scholarly journals Landau effective Hamiltonian and its application to magnetic systems

2018 ◽  
Vol 26 (1) ◽  
pp. 19-28
Author(s):  
K. M. Haponenko ◽  
A. I. Sokolovsky
Keyword(s):  
Free Energy ◽  
Landau Theory ◽  
Microscopic Theory ◽  
Order Parameters ◽  
Effective Hamiltonian ◽  
Magnetic Systems ◽  
Nonequilibrium States ◽  
Ferromagnetic System ◽  
Definition Of ◽  
Phenomenological Landau Theory

The Landau definition of the effective Hamiltonian (of the nonequilibrium free energy) is realized in a microscopic theory. According to Landau remark, the consideration is based on classical statistical mechanics. In his approach nonequilibrium states coinciding with equilibrium fluctuations are taken into account (the Onsager principle). The definition leads to the exact fulfillment of the Boltzmann principle written in the form with the complete free energy. The considered system is assumed to consist of two subsystems. The first subsystem is an equilibrium one. The second subsystem is a nonequilibrium one and its state is described by quantities that are considered as order parameters. The effective Hamiltonian is calculated near equilibrium in the form of a series in powers of deviations of the order parameters from their equilibrium values. The coefficients of the series are expressed through equilibrium correlation functions of the order parameters. In the final approximation correlations of six and more order parameters are neglected and correlations of four parameters are assumed to be small that leads to the corresponding perturbation theory. The developed theory is compared with the phenomenological Landau theory of phase transitions of the second kind. The obtained results are concretized for paramagnetic-ferromagnetic system. The consideration is restricted by paramagnetic phase.

scholarly journals Realization of the Landau definitions of effective Hamiltonian and nonequilibrium free energy in microscopic theory

2020 ◽  
Vol 28 (2) ◽  
pp. 63-74
Author(s):  
A. I. Sokolovsky
Keyword(s):  
Free Energy ◽  
Phase Transitions ◽  
General Formula ◽  
Correlation Functions ◽  
Nonequilibrium Thermodynamic ◽  
Microscopic Theory ◽  
Effective Hamiltonian ◽  
Equilibrium Fluctuations ◽  
Thermodynamic Potentials ◽  
Definition Of

Equilibrium fluctuations of some set of parameters in the states described by the canonical Gibbs distribution are investigated. In the theory of phase transitions of the second kind, these parameters are components of the order parameter. The microscopic realization of the Landau definition of the effective Hamiltonian of the system for studying the equilibrium fluctuations of the specified system of parameters is discussed in the terms of the probability density of their values. A general formula for this function is obtained and it is expressed through the equilibrium correlation functions of these parameters. An expression for the effective Hamiltonian in terms of deviations of the parameters from their equilibrium values is obtained. The deviations are considered small for conducting the calculations. The possibility of calculating the exact free energy of the system using the found effective Hamiltonian is discussed. In the microscopic theory, the implementation of the Landau definition of nonequilibrium thermodynamic potentials introduced in his phenomenological theory of phase transitions of the second kind is investigated. Nonequilibrium states of a fluctuating system described with some sets of parameters are considered. A general formula for nonequilibrium free energy expressed through the correlation functions of these parameters is obtained as for the effective Hamiltonian above. Like the previous case, the free energy expression via parameter deviations from the equilibrium values is obtained and small deviations are considered for calculations. The idea of the identity of the effective Hamiltonian of the system and its nonequilibrium free energy is discussed in connection with the Boltzmann distribution. The Gaussian approximation of both developed formalisms is considered. A generalization of the constructed theory for the case of spatially inhomogeneous states and the study of long-wave fluctuations are developed.

GENERALISED GINZBURG-LANDAU THEORY FOR HIGH Tc SUPERCONDUCTORS

1988 ◽  
Vol 02 (06) ◽  
pp. 1513-1536 ◽  
Author(s):  
M. P. DAS ◽  
HONG-XING HE ◽  
T. C. CHOY
Keyword(s):  
High Temperature Superconductivity ◽  
Landau Theory ◽  
Strong Support ◽  
Microscopic Theory ◽  
Order Parameters ◽  
Abrikosov Vortex ◽  
Ginzburg Landau ◽  
Structural Distortions ◽  
Coupling Parameters ◽  
Local Gauge Invariance

In the absence of a consensus for the correct microscopic theory for high temperature superconductivity we have devoted earlier efforts to obtain a generalised Ginzburg-Landau (GL) phenomenological model. Originally the main motivation was to examine how GL theory could be generalised. Neglecting secondary order parameters like structural distortions, oxygen vacancies etc. whose effects are integrated out and phenomenologically treated in the GL coupling parameters, we concentrate on the superconducting order parameters. The resulting theory which emerged indicates severe constraints in the parameter space of models due to local gauge invariance. Now recent experiments by several groups on specific heat and conductivity fluctuations lend strong support to this theory. Additional predictions on gap parameters and tunnelling properties are exotic and could be verified. The magnetic and Abrikosov vortex states appear to be complicated and require further study.

