arXiv subjects

Peter Hänggi

Publications and source records attributed to Peter Hänggi.

At least 73 records · Page 4Linked to original sources

arXiv2011

Active motion assisted by correlated stochastic torques

The stochastic dynamics of an active particle undergoing a constant speed and additionally driven by an overall fluctuating torque is investigated. The random torque forces are expressed by a stochastic differential equation for the angular dynamics of the particle determining the orientation of motion. In addition to a constant torque, the particle is supplemented by random torques which are modeled as an Ornstein-Uhlenbeck process with given correlation time $τ_c$. These nonvanishing correlations cause a persistence of the particles' trajectories and a change of the effective spatial diffusion coefficient. We discuss the mean square displacement as a function of the correlation time and the noise intensity and detect a nonmonotonic dependence of the effective diffusion coefficient with respect to both correlation time and noise strength. A maximal diffusion behavior is obtained if the correlated angular noise straightens the curved trajectories, interrupted by small pirouettes, whereby the correlated noise amplifies a straightening of the curved trajectories caused by the constant torque.

cond-mat.stat-mech↗

arXiv2011

Fluctuation, Dissipation and the Arrow of Time

The recent development of the theory of fluctuation relations has led to new insights into the ever-lasting question of how irreversible behavior emerges from time-reversal symmetric microscopic dynamics. We provide an introduction to fluctuation relations, examine their relation to dissipation and discuss their impact on the arrow of time question.

physics.pop-ph↗

arXiv2011

Biased Brownian motion in extreme corrugated tubes

Biased Brownian motion of point-size particles in a three-dimensional tube with smoothly varying cross-section is investigated. In the fashion of our recent work [Martens et al., PRE 83,051135] we employ an asymptotic analysis to the stationary probability density in a geometric parameter of the tube geometry. We demonstrate that the leading order term is equivalent to the Fick-Jacobs approximation. Expression for the higher order corrections to the probability density are derived. Using this expansion orders we obtain that in the diffusion dominated regime the average particle current equals the zeroth-order Fick-Jacobs result corrected by a factor including the corrugation of the tube geometry. In particular we demonstrate that this estimate is more accurate for extreme corrugated geometries compared to the common applied method using the spatially dependent diffusion coefficient D(x,f). The analytic findings are corroborated with the finite element calculation of a sinusoidal-shaped tube.

cond-mat.stat-mech↗

arXiv2011

Time-resolved qubit readout via nonlinear Josephson inductance

We propose a generalisation of dispersive qubit readout which provides the time evolution of a flux qubit observable. Our proposal relies on the non-linear coupling of the qubit to a harmonic oscillator with high frequency, representing a dc-SQUID. Information about the qubit dynamics is obtained by recording the oscillator response to resonant driving and subsequent lock-in detection. The measurement process is simulated for the example of coherent qubit oscillations. This corroborates the underlying measurement relation and also reveals that the measurement scheme possesses low backaction and high fidelity.

cond-mat.supr-con↗

arXiv2011

Colloquium. Quantum Fluctuation Relations: Foundations and Applications

Two fundamental ingredients play a decisive role in the foundation of fluctuation relations: the principle of microreversibility and the fact that thermal equilibrium is described by the Gibbs canonical ensemble. Building on these two pillars we guide the reader through a self-contained exposition of the theory and applications of quantum fluctuation relations. These are exact results that constitute the fulcrum of the recent development of nonequilibrium thermodynamics beyond the linear response regime. The material is organized in a way that emphasizes the historical connection between quantum fluctuation relations and (non)-linear response theory. We also attempt to clarify a number of fundamental issues which were not completely settled in the prior literature. The main focus is on (i) work fluctuation relations for transiently driven closed or open quantum systems, and (ii) on fluctuation relations for heat and matter exchange in quantum transport settings. Recently performed and proposed experimental applications are presented and discussed.

cond-mat.stat-mech↗

arXiv2011

Distance between quantum states in presence of initial qubit-environment correlations: a comparative study

The time evolution of the trace distance between two states of an open quantum system may increase due to initial system-environment correlations, thus exhibiting a breakdown of distance contractivity of the reduced dynamics. We analyze how the time evolution of the distance depends on the chosen distance measure. Here we elucidate the behavior of the trace distance, the Hilbert- Schmidt distance, the Bures distance, the Hellinger distance and the quantum Jensen-Shannon divergence for two system-environment setups, namely a qubit bi-linearly coupled to an infinite and a finite size environment with the latter composed of harmonic oscillators.

