arXiv subjects

Jochen Gemmer

Publications and source records attributed to Jochen Gemmer.

At least 73 records · Page 4Linked to original sources

arXiv2014

Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems

In the ongoing discussion on thermalization in closed quantum many-body systems, the eigenstate thermalization hypothesis (ETH) has recently been proposed as a universal concept which attracted considerable attention. So far this concept is, as the name states, hypothetical. The majority of attempts to overcome this hypothetical character is based on exact diagonalization which implies for, e.g., spin systems a limitation to roughly 15 spins. In this Letter we present an approach which pushes this limit up to system sizes of roughly 35 spins, thereby going significantly beyond what is possible with exact diagonalization. A concrete application to a Heisenberg spin-ladder which yields conclusive results is demonstrated.

cond-mat.stat-mech↗

arXiv2013

Effect of short-range order on transport in one-particle, tight-binding models

We investigate transport properties of topologically disordered, three-dimensional, one-particle, tight binding models, featuring site distance dependent hopping terms. We start from entirely disordered systems into which we gradually introduce some short range order by numerically performing a pertinent structural relaxation using local site-pair interactions. Transport properties of the resulting models within the delocalized regime are analyzed numerically using linear response theory. We find that even though the generated order is very short ranged, transport properties such as conductivity or mean free path scale significantly with the degree of order. Mean free paths may exceed site-pair correlation length. It is furthermore demonstrated that, while the totally disordered model is not in accord with a Drude- or Boltzmann-type description, moderate degrees of order suffice to render such a picture valid.

cond-mat.dis-nn↗

arXiv2012

Onset of Fokker-Planck dynamics within a Closed Finite Spin System

Relaxation according to Fokker-Planck equations is a standard scenario in classical statistical mechanics. It is however not obvious how such an equilibration may emerge within a closed, finite quantum system. We present an analytical and numerical analysis of a system comprising sixteen spins in which spatial inhomogeneities of the magnetization relax approximately in accord with a standard Fokker-Planck equation for a Brownian particle in a parabolic potential.

quant-ph↗

arXiv2012

Boltzmann-type approach to transport in weakly interacting one-dimensional fermionic systems

We investigate transport properties of one-dimensional fermionic tight binding models featuring nearest and next-nearest neighbor hopping, where the fermions are additionally subject to a weak short range mutual interaction. To this end we employ a pertinent approach which allows for a mapping of the underlying Schrödinger dynamics onto an adequate linear quantum Boltzmann equation. This approach is based on a suitable projection operator method. From this Boltzmann equation we are able to numerically obtain diffusion coefficients in the case of non-vanishing next-nearest neighbor hopping, i.e., the non-integrable case, whereas the diffusion coefficient diverges without next-nearest neighbor hopping. For the latter case we analytically investigate the decay behavior of the current with the result that arbitrarily small parts of the current relax arbitrarily slowly which suggests anomalous diffusive transport behavior within the scope of our approach.

cond-mat.quant-gas↗

arXiv2011

Transient fluctuation theorem in closed quantum systems

Our point of departure are the unitary dynamics of closed quantum systems as generated from the Schrödinger equation. We focus on a class of quantum models that typically exhibit roughly exponential relaxation of some observable within this framework. Furthermore, we focus on pure state evolutions. An entropy in accord with Jaynes principle is defined on the basis of the quantum expectation value of the above observable. It is demonstrated that the resulting deterministic entropy dynamics are in a sense in accord with a transient fluctuation theorem. Moreover, we demonstrate that the dynamics of the expectation value are describable in terms of an Ornstein-Uhlenbeck process. These findings are demonstrated numerically and supported by analytical considerations based on quantum typicality.

quant-ph↗

arXiv2011

Finite size effects on transport coefficients for models of atomic wires coupled to phonons

