arXiv subjects

P. Hänggi

Publications and source records attributed to P. Hänggi.

At least 55 records · Page 3Linked to original sources

arXiv2007

Analytically solvable model of a driven system with quenched dichotomous disorder

We perform a time-dependent study of the driven dynamics of overdamped particles which are placed in a one-dimensional, piecewise linear random potential. This set-up of spatially quenched disorder then exerts a dichotomous varying random force on the particles. We derive the path integral representation of the resulting probability density function for the position of the particles and transform this quantity of interest into the form of a Fourier integral. In doing so, the evolution of the probability density can be investigated analytically for finite times. It is demonstrated that the probability density contains both a $δ$-singular contribution and a regular part. While the former part plays a dominant role at short times, the latter rules the behavior at large evolution times. The slow approach of the probability density to a limiting Gaussian form as time tends to infinity is elucidated in detail.

cond-mat.stat-mech↗

arXiv2007

Rapidly driven nanoparticles: Mean first-passage times and relaxation of the magnetic moment

We present an analytical method of calculating the mean first-passage times (MFPTs) for the magnetic moment of a uniaxial nanoparticle which is driven by a rapidly rotating, circularly polarized magnetic field and interacts with a heat bath. The method is based on the solution of the equation for the MFPT derived from the two-dimensional backward Fokker-Planck equation in the rotating frame. We solve these equations in the high-frequency limit and perform precise, numerical simulations which verify the analytical findings. The results are used for the description of the rates of escape from the metastable domains which in turn determine the magnetic relaxation dynamics. A main finding is that the presence of a rotating field can cause a drastic decrease of the relaxation time and a strong magnetization of the nanoparticle system. The resulting stationary magnetization along the direction of the easy axis is compared with the mean magnetization following from the stationary solution of the Fokker-Planck equation.

cond-mat.stat-mech↗

arXiv2007

Use and Abuse of a Fractional Fokker-Planck Dynamics for Time-Dependent Driving

We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in time-varying potential landscapes and thereby disclose the failure of the fractional Fokker-Planck equation (FFPE) in its commonly used form when generalized in an {\it ad hoc} manner to time-dependent forces. A modified FFPE (MFFPE) is rigorously derived, being valid for a family of dichotomously alternating force-fields. This MFFPE is numerically validated for a rectangular time-dependent force with zero average bias. For this case subdiffusion is shown to become enhanced as compared to the force free case. We question, however, the existence of any physically valid FFPE for arbitrary varying time-dependent fields that differ from this dichotomous varying family.

cond-mat.stat-mech↗

arXiv2007

Relaxation and phase space singularities in time series of human magnetoencephalograms as indicator of photosensitive epilepsy

To analyze the crucial role of fluctuation and relaxation effects for the function of the human brain we studied some statistical quantifiers that support the information characteristics of neuromagnetic brain responses (magnetoencephalogram, MEG). The signals to a flickering stimulus of different color combinations have been obtained from a group of control subjects which is then contrasted with those of a patient suffering photosensitive epilepsy (PSE). We found that the existence of the specific stratification of the phase clouds and the concomitant relaxation singularities of the corresponding nonequilibrium dynamics of the chaotic behavior of the signals in separate areas in a patient provide likely indicators for the zones which are responsible for the appearance of PSE.

physics.med-ph↗

arXiv2007

Non-Markov statistical effects of X-ray emission intensity of the microquasar GRS 1915+105

In this paper we develop the new approach in time series analysis with a variable time step and present the results of quantitative and qualitative estimation of randomness and regularity, and the study of non-Markovian effects of the X-ray emission intensity of the microquasar GRS 1915+105. Our estimation is based on the application of the theory of discrete non-Markovian stochastic processes and gives a wide set of quantitative characteristics and parameters of the studied system with a variable time step. This set reflects the change of the effects of randomness and regularity, the alternation of Markovian and non-Markovian processes in the initial time signals. Initially these characteristics were determined for the simple model systems constructed by means of a molecular dynamics method. Further the calculation of these parameters was executed for the X-ray emission intensity of the microquasar GRS 1915+105. We have developed a theoretical scheme for the detailed analysis of the time series with a variable time step. The new theory allows us to extract more detailed information about the X-ray emission of the microquasar GRS 1915+105 from the experimental time series. The received set of the parameters allows to estimate accurately randomness and stochastic behavior, regularity and robustness, non-Markovian effects of statistical memory in the intensity of the X-ray emission. The analysis of the experimental data with a constant and variable time step is carried out by means of phase portraits, power spectra of the initial time and event correlation function (TCF and ECF), and memory functions (MF) of the junior order, the first three points of non-Markovity parameter.