quant-ph↗

arXiv2011

Temperature-resonant cyclotron spectra in confined geometries

We consider a two-dimensional gas of colliding charged particles confined to finite size containers of various geometries and subjected to a uniform orthogonal magnetic field. The gas spectral densities are characterized by a broad peak at the cyclotron frequency. Unlike for infinitely extended gases, where the amplitude of the cyclotron peak grows linearly with temperature, here confinement causes such a peak to go through a maximum for an optimal temperature. In view of the fluctuation-dissipation theorem, the reported resonance effect has a direct counterpart in the electric susceptibility of the confined magnetized gas.

nlin.CD↗

arXiv2011

Entropic particle transport: higher order corrections to the Fick-Jacobs diffusion equation

Transport of point-size Brownian particles under the influence of a constant and uniform force field through a three-dimensional channel with smoothly varying periodic cross-section is investigated. Here, we employ an asymptotic analysis in the ratio between the difference of the widest and the most narrow constriction divided through the period length of the channel geometry. We demonstrate that the leading order term is equivalent to the Fick-Jacobs approximation. By use of the higher order corrections to the probability density we derive an expression for the spatially dependent diffusion coefficient D(x) which substitutes the constant diffusion coefficient present in the common Fick-Jacobs equation. In addition, we show that in the diffusion dominated regime the average transport velocity is obtained as the product of the zeroth-order Fick-Jacobs result and the expectation value of the spatially dependent diffusion coefficient . The analytic findings are corroborated with the precise numerical results of a finite element calculation of the Smoluchowski diffusive particle dynamics occurring in a reflection symmetric sinusoidal-shaped channel.

cond-mat.stat-mech↗

arXiv2011

Influence of measurements on the statistics of work performed on a quantum system

The recently demonstrated robustness of fluctuation theorems against measurements [M. Campisi \emph{et al.}, Phys. Rev. Lett. \textbf{105} 140601 (2010)] does not imply that the probability distributions of nonequilibrium quantities, such as heat and work, remain unaffected. We determine the impact of measurements that are performed during a running force protocol on the characteristic function of work. The results are illustrated by means of the Landau-Zener(-Stückelberg-Majorana) model. In the limit of continuous measurements the quantum Zeno effect suppresses any unitary dynamics. It is demonstrated that the characteristic function of work is the same as for an adiabatic protocol when the continuously measured quantity coincides with the Hamiltonian governing the unitary dynamics of the system in the absence of measurements.

cond-mat.stat-mech↗

arXiv2011

Thermal equilibration between two quantum systems

Two identical finite quantum systems prepared initially at different temperatures, isolated from the environment, and subsequently brought into contact are demonstrated to relax towards Gibbs-like quasi-equilibrium states with a common temperature and small fluctuations around the time-averaged expectation values of generic observables. The temporal thermalization process proceeds via a chain of intermediate Gibbs-like states. We specify the conditions under which this scenario occurs and corroborate the quantum equilibration with two different models.

cond-mat.stat-mech↗

arXiv2010

Monitoring Entanglement Evolution and Collective Quantum Dynamics

We generalize a recently developed scheme for monitoring coherent quantum dynamics with good time-resolution and low backaction [Reuther et al., Phys. Rev. Lett. 102, 033602 (2009)] to the case of more complex quantum dynamics of one or several qubits. The underlying idea is to measure with lock-in techniques the response of the quantum system to a high-frequency ac field. We demonstrate that this scheme also allows one to observe quantum dynamics with many frequency scales, such as that of a qubit undergoing Landau-Zener transitions. Moreover, we propose how to measure the entanglement between two qubits as well as the collective dynamics of qubit arrays.

cond-mat.supr-con↗

arXiv2010

Fluctuation theorems for continuously monitored quantum fluxes

It is shown that quantum fluctuation theorems remain unaffected if measurements of any kind and number of observables are performed during the action of a force protocol. That is, although the backward and forward probabilities entering the fluctuation theorems are both altered by these measurements, their ratio remains unchanged. This observation allows to describe the measurement of fluxes through interfaces and, in this way, to bridge the gap between the current theory, based on only two measurements performed at the beginning and end of the protocol, and experiments that are based on continuous monitoring.

cond-mat.stat-mech↗

arXiv2010

Berry-Phase induced Heat Pumping and its Impact on the Fluctuation Theorem

Applying adiabatic, cyclic two parameter modulations we investigate quantum heat transfer across an anharmonic molecular junction contacted with two heat baths. We demonstrate that the pumped heat typically exhibits a Berry phase effect in providing an additional geometric contribution to heat flux. Remarkably, a robust fractional quantized geometric phonon response is identified as well. The presence of this geometric phase contribution in turn causes a breakdown of the fluctuation theorem of the Gallavotti-Cohen type for quantum heat transfer. This can be restored only if (i) the geometric phase contribution vanishes and if (ii) the cyclic protocol preserves the detailed balance symmetry.

