First, second, and fourth moments of the Green function of stochastic wave equation for dispersive and Gaussian media: Monte Carlo method and path integrals

1994 ◽  
Author(s):  
Vladimir S. Filinov
Keyword(s):  
Monte Carlo ◽  
Wave Equation ◽  
Monte Carlo Method ◽  
Green Function ◽  
Path Integrals ◽  
Stochastic Wave Equation ◽  
The Green Function

scholarly journals Pauli Potential and Green-Function Monte-Carlo Method for Many-Fermion Systems

1998 ◽  
Vol 25 (1-3) ◽  
pp. 101-113 ◽  
Author(s):  
B. L. G. Bakker ◽  
M. I. Polikarpov ◽  
A. I. Veselov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Green Function ◽  
Pauli Potential ◽  
Fermion Systems

scholarly journals THE FOURTH VIRIAL COEFFICIENT OF ANYONS

1998 ◽  
Vol 13 (21) ◽  
pp. 3723-3747 ◽  
Author(s):  
ANDERS KRISTOFFERSEN ◽  
STEFAN MASHKEVICH ◽  
JAN MYRHEM ◽  
KÅRE OLAUSSEN
Keyword(s):  
Monte Carlo ◽  
Fourier Series ◽  
Monte Carlo Method ◽  
Path Integral ◽  
Virial Coefficient ◽  
Path Integrals ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Partition Functions ◽  
Two Dimensional

We have computed by a Monte Carlo method the fourth virial coefficient of free anyons, as a function of the statistics angle θ. It can be fitted by a four term Fourier series, in which two coefficients are fixed by the known perturbative results at the boson and fermion points. We compute partition functions by means of path integrals, which we represent diagramatically in such a way that the connected diagrams give the cluster coefficients. This provides a general proof that all cluster and virial coefficients are finite. We give explicit polynomial approximations for all path integral contributions to all cluster coefficients, implying that only the second virial coefficient is statistics dependent, as is the case for two-dimensional exclusion statistics. The assumption leading to these approximations is that the tree diagrams dominate and factorize.

scholarly journals Lecture notes on Diagrammatic Monte Carlo for the Fröhlich polaron

2018 ◽  
Author(s):  
Jonas Greitemann ◽  
Lode Pollet
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fourier Transforms ◽  
Full Detail ◽  
Many Body ◽  
Sampling Schemes ◽  
Self Energy ◽  
Extensive Documentation ◽  
Many Body Systems ◽  
The Green Function

These notes are intended as a detailed discussion on how to implement the diagrammatic Monte Carlo method for a physical system which is technically simple and where it works extremely well, namely the Fröhlich polaron problem. Sampling schemes for the Green function as well as the self-energy in the bare and skeleton (bold) expansion are disclosed in full detail. We discuss the Monte Carlo updates, possible implementations in terms of common data structures, as well as techniques on how to perform the Fourier transforms for functions with discontinuities. Control over the variety of parameters, especially in the bold scheme, is demonstrated. Sample codes are made available online along with extensive documentation. Towards the end, we discuss various extensions of the method and their applications. After working through these notes, the reader will be well equipped to explore the richness of the diagrammatic Monte Carlo method for quantum many-body systems.

Sign in / Sign up

Export Citation Format

Share Document