physics.space-ph↗

arXiv2007

Mean first-passage times for an ac-driven magnetic moment of a nanoparticle

The two-dimensional backward Fokker-Planck equation is used to calculate the mean first-passage times (MFPTs) of the magnetic moment of a nanoparticle driven by a rotating magnetic field. It is shown that a magnetic field that is rapidly rotating in the plane {\it perpendicular} to the easy axis of the nanoparticle governs the MFPTs just in the same way as a static magnetic field that is applied {\it along} the easy axis. Within this framework, the features of the magnetic relaxation and net magnetization of systems composed of ferromagnetic nanoparticles arising from the action of the rotating field are revealed.

cond-mat.stat-mech↗

arXiv2006

Analysis of the Dynamics of Liquid Aluminium: Recurrent Relation Approach

By use of the recurrent relation approach (RRA) we study the microscopic dynamics of liquid aluminium at T=973 K and develop a theoretical model which satisfies all the corresponding sum rules. The investigation covers the inelastic features as well as the crossover of our theory into the hydrodynamical and the free-particle regimes. A comparison between our theoretical results with those following from a generalized hydrodynamical approach is also presented. In addition to this we report the results of our molecular dynamics simulations for liquid aluminium, which are also discussed and compared to experimental data. The received results reveal that (i) the microscopical dynamics of density fluctuations is defined mainly by the first four even frequency moments of the dynamic structure factor, and (ii) the inherent relation of the high-frequency collective excitations observed in experimental spectra of dynamic structure factor $S(k,ω)$ with the two-, three- and four-particle correlations.

cond-mat.dis-nn↗

arXiv2006

Strong Memory in Time Series of Human Magnetoencephalograms Can Identify Photosensitive Epilepsy

To discuss the salient role of the statistical memory effects in the human brain functioning we have analyzed a set of stochastic memory quantifiers that reflects the dynamical characteristics of neuromagnetic brain responses to a flickering stimulus of different color combinations from a group of control subjects which is contrasted with those from a patient with photosensitive epilepsy (PSE). We have discovered the emergence of strong memory and the accompanying transition to a regular and robust regime of chaotic behavior of the signals in the separate areas for a patient with PSE. This finding most likely identifies the regions of the location the protective mechanism in a human organism against occurrence of PSE.

physics.med-ph↗

arXiv2006

Magnetization of nanoparticle systems in a rotating magnetic field

The investigation of a sizable thermal enhancement of magnetization is put forward for uniaxial ferromagnetic nanoparticles that are placed in a rotating magnetic field. We elucidate the nature of this phenomenon and evaluate the resonant frequency dependence of the induced magnetization. Moreover, we reveal the role of magnetic dipolar interactions, point out potential applications and reason the feasibility of an experimental observation of this effect.

cond-mat.stat-mech↗

arXiv2006

Dynamical and thermal effects in nanoparticle systems driven by a rotating magnetic field

We study dynamical and thermal effects that are induced in nanoparticle systems by a rotating magnetic field. Using the deterministic Landau-Lifshitz equation and appropriate rotating coordinate systems, we derive the equations that characterize the steady-state precession of the nanoparticle magnetic moments and study a stability criterion for this type of motion. On this basis, we describe (i) the influence of the rotating field on the stability of the small-angle precession, (ii) the dynamical magnetization of nanoparticle systems, and (iii) the switching of the magnetic moments under the action of the rotating field. Using the backward Fokker-Planck equation, which corresponds to the stochastic Landau-Lifshitz equation, we develop a method for calculating the mean residence times that the driven magnetic moments dwell in the up and down states. Within this framework, the features of the induced magnetization and magnetic relaxation are elucidated.

cond-mat.stat-mech↗

arXiv2006

Entropic transport: Kinetics, scaling and control mechanisms

We show that transport in the presence of entropic barriers exhibits peculiar characteristics which makes it distinctly different from that occurring through energy barriers. The constrained dynamics yields a scaling regime for the particle current and the diffusion coefficient in terms of the ratio between the work done to the particles and available thermal energy. This interesting property, genuine to the entropic nature of the barriers, can be utilized to effectively control transport through quasi one-dimensional structures in which irregularities or tortuosity of the boundaries cause entropic effects. The accuracy of the kinetic description has been corroborated by simulations. Applications to different dynamic situations involving entropic barriers are outlined.

