Next Article in Journal / Special Issue
Analysis of Time Reversible Born-Oppenheimer Molecular Dynamics
Previous Article in Journal / Special Issue
Nonadiabatic Molecular Dynamics Based on Trajectories
Article Menu

Export Article

Open AccessArticle
Entropy 2014, 16(1), 86-109; doi:10.3390/e16010086

Approximating Time-Dependent Quantum Statistical Properties

Department of Physics and CNISM Unit 1, University of Rome "La Sapienza", Ple A. Moro 5, 00185 Rome, Italy
*
Author to whom correspondence should be addressed.
Received: 11 November 2013 / Revised: 10 December 2013 / Accepted: 19 December 2013 / Published: 27 December 2013
(This article belongs to the Special Issue Molecular Dynamics Simulation)
View Full-Text   |   Download PDF [518 KB, 24 February 2015; original version 24 February 2015]   |  

Abstract

Computing quantum dynamics in condensed matter systems is an open challenge due to the exponential scaling of exact algorithms with the number of degrees of freedom. Current methods try to reduce the cost of the calculation using classical dynamics as the key ingredient of approximations of the quantum time evolution. Two main approaches exist, quantum classical and semi-classical, but they suffer from various difficulties, in particular when trying to go beyond the classical approximation. It may then be useful to reconsider the problem focusing on statistical time-dependent averages rather than directly on the dynamics. In this paper, we discuss a recently developed scheme for calculating symmetrized correlation functions. In this scheme, the full (complex time) evolution is broken into segments alternating thermal and real-time propagation, and the latter is reduced to classical dynamics via a linearization approximation. Increasing the number of segments systematically improves the result with respect to full classical dynamics, but at a cost which is still prohibitive. If only one segment is considered, a cumulant expansion can be used to obtain a computationally efficient algorithm, which has proven accurate for condensed phase systems in moderately quantum regimes. This scheme is summarized in the second part of the paper. We conclude by outlining how the cumulant expansion formally provides a way to improve convergence also for more than one segment. Future work will focus on testing the numerical performance of this extension and, more importantly, on investigating the limit for the number of segments that goes to infinity of the approximate expression for the symmetrized correlation function to assess formally its convergence to the exact result. View Full-Text
Keywords: semiclassical statistical properties; time correlation functions; mixed quantum classical dynamics semiclassical statistical properties; time correlation functions; mixed quantum classical dynamics
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Bonella, S.; Ciccotti, G. Approximating Time-Dependent Quantum Statistical Properties. Entropy 2014, 16, 86-109.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top