Simulation of quantum electrons in disordered system of scatterers by path integrals and complex-valued Monte Carlo method

1995 ◽  
Vol 52 (4) ◽  
pp. 356-359
Author(s):  
V S Filinov ◽  
L I Podlubny
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Path Integrals ◽  
Disordered System ◽  
Complex Valued

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.

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