THE UNDERLYING PHYSICS OF q-DEFORMED PSEUDOSPIN MODELS

1996 ◽  
Vol 05 (02) ◽  
pp. 403-421 ◽  
Author(s):  
S.S. AVANCINI ◽  
D.P. MENEZES ◽  
F.F. DE SOUZA CRUZ ◽  
M.M. WATANABE DE MORAES
Keyword(s):  
Free Energy ◽  
Variational Method ◽  
Temperature Effects ◽  
Helmholtz Free Energy ◽  
Time Dependent ◽  
Quantum Algebras ◽  
Hartree Fock

In this paper, we have used the q-deformed version of the Lipkin-Meshkov-Glick (LMG) model to summarize the utilization of quantum algebras already applied to soluble pseudospin models. Within the suq(2) context, we have checked the validity of the co herent states variational method, then used the Time Dependent Hartree-Fock (TDHF) approximation to compare with the exact evolution in time of the system, and finally observed the temperature effects undergone by the system, through the study of the Helmholtz free energy. We have also investigated the LMG model within the contexts of the supq(2) and suq(3) algebras and some of the features mentioned above have been rediscussed.

scholarly journals Temperature dependence of the Helmholtz free energy of liquid alkali metals

BIBECHANA ◽  
2012 ◽  
Vol 9 ◽  
pp. 7-12
Author(s):  
BK Singh ◽  
Sudhir Singh
Keyword(s):  
Free Energy ◽  
Correlation Function ◽  
Variational Method ◽  
Temperature Dependence ◽  
Alkali Metals ◽  
Helmholtz Free Energy ◽  
Model Potential ◽  
Type Model ◽  
Liquid Alkali Metals ◽  
Good Agreement

The Gibbs-Bogoliubov variational method has been considered to study the Helmholtz free energy of liquid alkali metals (Na, K, Rb and Cs) as a function of temperature, using Heine Abarenkov type model potential with Hubbard-Sham exchange and correlation function. The computed values are in very good agreement with experimental observations. DOI: http://dx.doi.org/10.3126/bibechana.v9i0.7144 BIBECHANA 9 (2013) 7-12

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

scholarly journals Free Energy of Metals from Quasi-Harmonic Models of Thermal Disorder

Metals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 195
Author(s):  
Pavel A. Korzhavyi ◽  
Jing Zhang
Keyword(s):  
Free Energy ◽  
First Principles ◽  
Density Functional ◽  
Helmholtz Free Energy ◽  
Complex Materials ◽  
Predictive Capability ◽  
Temperature Dependent ◽  
Disordered Alloys ◽  
Thermal Disorder ◽  
Structure Calculations

A simple modeling method to extend first-principles electronic structure calculations to finite temperatures is presented. The method is applicable to crystalline solids exhibiting complex thermal disorder and employs quasi-harmonic models to represent the vibrational and magnetic free energy contributions. The main outcome is the Helmholtz free energy, calculated as a function of volume and temperature, from which the other related thermophysical properties (such as temperature-dependent lattice and elastic constants) can be derived. Our test calculations for Fe, Ni, Ti, and W metals in the paramagnetic state at temperatures of up to 1600 K show that the predictive capability of the quasi-harmonic modeling approach is mainly limited by the electron density functional approximation used and, in the second place, by the neglect of higher-order anharmonic effects. The developed methodology is equally applicable to disordered alloys and ordered compounds and can therefore be useful in modeling realistically complex materials.

Thermodynamics Energy for Both Supervised and Unsupervised Learning Neural Nets at a Constant Temperature

1999 ◽  
Vol 09 (03) ◽  
pp. 175-186 ◽  
Author(s):  
HAROLD SZU
Keyword(s):  
Free Energy ◽  
Constant Temperature ◽  
Helmholtz Free Energy ◽  
Principal Component ◽  
Neural Nets ◽  
Mixing Condition ◽  
Smart Cameras ◽  
Minimization Principle ◽  
Output Entropy ◽  
Artificial Neural Network Ann

Unified Lyaponov function is given for the first time to prove the learning methodologies convergence of artificial neural network (ANN), both supervised and unsupervised, from the viewpoint of the minimization of the Helmholtz free energy at the constant temperature. Early in 1982, Hopfield has proven the supervised learning by the energy minimization principle. Recently in 1996, Bell & Sejnowski has algorithmically demonstrated. Independent Component Analyses (ICA) generalizing the Principal Component Analyses (PCA) that the continuing reduction of early vision redundancy happens towards the "sparse edge maps" by maximization of the ANN output entropy. We explore the combination of both as Lyaponov function of which the proven convergence gives both learning methodologies. The unification is possible because of the thermodynamics Helmholtz free energy at a constant temperature. The blind de-mixing condition for more than two objects using two sensor measurement. We design two smart cameras with short term working memory to do better image de-mixing of more than two objects. We consider channel communication application that we can efficiently mix four images using matrices [AO] and [Al] to send through two channels.

scholarly journals Theoretical and experimental comparative studies of nonlinear optical properties for selected melaminium compounds

2010 ◽  
Vol 8 (6) ◽  
pp. 1192-1202 ◽  
Author(s):  
Marek Drozd ◽  
Mariusz Marchewka
Keyword(s):  
Optical Properties ◽  
Acetic Acid ◽  
Nonlinear Optical ◽  
Time Dependent ◽  
X Ray ◽  
Hartree Fock ◽  
Optical Applications ◽  
Experimental Values ◽  
Nonlinear Optical Applications ◽  
Theoretical Results

AbstractThe bis(melaminium) sulphate dihydrate, 2,4,6-triamine-1,3,5-triazin-1,3-ium tartrate monohydrate, 2,4,6-triamine-1,3,5-triazin-1-ium hydrogenphthalate, 2,4,6-triamine-1,3,5-triazin-1-ium acetate acetic acid solvate monohydrate, 2,4,6-triamine-1,3,5-triazin-1-ium bis(selenate) trihydrate, melaminium diperchlorate hydrate, melaminium bis(trichloroacetate) monohydrate and melaminium bis(4-hydroxybenzenesulphonate) dihydrate were discovered recently as perspective materials for nonlinear optical applications. On the basis of X-ray structures for eight melaminium compounds the time dependent Hartree Fock (TDHF) method was used for calculation of the polarizability, and first and second hyperpolarizability. Detailed directional studies of calculated hyperpolarizability for all investigated melaminium compounds are shown. The theoretical results are compared with experimental values of β.

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