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.

Coordinate uncertainty principle in a generalized phase space

2014 ◽  
Vol 90 (2) ◽  
pp. 628-630 ◽  
Author(s):  
B. I. Sadovnikov ◽  
E. E. Perepelkin ◽  
N. G. Inozemtseva
Keyword(s):  
Phase Space ◽  
Uncertainty Principle ◽  
Generalized Phase Space

On the Uncertainty Principle for Positive Definite Densities

1996 ◽  
Vol 15 (4) ◽  
pp. 1015-1023 ◽  
Author(s):  
I. Dreier
Keyword(s):  
Uncertainty Principle ◽  
Positive Definite

The Duflo non-commutative Fourier transform for the Lorentz group

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040011
Author(s):  
Giacomo Rosati
Keyword(s):  
Fourier Transform ◽  
Phase Space ◽  
Quantum System ◽  
Lie Group ◽  
Lorentz Group ◽  
Commutative Algebra ◽  
Cotangent Bundle ◽  
Irreducible Representations ◽  
Algebra Representation

For a quantum system whose phase space is the cotangent bundle of a Lie group, like for systems endowed with particular cases of curved geometry, one usually resorts to a description in terms of the irreducible representations of the Lie group, where the role of (non-commutative) phase space variables remains obscure. However, a non-commutative Fourier transform can be defined, intertwining the group and (non-commutative) algebra representation, depending on the specific quantization map. We discuss the construction of the non-commutative Fourier transform and the non-commutative algebra representation, via the Duflo quantization map, for a system whose phase space is the cotangent bundle of the Lorentz group.

Zur Berechnung von spezifischer Wärme und Entropie in der Quantenstatistik

1965 ◽  
Vol 20 (12) ◽  
pp. 1553-1556
Author(s):  
F. Wagner ◽  
H. Koppe
Keyword(s):  
Free Energy ◽  
Variational Principle ◽  
Helmholtz Equation ◽  
Specific Heat ◽  
Quantum System ◽  
Thermodynamic Function ◽  
Variational Parameter ◽  
Statistical Operator

Applying the variational principle of BOGOLIUBOV to calculate the free energy of a quantum system one does not get, automatically, physical meaningful results for entropy and specific heat. By using the temperature in the ansatz for the statistical operator as a variational parameter it is proved, that at any rate, the approximation expression for free energy has the properties of a thermodynamic function, that means, it leads to positive values for specific heat and entropy, and to a GIBBS—HELMHOLTZ equation for entropy and free energy.

Phase space quantization and the uncertainty principle

2003 ◽  
Vol 317 (5-6) ◽  
pp. 365-369 ◽  
Author(s):  
Maurice A de Gosson
Keyword(s):  
Phase Space ◽  
Uncertainty Principle

Generalized phase space version of Langevin equations and associated Fokker-Planck equations

2000 ◽  
Vol 15 (2) ◽  
pp. 305-311 ◽  
Author(s):  
W.C. Kerr ◽  
A.J. Graham
Keyword(s):  
Phase Space ◽  
Langevin Equations ◽  
Fokker Planck Equations ◽  
Generalized Phase Space ◽  
Fokker Planck

scholarly journals Kinetic derivation of generalized phase space Chern-Simons theory

2017 ◽  
Vol 95 (12) ◽  
Author(s):  
Tomoya Hayata ◽  
Yoshimasa Hidaka
Keyword(s):  
Phase Space ◽  
Simons Theory ◽  
Chern Simons ◽  
Generalized Phase Space ◽  
Chern Simons Theory

Generalized phase space and conservative systems

2013 ◽  
Vol 88 (1) ◽  
pp. 457-459 ◽  
Author(s):  
B. I. Sadovnikov ◽  
N. G. Inozemtseva ◽  
E. E. Perepelkin
Keyword(s):  
Phase Space ◽  
Conservative Systems ◽  
Generalized Phase Space

A Generalized Phase Space Optical Analysis of X-Ray Optical Systems Using Crystal Monochromators

1978 ◽  
Vol 17 (S2) ◽  
pp. 449 ◽  
Author(s):  
Tadashi Matsushita ◽  
Ukyo Kaminaga ◽  
Kazutake Kohra
Keyword(s):  
Phase Space ◽  
Optical Systems ◽  
Optical Analysis ◽  
X Ray ◽  
Generalized Phase Space
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