cond-mat.stat-mech↗

arXiv2006

Fractional Fokker-Planck dynamics: Numerical algorithm and simulations

Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying CTRW. An efficient numerical algorithm is developed which is applicable for an arbitrary potential. This algorithm is then applied to investigate the fractional current and the corresponding nonlinear mobility in different washboard potentials. Normal and fractional diffusion are compared through their time evolution of the probability density in state space. Moreover, we discuss the stationary probability density of the fractional current values.

cond-mat.stat-mech↗

arXiv2006

Ratchet transport for a chain of interacting charged particles

We study analytically and numerically the overdamped, deterministic dynamics of a chain of {\it charged}, interacting particles driven by a longitudinal alternating electric field and additionally interacting with a smooth ratchet potential. We derive the equations of motion, analyze the general properties of their solutions and find the drift criterion for chain motion. For ratchet potentials of the form of a double-sine and a phase-modulated sine it is demonstrated that both, a so-called integer and fractional transport of the chain can occur. Explicit results for the directed chain transport for these two classes of ratchet potentials are presented.

cond-mat.soft↗

arXiv2006

Domain statistics in a finite Ising chain

We present a comprehensive study for the statistical properties of random variables that describe the domain structure of a finite Ising chain with nearest-neighbor exchange interactions and free boundary conditions. By use of extensive combinatorics we succeed in obtaining the one-variable probability functions for (i) the number of domain walls, (ii) the number of up domains, and (iii) the number of spins in an up domain. The corresponding averages and variances of these probability distributions are calculated and the limiting case of an infinite chain is considered. Analyzing the averages and the transition time between differing chain states at low temperatures, we also introduce a criterion of the ferromagnetic-like behavior of a finite Ising chain. The results can be used to characterize magnetism in monatomic metal wires and atomic-scale memory devices.

cond-mat.stat-mech↗

arXiv2006

Levy--Brownian motion on finite intervals: Mean first passage time analysis

We present the analysis of the first passage time problem on a finite interval for the generalized Wiener process that is driven by Lévy stable noises. The complexity of the first passage time statistics (mean first passage time, cumulative first passage time distribution) is elucidated together with a discussion of the proper setup of corresponding boundary conditions that correctly yield the statistics of first passages for these non-Gaussian noises. The validity of the method is tested numerically and compared against analytical formulae when the stability index $α$ approaches 2, recovering in this limit the standard results for the Fokker-Planck dynamics driven by Gaussian white noise.

cond-mat.stat-mech↗

arXiv2006

Anomalous diffusion for overdamped particles driven by cross-correlated white noise sources

We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact probability distribution function for the particle positions, calculate its moments and find their corresponding long-time, asymptotic behaviors. The generally anomalous diffusive regimes of the particles are classified, and their dependence on the friction coefficient and the characteristics of the noises is analyzed in detail. The asymptotic predictions are confirmed by exact solutions for two examples.

cond-mat.stat-mech↗

arXiv2005

Quantum diffusion in biased washboard potentials: strong friction limit

Diffusive transport properties of a quantum Brownian particle moving in a tilted spatially periodic potential and strongly interacting with a thermostat are explored. Apart from the average stationary velocity, we foremost investigate the diffusive behavior by evaluating the effective diffusion coefficient together with the corresponding Peclet number. Corrections due to quantum effects, such as quantum tunneling and quantum fluctuations, are shown to substantially enhance the effectiveness of diffusive transport if only the thermostat temperature resides within an appropriate interval of intermediate values.

cond-mat.stat-mech↗

arXiv2004

Brownian motors

In systems possessing a spatial or dynamical symmetry breaking thermal Brownian motion combined with unbiased, non-equilibrium noise gives rise to a channelling of chance that can be used to exercise control over systems at the micro- and even on the nano-scale. This theme is known as ``Brownian motor'' concept. The constructive role of (the generally overdamped) Brownian motion is exemplified for a noise-induced transport of particles within various set-ups. We first present the working principles and characteristics with a proof-of-principle device, a diffusive temperature Brownian motor. Next, we consider very recent applications based on the phenomenon of signal mixing. The latter is particularly simple to implement experimentally in order to optimize and selectively control a rich variety of directed transport behaviors. The subtleties and also the potential for Brownian motors operating in the quantum regime are outlined and some state-of-the-art applications, together with future roadways, are presented.

cond-mat.stat-mech↗