scholarly journals THERMODYNAMICS OF PSEUDO-HERMITIAN SYSTEMS IN EQUILIBRIUM

2007 ◽  
Vol 22 (15) ◽  
pp. 1075-1084 ◽  
Author(s):  
VÍT JAKUBSKÝ
Keyword(s):  
Thermodynamic Properties ◽  
Physical Interpretation ◽  
Explicit Knowledge ◽  
Positive Definite ◽  
Explicit Calculation ◽  
Constant Number ◽  
Metric Operator ◽  
Number Of Particles

In the study of pseudo(quasi)-hermitian operators, the key role is played by the positive-definite metric operator. It enables physical interpretation of the considered systems. In this paper, we study the pseudo-hermitian systems with constant number of particles in equilibrium. We show that the explicit knowledge of the metric operator is not essential for the study of thermodynamic properties of the system. We introduce a simple example where the physically relevant quantities are derived without explicit calculation of either metric operator or spectrum of the Hamiltonian.

DIFFUSION IN MULTICOMPONENT METALLIC SYSTEMS: VI. SOME THERMODYNAMIC PROPERTIES OF THE D MATRIX AND THE CORRESPONDING SOLUTIONS OF THE DIFFUSION EQUATIONS

1963 ◽  
Vol 41 (12) ◽  
pp. 2166-2173 ◽  
Author(s):  
J. S. Kirkaldy ◽  
D. Weichert ◽  
Zia-Ul- Haq
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Stability Condition ◽  
Stable Solution ◽  
Positive Definite ◽  
Diffusion Equations ◽  
Second Law ◽  
Isothermal Diffusion ◽  
Gibb’S Free Energy ◽  
The Stability

The second law requirement that the Onsager L matrix for isothermal diffusion in a stable solution be positive definite and the stability condition for such a solution that the Hessian of the Gibb's free energy be positive definite impose on the diffusion D matrix the condition that it always have real and positive eigenvalues. This condition ensures that solutions of the differential equations for diffusion will always relax in a nonperiodic way.

scholarly journals THERMODYNAMIC PROPERTIES OF A QUANTUM GROUP BOSON GAS GLp,q(2)

2002 ◽  
Vol 17 (12) ◽  
pp. 701-710 ◽  
Author(s):  
AHMED JELLAL
Keyword(s):  
Thermodynamic Properties ◽  
Quantum Group ◽  
Present System ◽  
Bosonic System ◽  
Deformation Parameters ◽  
Number Of Particles

An approach is proposed enabling to effectively describe the behavior of a bosonic system. The approach uses the quantum group GL p,q(2) formalism. Indeed, considering a bosonic Hamiltonian in terms of the GL p,q(2) generators, it is shown that its thermodynamic properties are connected to deformation parameters p and q. For instance, the average number of particles and the pressure have been computed. If p is fixed to be the same value for q, our approach coincides perfectly with some results developed recently in this subject. The ordinary results, of the present system, can be found when we take the limit p = q = 1.

scholarly journals DISTRIBUTION OF PARASTATISTICS FUNCTIONS: AN OVERVIEW OF THERMODYNAMICS PROPERTIES

2016 ◽  
Vol 4 (2) ◽  
pp. 179
Author(s):  
R. Yosi Aprian Sari ◽  
W. S. B. Dwandaru
Keyword(s):  
Partition Function ◽  
Thermodynamic Properties ◽  
Thermodynamic Functions ◽  
Energy Levels ◽  
Canonical Partition Function ◽  
Thermodynamics Properties ◽  
Grand Canonical Partition Function ◽  
Bose Einstein ◽  
Grand Canonical ◽  
Number Of Particles

This study aims to determine the thermodynamic properties of the parastatistics system of order two. The thermodynamic properties to be searched include the Grand Canonical Partition Function (GCPF) Z, and the average number of particles N. These parastatistics systems is in a more general form compared to quantum statistical distribution that has been known previously, i.e.: the Fermi-Dirac (FD) and Bose-Einstein (BE). Starting from the recursion relation of grand canonical partition function for parastatistics system of order two that has been known, recuresion linkages for some simple thermodynamic functions for parastatistics system of order two are derived. The recursion linkages are then used to calculate the thermodynamic functions of the model system of identical particles with limited energy levels which is similar to the harmonic oscillator. From these results we concluded that from the Grand Canonical Partition Function (GCPF), Z, the thermodynamics properties of parastatistics system of order two (paraboson and parafermion) can be derived and have similar shape with parastatistics system of order one (Boson and Fermion). The similarity of the graph shows similar thermodynamic properties. Keywords: parastatistics, thermodynamic properties

Negative probability

1945 ◽  
Vol 41 (1) ◽  
pp. 71-73 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Probability Theory ◽  
Quantum Theory ◽  
Physical Interpretation ◽  
Random Variables ◽  
Characteristic Functions ◽  
Negative Probability ◽  
Number Of Particles

SummaryIt has been shown that orthodox probability theory may consistently be extended to include probability numbers outside the conventional range, and in particular negative probabilities. Random variables are correspondingly generalized to include extraordiary random variables; these have been defined in general, however, only through their characteristic functions.This generalized theory implies redundancy, and its use is a matter of convenience. Eddington(3) has employed it in this sense to introduce a correction to the fluctuation in number of particles within a given volume.Negative probabilities must always be combined with positive ones to give an ordinary probability before a physical interpretation is admissible. This suggests that where negative probabilities have appeared spontaneously in quantum theory it is due to the mathematical segregation of systems or states which physically only exist in combination.

scholarly journals PSEUDO-HERMITIAN INTERACTIONS IN DIRAC THEORY: EXAMPLES

2010 ◽  
Vol 25 (20) ◽  
pp. 1723-1732 ◽  
Author(s):  
BHABANI PRASAD MANDAl ◽  
SAURABH GUPTA
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Positive Definite ◽  
The Other ◽  
Relativistic Quantum Mechanics ◽  
Arbitrary Parameter ◽  
Scalar Interaction ◽  
Dirac Theory ◽  
Metric Operator ◽  
Dirac Hamiltonian

We consider a couple of examples to study the pseudo-Hermitian interaction in relativistic quantum mechanics. Rasbha interaction, commonly used to study the spin Hall effect, is considered with imaginary coupling. The corresponding Dirac Hamiltonian is shown to be parity pseudo-Hermitian. In the other example we consider parity pseudo-Hermitian scalar interaction with arbitrary parameter in Dirac theory. In both cases we show that the energy spectrum is real and all the other features of nonrelativistic pseudo-Hermitian formulation are present. Using the spectral method, the positive definite metric operator (η) has been calculated explicitly for both the models to ensure positive definite norms for the state vectors.

A hybrid formulation for fast explicit calculation of thermodynamic properties of refrigerants

2012 ◽  
Vol 35 (4) ◽  
pp. 1021-1034 ◽  
Author(s):  
Jaime Sieres ◽  
Fernando Varas ◽  
Jose Antonio Martínez-Suárez
Keyword(s):  
Thermodynamic Properties ◽  
Explicit Calculation ◽  
Hybrid Formulation
Sign in / Sign up

Export Citation Format

Share Document