arXiv subjects

Peter Talkner

Publications and source records attributed to Peter Talkner.

70 records · Page 4Linked to original sources

arXiv2007

Accumulating Particles at the Boundaries of a Laminar Flow

The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a Fokker-Planck equation for the particle density. It is shown that in the limit of vanishing particle size a uniform particle distribution is always approached in the long time limit. For extended spherical particles, conditions are specified that lead to inhomogeneous densities and consequently to particle accumulation and depletion. Hereby the boundary conditions for the particle density play a decisive role: The centers of spherical particles must keep the minimal distance of their radius from the fluid boundaries. The normal components of the forces acting on the sphere then may assume finite values which are diffusively transported into the bulk of the fluid.

cond-mat.soft↗

arXiv2007

Fluctuation theorems: Work is not an observable

The characteristic function of the work performed by an external time-dependent force on a Hamiltonian quantum system is identified with the time-ordered correlation function of the exponentiated system's Hamiltonian. A similar expression is obtained for the averaged exponential work which is related to the free energy difference of equilibrium systems by the Jarzynski work theorem.

cond-mat.stat-mech↗

arXiv2007

The Tasaki-Crooks quantum fluctuation theorem

Starting out from the recently established quantum correlation function expression of the characteristic function for the work performed by a force protocol on the system [cond-mat/0703213] the quantum version of the Crooks fluctuation theorem is shown to emerge almost immediately by the mere application of an inverse Fourier transformation.

cond-mat.stat-mech↗

arXiv2007

Relative entropy, Haar measures and relativistic canonical velocity distributions

The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy. The latter characterizes probability distributions with respect to a pre-specified reference measure. To identify the canonical BGS entropy with a relative entropy is appealing for two reasons: (i) the maximum entropy principle assumes a coordinate invariant form; (ii) thermodynamic equilibrium distributions, which are obtained as solutions of the maximum entropy problem, may be characterized in terms of the transformation properties of the underlying reference measure (e.g., invariance under group transformations). As examples, we analyze two frequently considered candidates for the one-particle equilibrium velocity distribution of an ideal gas of relativistic particles. It becomes evident that the standard Jüttner distribution is related to the (additive) translation group on momentum space. Alternatively, imposing Lorentz invariance of the reference measure leads to a so-called modified Jüttner function, which differs from the standard Jüttner distribution by a prefactor, proportional to the inverse particle energy.

cond-mat.stat-mech↗

arXiv2007

Relativistic diffusion processes and random walk models

The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (non-continuous) diffusion fronts on the light cone, which are unlikely to exist for massive particles. It is therefore advisable to explore other alternatives as well. In this paper, a generalized Wiener process is proposed that is continuous, avoids superluminal propagation, and reduces to the standard Wiener process in the non-relativistic limit. The corresponding relativistic diffusion propagator is obtained directly from the nonrelativistic Wiener propagator, by rewriting the latter in terms of an integral over actions. The resulting relativistic process is non-Markovian, in accordance with the known fact that nontrivial continuous, relativistic Markov processes in position space cannot exist. Hence, the proposed process defines a consistent relativistic diffusion model for massive particles and provides a viable alternative to the solutions of the telegraph equation.

cond-mat.stat-mech↗

arXiv2007

Transport of Forced Quantum Motors in the Strong Friction Limit

The directed transport of an overdamped Brownian motor moving in a spatially periodic potential that lacks reflection symmetry (i.e. a ratchet potential) is studied when driven by thermal and dichotomic nonequilibrium noise in the presence of an external, constant load force. We consider both, the classical and the quantum tunneling assisted regimes. The current-load characteristics are investigated as a function of the system parameters like the load force, the temperature and the amplitude strength of the applied two-state noise.

cond-mat.soft↗

arXiv2006

Optimal strategy for controlling transport in inertial Brownian motors

In order to optimize the directed motion of an inertial Brownian motor, we identify the operating conditions that both maximize the motor current and minimize its dispersion. Extensive numerical simulation of an inertial rocked ratchet displays that two quantifiers, namely the energetic efficiency and the Péclet number (or equivalently the Fano factor), suffice to determine the regimes of optimal transport. The effective diffusion of this rocked inertial Brownian motor can be expressed as a generalized fluctuation theorem of the Green -- Kubo type. Addendum and Erratum The expression for the effective diffusion of an inertial, periodically driven Brownian particle in an asymmetric, periodic potential is compared with the step number diffusion which is extracted from the corresponding coarse grained hopping process specifying the number of covered spatial periods within each temporal period. The two expressions are typically different and involve the correlations between the number of hops.

cond-mat.stat-mech↗

arXiv2006

Escape rates in periodically driven Markov processes

We present an approximate analytical expression for the escape rate of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrate-and-fire model for neural spiking. The novel approximation is based on a discrete state Markovian modeling of the full long-time dynamics with time-dependent rates. It is valid in a wide parameter regime beyond the restraining limits of weak driving (linear response) and/or weak noise. The scheme is carefully tested and yields excellent agreement with three different numerical methods based on the Langevin equation, the Fokker-Planck equation and an integral equation.

physics.data-an↗

arXiv2006

Statistics of transition times, phase diffusion and synchronization in periodically driven bistable systems

