arXiv subjects

Mathias Michel

Publications and source records attributed to Mathias Michel.

17 recordsLinked to original sources

arXiv2008

Transport in open spin chains: A Monte Carlo wave-function approach

We investigate energy transport in several two-level atom or spin-1/2 models by a direct coupling to heat baths of different temperatures. The analysis is carried out on the basis of a recently derived quantum master equation which describes the nonequilibrium properties of internally weakly coupled systems appropriately. For the computation of the stationary state of the dynamical equations, we employ a Monte Carlo wave-function approach. The analysis directly indicates normal diffusive or ballistic transport in finite models and hints toward an extrapolation of the transport behavior of infinite models.

quant-ph↗

arXiv2008

Transport in anisotropic model systems analyzed by a correlated projection superoperator technique

By using a correlated projection operator, the time-convolutionless (TCL) method to derive a quantum master equation can be utilized to investigate the transport behavior of quantum systems as well. Here, we analyze a three-dimensional anisotropic quantum model system according to this technique. The system consists of Heisenberg coupled two-level systems in one direction and weak random interactions in all other ones. Depending on the partition chosen, we obtain ballistic behavior along the chains and normal transport in the perpendicular direction. These results are perfectly confirmed by the numerical solution of the full time-dependent Schrödinger equation.

quant-ph↗

arXiv2007

Modeling heat transport through completely positive maps

We investigate heat transport in a spin-1/2 Heisenberg chain, coupled locally to independent thermal baths of different temperature. The analysis is carried out within the framework of the theory of open systems by means of appropriate quantum master equations. The standard microscopic derivation of the weak-coupling Lindblad equation in the secular approximation is considered, and shown to be inadequate for the description of stationary nonequilibrium properties like a non-vanishing energy current. Furthermore, we derive an alternative master equation that is capable to describe a stationary energy current and, at the same time, leads to a completely positive dynamical map. This paves the way for efficient numerical investigations of heat transport in larger systems based on Monte Carlo wave function techniques.

quant-ph↗

arXiv2006

Finite quantum environments as thermostats: an analysis based on the Hilbert space average method

We consider discrete quantum systems coupled to finite environments which may possibly consist of only one particle in contrast to the standard baths which usually consist of continua of oscillators, spins, etc. We find that such finite environments may, nevertheless, act as thermostats, i.e., equilibrate the system though not necessarily in the way predicted by standard open system techniques. Thus, we apply a novel technique called the Hilbert space Average Method (HAM) and verify its results numerically.

quant-ph↗

arXiv2006

Microscopic Quantum Mechanical Foundation of Fourier's Law

Besides the growing interest in old concepts like temperature and entropy at the nanoscale, theories of relaxation and transport have recently regained a lot of attention. With the electronic circuits and computer chips getting smaller and smaller, a fresh look should be appropriate on the equilibrium and nonequilibrium thermodynamics at small length scales far below the thermodynamic limit, i.e. on the theoretical understanding of original macroscopic processes, e.g. transport of energy, heat, charge, mass, magnetization etc. Only from the foundations of a theory its limits of applicability may be inferred. This review tries to give an overview of the background and recent developments in the field of nonequilibrium quantum thermodynamics focusing on the transport of heat in small quantum systems.

cond-mat.stat-mech↗

arXiv2006

Normal Transport Behavior in Finite One-Dimensional Chaotic Quantum Systems

We investigate the transport of energy, magnetization, etc. in several finite one-dimensional (1D) quantum systems only by solving the corresponding time-dependent Schroedinger equation. We explicitly renounce on any other transport-analysis technique. Varying model parameters we find a sharp transition from non-normal to normal transport and a transition from integrability to chaos, i.e., from Poissonian to Wigner-like level statistics. These transitions always appear in conjunction with each other. We investigate some rather abstract design models and a (locally perturbed) Heisenberg spin chain.

cond-mat.stat-mech↗

arXiv2006

Limited validity of the Kubo formula for thermal conduction in modular quantum systems

The Kubo formula describes a current as a response to an external field. In the case of heat conduction there is no such external field. We analyze why and to what extend it is nevertheless justified to describe heat conduction in modular quantum systems by the Kubo formula. Modular we call systems that may be described as consisting of weakly coupled identical subsystems. We explain in what sense this description applies to a large class of systems. Furthermore, we numerically evaluate the Kubo formula for some finite modular systems. We compare the results with data obtained from the direct numerical solution of the corresponding time-dependent Schroedinger equation.

cond-mat.stat-mech↗

arXiv2006

Non-Markovian quantum dynamics: Correlated projection superoperators and Hilbert space averaging

The time-convolutionless (TCL) projection operator technique allows a systematic analysis of the non-Markovian quantum dynamics of open systems. We introduce a class of projection superoperators which project the states of the total system onto certain correlated system-environment states. It is shown that the application of the TCL technique to this class of correlated superoperators enables the non-perturbative treatment of the dynamics of system-environment models for which the standard approach fails in any finite order of the coupling strength. We demonstrate further that the correlated superoperators correspond to the idea of a best guess of conditional quantum expectations which is determined by a suitable Hilbert space average. The general approach is illustrated by means of the model of a spin which interacts through randomly distributed couplings with a finite reservoir consisting of two energy bands. Extensive numerical simulations of the full Schroedinger equation of the model reveal the power and efficiency of the method.

