Fluctuations thermodynamiques

Résumé

Les fluctuations thermodynamiques des atomes ou molécules à l'intérieur d'un système sont les faibles écarts statistiques à l'équilibre thermodynamique de ce système. Ils sont décrits par la physique statistique hors d'équilibre. Ces fluctuations affectent tous les degrés de liberté : translation, rotation, vibration et énergie interne des molécules dans un gaz, translation pour un atome adsorbé sur une surface ou constituant un élément étranger dans une structure cristalline. Dans ces derniers cas ce phénomène est lié au mouvement des atomes constituant le solide (phonons). On peut relier ces phénomènes à la diffusion et à la dissipation de l'énergie. Distribution gaussienne des fluctuations Physique statistique hors d'équilibre Les systèmes auxquels on s'intéresse, qu'ils soient solides, liquides ou gazeux, sont décrits par un nombre faible de variables extensives (conservatives) décrivant une collection d'états du système à l'échelle microscopique appelé ensemble de

Source officielle

https://fr.wikipedia.org/wiki/Fluctuations_thermodynamiques

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The principal aim of this thesis is to gain a better understanding of the competition between magnetic and quadrupolar degrees of freedom on two-dimensional lattices. Recent experimental investigations of the material NiGa2S4 revealed several anomalous properties that might be accounted for within the framework of quadrupolar ordering. Exhibiting both a ferroquadrupolar and an antiferroquadrupolar phase, the S = 1 bilinear-biquadratic Heisenberg model on the triangular lattice is a possible candidate for describing the low-temperature behaviour of the system. In this work, we put forward a more realistic model that includes single-ion anisotropy. We perform a thorough investigation of the variational phase diagram of this model and we show that it exhibits a variety of unconventional phases. We derive the excitation spectrum of the quadrupolar phases in the phase diagram and we point out that ferroquadrupolar order is particularly sensitive to the nature of anisotropy. Finally, we study quantum effects in the perturbative limit of large anisotropy and we argue that the non-trivial degeneracy of the mean-field solution is lifted by an emergent supersolid phase. We also discuss our results in the context of NiGa2S4. In the second part of the thesis, we aim at gaining an insight into the interplay between geometrical frustration and quadrupolar degrees of freedom by mapping out the phase diagram of the spin-one bilinear-biquadratic model on the square lattice. Our variational approach reveals a remarkable 1/2-magnetization plateau of mixed quadrupolar and magnetic character above the classically degenerate "semi-ordered" phase, and this finding is corroborated by exact diagonalization of finite clusters. "Order-by-disorder" phenomenon gives rise to a state featuring three-sublattice antiferroquadrupolar order below the plateau, which is truly surprising given the bipartite nature of the square lattice. We place particular emphasis on investigating the properties of the SU(3) Heisenberg model, which is shown to feature a subtle competition between quantum and thermal fluctuations. Our results suggest a suppression of two-sublattice Néel order in a finite window below the SU(3) point. Experimental implications for the Mott-insulating states of three-flavour fermionic atoms in optical lattices are discussed.

EPFL2011

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Local excitations in amorphous solids

Wencheng Ji

Amorphous solids are structurally disordered. They are very common and include glasses, colloids, and granular materials, but are far less understood than crystalline solids. Key aspects of these materials are controlled by the presence of excitations in which a group of particles rearranges. This motion can be triggered by (a) quantum fluctuations associated with two-level systems (TLS), which dominate the low temperature properties of conventional glasses and have practical importance on superconducting qubits; by (b) thermal fluctuations associated with activations, which are related to the famous and challenging

glass transition'' problem; or by (c) exerting an external stress or strain associated with shear transformations, which control the plasticity. Hence, it is important to understand how temperature and system preparation determines the density and geometry of these excitations. The possible unification of these excitations into a common description is also a fundamental problem.  These local excitations are thought to have a close relationship with

Quasi-localised modes (QLMs)'' which are present in the low-frequency vibrational spectrum in amorphous solids. Understanding the properties of QLMs and clarifying the relation between QLMs and these local excitations are important to the study of the latter. In this thesis: (1) we provide a theory for the QLMs, D_L(omega) ~ omega^alpha, that establishes the link between QLMs and shear transformations for systems under quasi-static loading. It predicts two regimes depending on the density of shear transformations P(x)~ x^theta (with x the additional stress needed to trigger a shear transformation). If theta>1/4, alpha=4 and a finite fraction of quasi-localised modes form shear transformations, whose amplitudes vanish at low frequencies. If theta

EPFL2021

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Universal Aspects of Metamagnetic Transitions in Frustrated Ising Chains

Nagabhushan Ganesh Hegde

The study of magnetic frustration has been interesting due to the variety of magnetic ordering observed at low temperatures. At these temperatures thermal fluctuations become redundant and quantum fluctuations play a significant role in the determining the ground state of the system. Frustration can happen due to randomness or geometry. In our research, we have focused on triangle-based geometrically frustrated systems where stronger FM coupling is present along the c- axis and weaker AFM coupling in the ab- plane. Such quasi-1D behavior gives rise to several interesting features and metamagnetic phase transitions are one among them. In triangle based Ising geometry 1st order metamagnetic phase transitions are observed between 1/3Ms and Ms (saturation magnetization). Since most of the research has been dedicated to explain the formation of these plateaus, there is a lack of clear understanding of the dynamics of this transition. Our primary aim is to construct analytical models that can explain the dynamics of metamagnetic transitions using bulk and microscopic methods. Further, we would like to expand our quest to focus on finding out universal behavior of these transitions in different materials.

EPFL2021

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EPFL2011