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Landau theory
About: Landau theory is a research topic. Over the lifetime, 2882 publications have been published within this topic receiving 57078 citations.
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TL;DR: In this article, the authors extend the time-dependent effective theory for the Goldstone field (the phase of the pair field) with s-wave interactions to finite temperature and show that when Landau damping is neglected, the effective theory can be written as a local timedependent non-linear Schrodinger Lagrangian (TDNLSL) which preserves the Galilean invariance of the zero temperature effective theory and is identified with the superfluid component.
Abstract: We extend to finite temperature the time-dependent effective theory for the Goldstone field (the phase of the pair field) $ \theta $ which is appropriate for a superfluid containing one species of fermions with s-wave interactions, described by the BCS Lagrangian. We show that, when Landau damping is neglected, the effective theory can be written as a local time-dependent non-linear Schrodinger Lagrangian (TDNLSL) which preserves the Galilean invariance of the zero temperature effective theory and is identified with the superfluid component. We then calculate the relevant Landau terms which are non-local and which destroy the Galilean invariance. We show that the retarded $\theta$-propagator (in momentum space) can be well represented by two poles in the lower-half frequency plane, describing damping with a predicted temperature, frequency and momentum dependence. It is argued that the real parts of the Landau terms can be approximately interpreted as contributing to the normal fluid component.
19 citations
TL;DR: In this article, the correlated density matrix theory is employed and further developed to analyze the one-body density matrix ρ1(|rcffff 1-rcffff 2|) of the normal and superfluid phases of a strongly interacting Bose system at non-zero temperature.
Abstract: The correlated density matrix theory is employed and further developed to analyze the one-body density matrix ρ1(|r
1-r
2|) of the normal and superfluid phases of a strongly interacting Bose system at non-zero temperature. The approach continues the formal development described in an earlier article and is based on a suitable trial ansatz for the many-body density matrixW(R, R′)∼Φ(R) Q(R, R′) Φ(R′) with the wave function Φ and incoherence factorQ incorporating the essential statistical and dynamical correlations. Special attention is given to the appearance of off-diagonal long-range order in function ρ1(|r
1-r
2|) and its relation to the condensation strength Bcc characterizing the degree of coherence in the superfluid phase. We derive a number of structural relations that have counterparts in known results on ρ1 in the Jastrow variational theory of the Bose ground state. We discuss Bose-Einstein condensation and make contact to Landau's phenomenological theory of continuous phase transitions. Numerical estimates are presented on the condensation strength and the condensate fraction of liquid4He as functions of the temperature.
19 citations
TL;DR: In this paper, a fully parameterised Landau model of the Pm3m ↔ I4/mcm transition as a function of temperature, pressure and composition is presented.
Abstract: Octahedral tilting transitions in perovskites are usually identified by the significant lattice distortions which accompany them. The underlying mechanism of coupling between the tilts and the macroscopic strain also gives rise to large anomalies in single crystal and bulk elastic moduli. Landau theory provides an effective framework for describing these different changes in properties and relating them, quantitatively, to the evolution of the driving order parameter for the transition. This approach has been used to analyse the overall elastic behaviour of perovskites belonging to the CaTiO3-SrTiO3 (CST) solid solution, which is expected to be closely analogous to the behaviour of silicate perovskites at higher pressures and temperatures. Pm3m ↔ I4/mcm and I4/mcm ↔ Pnma transitions in CST perovskites are marked by changes in the shear modulus of ∼ 10-30%. The evolution of the order parameter and, hence, of the octahedral tilt angles through these can be followed through the variations of spontaneous strains extracted from high resolution lattice parameter data. Contributions to the elastic softening which are due to strain/octahedral tilt coupling have been calculated using a fully parameterised Landau model of the Pm3m ↔ I4/mcm transition as a function of temperature, pressure and composition. Differences between calculated elastic constants and experimental data from Dynamical Mechanical Analysis, pulse-echo ultrasonics and Resonant Ultrasound Spectroscopy suggest that a proportion of the total softening in tetragonal samples may be due to anelastic effects. The anelastic contributions are observed at frequencies of both a few Hz and 10's of MHz, and can be understood in terms of strain contributions arising from movements of transformation twin walls in response to an externally applied shear stress. Similar transitions in other perovskites are likely to display small anomalies in the bulk modulus, due to weak coupling between octahedral tilts and volume strain, but much larger anomalies in the shear modulus. The elastic properties of tetragonal and orthorhombic structures are likely to be quite different due to different anelastic contributions from twin wall displacements.
19 citations
TL;DR: In this paper, the critical behavior of the phase transition using numerical Monte Carlo simulations of the three-dimensional integer-valued lattice gauge theory was investigated, and it was shown that the penetration depth exhibits critical scaling only very close to the transition point.
Abstract: The three-dimensional integer-valued lattice gauge theory, which is also known as a ``frozen superconductor,'' can be obtained as a certain limit of the Ginzburg-Landau theory of superconductivity, and is believed to be in the same universality class. It is also exactly dual to the three-dimensional XY model. We use this duality to demonstrate the practicality of recently developed methods for studying topological defects, and investigate the critical behavior of the phase transition using numerical Monte Carlo simulations of both theories. On the gauge theory side, we concentrate on the vortex tension and the penetration depth, which map onto the correlation lengths of the order parameter and the Noether current in the XY model, respectively. We show how these quantities behave near the critical point, and that the penetration depth exhibits critical scaling only very close to the transition point. This may explain the failure of superconductor experiments to see the inverted XY model scaling.
19 citations
TL;DR: The Ginzburg-Landau free energy functional for hard spheres is constructed using the fundamental measure theory approach to density functional theory as a starting point and it is found that the properties of the solid clusters are consistent with classical nucleation theory.
Abstract: The Ginzburg-Landau free energy functional for hard spheres is constructed using the fundamental measure theory approach to density functional theory as a starting point. The functional is used to study the liquid-fcc solid planer interface and the properties of small solid clusters nucleating within a liquid. The surface tension for planer interfaces agrees well with simulation and it is found that the properties of the solid clusters are consistent with classical nucleation theory.
19 citations