Steffen Trimper

• Professor
• Senior Researcher at Martin Luther University Halle-Wittenberg

Based on a microscopic model and the Green's function theory, the temperature, size, magnetic field, and ion doping dependence of the magnetic, electric, and dielectric properties in Fe‐and Nd‐doped ferroelectric Bi 4 Ti 3 O 12 bulk and nanoparticles is investigated. The multiferroism can be achieved in two ways. At once the magnetism appears by su...

Magnetoelectroporation is an effective method of opening nanopores in cell membranes using magnetoelectric nanoparticles (MENPs) for the purpose of delivery of in vivo and in vitro of drug substances to cancer cells. We propose a microscopic approach as theoretical basis for that phenomenon. The underlying Hamiltonian includes the magnetic and ferr...

The dielectric properties of CuCrO2 bulk and thin films are studied by evaluating the complex dielectric function ϵ. In addition to the small peak near to the Neel temperature TN, we find a secondary broad peak at high temperatures around Tm = 450K ≫ TN. As a feature of relaxor ferroelectrics the maximum temperature Tm increases with increasing fre...

Different properties of pure, Ni, Zr and Sm doped BaFe12O19 – bulk and nanoparticles are investigated using a microscopic model and the Green’s function technique. The magnetization M s increases whereas the coercive field H c decreases with increasing particle size. The doping leads to a decreasing of M s and the band gap energy E g with increasin...

The size, doping concentration, and magnetic field dependences of the magnetization M and the real part of the dielectric function ε ' in doped LaFe 1 − x M x O 3 nanoparticles (NPs) are studied using a microscopic model. Although M increases, ε ′ decreases with decreasing NPs size in pure LaFeO 3 . Doping with different ions causes different strai...

The remanent polarization Pr and remanent magnetization Mr for different Sm-concentrations x in Sm-doped BiFeO3 is investigated using a microscopic model and the Green's function technique. For pure BiFeO3 with a rhombohedral symmetry we obtain a hysteresis loop P(E) which is typical for a ferroelectric material. Further increase of x (x = 0.16) le...

It is demonstrated theoretically that the magnetization of FeS2 nanoparticles is originated by the appearance of sulfur vacancies at the surface, where FeS2 undergoes a reduction to FeS. This change is accompanied by a transition from the zero spin configuration of Fe²⁺ ions to a spin S = 2 state. Additionally there are uncompensated Fe spins on th...

Using a microscopic model taking into account the spin–phonon interactions we have studied the magnetic properties of pure and ion-doped SnO2 nanoparticles (NPs). The magnetization M in pure SnO2 NPs is due to surface oxygen vacancies. By doping with magnetic Co ion we observe a maximum in M for small Co-concentration, x = 1%, whereas for nonmagnet...

We propose a microscopic model in order to study the multiferroic properties of the triangular compound CuCrO 2 taking into account antiferromagnetic interactions in the ab plane, spin-phonon interactions and quadratic magnetoelectric (ME) coupling. The temperature and magnetic field dependence of the polarization P ab and dielectric constant ϵ ab...

We have studied the electric properties of multiferroic BiFeO3 (BFO) using the transverse Ising model in terms of pseudo-spin variables with S= 7/2 and the Green's function method. Mechanisms of magnetoelectric (ME) couplings and electric field-induced spin-reorientation (SR) transition in BFO ( in-plane and out-of-plane switching) are examined. It...

This chapter highlights the aspects of transient operation and measurements of thermoelectric (TE) materials and systems. If the timescale of changes in the working or boundary conditions is much greater than the response time of the TE system, a quasi-stationary approach is suitable to describe the transient behavior of the system. A dynamically s...

The class of RMn2O5 (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisen...

Abstractauthoren We propose a microscopic model in order to study the multiferroic properties of LiZrCuO at low temperatures taking into account the competing nearest and next-nearest magnetic interactions, frustration, and a linear magnetoelectric coupling. To understand the experimental observation an anti-ferroelectric interaction between the Cu...

We propose a microscopic model in order to study the multiferroic (MF) properties of LiCuVO4 (LCVO) taking into account the competing nearest and next-nearest magnetic interactions, frustration and a linear magnetoelectric (ME) coupling. We obtain for α = |J2∕J1| = 0.76. The temperature and magnetic field dependence of the polarization Pa and Pc is...

