic feeding costs on animal-based commodities with particular
focus on aquaculture. More specifically, we use soybean futures to infer on the stochastic …
focus on aquaculture. More specifically, we use soybean futures to infer on the stochastic …
Qubit fidelity under stochastic Schr\" odinger equations driven by colored noise
Environmental noise on a controlled quantum system is generally modeled by a dissipative
Lindblad equation. This equation describes the average state of the system via the density …
Lindblad equation. This equation describes the average state of the system via the density …
[HTML][HTML] Numerical solution of kinetic SPDEs via stochastic Magnus expansion
In this paper, we show how the Itô-stochastic Magnus expansion can be used to efficiently
solve stochastic partial differential equations (SPDE) with two space variables numerically …
solve stochastic partial differential equations (SPDE) with two space variables numerically …