Théorie de Landau

Résumé

En physique, la théorie de Landau est une théorie des transitions de phases. Elle doit son nom au théoricien russe Lev Landau. Cette théorie repose sur un développement polynomial de l'énergie libre en fonction d'un paramètre, appelé paramètre d'ordre, au voisinage de la transition. Cette théorie s'applique aux transitions de phases marquées par la perte de certains éléments de symétrie. La forme du potentiel de Landau est alors contrainte par les symétries des phases en présence, et peut être donnée par la théorie des groupes. De fait, la théorie de Landau constitue la première application de la théorie des groupes à la thermodynamique. Les principes généraux de la théorie ont été posés par Lev Landau en 1937. Par la suite, différentes travaux ont appliqué cette théorie générale à des cas plus spécifiques qu'on désigne parfois par des noms légèrement différents : théorie de Ginzburg-Landau pour les supraconducteurs, théorie de Landau-Devonshire pour les ferroélectriques etc.

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Liouvillian spectral collapse in the Scully-Lamb laser model

Fabrizio Minganti

Phase transitions of thermal systems and the laser threshold were first connected more than forty years ago. Despite the nonequilibrium nature of the laser, the Landau theory of thermal phase transitions, applied directly to the Scully-Lamb laser model (SLLM), indicates that the laser threshold is a second-order phase transition, associated with a U(1) spontaneous symmetry breaking (SSB). To capture the genuine nonequilibrium phase transition of the SLLM (i.e., a single-mode laser without a saturable absorber), here we employ a quantum theory of dissipative phase transitions. Our results confirm that the U(1) SSB can occur at the lasing threshold but, in contrast to the Landau theory and semiclassical approximation, they signal that the SLLM "fundamental" transition is a different phenomenon, which we call Liouvillian spectral collapse; that is, the emergence of diabolic points of infinite degeneracy. By considering a generalized SLLM with additional dephasing, we witness a second-order phase transition, with a Liouvillian spectral collapse, but in the absence of symmetry breaking. Most surprisingly, the phase transition corresponds to the emergence of dynamical multistability even without SSB. Normally, bistability is suppressed by quantum fluctuations, while in this case, the very presence of quantum fluctuations enables bistability. This rather anomalous bistability, characterizing the truly dissipative and quantum origin of lasing, can be an experimental signature of our predictions, and we show that it is associated with an emergent dynamical hysteresis.

AMER PHYSICAL SOC2021

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The macroscopic properties of ferroelectric materials depend directly on the domain configuration and the structure of the domain boundaries. For this reason, their study is of great scientific and technological interest. Several models have been developed to describe the properties of domain walls (structure, thickness, stress at the interface, mobility, …). However, few quantitative experimental observations of ferroelectric domain walls at an atomic scale have been reported, and even less results exist at higher temperatures. The ferroelectric domain-wall thickness is an important parameter whose behavior as a function of temperature is directly related to the order of the phase transition. In a second-order system, the temperature dependence of the domain-wall thickness follows a power law L ~ (Tc - T)-ω where ω is the critical exponent characterizing the divergence of L near the critical temperature Tc The predictions concerning the numerical value of are different depending on the theoretical model considered. Nevertheless, the majority of ferroelectric materials are known to undergo a first-order transition. In these systems the domain-wall thickness increases when the transition temperature is approached, but without diverging as for a second-order phase transition. The major objective of this work was to measure this broadening predicted by the theory for the first time at the approach of the phase transition temperature. We have shown that high resolution transmission electron microscopy is powerful technique for the study of ferroelectric domain walls not only at room temperature but also at higher temperatures. This method allows a direct and local observation of interfaces at an atomic scale which is a considerable advantage over diffraction techniques (X-ray, neutron, electron) and most of the other electron microscopy methods. However, the requirements of this method concerning the performance of the optical system of the microscope, the quality of the specimen and its stability in the column are very high, and today high resolution microscopy at high temperature remains a major challenge. The domain-wall thickness is obtained from the measurement of the crystal lattice distortion near the interface using two different numerical techniques of image analysis. The first method is based on the accurate determination of the center of bright peaks which appear on high resolution images for a judicious choice of the experimental parameters (delocalization and crystal thickness) and which represent the crystal lattice nodes. The second technique consists in selecting a circular region of the power spectrum around a reflection peak, centering the Fourier space on this reflection and performing the inverse Fourier transform. The information about the local displacement of atomic planes corresponding to the selected reflection is extracted form the phase component of the obtained complex image. Both techniques have been successfully applied to the measurement of the thickness of the 90° ferroelectric domain walls in PbTiO3 single crystals. This perovskite presents a first order phase transition at Tc = 492.2°C. which corresponds to the transformation of the crystal from the high-temperature paraelectric cubic phase to the low-temperature ferroelectric tetragonal phase. For the first time, the thermal broadening of domain walls has been measured quantitatively using HRTEM. The results are compared with the predictions made by phenomenological theories. We find that the domain wall thickness increases continuously from 0.7 nm at room temperature up to 5.5 nm near the transition temperature. Our results are consistent with those obtained by other authors at room temperature and those of a very recent study performed at higher temperatures using weak-beam microscopy. The measured domain-wall broadening is greater than the one predicted by a three-dimensional Ginzburg-Landau model where the polarization which is the primary order parameter is coupled to the elastic strain which plays the role of secondary order parameter. Our results are better described by a one-dimensional Ginzburg-Landau model without secondary order parameter. In this case the gradient coupling coefficient κ of the Ginzburg-Landau free energy is found to be 1.3 · 10-10 m3F-1. The methods developed for the measurement of the domain-wall thickness can by applied not only to other first-order ferroelectric crystals but also to ferroelectric systems presenting a second-order phase transition thus allowing the determination of the critical exponent ω. Characteristics only present in 2-D systems could also be detected by studying very thin specimens. Moreover, the same techniques can be adapted to the study of domain walls in purely ferroelastic materials.

EPFL2000

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Superfluidity and Critical Velocities in Nonequilibrium Bose-Einstein Condensates

We theoretically study the superfluidity properties of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity under incoherent pumping. The dynamics of the condensate is described at mean-field level in terms of a generalized Gross-Pitaevskii equation. The drag force on a small moving object and the onset of fringes in the density profile are shown to have a sharp threshold as a function of the velocity; a generalized Landau criterion is developed to explain this behavior in terms of the dispersion of elementary excitations. Metastability of supercurrents in multiply-connected geometries is shown to persist up to higher flow speeds.

2010

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