Generalized Phase-Space Method in the Langevin-Equation Approach

1978 ◽  
Vol 44 (5) ◽  
pp. 1435-1448 ◽  
Author(s):  
Fumiaki Shibata ◽  
Natsuki Hashitsume
Keyword(s):  
Phase Space ◽  
Langevin Equation ◽  
Equation Approach ◽  
Space Method ◽  
Generalized Phase Space

TOPOLOGICAL ASPECTS OF THE SPECIFIC HEAT

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4170-4185 ◽  
Author(s):  
C. M. SARRIS ◽  
A. N. PROTO
Keyword(s):  
Phase Space ◽  
Specific Heat ◽  
Quantum System ◽  
Uncertainty Principle ◽  
Positive Definite ◽  
Metric Tensor ◽  
Quantum Nature ◽  
Generalized Phase Space

We describe how the specific heat of a quantum system is related to a positive definite metric defined on the generalized phase space in which the dynamics and thermodynamics of the system take place. This relationship is given through the components of a second-rank covariant metric tensor, enhancing a topological nature of the specific heat. We also present two examples where it can be seen how the uncertainty principle imposes strong constraints on the values achieved by the specific heat showing its inherent quantum nature.

scholarly journals Dissipative quantum tunneling: quantum Langevin equation approach

1988 ◽  
Vol 128 (1-2) ◽  
pp. 29-34 ◽  
Author(s):  
G.W. Ford ◽  
J.T. Lewis ◽  
R.F. O'Connell
Keyword(s):  
Langevin Equation ◽  
Quantum Tunneling ◽  
Equation Approach ◽  
Quantum Langevin Equation
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