The statistics of transitions between the metastable states of a periodically driven bistable Brownian oscillator are investigated on the basis of a two-state description by means of a master equation with time-dependent rates. The results are compared with extensive numerical simulations of the Langevin equation for a sinusoidal driving force. Very good agreement is achieved both for the counting statistics of the number of transitions and the residence time distribution of the process in either state. The counting statistics corroborate in a consistent way the interpretation of stochastic resonance as a synchronisation phenomenon for a properly defined generalized Rice phase.

physics.data-an↗

arXiv2006

Switching Time Statistics for Driven Neuron Models: Analytic Expressions versus Numerics

Analytical expressions are put forward to investigate the forced spiking activity of abstract neuron models such as the driven leaky integrate-and-fire (LIF) model. The method is valid in a wide parameter regime beyond the restraining limits of weak driving (linear response) and/or weak noise. The novel approximation is based on a discrete state Markovian modeling of the full dynamics with time-dependent rates. The scheme yields very good agreement with numerical Langevin and Fokker-Planck simulations of the full non-stationary dynamics for both, the first-passage time statistics and the interspike interval (residence time) distributions.

q-bio.NC↗

arXiv2005

Forcing inertial Brownian motors: efficiency and negative differential mobility

The noise-assisted, directed transport in a one-dimensional dissipative, inertial Brownian motor of the rocking type that is exposed to an external bias is investigated. We demonstrate that the velocity-load characteristics is distinctly non-monotonic, possessing regimes with a {\em negative differential mobility}. In addition, we evaluate several possible efficiency quantifiers which are compared among each other. These quantifiers characterize the mutual interplay between the viscous drag and the external load differently, weighing the inherent rectification features from different physical perspectives.

cond-mat.stat-mech↗

arXiv2005

Chiral separation in microflows

Molecules that only differ by their chirality, so called enantiomers, often possess different properties with respect to their biological function. Therefore, the separation of enantiomers presents a prominent challenge in molecular biology and belongs to the ``Holy Grail'' of organic chemistry. We suggest a new separation technique for chiral molecules that is based on the transport properties in a microfluidic flow with spatially variable vorticity. Because of their size the thermal fluctuating motion of the molecules must be taken into account. These fluctuations play a decisive role in the proposed separation mechanism.

cond-mat.soft↗

arXiv2005

Anticipated synchronization in coupled inertia ratchets with time-delayed feedback: a numerical study

We investigate anticipated synchronization between two periodically driven deterministic, dissipative inertia ratchets that are able to exhibit directed transport with a finite velocity. The two ratchets interact through an unidirectional delay coupling: one is acting as a master system while the other one represents the slave system. Each of the two dissipative deterministic ratchets is driven externally by a common periodic force. The delay coupling involves two parameters: the coupling strength and the (positive-valued) delay time. We study the synchronization features for the unbounded, current carrying trajectories of the master and the slave, respectively, for four different strengths of the driving amplitude. These in turn characterize differing phase space dynamics of the transporting ratchet dynamics: regular, intermittent and a chaotic transport regime. We find that the slave ratchet can respond in exactly the same way as the master will respond in the future, thereby anticipating the nonlinear directed transport.

cond-mat.soft↗

arXiv2003

Is the dynamics of open quantum systems always linear?

We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system density matrix and a bath density matrix the time evolution generally is no longer governed by a linear map nor is this map affine. Put differently, the evolution is truly nonlinear and cannot be cast into the form of a linear map plus a term that is independent of the initial density matrix of the open quantum system. As a consequence, the inhomogeneity that emerges in formally exact generalized master equations is in fact a nonlinear term that vanishes for a factorizing initial state. The general results are elucidated with the example of two interacting spins prepared at thermal equilibrium with one spin subjected to an external field. The second spin represents the environment. The field allows the preparation of mixed density matrices of the first spin that can be represented as a convex combination of two limiting pure states, i.e. the preparable reduced density matrices make up a convex set. Moreover, the map from these reduced density matrices onto the corresponding density matrices of the total system is affine only for vanishing coupling between the spins. In general, the set of the accessible total density matrices is nonconvex.

quant-ph↗

arXiv2003

Rate description of Fokker-Planck processes with time dependent parameters

The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time dependent parameters such as periodic external forces or slowly fluctuating barrier heights. A quantitative criterion is provided under which condition a kinetic description with time dependent frozen rates applies. Finally it is shown how the long time behavior of the underlying continuous process can be retrieved from the knowledge of the discrete process by means of an appropriate random decoration of the discrete states. As a particular example of the presented theory an over-damped bistable Brownian oscillator with periodic driving is discussed.

cond-mat.stat-mech↗

arXiv2000

A Stochastic Cascade Model for FX Dynamics

A time series model for the FX dynamics is presented which takes into account structural peculiarities of the market, namely its heterogeneity and an information flow from long to short time horizons. The model emerges from an analogy between FX dynamics and hydrodynamic turbulence. The heterogeneity of the market is modeled in form of a multiplicative cascade of time scales ranging from several minutes to a few months, analogous to the Kolmogorov cascade in turbulence. The model reproduces well the important empirical characteristics of FX rates for major currencies, as the heavy-tailed distribution of returns, their change in shape with increasing time interval, and the persistence of volatility.

cond-mat.stat-mech↗