Karsten Balzer

Nonequilibrium Green's Functions Approach to Inhomogeneous Systems

Part I Introduction.- Quantum Many-Particle Systems out of Equilibrium.- Part II Theory.- Nonequilibrium Greens Functions.- Part III Computational Methods.- Representations of the Nonequilibrium Greens Function.- Computation of Equilibrium States and Time-Propatation.- Part IV Applications for Inhomogeneous Systems.- Lattice Systems.- Non-Lattics Systems.- Conclusion and Outlook.- Second Quantization.- Perturbation Expansion.- Index.

Nonequilibrium Green's function approach to strongly correlated few-electron quantum dots

The effect of electron-electron scattering on the equilibrium properties of few-electron quantum dots is investigated by means of nonequilibrium Greens function theory. The ground and equilibrium states are self-consistently computed from the Matsubara (imaginary time) Greens function for the spatially inhomogeneous quantum dot system whose constituent charge carriers are treated as spin-polarized. To include correlations, the Dyson equation is solved, starting from a Hartree-Fock reference state, within a conserving (second-order) self-energy approximation where direct and exchange contributions to the electron-electron interaction are included on the same footing. We present results for the zero and finite temperature charge carrier densities, the orbital-resolved distribution functions, and the self-consistent total energies and spectral functions for isotropic two-dimensional parabolic confinement as well as for the limit of large anisotropy\char22{}quasi-one-dimensional entrapment. For the considered quantum dots with

Quantum breathing mode of trapped bosons and fermions at arbitrary coupling

N=2

Multiconfiguration time-dependent Hartree impurity solver for nonequilibrium dynamical mean-field theory

, 3, and 6 electrons, the analysis comprises the crossover from Fermi gas or liquid (at large carrier density) to Wigner molecule or crystal behavior (in the low-density limit).

Hamiltonian-based impurity solver for nonequilibrium dynamical mean-field theory

Interacting particles in a harmonic trap are known to possess a radial collective oscillation--the breathing mode (BM). We show that a quantum system has two BMs and analyze their properties by exactly solving the time-dependent Schroedinger equation. We report that the frequency of one BM changes with system dimensionality, the particle spin and the strength of the pair interaction and propose a scheme that gives direct access to key properties of trapped particles, including their many-body effects.

Electronic double excitations in quantum wells: Solving the two-time Kadanoff-Baym equations

Nonequilibrium dynamical mean-field theory (DMFT) solves correlated lattice models by obtaining their local correlation functions from an effective model consisting of a single impurity in a self-consistently determined bath. The recently developed mapping of this impurity problem from the Keldysh time contour onto a time-dependent single-impurity Anderson model (SIAM) [C. Gramsch et al., Phys. Rev. B 88, 235106 (2013)] allows one to use wave function-based methods in the context of nonequilibrium DMFT. Within this mapping, long times in the DMFT simulation become accessible by an increasing number of bath orbitals, which requires efficient representations of the time-dependent SIAM wave function. These can be achieved by the multiconfiguration time-dependent Hartree (MCTDH) method and its multi-layer extensions. We find that MCTDH outperforms exact diagonalization for large baths in which the latter approach is still within reach and allows for the calculation of SIAMs beyond the system size accessible by exact diagonalization. Moreover, we illustrate the computation of the self-consistent two-time impurity Greens function within the MCTDH second quantization representation.

The generalized Kadanoff-Baym ansatz. Computing nonlinear response properties of finite systems

We derive an exact mapping from the action of nonequilibrium dynamical mean-field theory (DMFT) to a single-impurity Anderson model (SIAM) with time-dependent parameters, which can be solved numerically by exact diagonalization. The representability of the nonequilibrium DMFT action by a SIAM is established as a rather general property of nonequilibrium Green functions. We also obtain the nonequilibrium DMFT equations using the cavity method alone. We show how to numerically obtain the SIAM parameters using Cholesky or eigenvector matrix decompositions. As an application, we use a Krylov-based time propagation method to investigate the Hubbard model in which the hopping is switched on, starting from the atomic limit. Possible future developments are discussed.

The non-equilibrium Green function approach to inhomogeneous quantum many-body systems using the generalized Kadanoff–Baym ansatz

For a quantum many-body system, the direct population of states of double-excitation character is a clear indication that correlations importantly contribute to its nonequilibrium properties. We analyze such correlation-induced transitions by propagating the nonequilibrium Greens functions in real time within the second Born approximation. As crucial benchmarks, we compute the absorption spectrum of few electrons confined in quantum wells of different width. Our results include the full two-time solution of the Kadanoff-Baym equations as well as of their time-diagonal limit and are compared to Hartree-Fock and exact diagonalization data.

Tuning correlations in multi-component plasmas

For a minimal Hubbard-type system at different interaction strengths U, we investigate the density-response for an excitation beyond the linear regime using the generalized Kadanoff-Baym ansatz (GKBA) and the second Born (2B) approximation. We find strong correlation features in the response spectra and establish the connection to an involved double excitation process. By comparing approximate and exact Greens function results, we also observe an anomalous U-dependence of the energy of this double excitation in 2B+GKBA. This is in accordance with earlier findings [K. Balzer et al., EPL 98, 67002 (2012)] on double excitations in quantum wells.

Electronic correlations in double ionization of atoms in pump-probe experiments

In the non-equilibrium Green function calculations, the use of the generalized Kadanoff–Baym ansatz (GKBA) allows for a simple approximate reconstruction of the two-time Green function from its time-diagonal value. With this, a drastic reduction of the computational needs is achieved in time-dependent calculations, making longer time propagation possible and more complex systems accessible. This paper gives credit to the GKBA that was introduced 25 years ago. After a detailed derivation of the GKBA, we recall its application to homogeneous systems and show how to extend it to strongly correlated, inhomogeneous systems. As a proof of concept, we present the results for a two-electron quantum well, where the correct treatment of the correlated electron dynamics is crucial for a correct description of the equilibrium and dynamic properties.