Concept# Fermi–Dirac statistics

Summary

Fermi–Dirac statistics (F–D statistics) is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul Dirac, each of whom derived the distribution independently in 1926 (although Fermi derived it before Dirac). Fermi–Dirac statistics is a part of the field of statistical mechanics and uses the principles of quantum mechanics.
F–D statistics applies to identical and indistinguishable particles with half-integer spin (1/2, 3/2, etc.), called fermions, in thermodynamic equilibrium. For the case of negligible interaction between particles, the system can be described in terms of single-particle energy states. A result is the F–D distribution of particles over these states where no two particles can occupy the same state, whic

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related publications (22)

Related people (1)

Loading

Loading

Loading

Related concepts (66)

A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic

Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. Spin should not be understood as in the "rotat

In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system

Related units (1)

Related courses (46)

ME-469: Nano-scale heat transfer

In this course we study heat transfer (and energy conversion) from a microscopic perspective. This allows us to understand why classical laws (i.e. Fourier Law) are what they are and what are their limits of validity . We will then discuss emerging opprotunities in nanoscale devices.

PHYS-315: Statistical physics I

L'objectif du cours est d'introduire les concepts fondamentaux de la physique statistique.

PHYS-314: Quantum physics II

L'objectif de ce cours est de familiariser l'étudiant avec les concepts, les méthodes et les conséquences de la physique quantique. En particulier, le moment cinétique, la théorie de perturbation, les systèmes à plusieurs particules, les symétries, et les corrélations quantique seront traité

Related lectures (97)

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.

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.

2008Romain 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