arXiv subjects

Joachim Ankerhold

Publications and source records attributed to Joachim Ankerhold.

At least 109 records · Page 6Linked to original sources

arXiv2010

Low-temperature quantum fluctuations in overdamped ratchets

At low temperatures and strong friction the time evolution of the density distribution in position follows a quantum Smoluchowski equation. Recently, also higher-order contributions of quantum fluctuations to drift and diffusion coefficients have been systematically derived. As a non-trivial situation to reveal the impact of subleading quantum corrections and to demonstrate convergence properties of the perturbation series, directed transport in ratchets is studied. It is shown that the perturbation series typically has a non-monotonous behavior. Depending on symmetry properties higher order contributions may even compensate current reversals induced by leading quantum fluctuations. This analysis demonstrates how to consistently treat the dynamics of overdamped quantum systems at low temperatures also in numerical applications.

cond-mat.stat-mech↗

arXiv2010

Quantum Smoluchowski equation: A systematic study

The strong friction regime at low temperatures is analyzed systematically starting from the formally exact path integral expression for the reduced dynamics. This quantum Smoluchowski regime allows for a type of semiclassical treatment in the inverse friction strength so that higher order quantum corrections to the original quantum Smoluchowski equation [PRL 87, 086802 (2001), PRL 101, 11903 (2008)] can be derived. Drift and diffusion coefficients are determined by the equilibrium distribution in position and are directly related to the corresponding action of extremal paths and fluctuations around them. It is shown that the inclusion of higher order corrections reproduces the quantum enhancement above crossover for the decay rate out of a metastable well exactly.

cond-mat.stat-mech↗

arXiv2010

Dissipation in a rotating frame: master equation, effective temperature and Lamb-shift

Motivated by recent realizations of microwave-driven nonlinear resonators in superconducting circuits, the impact of environmental degrees of freedom is analyzed as seen from a rotating frame. A system plus reservoir model is applied to consistently derive in the weak coupling limit the master equation for the reduced density in the moving frame and near the first bifurcation threshold. It turns out that additional interactions between momenta of system and bath appear which have been omitted in previous studies. Explicit expressions for the effective temperature and the Lamb-shift are given which for ohmic baths are in agreement with experimental findings, while for structured environments population inversion is predicted that may qualitatively explain recent observations.

cond-mat.other↗

arXiv2009

Semiclassical theory of energy diffusive escape

Thermal escape out of a metastable well is considered in the weak friction regime, where the bottleneck for decay is energy diffusion, and at lower temperatures, where quantum tunneling becomes relevant. Within a systematic semiclassical formalism an extension of the classical diffusion equation is derived starting from a quantum mechanical master equation. In contrast to previous approaches finite barrier transmission also affects transition probabilities. The decay rate is obtained from the stationary non-equilibrium solution and captures the intimate interplay between thermal and quantum fluctuations above the crossover to the deep quantum regime.

cond-mat.stat-mech↗

arXiv2009

Nonadiabatic transitions between adiabatic surfaces: phase diffusion in superconducting atomic point contacts

Motivated by experiments with current biased superconducting atomic point contacts the general problem of nonadiabatic transitions between adiabatic surfaces in presence of strong dissipation is studied. For a single channel device the supercurrent is determined by the diffusive motion of the superconducting phase difference on two Andreev levels. These surfaces are uncoupled only in the adiabatic limit of low to moderate transmissions, while for high transmissions curve crossings are important. Starting from a general master equation of the full density matrix an approximate time evolution equation for the populations on the adiabatic surfaces in the overdamped limit is derived from which the relevant observables can be obtained. Specific results for the case of atomic point contacts are in agreement with experimental observations that cannot be explained by conventional theory.

cond-mat.mes-hall↗

arXiv2008

Non-Markovian Dissipative Semiclassical Dynamics

The exact stochastic decomposition of non-Markovian dissipative quantum dynamics is combined with the time-dependent semiclassical initial value formalism. It is shown that even in the challenging regime of moderate friction and low temperatures, where non-Markovian effects are substantial, this approach allows for the accurate description of dissipative dynamics in anharmonic potentials over many oscillation periods until thermalization is reached. The problem of convergence of the stochastic average at long times, which plagues full quantum mechanical implementations, is avoided through a joint sampling of the stochastic noise and the semiclassical phase space distribution.

