The Path-Integral Simulation of Quantum Systems

1990 ◽  
pp. 155-188 ◽  
Author(s):  
M. J. Gillan
Keyword(s):  
Path Integral ◽  
Quantum Systems

A non-perturbative path-integral based thermal cluster expansion approach for grand partition function of quantum systems

2002 ◽  
Vol 352 (1-2) ◽  
pp. 63-69 ◽  
Author(s):  
Sheikh Hannan Mandal ◽  
Rathindranath Ghosh ◽  
Goutam Sanyal ◽  
Debashis Mukherjee
Keyword(s):  
Partition Function ◽  
Path Integral ◽  
Cluster Expansion ◽  
Quantum Systems ◽  
Grand Partition Function

scholarly journals Matrix models and deformations of JT gravity

2020 ◽  
Vol 476 (2244) ◽  
pp. 20200582
Author(s):  
Edward Witten
Keyword(s):  
Matrix Models ◽  
Path Integral ◽  
Matrix Model ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Two Dimensional ◽  
Quantum Mechanical System ◽  
Specific Procedure ◽  
Dimensional Theory ◽  
Specific Quantum

Recently, it has been found that Jackiw-Teitelboim (JT) gravity, which is a two-dimensional theory with bulk action − 1 / 2 ∫ d 2 x g ϕ ( R + 2 ) , is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action − 1 / 2 ∫ d 2 x g ( ϕ R + W ( ϕ ) ) is likewise dual to a matrix model. With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model. There is a simple answer if W (0) = 0, and otherwise a rather complicated answer.

Interacting Quantum Systems

2014 ◽  
pp. 1-37
Keyword(s):  
Density Matrix ◽  
Integral Equations ◽  
Time Evolution ◽  
Path Integral ◽  
Quantum Systems ◽  
Transition Rates ◽  
Feynman Path Integral ◽  
Matrix Representations ◽  
Evolution Operators ◽  
Feynman Path

In this chapter, basic quantum tools such as time-evolution operators, transition rates and amplitudes, statistical and projector operators, and interaction and density matrix representations are employed to characterize the open and interacting quantum systems with the aid of Schrödinger, quantum master, Fokker-Planck, and Feynman path integral equations and formulations.

Sign in / Sign up

Export Citation Format

Share Document