Quantum Chaos and Regularity in Ultracold Fermi Gases

Quantum fluctuation of the energy is studied for an ultracold gas of interacting fermions trapped in a three-dimensional potential. Periodic-orbit theory is explored, and energy fluctuations are studied versus particle number for generic regular and chaotic systems, as well for a system defined by a harmonic confinement potential. Temperature effects on the energy fluctuations are investigated.Comment: 4 pages, 5 figure

Can we always get the entanglement entropy from the Kadanoff-Baym equations? The case of the T-matrix approximation

We study the time-dependent transmission of entanglement entropy through an out-of-equilibrium model interacting device in a quantum transport set-up. The dynamics is performed via the Kadanoff-Baym equations within many-body perturbation theory. The double occupancy $< \hat{n}_{R \uparrow} \hat{n}_{R \downarrow} >$, needed to determine the entanglement entropy, is obtained from the equations of motion of the single-particle Green's function. A remarkable result of our calculations is that $< \hat{n}_{R \uparrow} \hat{n}_{R \downarrow} >$ can become negative, thus not permitting to evaluate the entanglement entropy. This is a shortcoming of approximate, and yet conserving, many-body self-energies. Among the tested perturbation schemes, the $T$-matrix approximation stands out for two reasons: it compares well to exact results in the low density regime and it always provides a non-negative $< \hat{n}_{R \uparrow} \hat{n}_{R \downarrow} >$. For the second part of this statement, we give an analytical proof. Finally, the transmission of entanglement across the device is diminished by interactions but can be amplified by a current flowing through the system.Comment: 6 pages, 6 figure

Kadanoff-Baym approach to time-dependent quantum transport in AC and DC fields

We have developed a method based on the embedded Kadanoff-Baym equations to study the time evolution of open and inhomogeneous systems. The equation of motion for the Green's function on the Keldysh contour is solved using different conserving many-body approximations for the self-energy. Our formulation incorporates basic conservation laws, such as particle conservation, and includes both initial correlations and initial embedding effects, without restrictions on the time-dependence of the external driving field. We present results for the time-dependent density, current and dipole moment for a correlated tight binding chain connected to one-dimensional non-interacting leads exposed to DC and AC biases of various forms. We find that the self-consistent 2B and GW approximations are in extremely good agreement with each other at all times, for the long-range interactions that we consider. In the DC case we show that the oscillations in the transients can be understood from interchain and lead-chain transitions in the system and find that the dominant frequency corresponds to the HOMO-LUMO transition of the central wire. For AC biases with odd inversion symmetry odd harmonics to high harmonic order in the driving frequency are observed in the dipole moment, whereas for asymmetric applied bias also even harmonics have considerable intensity. In both cases we find that the HOMO-LUMO transition strongly mixes with the harmonics leading to harmonic peaks with enhanced intensity at the HOMO-LUMO transition energy.Comment: 16 pages, 9 figures. Submitted at "Progress in Nonequilibrium Green's Functions IV" conferenc

Some open questions in TDDFT: Clues from Lattice Models and Kadanoff-Baym Dynamics

Two aspects of TDDFT, the linear response approach and the adiabatic local density approximation, are examined from the perspective of lattice models. To this end, we review the DFT formulations on the lattice and give a concise presentation of the time-dependent Kadanoff-Baym equations, used to asses the limitations of the adiabatic approximation in TDDFT. We present results for the density response function of the 3D homogeneous Hubbard model, and point out a drawback of the linear response scheme based on the linearized Sham-Schl\"uter equation. We then suggest a prescription on how to amend it. Finally, we analyze the time evolution of the density in a small cubic cluster, and compare exact, adiabatic-TDDFT and Kadanoff-Baym-Equations densities. Our results show that non-perturbative (in the interaction) adiabatic potentials can perform quite well for slow perturbations but that, for faster external fields, memory effects, as already present in simple many-body approximations, are clearly required.Comment: 15 pages, submitted to Chemical Physic

Successes and Failures of Kadanoff-Baym Dynamics in Hubbard Nanoclusters

We study the non-equilibrium dynamics of small, strongly correlated clusters, described by a Hubbard Hamiltonian, by propagating in time the Kadanoff-Baym equations within the Hartree-Fock, 2nd Born, GW and T-matrix approximations. We compare the results to exact numerical solutions. We find that the T-matrix is overall superior to the other approximations, and is in good agreement with the exact results in the low-density regime. In the long time limit, the many-body approximations attain an unphysical steady state which we attribute to the implicit inclusion of infinite order diagrams in a few-body system.Comment: 4 pages, 4 figure

Finite elements and the discrete variable representation in nonequilibrium Green's function calculations. Atomic and molecular models

In this contribution, we discuss the finite-element discrete variable representation (FE-DVR) of the nonequilibrium Green's function and its implications on the description of strongly inhomogeneous quantum systems. In detail, we show that the complementary features of FEs and the DVR allows for a notably more efficient solution of the two-time Schwinger/Keldysh/Kadanoff-Baym equations compared to a general basis approach. Particularly, the use of the FE-DVR leads to an essential speedup in computing the self-energies. As atomic and molecular examples we consider the He atom and the linear version of H$_3^+$ in one spatial dimension. For these closed-shell models we, in Hartree-Fock and second Born approximation, compute the ground-state properties and compare with the exact findings obtained from the solution of the few-particle time-dependent Schr\"odinger equation.Comment: 12 pages, 3 figures, submitted as proceedings of conference "PNGF IV

Optical absorption spectra of finite systems from a conserving Bethe-Salpeter equation approach

We present a method for computing optical absorption spectra by means of a Bethe-Salpeter equation approach, which is based on a conserving linear response calculation for electron-hole coherences in the presence of an external electromagnetic field. This procedure allows, in principle, for the determination of the electron-hole correlation function self-consistently with the corresponding single-particle Green function. We analyze the general approach for a "one-shot" calculation of the photoabsorption cross section of finite systems, and discuss the importance of scattering and dephasing contributions in this approach. We apply the method to the closed-shell clusters Na_4, Na^+_9 and Na^+_(21), treating one active electron per Na atom.Comment: 9 pages, 3 figure