Application of Discrete Variable Methods to Trapped Fermi Gases

Pasquale Calabrese, Pierre Le Doussal, Satya N. Majumdar

We exploit and clarify the use of random matrix theory for the calculation of the entanglement entropy of free Fermi gases. We apply this method to obtain analytic predictions for R\'enyi entanglement entropies of a one-dimensional gas trapped by a harmonic potential in all the relevant scaling regimes. We confirm our findings with accurate numerical calculations obtained by means of an ingenious discretization of the reduced correlation matrix.

Le Tri Dat, Vinh N. T. Pham

Abstract In this work, the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable. Afterward, the applicability of the analytical formulas is validated by comparison with the numerical calculation. The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5% in the vicinity of the critical temperature T c in the case of Bose gases. Meanwhile, for Fermi gases, although the analytical formula fits well at very low- and high-temperature regimes, it cannot be applied at temperature in the range [ 0.3 - 0.5 ] T F , where T F is the Fermi temperature. In addition, the consistency between our formulas and classical ones at significantly high temperatures is also discussed.

Javier von Stecher, Seth T. Rittenhouse, Chris H. Greene

A. Sindona, Michele Pisarra, Mario Gravina +4 more

The sudden introduction of a local impurity in a Fermi sea leads to an anomalous disturbance of its quantum state that represents a local quench, leaving the system out of equilibrium and giving rise to the Anderson orthogonality catastrophe. The statistics of the work done describe the energy fluctuations produced by the quench, providing an accurate and detailed insight into the fundamental physics of the process. We present here a numerical approach to the non-equilibrium work distribution, supported by applications to phenomena occurring at very diverse energy ranges. One of them is the valence electron shake-up induced by photo-ionization of a core state in a fullerene molecule. The other is the response of an ultra-cold gas of trapped fermions to an embedded two-level atom excited by a fast pulse. Working at low thermal energies, we detect the primary role played by many-particle states of the perturbed system with one or two excited fermions. We validate our approach through the comparison with some photoemission data on fullerene films and previous analytical calculations on harmonically trapped Fermi gases.

M.Ya. Amusia, A.Z. Msezane, Vasily R. Shaginyan