We consider models of quasi-1-d, planar atomic wires consisting of several, laterally coupled rows of atoms, with mutually non-interacting electrons. This electronic wire system is coupled to phonons, corresponding, e.g., to some substrate. We aim at computing diffusion coefficients in dependence on the wire widths and the lateral coupling. To this end we firstly construct a numerically manageable linear collision term for the dynamics of the electronic occupation numbers by following a certain projection operator approach. By means of this collision term we set up a linear Boltzmann equation. A formula for extracting diffusion coefficients from such Boltzmann equations is given. We find in the regime of a few atomic rows and intermediate lateral coupling a significant and non-trivial dependence of the diffusion coefficient on both, the width and the lateral coupling. These results, in principle, suggest the possible applicability of such atomic wires as electronic devices, such as, e.g., switches.

cond-mat.mes-hall↗

arXiv2010

Transport in the 3-dimensional Anderson model: an analysis of the dynamics on scales below the localization length

Single-particle transport in disordered potentials is investigated on scales below the localization length. The dynamics on those scales is concretely analyzed for the 3-dimensional Anderson model with Gaussian on-site disorder. This analysis particularly includes the dependence of characteristic transport quantities on the amount of disorder and the energy interval, e.g., the mean free path which separates ballistic and diffusive transport regimes. For these regimes mean velocities, respectively diffusion constants are quantitatively given. By the use of the Boltzmann equation in the limit of weak disorder we reveal the known energy-dependencies of transport quantities. By an application of the time-convolutionless (TCL) projection operator technique in the limit of strong disorder we find evidence for much less pronounced energy dependencies. All our results are partially confirmed by the numerically exact solution of the time-dependent Schroedinger equation or by approximative numerical integrators. A comparison with other findings in the literature is additionally provided.

cond-mat.stat-mech↗

arXiv2010

Projection operator approach to master equations for coarse grained occupation numbers in non-ideal quantum gases

We aim at deriving an equation of motion for specific sums of momentum mode occupation numbers from models for electrons in periodic lattices experiencing elastic scattering, electron-phonon scattering or electron-electron scattering. These sums correspond to "grains" in momentum space. This equation of motion is supposed to involve only a moderate number of dynamical variables and/or exhibit a sufficiently simple structure such that neither its construction nor its analyzation/solution requires substantial numerical effort. To this we end compute, by means of a projection operator technique, a linear(ized) collision term which determines the dynamics of the above grain-sums. This collision term results as non-singular, finite dimensional rate matrix and may thus be inverted regardless of any symmetry of the underlying model. This facilitates calculations of, e.g., transport coefficients, as we demonstrate for a 3-dim. Anderson model featuring weak disorder.

cond-mat.quant-gas↗

arXiv2009

Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales

We investigate transport in several translationally invariant spin-1/2 chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating field, and energy transport in an Ising chain which is exposed to a tilted field. Our approach is essentially based on a connection between the evolution of the variance of an inhomogeneous non-equilibrium density and the current auto-correlation function at finite times. Although this relationship is not restricted to the case of diffusive transport, it allows to extract a quantitative value for the diffusion constant in that case. By means of numerically exact diagonalization we indeed observe diffusive behavior in the considered spin chains for a range of model parameters and confirm the diffusion coefficients which were obtained for these systems from non-equilibrium bath scenarios.

cond-mat.stat-mech↗

arXiv2009

Density dynamics from current auto-correlations at finite time- and length-scales

We consider the increase of the spatial variance of some inhomogeneous, non-equilibrium density (particles, energy, etc.) in a periodic quantum system of condensed matter-type. This is done for a certain class of initial quantum states which is supported by static linear response and typicality arguments. We directly relate the broadening to some current auto-correlation function at finite times. Our result is not limited to diffusive behavior, however, in that case it yields a generalized Einstein relation. These findings facilitate the approximation of diffusion constants/conductivities on the basis of current auto-correlation functions at finite times for finite systems. Pursuing this, we quantitatively confirm the magnetization diffusion constant in a spin chain which was recently found from non-equilibrium bath scenarios.

