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Concept# Fermi gas

Summary

A Fermi gas is an idealized model, an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer spin. These statistics determine the energy distribution of fermions in a Fermi gas in thermal equilibrium, and is characterized by their number density, temperature, and the set of available energy states. The model is named after the Italian physicist Enrico Fermi.
This physical model is useful for certain systems with many fermions. Some key examples are the behaviour of charge carriers in a metal, nucleons in an atomic nucleus, neutrons in a neutron star, and electrons in a white dwarf.
Description
An ideal Fermi gas or free Fermi gas is a physical model assuming a collection of non-interacting fermions in a constant potential well. Fermions are elementary or composite particles with half-integer spin, thus follow Fermi-Dirac statistics. The equivale

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Starting from the quantum statistical master equation derived in [1] we show how the connection to the semi-classical Boltzmann equation (SCBE) can be established and how irreversibility is related to the problem of separability of quantum mechanics. Our principle goal is to find a sound theoretical basis for the description of the evolution of an electron gas in the intermediate regime between pure classical behavior and pure quantum behavior. We investigate the evolution of one-particle properties in a weakly interacting N-electron system confined to a finite spatial region in a near-equilibrium situation that is weakly coupled to a statistical environment. The equations for the reduced n-particle density matrices, with n < N are hierarchically coupled through two-particle interactions. In order to elucidate the role of this type of coupling and of the inter-particle correlations generated by the interaction, we examine first the particular situation where energy transfer between the N-electron system and the statistical environment is negligible, but where the system has a finite memory. We then formulate the general master equation that describes the evolution of the coarse grained one-particle density matrix of an interacting confined electron gas including energy transfer with one or more bath subsystems, which is called the quantum Boltzmann equation (QBE). The connection with phase space is established by expressing the one-particle states in terms of the overcomplete basis of coherent states, which are localized in phase space. In this way we obtain the QBE in phase space. After performing an additional coarse-graining procedure in phase space, and assuming that the interaction of the electron gas and the bath subsystems is local in real space, we obtain the semi-classical Boltzmann equation. The validity range of the classical description, which introduces local dynamics in phase space is discussed.

This thesis work focuses on impact and diffusion processes as well as equilibrium positions of a metal deposited on a surface. The metal is deposited in the form of clusters containing n atoms in a controlled way. Gold or silver clusters cations (Au+n and Ag+n ) are used. Their size (n ∈ [1, 9]), charge state and deposition energy (E = 10 - 4500 eV) are well defined. The surface being at room temperature during the deposition, can be annealed and transferred in a scanning tunnelling microscope (STM) after deposition. The variable temperature microscope was developed during this thesis. The approach of the tip is carried out by an axial motor, which renders the microscope very stable. The first part of this work treats of the evolution of gold deposited on a TiO2(110) surface. Position and size of gold islands created by cluster or atomic depositions are determined by STM. Compared to atomic deposition at the same energy (10 < E < 100 eV), the cluster deposition produces smaller islands with a large islands density after annealing at 800 K. Regardless the deposition conditions, gold atoms diffuse on the surface already at 300 K. The impact energy is the key parameter to reduce the diffusion by cluster or atomic implantation or defect creation. Upon a high energy deposition, part of the deposited gold is invisible to the STM. The fate of these gold atoms is unclear : they are either buried under the surface or ejected in vacuum at the impact. The control of the islands size should permit the creation of a stable system with an optimum catalytic activity (i. e. CO combustion). Research groups have shown that this activity is strongly influenced by the islands size. It is equal to zero if the diameter is greater than 5 nm. The second part of this work is devoted to the electron emission γ induced by the impact of silver clusters Ag+n on a Pt and HOPG surface. Measurements are made by varying the impact energy (and so the speed v) of size-selected clusters on a defined surface. Impact velocity ranges from 104 to 105 m/s, which is lower than the classical threshold. Nevertheless every cluster size produces an electron emission. A potential emission (γ(v=0) ≠ 0) is observed for the monomer on both surfaces, which is caused by excited ions in a metastable state. The γ(v) curves are increasing, and no mesurable oscillation are observed. This does not confirm earlier work by Meiwes-Broer et al. These authors found oscillations in γ on similar systems relating them to the electronic structure of the clusters and the surface. A model based on heating of the electron gas is developed. This model gives good agreements with the γ(v) curves. The electronic temperature is estimated to 3000-8000 K. Similar behavior on both surfaces (Pt and HOPG) depending of the cluster size is shown. This behavior is probably related to the geometrical structure of the clusters. Finally, a more pronounced molecular effect is observed for the HOPG : the number of electrons emitted by the impact of a Ag+n is up to 7 times higher than the number of electrons emitted by impacts of n independent atoms. This value is smaller than 2 for the Pt surface.

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We study a Fermi gas with strong, tunable interactions dispersively coupled to a high-finesse cavity. Upon probing the system along the cavity axis, we observe a strong optomechanical Kerr nonlinearity originating from the density response of the gas to the intracavity field and measure it as a function of interaction strength. We find that the zero-frequency density response function of the Fermi gas increases by a factor of two from the Bardeen-Cooper-Schrieffer to the Bose-Einstein condensate regime. The results are in quantitative agreement with a theory based on operator-product expansion, expressing the density response in terms of universal functions of the interactions, the contact, and the internal energy of the gas. This provides an example of a driven-dissipative, strongly correlated system with a strong nonlinear response, opening up perspectives for the sensing of weak perturbations or inducing long-range interactions in Fermi gases.

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