CaltechAUTHORS
  A Caltech Library Service

Numerical ansatz for solving integro-differential equations with increasingly smooth memory kernels: spin-boson model and beyond

Zwolak, Michael (2008) Numerical ansatz for solving integro-differential equations with increasingly smooth memory kernels: spin-boson model and beyond. Computational Science and Discovery, 1 . Art No. 015002. ISSN 1749-4699. https://resolver.caltech.edu/CaltechAUTHORS:ZWOcsd08

[img]
Preview
PDF - Published Version
See Usage Policy.

556Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:ZWOcsd08

Abstract

We present an efficient and stable numerical ansatz for solving a class of integro-differential equations. We define the class as integro-differential equations with increasingly smooth memory kernels. The resulting algorithm reduces the computational cost from the usual T^2 to TC(T), where T is the total simulation time and C(T) is some function. For instance, C(T ) is equal to ln T for polynomially decaying memory kernels. Due to the common occurrence of increasingly smooth memory kernels in physical, chemical and biological systems, the algorithm can be applied in quite a wide variety of situations. We demonstrate the performance of the algorithm by examining two cases. Firstly, we compare the algorithm to a typical numerical procedure for a simple integro-differential equation. Secondly, we solve the non-interacting blip approximation equations for the spin-boson model in real time.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1088/1749-4699/1/1/015002DOIUNSPECIFIED
http://www.iop.org/EJ/abstract/1749-4699/1/1/015002/PublisherUNSPECIFIED
Additional Information:© 2008 IOP Publishing Ltd. Received 5 March 2007, in final form 11 December 2007. Published 20 November 2008. The author would like to thank G Vidal and G Refael for helpful discussions. This research was supported by the National Science Foundation through its Graduate Fellowship program and a Sigma Xi Grant-in-Aid of Research.
Funders:
Funding AgencyGrant Number
National Science FoundationUNSPECIFIED
Sigma XiUNSPECIFIED
Record Number:CaltechAUTHORS:ZWOcsd08
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:ZWOcsd08
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13245
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:05 Feb 2009 22:13
Last Modified:03 Oct 2019 00:35

Repository Staff Only: item control page