cond-mat.stat-mech↗

arXiv2007

Dissipation can enhance quantum effects

Usually one finds that dissipation tends to make a quantum system more classical in nature. In this paper we study the effect of momentum dissipation on a quantum system. The momentum of the particle is coupled bilinearly to the momenta of a harmonic oscillator heat bath. For a harmonic oscillator system we find that the position and momentum variances for momentum coupling are respectively identical to momentum and position variances for spatial friction. This implies that momentum coupling leads to an increase in the fluctuations in position as the temperature is lowered, exactly the opposite of the classical like localization of the oscillator, found with spatial friction. For a parabolic barrier, momentum coupling causes an {\it increase} in the unstable normal mode barrier frequency, as compared to the lowering of the barrier frequency in the presence of purely spatial coupling. This increase in the frequency leads to an enhancement of the thermal tunneling flux, which below the crossover temperature becomes exponentially large. The crossover temperature between tunneling and thermal activation {\it increases} with momentum friction so that quantum effects in the escape are relevant at higher temperatures.

cond-mat.stat-mech↗

arXiv2006

Detecting charge noise with a Josephson junction: A problem of thermal escape in presence of non-Gaussian fluctuations

Motivated by several experimental activities to detect charge noise produced by a mesoscopic conductor with a Josephson junction as on-chip detector, the switching rate out of its zero-voltage state is studied. This process is related to the fundamental problem of thermal escape in presence of non-Gaussian fluctuations. In the relevant case of weak higher than second order cumulants, an effective Fokker-Planck equation is derived, which is then used to obtain an explicit expression for the escape rate. Specific results for the rate asymmetry due to the third moment of current noise allow to analyse experimental data and to optimize detection circuits.

cond-mat.mes-hall↗

arXiv2006

Nonequilibrium many-body dynamics along a dissipative Hubbard chain: Symmetries and Quantum Monte Carlo simulations

The nonequilibrium dynamics of correlated charge transfer along a one-dimensional chain in presence of a phonon environment is investigated within a dissipative Hubbard model. For this generalization of the ubiquitous spin-boson model the crucial role of symmetries is analysed in detail and corresponding invariant subspaces are identified. It is shown that the time evolution typically occurs in each of the disjunct subspaces independently leading e.g. asymptotically to a non-Boltzmann equilibrium state. Based on these findings explicit results are obtained for two interacting electrons by means of a substantially improved real-time quantum Monte Carlo approach. In the incoherent regime an appropriate mapping of the many-body dynamics onto an isomorphic single particle motion allows for an approximate description of the numerical data in terms of rate equations. These results may lead to new control schemes of charge transport in tailored quantum systems as e.g. molecular chains or quantum dot arrays.

cond-mat.stat-mech↗

arXiv2006

Real-time Monte-Carlo simulations for dissipative tight-binding systems and time local master equations

The numerically exact path integral Monte Carlo approach for the real-time evolution of dissipative quantum systems (PIMC), particularly suited for systems with discrete configuration space (tight-binding systems), is extended to treat spatially continuous and correlated many-body systems. This way, one has to consider generalized tight-binding lattices with either non-equidistant spacing or in higher dimensions, which in turn allows to analyze to what extent Markovian master equations can be applied beyond the usually studied spin-boson type of models.

cond-mat.stat-mech↗

arXiv2005

How to detect the fourth order cumulant of electrical noise

It is proposed to measure the current noise generated in a mesoscopic conductor by macroscopic quantum tunneling (MQT) in a current biased Josephson junction placed in parallel to the conductor. The theoretical description of this set-up takes into account the complete dynamics of detector and noise source. Explicit results are given for the specific case of current fluctuations in an oxide layer tunnel junction, and it is shown how the device allows to extract the fourth order cumulant of the noise from the MQT data for realistic experimental parameters.