We propose a microscopic model in order to study the multiferroic properties of LuFe2O4. It is shown that the real part of the dielectric constant ϵ has a plateau near the magnetic phase transition . At room temperature ϵ decreases strongly by applying an external magnetic field H. This behavior is an evidence for a strong coupling of spins and ele...

Experimentally the polarization P and the magnetization M of BaTiO (BTO) nanoparticles are altered under doping with transition metals as Fe-ions. Using a modified spin model for the magnetic and the ferroelectric part as well as the magnetoelectric coupling we have calculated the dependence of M and P on the Fe-doping content in BTO nanoparticles....

Following the theoretical approach by Xiao et al [Phys. Rev. B 81, 214418 (2010)] to the spin Seebeck effect, we calculate the mean value of the total spin current flowing through a normalmetal/ ferromagnet interface. The spin current emitted from the ferromagnet to the normal metal is evaluated in the framework of the Fokker-Planck approach for th...

We study the role of thermal fluctuations on the spin dynamics of a thin permalloy film with a focus on the behavior of spin torque and find that the thermally assisted spin torque results in new aspects of the magnetization dynamics. In particular, we uncover the formation of a finite, spin torque-induced, in-plane magnetization component. The ori...

The multiferroic properties of bulk CuO are manifested in the dielectric function which can be triggered by an external magnetic field h and by the temperature T. Within a microscopic model and a Green's function technique we have calculated the dielectric function \varepsilon ({\bf k};T,\;h). At the magnetic phase transition temperature T_{{\rm N}...

The multiferroic behavior of rare-earth manganites is studied within a microscopic model including a symmetry-allowed magnetoelectric coupling between polarization and magnetization. The magnetic subsystem is described by a frustrated Heisenberg spin model, whereas the ferroelectric subsystem is characterized by an Ising model in a transverse field...

For almost a decade the consensus has held that the random walk propagator for the elephant random walk (ERW) model is a Gaussian. Here we present strong numerical evidence that the propagator is, in general, non-Gaussian and, in fact, non-Lévy. Motivated by this surprising finding, we seek a second, non-Gaussian solution to the associated Fokker-P...

Multiferroic rare-earth manganites are theoretically studied by focusing on the coupling to the lattice degrees of freedom. We demonstrate analytically that the phonon excitations in the multiferroic phase are strongly affected by the magnetoelectric coupling, the spin-phonon interaction and the anharmonic phonon-phonon interaction. Based on a micr...

Energy excitations in ferromagnets are studied in case a temperature gradient is coupled to the local magnetization. Due to different time scales only the coupling between the spatially varying part of the temperature field and the magnetization is relevant. The magnetothermal coupling with a definite sign breaks the time inversion symmetry and lea...

Based on a microscopic model with a biquadratic magnetoelectric coupling the properties of Bi2NiMnO6 thin films are investigated. Using Green's functions the phonon spectrum is calculated which is determined by the polarization and the magnetization. The phonon energy and its damping offer a kink at the magnetic phase transition temperature. The ph...

Ferromagnetic resonance in thin films is analyzed under the influence of spatiotemporal feedback effects. The equation of motion for the magnetization dynamics is nonlocal in both space and time and includes isotropic, anisotropic and dipolar energy contributions as well as the conserved Gilbert- and the non-conserved Bloch-damping. We derive an an...

Random walks in one-dimensional environments with an additional dynamical feedback-coupling is analyzed numerically. The feedback introduced via a generalized master equation is controlled by a memory kernel of strength λ the explicit form of which is motivated by arguments used in mode-coupling theories. Introducing several realizations of the fee...

A symmetric binary polymer electrolyte subjected to an AC voltage is considered. The analytical solution of the Poisson–Nernst–Planck equations (PNP) is found and analyzed for small applied voltages. Three distinct time regimes offering different behavior can be discriminated. The experimentally realized stationary behavior is discussed in detail....

The dynamics of the n-spin facilitated kinetic Ising model (Fredrickson–Andersen model) with mobile vacancies as a model for the glassy materials are studied analytically by means of the Fock-space representation of the master equation. The system is mapped onto a three state model characterizing mobile, immobile and vacant cells. The characteristi...

Using microscopically models and Green’s function techniques we demonstrate how one can get information of ferroelectric nanoparticles. The approach can be extended to multiferroic systems which are defined as materials possessing two or more ferroic orders in a single phase. In detail we show that the unexpected ferromagnetic properties of BaTiO3...

