Statistique de Fermi-Dirac | EPFL Graph Search

En mécanique quantique et en physique statistique, la statistique de Fermi-Dirac désigne la distribution statistique de fermions indiscernables (tous similaires) sur les états d'énergie d'un système à l'équilibre thermodynamique. La distribution en question tient à une particularité des fermions : les particules de spin demi-entier sont assujetties au principe d'exclusion de Pauli, à savoir que deux particules ne peuvent occuper simultanément un même état quantique (voir l'article Gaz de Fermi). Note historique Avant l'avènement de la distribution de Fermi-Dirac dans les années 1920, la compréhension du comportement des électrons dans les métaux était très rudimentaire. Le modèle de Drude utilisait la statistique classique de Maxwell-Boltzmann pour décrire la dynamique des électrons. Ainsi les scientifiques ne comprenaient pas bien pourquoi les électrons participaient en grand nombre dans la conduction du courant électrique dans un métal et que ce nombre devenait extrêmemen

Tilted double Dirac cone and anisotropic quantum-spin-Hall topological insulator in mechanical granular graphene

Romain Christophe Rémy Fleury, Georgios Theocharis

Dirac degeneracies are essential ingredients to control topological charge exchanges between bands and trigger the unique edge transport properties of topological materials. In addition, when Dirac cones are tilted, exotic phenomena can emerge such as anomalous Hall effect or unconventional Klein tunneling. However, the unique topological transport properties arising from the opening of tilted Dirac cone degeneracies have been left completely uncharted. Here, we demonstrate a new form of Dirac degeneracy that occurs in mechanical granular graphene (MGG): a tilted double Dirac cone, composed of two counter-tilted type-I Dirac cones. Different from the reported C 6 systems, we show that the tilted double Dirac cone is present in a C 2 granular graphene. Remarkably, a pair of anisotropic helical edge waves appears when the degeneracy is lifted. This leads to an anisotropic quantum spin-Hall topological insulator that possesses unique wave propagation properties, including anisotropic edge dispersion and direction-dependent edge-bulk mode conversion.

2020

Some issues concerning large-eddy simulation of inertial particle dispersion in turbulent bounded flows

Alfredo Soldati

The problem of accurate Eulerian-Lagrangian modeling of inertial particle dispersion in large-eddy simulation (LES) of turbulent wall-bounded flows is addressed. We run direct numerical simulation (DNS) of turbulent channel flow at shear Reynolds number Re-tau=150 and corresponding a priori and a posteriori LES on two coarser grids. For each flow field, we tracked swarms of particles with different inertia to examine the behavior of particle statistics, specifically focusing on particle preferential segregation and accumulation at the wall. Our object is to discuss the necessity of a closure model for the particle equations when using LES and we verify if the influence of the subgrid turbulence filtered by LES is an important effect on particle motion according to particle size. The results show that well-resolved LES gives particle velocity statistics in satisfactory agreement with DNS. However, independent of the grid, quantitatively inaccurate predictions are obtained for local particle preferential segregation, particularly in the near-wall region. Inaccuracies are observed for the entire range of particle size considered in this study, even when the particle response time is much larger than the flow time scales not resolved in LES. The satisfactory behavior of LES in reproducing particle velocity statistics is thus counterbalanced by the inaccurate representation of local segregation phenomena, indicating that closure models supplying the particle motion equation with an adequate rendering of the flow field might be needed. Finally, we remark that recovering the level of fluid and particle velocity fluctuations in the particle equations does not ensure a quantitative replica of the subgrid turbulence effects, thus implying that accurate subgrid closure models for particles may require information also proportional to the higher-order moments of the velocity fluctuations. (c) 2008 American Institute of Physics.

2008

Quantum phase transitions in low-dimensional weakly interacting disordered Bose gases

Joseph Saliba

In this thesis, we study the quantum phase transition triggered by an external random po- tential in ultra-cold low-dimensional weakly-interacting Bose gases at zero temperature. In one-dimensional systems, the quantum phases are characterized by the decay at long-range of the one-body density matrix. This decay exhibits an algebraic behaviour in the superfluid quasi-condensed phase while in the insulating Bose glass phase this it becomes exponen- tial, signaling the complete loss of coherence in the system. In two-dimensional systems, a characterization based on the long-range behaviour of the one-body density matrix appears to be highly demanding from a computational point of view. We therefore characterized the superfluid-insulator transition in two-dimensional systems by the low-energy behaviour of the cumulative density of states of the Bogoliubov excitations. While in the superfluid condensed phase this quantity grows as the square of the excitation energy in agreement with the existence of a finite velocity of sound, in the insulating Bose glass phase this power law is less than quadratic. This study is performed in the framework of an extended Bogoliubov approach properly adapted to treat low-dimensional Bose gases. Using a systematic numerical study, we draw the interaction-disorder phase diagrams of the superfluid-insulator transition in 1D and 2D. The phase boundary follows two different power- laws depending on the length scales characterizing the spatial correlations of the disorder and the strength of interactions. The power-law exponents were found to be in agreement with the ones predicted by scaling arguments, both in the white noise and the Thomas-Fermi regimes. In the two-dimensional system, the classical percolation threshold in the Thomas-Fermi limit was found to overestimate the critical disorder below which the onset of superfluidity should be observed for a given interaction strength.