scholarly journals Nonlinear density response from imaginary-time correlation functions: Ab initio path integral Monte Carlo simulations of the warm dense electron gas

2021 ◽  
Vol 155 (5) ◽  
pp. 054110
Author(s):  
Tobias Dornheim ◽  
Zhandos A. Moldabekov ◽  
Jan Vorberger
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Path Integral ◽  
Correlation Functions ◽  
Electron Gas ◽  
Time Correlation ◽  
Time Correlation Functions ◽  
Imaginary Time ◽  
Path Integral Monte Carlo ◽  
Density Response

ON THE CALCULATION OF THE HEAT CAPACITY IN PATH INTEGRAL MONTE CARLO SIMULATIONS

1992 ◽  
Vol 03 (02) ◽  
pp. 337-346 ◽  
Author(s):  
D. MARX ◽  
P. NIELABA ◽  
K. BINDER
Keyword(s):  
Heat Capacity ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Path Integral ◽  
General Relation ◽  
Absolute Magnitude ◽  
Computational Effort ◽  
Imaginary Time ◽  
Time Dimension ◽  
Path Integral Monte Carlo

In Path Integral Monte Carlo simulations the systems partition function is mapped to an equivalent classical one at the expense of a temperature-dependent Hamiltonian with an additional imaginary time dimension. As a consequence the standard relation linking the heat capacity Cv to the energy fluctuations, <E2>−<E>2, which is useful in standard classical problems with temperature-independent Hamiltonian, becomes invalid. Instead, it gets replaced by the general relation [Formula: see text] for the intensive heat capacity estimator; β being the inverse temperature and the subscript P indicates the P-fold discretization in the imaginary time direction. This heatcapacity estimator has the advantage of being based directly on the energy estimatorand thus requires no extra computational effort and is suited for extensive phase diagramstudies. As an example, numerical results are presented for a two-dimensional fluid withinternal magnetic quantum degrees of freedom. We discuss in detail origin and consequences of the excess term. Due to the subtraction of two relatively large contributions ofsimilar absolute magnitude a large statistical effort would be necessary for very accurateheat capacity estimates.

scholarly journals Dynamic properties of the warm dense electron gas based on ab initio path integral Monte Carlo simulations

2020 ◽  
Vol 102 (12) ◽  
Author(s):  
Paul Hamann ◽  
Tobias Dornheim ◽  
Jan Vorberger ◽  
Zhandos A. Moldabekov ◽  
Michael Bonitz
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Ab Initio ◽  
Path Integral ◽  
Dynamic Properties ◽  
Electron Gas ◽  
Path Integral Monte Carlo

Machine learning-assisted approximation of symmetrized quantum time correlation functions

2021 ◽  
Author(s):  
Arif Ullah
Keyword(s):  
Machine Learning ◽  
Molecular Dynamics ◽  
Real Time ◽  
Path Integral ◽  
Correlation Functions ◽  
Time Correlation ◽  
Time Correlation Functions ◽  
Imaginary Time ◽  
Quantum Time ◽  
Sampling Approach

Open-chain imaginary-time path-integral sampling approach known with the acronym OPSCF (J. Chem. Phys. 148, 102340 (2018)) is an approach to the calculation of approximate symmetrized quantum time correlation functions. In OPSCF approach, the real time t is treated as a parameter, and therefore for each real time t, a separate simulation on the imaginary time axis is needed to be run, which makes the OPSCF approach quite expensive and as a result, the approach loses the advantage of being a standard path-integral sampling approach. In this study, I propose that the use of OPSCF approach in combination with machine learning can reduce the computational cost by 75% to 90% (depending on the problem at hand). Combining OPSCF approach with ML is very straight forward which gives an upper hand to OPSCF approach over the trajectory-based methods such as the centroid molecular dynamics (CMD) and the ring-polymer molecular dynamics (RPMD).

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