The theory predicts that the spin-wave lifetime $\tau_L$ and the linewidth of ferromagnetic resonance $\Delta B$ can be governed by random fields and spatial memory. To that aim the effective field around which the magnetic moments perform a precession is superimposed by a stochastic time dependent magnetic field with finite correlation time. The m...

The Green's function (GF) method is a powerful technique to describe non-equilibrium processes under inclusion of a broad class of boundary and initial conditions. Based on the Onsager theory of non-equilibrium the applicability of GFs is demonstrated to find the steady-state solution for the thermoelectric behaviour in one dimension. The spatial t...

The polarization and susceptibility of thin antiferroelectric films are presented using a Green's function technique within an Ising model in a transverse field. Both quantities vary with the numbers of layers. Whereas at low temperatures the suceptibilty of the surface layer increases stronger than that of the second layer, the polarization of the...

Based on a microscopic approach we demonstrate that the unexpected ferromagnetic properties of BaTiO3 (BTO) or PTO observed recently at room temperature are due to oxygen vacancies at the surface of the nanocrystalline materials. Such vacancies lead to the appearance of Ti3+ or Ti2+ ions with nonzero net spin. The resulting different valence states...

Graded and segmented thermoelectric elements are studied in order to improve the performance of thermogenerators that are exposed to a large temperature difference. The linear thermodynamics of irreversible processes is extended by assuming spatially dependent material parameters like the Seebeck coefficient, the electrical and thermal conductiviti...

We consider a three-state model comprising tumor cells, effector cells, and tumor-detecting cells under the influence of noises. It is demonstrated that inevitable stochastic forces existing in all three cell species are able to suppress tumor cell growth completely. Whereas the deterministic model does not reveal a stable tumor-free state, the aut...

Antiferroelectric (AFE) thin films are studied under the influence of doping ions and the presence of substrates. Both induce a strong changing of the polarization and lead to a shift of the phase transition temperature. These effects can be understood within the Ising model in a transverse field with additional four spin interaction. To that aim d...

The analytical solution of the Poisson-Nernst-Planck equations is found in the linear regime as response to a dc-voltage. In deriving the results a new approach is suggested, which allows to fulfill all initial and boundary conditions and guarantees the absence of Faradaic processes explicitly. We obtain the spatiotemporal distribution of the elect...

A Lagrangian is introduced which includes the coupling between magnetic moments $\mathbf{m}$ and the degrees of freedom $\boldsymbol{\sigma}$ of a reservoir. In case the system-reservoir coupling breaks the time reversal symmetry the magnetic moments perform a damped precession around an effective field which is self-organized by the mutual interac...

We analyze the Landau-Lifshitz-Gilbert equation under the inclusion of retardation effects by introducing a memory kernel comprised of an instantaneous and a time-dependent part. Due to the delay term the spin waves become decoherent, leading to an additional damping process. Based on a linear spin-wave analysis, we find that the total damping proc...

A systematic microscopic theory of the magnetoelectric (ME) effect in multiferroic materials with well-separated phase-transition temperatures is presented. Whereas the ferroelectric subsystem is described by an Ising model in a transverse field, the magnetic one is characterized by the Heisenberg model with Dzyaloshinski-Moriya interaction (DMI)....

The asymmetric spin-wave dispersion relation observed recently [ Zakeri et al. Phys. Rev. Lett. 104 137203 (2010)], is explained within a quantum model consisting of an anisotropic Heisenberg coupling and the Dzyaloshinski-Moriya interaction (DMI). Applying a transformation of the spin operators into a representation without fixed quantization axis...

The exact steady state solution of the Poisson–Nernst–Planck equations (PNP) is given in terms of Jacobi elliptic functions. A more tractable approximate solution is derived which can be used to compare the results with experimental observations in binary electrolytes. The breakdown of the PNP for high concentration and high applied voltage is disc...

Graded and segmented thermoelectric elements have been studied for a long time with the aim of improving the performance of thermogenerators that are exposed to a large temperature difference. The global optimization of a performance parameter is commonly based on a one-dimensional continua-theoretical model. Following the proposal by Müller et al....

We analyze the Landau-Lifshitz-Gilbert equation when the precession motion of the magnetic moments is additionally subjected to an uniaxial anisotropy and is driven by a multiplicative coupled stochastic field with a finite correlation time $\tau$. The mean value for the spin wave components offers that the spin-wave dispersion relation and its dam...