quant-ph↗

arXiv2005

Application of the Hilbert Space Average Method on Heat Conduction Models

We analyze closed one-dimensional chains of weakly coupled many level systems, by means of the so-called Hilbert space average method (HAM). Subject to some concrete conditions on the Hamiltonian of the system, our theory predicts energy diffusion with respect to a coarse-grained description for almost all initial states. Close to the respective equilibrium we investigate this behavior in terms of heat transport and derive the heat conduction coefficient. Thus, we are able to show that both heat (energy) diffusive behavior as well as Fourier's law follows from and is compatible with a reversible Schroedinger dynamics on the complete level of description.

cond-mat.stat-mech↗

arXiv2005

Global and local relaxation of a spin-chain under exact Schroedinger and master-equation dynamics

We solve the Schroedinger equation for an interacting spin-chain locally coupled to a quantum environment with a specific degeneracy structure. The reduced dynamics of the whole spin-chain as well as of single spins is analyzed. We show, that the total spin-chain relaxes to a thermal equilibrium state independently of the internal interaction strength. In contrast, the asymptotic states of each individual spin are thermal for weak but non-thermal for stronger spin-spin coupling. The transition between both scenarios is found for couplings of the order of $0.1 \times ΔE$, with $ΔE$ denoting the Zeeman-splitting. We compare these results with a master equation treatment; when time averaged, both approaches lead to the same asymptotic state and finally with analytical results.

cond-mat.stat-mech↗

arXiv2005

Thermalization of quantum systems by finite baths

We consider a discrete quantum system coupled to a finite bath, which may consist of only one particle, in contrast to the standard baths which usually consist of continua of oscillators, spins, etc. We find that such finite baths may nevertheless equilibrate the system though not necessarily in the way predicted by standard open system techniques. This behavior results regardless of the initial state being correlated or not.

quant-ph↗

arXiv2005

Fourier's Law from Schroedinger Dynamics

We consider a class of one-dimensional chains of weakly coupled many level systems. We present a theory which predicts energy diffusion within these chains for almost all initial states, if some concrete conditions on their Hamiltonians are met. By numerically solving the time dependent Schroedinger equation, we verify this prediction. Close to equilibrium we analyze this behavior in terms of heat conduction and compute the respective coefficient directly from the theory.

cond-mat.stat-mech↗

arXiv2005

Emergence of thermodynamic behavior within composite quantum systems

Entanglement within a given device provides a potential resource for quantum information processing. Entanglement between system and environment leads to decoherence (thus suppressing non-classical features within the system) but also opens up a route to robust and universal control. The latter is related to thermodynamic equilibrium, a generic behavior of bi-partite quantum systems. Fingerprints of this equilibrium behavior (including relaxation and stability) show up already far from the thermodynamic limit, where a complete solution of the underlying Schroedinger dynamics of the total system is still feasible.

quant-ph↗

arXiv2005

From Pure Schroedingerian to Statistical Dynamics

Many processes in nature seem to be entirely controlled by transition rates and the corresponding statistical dynamics. Some of them are in essence quantum, like the decay of excited states, the tunneling through barriers or the decay of unstable nuclei. Thus, starting from first principles, those systems should be analyzed on the basis of the Schroedinger equation. In the present paper we consider a two level system coupled to an environment which is basically described by an two-band energy scheme. For appropriately tuned environment parameters, the excitation probability of the two level system exhibits statistical dynamics, while the full system follows the coherent, unitary pure state evolution generated by the Schroedinger equation.

quant-ph↗

arXiv2005

Quantum Heat Transport: Perturbation Theory in Liouville Space

We consider chains consisting of several identical subsystems weakly coupled by various types of next neighbor interactions. At both ends the chain is coupled to a respective heat bath with different temperature modeled by a Lindblad formalism. The temperature gradient introduced by this environment is then treated as an external perturbation. We propose a method to calculate the heat current and the local temperature profile of the resulting stationary state as well as the heat conductivity in such systems. This method is similar to Kubo techniques used e.g. for electrical transport but extended here to the Liouville space.

cond-mat.stat-mech↗

arXiv2005

Fourier's Law confirmed for a class of small quantum systems

Within the Lindblad formalism we consider an interacting spin chain coupled locally to heat baths. We investigate the dependence of the energy transport on the type of interaction in the system as well as on the overall interaction strength. For a large class of couplings we find a normal heat conduction and confirm Fourier's Law. In a fully quantum mechanical approach linear transport behavior appears to be generic even for small quantum systems.

cond-mat.stat-mech↗

arXiv2005

Heat conductivity in small quantum systems: Kubo formula in Liouville space

We consider chains consisting of several identical subsystems weakly coupled by various types of next neighbor interactions. At both ends the chain is coupled to a respective heat bath with different temperature modeled by a Lindblad formalism. The temperature gradient introduced by this environment is then treated as an external perturbation. We propose a method to evaluate the heat current and the local temperature profile of the resulting stationary state as well as the heat conductivity in such systems. This method is similar to Kubo techniques used e.g. for electrical transport but extended here to the Liouville space.

cond-mat.stat-mech↗