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Tree tensor network states (TTNS) decompose the system wavefunction to the product of low-rank tensors based on the tree topology, serving as the foundation of the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method. In this work, we present an algorithm that automatically constructs the optimal and exact tree tensor network operators (TTNO) for any sum-of-product symbolic quantum operator.The construction is based on the minimum vertex cover of a bipartite graph. With the optimal TTNO, we simulate open quantum systems such as spin relaxation dynamics in the spin-boson model and charge transport in molecular junctions. In these simulations, the environment is treated as discrete modes and its wavefunction is evolved on equal footing with the system. We employ the Cole-Davidson spectral density to model the glassy phonon environment, and incorporate temperature effects via thermo field dynamics. Our results show that the computational cost scales linearly with the number of discretized modes, demonstrating the efficiency of our approach.

We relate the memory kernel in the Nakajima-Zwanzig-Mori time-convolution approach to the reduced system propagator which is often used to obtain the kernel in the Tokuyama-Mori time-convolutionless approach. The connection provides a robust and simple formalism to compute the memory kernel for a generalized system-bath model circumventing the need to compute high order system-bath observables. We illustrate this for a model system with electron-electron and electron-phonon couplings, driven away from equilibrium.

Quantum transport is studied for the nonequilibrium Anderson impurity model at zero temperature employing the multilayer multiconfiguration time-dependent Hartree theory within the second quantization representation (ML-MCTDH-SQR) of Fock space. To adress both linear and nonlinear conductance in the Kondo regime, two new techniques of the ML-MCTDH-SQR simulation methodology are introduced: (i) the use of correlated initial states, which is achieved by imaginary time propagation of the overall Hamiltonian at zero voltage and (ii) the adoption of the logarithmic discretization of the electronic continuum. Employing the improved methodology, the signature of the Kondo effect is analyzed., Comment: arXiv admin note: substantial text overlap with arXiv:1301.4489, arXiv:1103.4945

Chinese font recognition (CFR) has gained significant attention in recent years. However, due to the sparsity of labeled font samples and the structural complexity of Chinese characters, CFR is still a challenging task. In this paper, a DropRegion method is proposed to generate a large number of stochastic variant font samples whose local regions are selectively disrupted and an inception font network (IFN) with two additional convolutional neural network (CNN) structure elements, i.e., a cascaded cross-channel parametric pooling (CCCP) and global average pooling, is designed. Because the distribution of strokes in a font image is non-stationary, an elastic meshing technique that adaptively constructs a set of local regions with equalized information is developed. Thus, DropRegion is seamlessly embedded in the IFN, which enables end-to-end training; the proposed DropRegion-IFN can be used for high performance CFR. Experimental results have confirmed the effectiveness of our new approach for CFR., Comment: 15 pages, 7 figures

The accuracy of the noninteracting electron approximation is examined for a model of vibrationally coupled electron transport in single molecule junction. In the absence of electronic-vibrational coupling, steady state transport in this model is described exactly by Landauer theory. Including coupling, both electronic-vibrational and vibrationally induced electron-electron correlation effects may contribute to the real time quantum dynamics. Using the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory to describe nuclear dynamics exactly while maintaining the noninteracting electron approximation for the electronic dynamics, the correlation effects are analyzed in different physical regimes. It is shown that although the noninteracting electron approximation may be reasonable for describing short time dynamics, it does not give the correct long time limit for certain initial conditions., Comment: arXiv admin note: text overlap with arXiv:1103.4945, arXiv:1301.4489

The transition from weakly damped coherent motion to localization in the context of the spin-boson model has been the subject of numerous studies with distinct behavior depending on the form of the phonon-bath spectral density, $J\left(\omega\right)\propto\omega^{s}$. Sub-Ohmic ($s<1$) and Ohmic ($s=1$) spectral densities show a clear localization transition at zero temperature and zero bias, while for super-Ohmic ($s>1$) spectral densities this transition disappears. In this work, we consider the influence of the phonon-bath spectral density on the \emph{nonequilibrium} dynamics of a quantum dot with electron-phonon interactions described by the extended Holstein model. Using the reduced density matrix formalism combined with the multi-layer multiconfiguration time-dependent Hartree approach, we investigate the dynamic response, the time scales for relaxation, as well as the existence of multiple long-lived solutions as the system-bath coupling changes from the sub- to the super-Ohmic cases. Bistability is shown to diminish for increasing powers of $s$ similar to the spin-boson case. However, the physical mechanism and the dependence on the model parameters such as the typical bath frequency $\omega_{c}$ and the polaron shift $\lambda$ are rather distinct., Comment: 10 pages, 6 figures

A general form of a many-body Hamiltonian is considered, which includes an interacting fermionic sub-system coupled to non-interacting extended fermionic and bosonic systems. We show that the exact dynamics of the extended bosonic system can be derived from the reduced density matrix of the sub-system alone, despite the fact that the latter contains information about the sub-system only. The advantage of the formalism is immediately clear: While the reduced density matrix of the sub-system is readily available, the formalism offers access to observables contained in the full density matrix, which is often difficult to obtain. As an example, we consider an extended Holstein model and study the nonequilibrium dynamics of the, so called, "reaction mode" for different model parameters. The effects of the phonon frequency, the strength of the electron-phonon couplings, and the source-drain bias voltage on the phonon dynamics across the bistability are discussed., Comment: 5 pages, 3 figures