cond-mat.mes-hall↗

arXiv2010

Two-resonator circuit QED: Dissipative Theory

We present a theoretical treatment for the dissipative two-resonator circuit quantum electrodynamics setup referred to as quantum switch. There, switchable coupling between two superconducting resonators is mediated by a superconducting qubit operating in the dispersive regime, where the qubit transition frequency is far detuned from those of the resonators. We derive an effective Hamiltonian for the quantum switch beyond the rotating wave approximation and study the dissipative dynamics within a Bloch-Redfield quantum master equation approach. We derive analytically how the qubit affects the quantum switch even if the qubit has no dynamics, and we estimate the strength of this influence. The analytical results are corroborated by numerical calculations, where coherent oscillations between the resonators, the decay of coherent and Fock states, and the decay of resonator-resonator entanglement are studied. Finally, we suggest an experimental protocol for extracting the damping constants of qubit and resonators by measuring the quadratures of the resonator fields.

cond-mat.supr-con↗

arXiv2010

Quantum Bochkov-Kuzovlev Work Fluctuation Theorems

The quantum version of the Bochkov-Kuzovlev identity is derived on the basis of the appropriate definition of work as the difference of the measured internal energies of a quantum system at the beginning and at the end of an external action on the system given by a prescribed protocol. According to the spirit of the original Bochkov-Kuzovlev approach, we adopt the "exclusive" viewpoint, meaning that the coupling to the external work-source is {\it not} counted as part of the internal energy. The corresponding canonical and microcanonical quantum fluctuation theorems are derived as well, and are compared to the respective theorems obtained within the "inclusive" approach. The relations between the quantum inclusive-work $w$, the exclusive-work $w_0$ and the dissipated-work $w_{dis}$, are discussed and clarified. We show by an explicit example that $w_0$ and $w_{dis}$ are distinct stochastic quantities obeying different statistics.

cond-mat.stat-mech↗

arXiv2010

Coherent charge transport through molecular wires: "Exciton blocking" and current from electronic excitations in the wire

We consider exciton effects on current in molecular nanojunctions, using a model comprising a two two-level sites bridge connecting free electron reservoirs. Expanding the density operator in the many-electron eigenstates of the uncoupled sites, we obtain a 16X16 density matrix in the bridge subspace whose dynamics is governed by Liuoville equation that takes into account interactions on the bridge as well as electron injection and damping to and from the leads. Our consideration can be considerably simplified by using the pseudospin description based on the symmetry properties of Lie group SU(2). We study the influence of the bias voltage, the Coulomb repulsion and the energy-transfer interactions on the steady-state current and in particular focus on the effect of the excitonic interaction between bridge sites. Our calculations show that in case of non-interacting electrons this interaction leads to reduction in the current at high voltage for a homodimer bridge. In other words, we predict the effect of \textquotedblleft exciton\textquotedblright blocking. The effect of \textquotedblleft exciton\textquotedblright blocking is modified for a heterodimer bridge, and disappears for strong Coulomb repulsion at sites. In the latter case the exciton type interactions can open new channels for electronic conduction. In particular, in the case of strong Coulomb repulsion, conduction exists even when the electronic connectivity does not exist.

cond-mat.str-el↗

arXiv2009

Molecular wires acting as quantum heat ratchets

We explore heat transfer in molecular junctions between two leads in the absence of a finite net thermal bias. The application of an unbiased, time-periodic temperature modulation of the leads entails a dynamical breaking of reflection symmetry, such that a directed heat current may emerge (ratchet effect). In particular, we consider two cases of adiabatically slow driving, namely (i) periodic temperature modulation of only one lead and (ii) temperature modulation of both leads with an ac driving that contains a second harmonic, thus generating harmonic mixing. Both scenarios yield sizeable directed heat currents which should be detectable with present techniques. Adding a static thermal bias, allows one to compute the heat current-thermal load characteristics which includes the ratchet effect of negative thermal bias with positive-valued heat flow against the thermal bias, up to the thermal stop-load. The ratchet heat flow in turn generates also an electric current. An applied electric stop-voltage, yielding effective zero electric current flow, then mimics a solely heat-ratchet-induced thermopower (``ratchet Seebeck effect''), although no net thermal bias is acting. Moreover, we find that the relative phase between the two harmonics in scenario (ii) enables steering the net heat current into a direction of choice.

cond-mat.mes-hall↗

arXiv2009

Finite Bath Fluctuation Theorem

We demonstrate that a Finite Bath Fluctuation Theorem of the Crooks type holds for systems that have been thermalized via weakly coupling it to a bath with energy independent finite specific heat. We show that this theorem reduces to the known canonical and microcanonical fluctuation theorems in the two respective limiting cases of infinite and vanishing specific heat of the bath. The result is elucidated by applying it to a 2D hard disk colliding elastically with few other hard disks in a rectangular box with perfectly reflecting walls.

cond-mat.stat-mech↗