System of thermodynamic quantities in the McMillan-Mayer solution theory

1985 ◽  
Vol 50 (4) ◽  
pp. 791-798 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Generating Function ◽  
Simple Form ◽  
Unit Volume ◽  
Thermodynamic Quantities ◽  
Solution Theory ◽  
Pure Solvent ◽  
Second Derivatives ◽  
Definition Of ◽  
Derivatives Of

The McMillan-Mayer (MM) free energy per unit volume of solution AMM, is employed as a generating function of the MM system of thermodynamic quantities for solutions in the state of osmotic equilibrium with pure solvent. This system can be defined by replacing the quantities G, T, P, and m in the definition of the Lewis-Randall (LR) system by AMM, T, P0, and c (P0 being the pure solvent pressure). Following this way the LR to MM conversion relations for the first derivatives of the free energy are obtained in a simple form. New relations are derived for its second derivatives.

scholarly journals Zilch vortical effect for fermions

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Artem Alexandrov ◽  
Pavel Mitkin
Keyword(s):  
Kinetic Theory ◽  
Spin Polarization ◽  
Wigner Function ◽  
Microscopic Theory ◽  
Chiral Media ◽  
Function Formalism ◽  
Chiral Effects ◽  
Definition Of ◽  
Theory Framework ◽  
Full Analogy

Abstract We consider the notion of zilch current that was recently discussed in the literature as an alternative helicity measure for photons. Developing this idea, we suggest the generalization of the zilch for the systems of fermions. We start with the definition of the photonic zilch current in chiral kinetic theory framework and work out field-theoretical definition of the fermionic zilch using the Wigner function formalism. This object has similar properties to the photonic zilch and is conserved in the non-interacting theory. We also show that, in full analogy with a case of photons, the fermionic zilch acquires a non-trivial contribution due to the medium rotation - zilch vortical effect (ZVE) for fermions. Combined with a previously studied ZVE for photons, these results form a wider set of chiral effects parameterized by the spin of the particles and the spin of the current. We briefly discuss the origin of the ZVE, its possible relation to the anomalies in the underlying microscopic theory and possible application for studying the spin polarization in chiral media.

scholarly journals Different length scales for order parameters in two-gap superconductors: Extended Ginzburg-Landau theory

2011 ◽  
Vol 84 (6) ◽  
Author(s):  
L. Komendová ◽  
M. V. Milošević ◽  
A. A. Shanenko ◽  
F. M. Peeters
Keyword(s):  
Landau Theory ◽  
Order Parameters ◽  
Ginzburg Landau ◽  
Length Scales

The Microscopic Theory of Superfluidity and Superconductivity Driven by Single Particle and Pair Condensation of Attracting Bosons

1998 ◽  
Vol 12 (21) ◽  
pp. 2151-2224 ◽  
Author(s):  
S. Dzhumanov
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Single Particle ◽  
Microscopic Theory ◽  
Order Parameters ◽  
Coupling Constants ◽  
Bose Liquid ◽  
Composite Bosons ◽  
Superfluidity And Superconductivity ◽  
Pair Condensation