cond-mat.stat-mech↗

arXiv2009

Equivalence of transport coefficients in bath-induced and dynamical scenarios

We investigate the transport of a single excitation through a chain of weakly coupled subunits. At both ends the chain is exposed to baths which are incorporated by means of a master equation in Lindblad form. This master equation is solved by the use of stochastic unraveling in order to obtain excitation profile and current in the steady state. Completely diffusive transport is found for a range of model parameters, whereas signatures of ballistic behavior are observed outside this range. In the diffusive regime the conductivity is rather independent from the strength of the bath coupling and quantitatively agrees with the diffusion coefficient which has been derived from an investigation of the same model without baths. Also the ballistic behavior in the non-diffusive regime is in accord with results from this alternative approach.

cond-mat.stat-mech↗

arXiv2009

Length scale dependent diffusion in the Anderson model at high temperatures

We investigate a single particle on a 3-dimensional, cubic lattice with a random on-site potential (3D Anderson model). We concretely address the question whether or not the dynamics of the particle is in full accord with the diffusion equation. Our approach is based on the time-convolutionless (TCL) projection operator technique and allows for a detailed investigation of this question at high temperatures. It turns out that diffusive dynamics is to be expected for a rather short range of wavelengths, even if the amount of disorder is tuned to maximize this range. Our results are partially counterchecked by the numerical solution of the full time-dependent Schroedinger equation.

cond-mat.stat-mech↗

arXiv2009

Projection operator approach to transport in complex single-particle quantum systems

We discuss the time-convolutionless (TCL) projection operator approach to transport in closed quantum systems. The projection onto local densities of quantities such as energy, magnetization, particle number, etc. yields the reduced dynamics of the respective quantities in terms of a systematic perturbation expansion. In particular, the lowest order contribution of this expansion is used as a strategy for the analysis of transport in "modular" quantum systems corresponding to quasi one-dimensional structures which consist of identical or similar many-level subunits. Such modular quantum systems are demonstrated to represent many physical situations and several examples of complex single-particle models are analyzed in detail. For these quantum systems lowest order TCL is shown to represent an efficient tool which also allows to investigate the dependence of transport on the considered length scale. To estimate the range of validity of the obtained equations of motion we extend the standard projection to include additional degrees of freedom which model non-Markovian effects of higher orders.

cond-mat.stat-mech↗

arXiv2009

Dynamical typicality of quantum expectation values

We show that the vast majority of all pure states featuring a common expectation value of some generic observable at a given time will yield very similar expectation values of the same observable at any later time. This is meant to apply to Schroedinger type dynamics in high dimensional Hilbert spaces. As a consequence individual dynamics of expectation values are then typically well described by the ensemble average. Our approach is based on the Hilbert space average method. We support the analytical investigations with numerics obtained by exact diagonalization of the full time-dependent Schroedinger equation for some pertinent, abstract Hamiltonian model. Furthermore, we discuss the implications on the applicability of projection operator methods with respect to initial states, as well as on irreversibility in general.

quant-ph↗

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

Occurrence of exponential relaxation in closed quantum systems

We investigate the occurrence of exponential relaxation in a certain class of closed, finite systems on the basis of a time-convolutionless (TCL) projection operator expansion for a specific class of initial states with vanishing inhomogeneity. It turns out that exponential behavior is to be expected only if the leading order predicts the standard separation of timescales and if, furthermore, all higher orders remain negligible for the full relaxation time. The latter, however, is shown to depend not only on the perturbation (interaction) strength, but also crucially on the structure of the perturbation matrix. It is shown that perturbations yielding exponential relaxation have to fulfill certain criteria, one of which relates to the so-called ``Van Hove structure''. All our results are verified by the numerical integration of the full time-dependent Schroedinger equation.

cond-mat.stat-mech↗

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↗