Solution of the Bloch Equation for Many-Particle Systems in Terms of the Path Integral

1973 ◽  
Vol 35 (4) ◽  
pp. 980-984 ◽  
Author(s):  
Tohru Morita
Keyword(s):  
Path Integral ◽  
Bloch Equation ◽  
Particle Systems

scholarly journals Coherent-state path-integral simulation of many-particle systems

1997 ◽  
Vol 55 (4) ◽  
pp. 3870-3877 ◽  
Author(s):  
M. Beccaria ◽  
B. Allés ◽  
F. Farchioni
Keyword(s):  
Coherent State ◽  
Path Integral ◽  
Particle Systems ◽  
State Path

scholarly journals Evaluation of Density Matrix and Helmholtz Free Energy for Harmonic Oscillator Asymmetric Potential via Feynmans Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Piyarut Moonsri ◽  
Artit Hutem
Keyword(s):  
Free Energy ◽  
Kinetic Energy ◽  
Density Matrix ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Integral Method ◽  
Helmholtz Free Energy ◽  
Unit Length ◽  
Bloch Equation ◽  
Path Integral Method

We apply a Feynmans technique for calculation of a canonical density matrix of a single particle under harmonic oscillator asymmetric potential and solving the Bloch equation of the statistical mechanics system. The density matrix (P^u) and kinetic energy per unit length (τ^L) can be directly evaluated from the solving solutions. From the evaluation, it was found that both of the density matrix and kinetic energy per unit length depended on the parameter of the value of asymmetric potential (λ), the value of axes-shift potential (g), and temperature (T). Comparison of the Helmholtz free energy was derived by the Feynmans technique and the path-integral method. The results illustrated are slightly different.

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