Density-Matrix Description of Optical Interactions based on a Tight-Binding Representation

V. L. Jacobs

V. L. Jacobs

Abhishek Dhar, Keiji Saito, Peter Hänggi A

With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the explicit result for the reduced density matrix of quantum transport when the system, the connecting reservoirs, and the system-reservoir interactions are described by quadratic Hamiltonians. Our procedure is detailed for both electronic transport described by the tight-binding Hamiltonian and for phonon transport described by harmonic Hamiltonians. For the special case of weak system-reservoir couplings, a more detailed description of the steady-state density matrix is obtained. Several paradigm transport setups for interelectrode electron transport and low-dimensional phonon heat flux are elucidated.

V. M. Axt, Shaul Mukamel

Sergei N. Taraskin, P. A. Fry, Xiaodong Zhang +2 more

Analytical results for the asymptotic spatial decay of the density matrix $\ensuremath{\rho}(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}})$ in the tight-binding model of the two-dimensional metal are presented. In various dimensions D, it is found analytically and numerically that the density matrix decays with distance according to the power law $\ensuremath{\rho}(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}})\ensuremath{\propto}|\mathbf{r}\ensuremath{-}{\mathbf{r}}^{\ensuremath{'}}{|}^{\ensuremath{-}(D+1)/2}.$

Pomorski, Krzysztof

The mathematical equivalence between finite state stochastic machine and non-dissipative and dissipative quantum tight-binding and Schroedinger model is derived. Stochastic Finite state machine is also expressed by classical epidemic model and can reproduce the quantum entanglement emerging in the case of electrostatically coupled qubits described by von-Neumann entropy both in non-dissipative and dissipative case. The obtained results shows that quantum mechanical phenomena might be simulated by classical statistical model as represented by finite state stochastic machine. It includes the quantum like entanglement and superposition of states. Therefore coupled epidemic models expressed by classical systems in terms of classical physics can be the base for possible incorporation of quantum technologies and in particular for quantum like computation and quantum like communication. The classical density matrix is derived and described by the equation of motion in terms of anticommutator. Existence of Rabi like oscillations is pointed in classical epidemic model. Furthermore the existence of Aharonov-Bohm effect in quantum systems can also be reproduced by the classical epidemic model or in broader sense by finite state stochastic machine. Every quantum system made from quantum dots and described by simplistic tight-binding model by use of position-based qubits can be effectively described by classical statistical model encoded in finite stochastic state machine with very specific structure of S matrix that has twice bigger size as it is the case of quantum matrix Hamiltonian. Furthermore the description of linear and non-linear stochastic finite state machine is mapped to tight-binding and Schroedinger model. The concept of N dimensional complex time is incorporated into tight-binding model, so the description of dissipation in most general case is possible.