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

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.

The Generalized Quasi-Variational Principles of NCS and Its Application in Mechanical Vibration

2007 ◽  
Author(s):  
Lifu Liang ◽  
Liming Dai ◽  
Qingyong Guo
Keyword(s):  
Phase Space ◽  
Variational Principles ◽  
Mechanical Vibration ◽  
Internal Force ◽  
Energy Principle ◽  
Force System ◽  
Conservative Systems ◽  
Generalized Displacements ◽  
Complementary Energy Principle ◽  
Two Kinds Of Variables

According to the corresponding relations between generalized forces and generalized displacements, the basic equations of elasto-dynamics in phase space are multiplied by corresponding virtual quantities, integrated and then added algebraically. By considering the character of fellow body and surface forces, the generalized quasi-variational principles of non-conservative systems are established in elasto-dynamics in phase space. By doing inverse Laplace transformation, the convolutional generalized quasi-variational principles of non-conservative systems of elasto-dynamics are established in original space. Applying the generalized quasi-complementary energy principle to the mechanical vibration problem of two kinds of variables, the authors of this paper present a calculation method for solving two kinds of variables simultaneously: the internal force and the displacement of a typical fellow force system.

CHAOTIC DIFFUSION IN MULTIDIMENSIONAL CONSERVATIVE MAPS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250237 ◽  
Author(s):  
PABLO M. CINCOTTA ◽  
CLAUDIA M. GIORDANO
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Resonance Interaction ◽  
Chaotic Diffusion ◽  
Conservative Systems

In the present paper, we provide results and discussions concerning the processes that lead to local and global chaotic diffusion in the phase space of multidimensional conservative systems. We investigate and provide a measure of the extent of the domain over which diffusion may occur. All these issues are thoroughly discussed by dealing with a multidimensional conservative map that would be representative of the dynamics of a resonance interaction, which is an important mechanism in many dynamical systems.

Generalized phase space representations in classical optics

2011 ◽  
Author(s):  
Miguel A. Alonso ◽  
Jonathan C. Petruccelli ◽  
Seongkeun Cho
Keyword(s):  
Phase Space ◽  
Generalized Phase Space
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