The nonequilibrium dynamics of a quantum dot with electron-phonon interactions described by a generalized Holstein model is presented. A combination of methodologies including the reduced density matrix formalism, the multilayer multiconfiguration time-dependent Hartree method, and a time-dependent nonequilibrium Green function approach, is used to explore the transient behavior on multiple timescales as the system approaches steady-state. The dot population dynamics on short to intermediate times is governed by the dot-lead hybridization parameter ($\Gamma$) and by the typical phonon frequency ($\omega_{c}$) and depends on the location of the energy level of the dot relative to the bias window. At longer times, the dynamics show a distinct behavior depending on whether the system is in the adiabatic or non-adiabatic regime, with a quantum dot occupation that may depend on the initial preparation of the phonons degrees of freedom. A "phase" diagram of this localization effect as a function of the polaron shift ($\lambda$) for various phonon frequencies is derived, suggesting the existence of bistability on experimentally observable timescales., Comment: 15 pages, 9 figures

The multilayer multiconfiguration time-dependent Hartree method is employed to study vibrationally coupled charge transport in models of single molecule junctions. To increase the efficiency of the simulation method, a representation of the Hamiltonian in terms of the scattering states of the underlying electronic Hamiltonian is used. It is found that with an appropriate choice of the scattering states the artificial electron correlation present in the original representation of the model is greatly reduced. This allows efficient simulation of the steady-state currents in a wide physical parameter space, which is demonstrated by several numerical examples., Comment: arXiv admin note: text overlap with arXiv:1301.4489

The existence of more than one steady-state in a many-body quantum system driven out-of-equilibrium has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. In this Letter, we combine a reduced density matrix formalism with the multilayer multiconfiguration time-dependent Hartree method to address this problem. This allows to obtain a converged numerical solution of the nonequilibrium dynamics. Considering a generic model for quantum transport through a quantum dot with electron-phonon interaction, we prove that a unique steady-state exists regardless of the initial electronic preparation of the quantum dot consistent with the converged numerical results. However, a bistability can be observed for different initial phonon preparations. The effects of the phonon frequency and strength of the electron-phonon couplings on the relaxation to steady-state and on the emergence of bistability is discussed.

The multilayer multiconfiguration time-dependent Hartree theory within second quantization representation of the Fock space is applied to study correlated electron transport in models of single-molecule junctions. Extending previous work, we consider models which include both electron-electron and electronic-vibrational interaction. The results show the influence of the interactions on the transient and the stationary electrical current. The underlying physical mechanisms are analyzed in conjunction with the nonequilibrium electronic population of the molecular bridge., Comment: arXiv admin note: substantial text overlap with arXiv:1103.4945

We investigate the transient nonequilibrium dynamics of a molecular junction biased by a finite voltage and strongly coupled to internal vibrational degrees of freedom. Using two different, numerical exact techniques, diagrammatic Monte Carlo and the multilayer multiconfiguration time-dependent Hartree method, we show that the steady state current through the junction may depend sensitively on the initial preparation of the system, thus revealing signatures of bistability. The influence of the bias voltage and the transient dynamics on the phenomenon of bistability is analyzed. Furthermore, a possible relation to the phenomenon of stochastic switching in nanoelectromecanical devices is discussed., Comment: 5 pages, 3 figures

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory within second quantization representation of the Fock space, a novel numerically exact methodology to treat many-body quantum dynamics for systems containing identical particles, is applied to study the effect of vibrational motion on electron transport in a generic model for single-molecule junctions. The results demonstrate the importance of electronic-vibrational coupling for the transport characteristics. For situations where the energy of the bridge state is located close to the Fermi energy, the simulations show the time-dependent formation of a polaron state that results in a pronounced suppression of the current corresponding to the phenomenon of phonon blockade. We show that this phenomenon cannot be explained solely by the polaron shift of the energy but requires methods that incorporate the dynamical effect of the vibrations on the transport. The accurate results obtained with the ML-MCTDH in this parameter regime are compared to results of nonequilibrium Green's function (NEGF) theory., Comment: 39 pages, 11 figures

An analog of the Meir-Wingreen formula for the steady-state heat current through a model molecular junction is derived. The expression relates the heat current to correlation functions that involve operators only acting on the degrees of freedom of the molecular junction. As a result, the macroscopic heat reservoirs are not treated explicitly. This allows one to exploit methods based on a reduced description of the dynamics of a relatively small part of the overall system to evaluate the heat current through a molecular junction. The derived expression is applied to calculate the steady-state heat current in a weak coupling limit, where Redfield theory is used to describe the reduced dynamics of the molecular junction. The results are compared with those from the previously developed approximate and numerically exact methods.

It is shown how to formulate the ubiquitous quantum chemistry problem of calculating the thermal rate constant on a quantum computer. The resulting exact algorithm scales exponentially faster with the dimensionality of the system than all known ``classical'' algorithms for this problem., Comment: 10 pages, no figures