Based on the Poisson-Nernst-Planck equations (PNP), the spatiotemporal charge, concentration profile, and the electric field in polyelectrolytes are analyzed. The system is subjected to a dc applied voltage. Different to recent papers we obtain an exact analytical solution of the PNP in the linear regime, which is characterized by an inevitable cou...

We analyze a stochastic model for tumor cell growth with both multiplicative and additive colored noises as well as nonzero cross correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term characterizing immunization, the birth rate is assumed to be stochastically changed due to biological motivated...

An exact expression for the Drude conductivity in one dimension is derived under the presence of an arbitrary potential. In getting the conductivity the influence of the electric field on the crystal potential is taken into account. This coupling leads to a systematic deformation of the potential and consequently to a significant modification of th...

The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible S can become infectious with an infection rate beta by an infectious I type provided that both are in contact. The I type may recover with a rate gamma and from then on stay...

We demonstrate the conventional Jarzynski relation (JR) is violated for a non-Markovian process with colored noise. As an example an exactly soluble model is considered with a simple protocol for the external work performed on the system along a non-equilibrium trajectory. For that model we derive an exact expression for the dissipative energy in t...

The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible $S$ can become infectious with an infection rate $\beta$ by an infectious $I$- type provided that both are in contact. The $I$- type may recover with a rate $\gamma$ and fro...

We perform molecular dynamics and Monte Carlo simulations of two-dimensional melting with dipole-dipole interactions. Both static and dynamic behaviors are examined. In the isotropic liquid phase, the bond orientational correlation length 6 and susceptibility 6 are measured, and the data are fitted to the theoretical ansatz. An algebraic decay is d...

The steady state of ions diffusion in polymer electrolytes at arbitrary applied voltage is analyzed in the framework of the Nernst-Planck-Poisson equation (NPP). The exact solution of the set of equations is found without the assumption of low ions concentration. The solution is independent of the kinetic properties of the system. At constant volta...

The spin polarized charge transport is systematically analyzed as a thermally driven stochastic process. The approach is based on Kramers' equation describing the semiclassical motion under the inclusion of stochastic and damping forces. Due to the relativistic spin-orbit coupling the damping experiences a relativistic correction leading to an addi...

The influence of doping effects on the polarization, the phase transition temperature and the hysteresis loop of ferroelectric nanoparticles is studied based on a modified Ising model in a transverse field. Due to the loss of translational invariance the physical quantities are figured out by a Green's function technique in real space. The spherica...

The reaction-diffusion process is generalized by including spatiotemporal delay effects. As a first example, we study the influence of a constant production term which is switched off after a finite time. In a second case, all diffusion-reaction processes within a distance R(t) = κtα around a certain spatial point are assumed to contribute to the i...

Ferroelectric nanostructures and multiferroic bulk systems are studied in a multiscale approach. The excitation energy, associated damping of ferroelectric modes and polarization are presented as a function of temperature, defect concentration, size and shape. The softening of the mode is strongly influenced by the kind of doping ions, the surface...

A random walk of N particles on a lattice with M sites is studied under the constraint that each lattice site is coupled to its own mesoscopic heat bath. Such a situation can be conveniently described by using the master equation in a quantized Hamiltonian formulation where the exclusion principle is included by using Pauli operators. If all reserv...

Motivated by the progress of a multiscale approach in magnetic materials, the dynamics of the Ising model in a transverse field as a basic model for ferroelectric order-disorder phase transition is reformulated in terms of a mesoscopic model and inherent microscopic parameters. The dynamics is governed by a reversible propagating part giving rise t...

Ferroelectric nanoparticles are described by a microscopic model which enables one to find the macroscopic polarization as well as the excitation energy of the soft mode and its damping with dependence on the temperature and the size of the particles. The constituents of the material are arranged in shells, and their interaction depends on both the...

We study the flip-processes in a two-level system, which is triggered by the coupling to a classical bath. When the bath is represented by a stochastic field, the time evolution of the density matrix leads to a stochastic equation with a multiplicative noise. Accordingly the Fokker–Planck-equation (FPE) depends on the matrix elements of the underly...

A Fock-space formalism is proposed which allows to get dynamical equations for averaged quantities from a master equation on a lattice with occupation numbers 0 and 1. Kinetic equations for restricted diffusion, non-penetrating diffusion-limited aggregation (DLA) and reaction-limited interface growth (RLA) are derived. We find a critical concentrat...