cond-mat.mes-hall↗

arXiv2005

Quantum Brownian Motion With Large Friction

Quantum Brownian motion in the strong friction limit is studied based on the exact path integral formulation of dissipative systems. In this limit the time-nonlocal reduced dynamics can be cast into an effective equation of motion, the quantum Smoluchowski equation. For strongly condensed phase environments it plays a similar role as master equations in the weak coupling range. Applications for chemical, mesoscopic, and soft matter systems are discussed and reveal the substantial role of quantum fluctuations.

cond-mat.stat-mech↗

arXiv2004

Path-integral Monte-Carlo simulations for electronic dynamics on molecular chains: II. Transport across impurities

Electron transfer (ET) across molecular chains including an impurity is studied based on a recently improved real-time path integral Monte Carlo (PIMC) approach [J. Chem. Phys. {\bf 121}, 12696 (2004)]. The reduced electronic dynamics is studied for various bridge lengths and defect site energies. By determining intersite hopping rates from PIMC simulations up to moderate times, the relaxation process in the extreme long time limit is captured within a sequential transfer model. The total transfer rate is extracted and shown to be enhanced for certain defect site energies. Further, it is revealed that the entire bridge compound approaches a steady state on a much shorter time scale than that related to the total transfer which allows for a simplified description of ET along donor-bridge-acceptor systems in the long time range.

cond-mat.mes-hall↗

arXiv2004

Overdamped quantum phase diffusion and charging effects in Josephson junctions

Exploiting the recently derived quantum Smoluchowski equation the classical Ivanchenko Zil'berman theory for overdamped diffusive phase motion of low capacitance Josephson junctions is extended to the low temperature quantum domain where charging effects appear. This formulation allows to derive explicit results for the current-voltage characteristics over a broad range of parameters that reduce to known findings in certain limits. In particular, the transparent analytical approach comprises Coulomb blockade physics, coherent Cooper pair transfer, and the precursors of macroscopic quantum tunneling and needs to be supplemented by more sophisticated methods only at very low temperatures.

cond-mat.mes-hall↗

arXiv2003

Low temperature electron transfer in strongly condensed phase

Electron transfer coupled to a collective vibronic degree of freedom is studied in strongly condensed phase and at lower temperatures where quantum fluctuations are essential. Based on an exact representation of the reduced density matrix of the electronic+reaction coordinate compound in terms of path integrals, recent findings on the overdamped limit in quantum dissipative systems are employed. This allows to give for the first time a consistent generalization of the well-known Zusman equations to the quantum domain. Detailed conditions for the range of validity are specified. Using the Wigner transform these results are also extended to the quantum dynamics in full phase space. As an important application electronic transfer rates are derived that comprise adiabatic and nonadiabatic processes in the low temperature regime including nuclear tunneling. Accurate agreement with precise quantum Monte Carlo data is observed.

cond-mat.stat-mech↗

arXiv2003

Dynamics of Dissipative Quantum Systems--from Path Integrals to Master Equations

The path integral approach offers not only an exact expression for the non- equilibrium dynamics of dissipative quantum systems, but is also a convenient starting point for perturbative treatments. An alternative way to explore the influence of friction in the quantum realm is based on master equations which require, however, in one or the other aspect approximations. Here it is discussed under which conditions and limitations Markovian master equations can be derived from exact path integrals thus providing a firm basis for their applicability.

cond-mat.stat-mech↗

arXiv2003

Enhancement of Macroscopic Quantum Tunneling by Landau-Zener Transitions

Motivated by recent realizations of qubits with a readout by macroscopic quantum tunneling in a Josephson junction, we study the problem of barrier penetration in presence of coupling to a spin-${1\over 2}$ system. It is shown that when the diabatic potentials for fixed spin intersect in the barrier region, Landau- -Zener transitions lead to an enhancement of the tunneling rate. The effect of these spin flips in imaginary time is in qualitative agreement with experimental observations.

cond-mat.mes-hall↗

arXiv2002

Phase space dynamics of overdamped quantum systems

The phase space dynamics of dissipative quantum systems in strongly condensed phase is considered. Based on the exact path integral approach it is shown that the Wigner transform of the reduced density matrix obeys a time evolution equation of Fokker-Planck type valid from high down to very low temperatures. The effect of quantum fluctuations is discussed and the accuracy of these findings is tested against exact data for a harmonic system.

cond-mat.stat-mech↗