A original microscopic theory of superfluidity and superconductivity driven by the single particle (SPC) and pair condensation (PC) of attracting bosons both in Fermi and in Bose systems is developed. This theory (as distinct from the existing theories) for Fermi systems contains two order parameters Δ F and Δ B characterizing the attracting fermion pairs and boson pairs, respectively. In such systems superconducting (SC) phase transition is accompanied, as a rule, by the formation of k-space composite bosons (e.g. Cooper pairs and bipolarons) with their subsequent transition to the superfluid (SF) state by attractive SPC and PC. A novel Fermi-liquid and SF Bose-liquid theories are elaborated for description this two-stage Fermi–Bose-liquid (FBL) scenario of SC (or SF) transition. The crossover from k- to real (r)-space pairing regime for BCS-like coupling constants γ F ≃ 0.7-0.9 and the irrelevance of r-space pairs to the superconductivity are shown. The developed SF Bose-liquid theory predicts the first-order phase transition SPC ↔ PC of attracting 3d-bosons with the kink-like behaviors of all SC (SF) parameters near [Formula: see text] in accordance with the observations in 4 He , 3 He and superconductors. It is argued that the coexistence of the order parameters Δ F and Δ B leads to the superconductivity by two FBL scenarios. One of these scenarios is realized in the so-called fermion (type I, II and III) superconductors (FSC) (where formation of k-space composite bosons and their condensation occur at the same temperature) and the other in the boson (type II and III) superconductors (BSC) (where BCS-like pairing take place in the normal state with manifesting of the second-order phase transition and opening of the pseudogap at T=T F > T c ). There the gapless superfluidity (superconductivity) is caused by the gapless excitation spectrum of bosons at [Formula: see text] and not by the presence of point or line nodes of the BCS-like gap Δ F assumed in some s-, p- and d-pairing models. The 3D- and 2D-insulator–metal–superconductor phase diagrams are presented. The necessary and sufficient microscopic criterions for superfluidity is formulated. The theory proposed are in close agreement with the observations in 4 He , 3 He , superconductors, nuclear and neutron star matter, cosmology, etc.

Variational thermodynamic derivation of the formula for pressure difference across a charged conducting liquid surface and its relation to the thermodynamics of electrical capacitance

1995 ◽  
Vol 450 (1938) ◽  
pp. 177-192 ◽  
Keyword(s):  
Free Energy ◽  
Pressure Difference ◽  
Liquid Surface ◽  
Field Energy ◽  
Conducting Liquid ◽  
Difference Formula ◽  
Direct Energy ◽  
Free Case ◽  
Definition Of ◽  
Work Done

The formula for pressure difference across a charged conducting liquid surface has conventionally been derived by adding a Maxwell stress term to the pressure-difference formula for the field-free case. As far as can be established, no derivation applying direct energy-based methods to the charged-surface case has ever been clearly formulated. This paper presents a first-principles variational derivation, starting from the laws of thermodynamics and modelled on Gibbs’s (1875) approach to the field-free case. The derivation applies to the static equilibrium situation. The method is to treat the charged liquid and its environment as a heterogeneous system in thermodynamic equilibrium, and consider the effects of a small virtual variation in the shape of the conducting-liquid surface. Expressions can be obtained for virtual changes in the free energies of relevant system components and for the virtual electrical work done on the system. By converting the space integral of the variation in electrostatic field energy to an integral over the surface of the liquid electrode, the usual pressure-difference formula is retrieved. It is also shown how the problem can be formulated, in various ways, as a free-energy problem in a situation involving electric stresses and capacitance. The most satisfactory approach involves the definition of an unfamiliar form of free energy, that can be seen as the electrical analogue of the Gibbs free energy and may have use in other contexts.

Alignment of carbon nanotubes under the influences of nematic liquid crystals and electric fields — an analytical study

2021 ◽  
Author(s):  
Setia Budi Sumandra ◽  
Bhisma Mahendra ◽  
Fahrudin Nugroho ◽  
Yusril Yusuf
Keyword(s):  
Carbon Nanotubes ◽  
Free Energy ◽  
Electric Field ◽  
Electric Fields ◽  
Analytical Study ◽  
Free Energy Density ◽  
Diameter Ratio ◽  
Order Parameters ◽  
Anchoring Strength ◽  
Length To Diameter Ratio

Carbon nanotubes (CNTs) have benefits in various fields, they are disadvantageous due to their tendency to form aggregates and poorly controlled alignment of the CNT molecules (characterized by order parameters). These deficiencies can be overcome by dispersing the CNTs in nematic liquid crystal (LC) and placing the mixture under the influence of an electric field. In this study, Doi and Landau–de Gennes free energy density equations are used to analytically confirm that an electric field increases the order parameters of CNTs and LCs in a dispersion mixture. The anchoring strength of the nematic LC is also found to affect the order parameters of the CNTs and LC. Further, increasing the length-to-diameter ratio of the CNTs increases their alignment without affecting the LC alignment. These findings indicate that CNT molecular alignment can be controlled by adjusting the CNT length-to-diameter ratio, anchoring the LCs, and adjusting the electric field strength.

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