Fermi Gas in D-Dimensional Space

Mingzhe Li, Zijun Yan, Jincan Chen +2 more

The properties of an ideal Fermi gas in an external potential in any dimensional space are studied, based on the semiclassical (Thomas-Fermi) approximation. The general analytical expressions of the total particle number $N,$ density of states $D(\ensuremath{\varepsilon}),$ Fermi energy ${E}_{F},$ total energy $E,$ and heat capacity $C$ have been derived, where $N,$ $E,$ and $C$ are expressed by the Fermi integration. Moreover, the analytical expressions of the total energy $E,$ chemical potential \ensuremath{\mu}, and heat capacity $C$ in the high- and low-temperature approximations are given. From these results, how the characteristics of the Fermi gas depend on an external potential and the dimension of space is discussed.

Michael Köhl

Henning Moritz, Kenneth G uenter, Thilo St oferle +2 more

Kristian Fenech

This thesis presents two measurements of the properties of a two-dimensional Fermi gas. The first series of measurements examine the role of interactions in defining the dimensionality of the system. From this, the parameter space where two-dimensional kinematics can be observed is established. Using this result, the thermodynamic properties and equations of state of an attractive Fermi gas in the normal phase are determined through the measurement of the density distribution of the trapped gas.

Hanoch Gutfreund

Manas Kulkarni, Goutam Mandal, Takeshi Morita

By exploring a phase-space hydrodynamics description of one-dimensional free Fermi gas, we discuss how systems settle down to steady states described by the generalized Gibbs ensembles through quantum quenches. We investigate time evolutions of the fermions which are trapped in external potentials or a circle for a variety of initial conditions and quench protocols. We analytically compute local observables such as particle density and show that they always exhibit power-law relaxation at late times. We find a simple rule which determines the power law exponent. Our findings are, in principle, observable in experiments in a one-dimensional free Fermi gas or Tonk's gas (Bose gas with infinite repulsion).