We investigate statistical properties of the German Dax and Chinese indices, including the volatility distribution, autocorrelation function, DFA function and return-volatility correlation function, with both the daily data and minutely data. At the minutely time scale, the Chinese indices may show irregular dynamic behavior. At the daily time scal...

We consider a reaction–diffusion process with retardation. The particles, initially immersed in traps, remain inactive until another particle is annihilated spontaneously with a rate λ at a certain point . In that case the traps within a sphere of radius R(t) = vtα around will be activated and a particle is released with a rate μ. Due to the compet...

We generalize the Fredrickson-Helfand theory of the microphase separation in symmetric diblock copolymer melts by taking into account the influence of a time-independent homogeneous electric field on the composition fluctuations within the self-consistent Hartree approximation. We predict that electric fields suppress composition fluctuations, and...

The nonthermal quantum relaxation of the magnetization under nonequilibrium initial conditions is studied for the transverse Ising chain and for the one-dimensional isotropic XY model. In the absence of a heat bath the transverse Ising system exhibits an oscillating relaxation with a decaying amplitude. At the critical transverse field some station...

We adapt the nonlinear σ model to study the nonequilibrium critical dynamics of O(n) symmetric ferromagnetic system. Using the renormalization group analysis in d = 2 + ε dimensions we investigate the pure relaxation of the system starting from a completely ordered state. We find that the average magnetization obeys the long-time scaling behaviour...

Based on the stochastic description of transport phenomena the relationship between a non-Markovian evolution equation and the Fokker-Planck equation with drift is investigated. Memory is included by direct coupling between initial and current values of probability density. We present the result for three different initial distributions.

We demonstrate the equivalence of a non-Markovian evolution equation with a linear memory-coupling and a Fokker–Planck equation (FPE). In case the feedback term offers a direct and permanent coupling of the current probability density to an initial distribution, the corresponding FPE offers a non-trivial drift term depending itself on the diffusion...

A microscopic model for describing ferroelectric nanoparticles is proposed which allows us to calculate the polarization as a function of an external electric field, the temperature, the defect concentration and the particle size. The interaction of the constituents of the material, arranged in layers, depends on both the coupling strength at the s...

Payoffs which depend on the scores of the strategies are introduced into the standard Minority Game (MG). The double-periodicity behavior of the standard model is consequently removed, and stylized facts arise, such as long-range volatility correlations and "fat-tails" of the probability distribution of the returns. Furthermore, the score-dependent...

A simple spin-flip process is analyzed under the presence of two heat reservoirs. While one flip process is triggered by a bath at temperature T, the inverse process is activated by a bath at a different temperature T'. The situation can be described by using a master equation approach in a second quantized Hamiltonian formulation. The stationary s...

Score-dependent and agent-dependent payoffs of the strategies are introduced into the standard minority game. The intrinsic periodicity is consequently removed, and the stylized facts arise, such as long-range volatility correlations and "fat tails" in the distribution of the returns. The agent dependence of the payoffs is essential in producing th...

The Glauber model is reconsidered based on a quantum formulation of the master equation. Unlike the conventional approach the temperature and the Ising energy are included from the beginning by introducing a Heisenberg-like picture of the second quantized operators. This method enables us to get an exact expression for the transition rate of a sing...

We investigate the return-volatility correlation both local and nonlocal in time with daily and minutely data of the German DAX and Chinese indices, and observe a leverage effect for the German DAX, while an antileverage effect for the Chinese indices. In the negative time direction, i.e., for the volatility-return correlation, an antileverage effe...

After filtering out the alpha and beta peaks in the power spectrum of the human brain electroencephalogram signals Y(t'), the probability distribution of the variation Delta Y(t') = Y(t' +Delta t) - Y(t') exhibits a dynamic scaling behavior. The autocorrelation functions, persistence probabilities and detrended fluctuation functions of the time ser...

The Glauber model is reconsidered based on a quantum formulation of the Master equation. Unlike the conventional approach the temperature and the Ising energy are included from the beginning by introducing a Heisenberg-like picture of the second quantized operators. This method enables us to get an exact expression for the transition rate of a sing...

We demonstrate the equivalence of a Non--Markovian evolution equation with a linear memory--coupling and a Fokker--Planck equation (FPE). In case the feedback term offers a direct and permanent coupling of the current probability density to an initial distribution, the corresponding FPE offers a non-trivial drift term depending itself on the diffus...

