Document Detail


Dynamical simulations of classical stochastic systems using matrix product states.
MedLine Citation:
PMID:  21230208     Owner:  NLM     Status:  In-Process    
Abstract/OtherAbstract:
We adapt the time-evolving block decimation (TEBD) algorithm, originally devised to simulate the dynamics of one-dimensional quantum systems, to simulate the time evolution of nonequilibrium stochastic systems. We describe this method in detail; a system's probability distribution is represented by a matrix product state (MPS) of finite dimension and then its time evolution is efficiently simulated by repeatedly updating and approximately refactorizing this representation. We examine the use of MPS as an approximation method, looking at parallels between the interpretations of applying it to quantum state vectors and probability distributions. In the context of stochastic systems we consider two types of factorization for use in the TEBD algorithm: non-negative matrix factorization (NMF), which ensures that the approximate probability distribution is manifestly non-negative, and the singular value decomposition (SVD). Comparing these factorizations, we find the accuracy of the SVD to be substantially greater than current NMF algorithms. We then apply TEBD to simulate the totally asymmetric simple exclusion process (TASEP) for systems of up to hundreds of lattice sites in size. Using exact analytic results for the TASEP steady state, we find that TEBD reproduces this state such that the error in calculating expectation values can be made negligible even when severely compressing the description of the system by restricting the dimension of the MPS to be very small. Out of the steady state we show for specific observables that expectation values converge as the dimension of the MPS is increased to a moderate size.
Authors:
T H Johnson; S R Clark; D Jaksch
Related Documents :
15152688 - Geometric leaf placement strategies.
19610288 - Fast convolution-superposition dose calculation on graphics hardware.
1004398 - On the application of a liquid-dielectric ionization chamber to 252 cf dosimetry.
9472828 - Validation of a new virtual wedge model.
17645208 - Cad of efficient tmmn0 single-mode elliptical applicators with coaxial excitation.
19503188 - Absolute left-handed behaviors in a triangular elliptical-rod photonic crystal.
Publication Detail:
Type:  Journal Article     Date:  2010-09-16
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  82     ISSN:  1550-2376     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2010 Sep 
Date Detail:
Created Date:  2011-01-14     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  United States    
Other Details:
Languages:  eng     Pagination:  036702     Citation Subset:  -    
Affiliation:
Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom. t.johnson1@physics.ox.ac.uk
Export Citation:
APA/MLA Format     Download EndNote     Download BibTex
MeSH Terms
Descriptor/Qualifier:

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine


Previous Document:  Comparative Monte Carlo efficiency by Monte Carlo analysis.
Next Document:  Application of the discrete dipole approximation to very large refractive indices: Filtered coupled ...