The short-time dynamics of the three-dimensional bond-diluted 4-state Potts model is investigated with Monte Carlo simulations. A recently suggested nonequilibrium reweighting method is applied, and the tricritical point is determined with the short-time dynamic approach. Based on the dynamic scaling form, both the dynamic and static critical expon...

We present a relatively detailed analysis of the persistence probability distributions in financial dynamics. Compared with the auto-correlation function, the persistence probability distributions describe dynamic correlations non-local in time. Universal and non-universal behaviors of the German DAX and Shanghai Index are analyzed, and numerical s...

We present the dynamics of the kinetically constrained Ising model, comprised of a system of spins coupled with the strength J and situated in a field which plays the role of activation energy. Due to kinetic constraints, glassy effects arise at low temperatures leading to a non-Arrhenius -relaxation time. The results of Monte Carlo simulations are...

The effect of random bonds on the phase transitions of the three-dimensional three-state Potts model is investigated with extensive dynamic Monte Carlo simulations. In the weakly disordered regime, the phase diagram is obtained with a recently suggested nonequilibrium reweighting method. The tricritical point separating the first- and second-order...

A Green's function technique for a modified Ising model in a transverse field is applied, which allows to calculate the damping of the elementary excitations and the phase transition temperature of ferroelectric thin films with structural defects. Based on an analytical expression for the damping function, we analyze its dependence on temperature,...

We present a simple model for growing up and depletion of parties due to the permanent communication between the participants of the events. Because of the rapid exchange of information, everybody is able to evaluate its own and and all other parties by means of the list of its friends. Therefore the number of participants at different parties can...

We present a simple model for growing up and depletion of parties due to the permanent communication between the participants of the events. Because of the rapid exchange of information, everybody is able to evaluate its own and and all other parties by means of the list of its friends. Therefore the number of participants at different parties can...

We adapt the non-linear $\sigma$ model to study the nonequilibrium critical dynamics of O(n) symmetric ferromagnetic system. Using the renormalization group analysis in $d=2+\epsilon$ dimensions we investigate the pure relaxation of the system starting from a completely ordered state. We find that the average magnetization obeys the long-time scali...

We study the asymptotic behavior of a Brownian particle under the influence of a dynamical feedback by numerical simulations and analytical considerations. The feedback is controlled by a memory coupling of strength λ. Whereas a negative memory strength yields a true self avoiding walk, a positive memory leads to a self-trapping of the particle. Th...

We present a relatively detailed analysis of the persistence probability distributions in financial dynamics. Compared with the auto-correlation function, the persistence probability distributions describe dynamic correlations nonlocal in time. Universal and non-universal behaviors of the German DAX and Shanghai Index are analyzed, and numerical si...

Based on a modified Ising model in a transverse field we demonstrate that defect layers in ferroelectric thin films, such as layers with impurities, vacancies or dislocations, are able to induce a strong increase or decrease of the polarization depending on the variation of the exchange interaction within the defect layers. A Green's function techn...

Memory effects require for their incorporation into random-walk models an extension of the conventional equations. The linear Fokker-Planck equation for the probability density p(r,t) is generalized by including nonlinear and nonlocal spatial-temporal memory effects. The realization of the memory kernel is restricted due the conservation of the bas...

The short-time critical dynamics of the two-dimensional eight-state random-bond Potts model is investigated with large-scale Monte Carlo simulations. Dynamic relaxation starting from a disordered and an ordered state is carefully analyzed. The continuous phase transition induced by disorder is studied, and both the dynamic and static critical expon...

A dynamic feed-back interaction is introduced to the Eguiluz–Zimmermann model (Phys. Rev. Lett. 85 (2000) 5659). In application to financial dynamics, transmission of information at time t′t′ is supposed to depend on the variation of the financial index at t′-1t′-1. The generated time series is strongly correlated in time at criticality. Both stati...

We consider a discrete-time random walk where the random increment at time step t depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition and on the memory parameter p . At a critical value p((1) )(c ) =1/2 where memory effects vanish there is a trans...

A microscopic model is studied numerically to describe wearless dry friction without thermal fluctuations between atomically flat contact interfaces. The analysis is based on a double-chain model with a Lennard-Jones interaction between the chains which are the respective upper flexible monolayers of the rigid bulk systems. Whereas below a critical...