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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 analytical expression for the peak-to-peak linewidth. It consists of four separate parts originated by Gilbert damping, Bloch-damping, a mixed Gilbert-Bloch component and a contribution arising from retardation. In an intermediate frequency regime the results are comparable with the commonly used Landau-Lifshitz-Gilbert theory combined with two-magnon processes. Retardation effects together with Gilbert damping lead to a linewidth the frequency dependence of which becomes strongly nonlinear. The relevance and the applicability of our approach to ferromagnetic resonance experiments is discussed., Comment: 22 pages, 9 figures

The dynamics of the low energy excitations in a ferromagnet is studied in case a temperature gradient is coupled to the local magnetization. Due to the different time scales of changing temperature and magnetization it is argued that only the coupling between the spatially varying part of the temperature field and the magnetization is relevant. Using variational principles the evolution equation for the magnetic system is found which is strongly influenced by the local temperature profile. The system offers damped spin wave excitations where the strength of damping is determined by the magneto-thermal coupling. Applying the model to nanowires it is demonstrated that the energy spectrum is significantly affected by the boundary conditions as well as the initial temperature distribution. In particular, the coupling between temperature and magnetization is expected to be several orders stronger for the open as for the isolated wire., Comment: 15 pages, 5 figures

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 magnetization dynamics is altered by inclusion of a spatial memory effect monitoring a non-local interaction of size $\xi$. The underlying Landau-Lifshitz-Gilbert equation (LLG) is modified accordingly. The stochastic LLG is equivalent to a Fokker-Planck equation which enables to calculate the mean values of the magnetization vector. Within the spin-wave approximation we present an analytical solution for the excitation energy and its damping. The lifetime and the linewidth are analyzed depending on the strength of the random field $D$ and its correlation time $\tau_c$ as well as the retardation strength $\Gamma_0$ and the size $\xi$. Whereas $\tau_L$ decreases with increasing $D$, retardation strength $\Gamma_0$ and $\tau_c$, the lifetime is enhanced for growing width $\xi$ of the spatial retardation kernel. In the same manner we calculate the experimentally measurable linewidth $\Delta B$ is increased strongly when the correlation time $\tau_c$ ranges in the nanosecond interval., Comment: 20 pages, 4 figures

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 auto-correlated noise combined with cross-correlation functions can either lead to tumor dormant states, tumor progression as well as to an elimination of tumor cells. The auto-correlation function exhibits a finite correlation time $\tau$ while the cross-correlation functions shows a white noise behavior. The evolution of each of the three kinds of cells leads to a multiplicative noise coupling. The model is investigated by means of a multivariate Fokker-Planck equation for small $\tau$. The different behavior of the system is above all determined by the variation of the correlation time and the strength of the cross-correlation between tumor and tumor detecting cells. The theoretical model is based on a biological background discussed in detail and the results are tested using realistic parameters from experimental observations., Comment: 20 pages, 4 figures, 1 table

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 interaction of the moments. The resulting evolution equation has the form of the Landau-Lifshitz-Gilbert equation. In case the bath variables are constant vector fields the moments $\mathbf{m}$ fulfill the reversible Landau-Lifshitz equation. Applying Noether's theorem we find conserved quantities under rotation in space and within the configuration space of the moments., Comment: 12 pages, 1 figure

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 damping is strongly influenced by the deterministic Gilbert damping parameter $\alpha$, the strength of the stochastic forces $D$ and its temporal range $\tau$. The spin-spin-correlation function can be calculated in the low correlation time limit by deriving an evolution equation for the joint probability function. The stability analysis enables us to find the phase diagram within the $\alpha-D$ plane for different values of $\tau$ where damped spin wave solutions are stable. Even for zero deterministic Gilbert damping the magnons offer a finite lifetime. We detect a parameter range where the deterministic and the stochastic damping mechanism are able to compensate each other leading to undamped spin-waves. The onset is characterized by a critical value of the correlation time. An enhancement of $\tau$ leads to an increase of the oscillations of the correlation function., Comment: 20 pages, 5 figures

We study a stochastic model for tumor cell growth with both multiplicative and additive colored noise as well as a non-zero 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 growth processes leading to a multiplicative internal noise. Moreover, the system is subjected to an external additive noise which mimics the influence of the environment of the tumor. The stationary probability distribution Ps is derived depending on the finite correlation time, the immunization rate and the strength of the crosscorrelation. Ps offers a maximum which becomes more pronounced for increasing immunization rate. The mean-first passage time is also calculated in order to find out under which conditions the tumor can suffer extinction. Its characteristics is again controlled by the degree of immunization and the strength of the cross-correlation. The behavior observed can be interpreted in terms of the three state model of a tumor population., Comment: 21 pages, 10 figures

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 terms of an arbitrary correlator of the noise characterized by an autocorrelation time $t_c$. As the result we find corrections to the JR in terms of $t_c$. In the limiting case of a Gaussian process as well as an infinitely slow process the conventional JR is retained. The result is valid for an arbitrary colored noise., Comment: 9 pages 1 figure

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 immune. Due to the coupling between the different individuals, the model is nonlinear and out of equilibrium. We adopt a stochastic individual-based description where individuals are represented by nodes of a graph and contact is defined by the links of the graph. Mapping the underlying Master equation into a quantum formulation in terms of spin operators, the hierarchy of evolution equations can be solved exactly for arbitrary initial conditions on a linear chain. In case of uncorrelated random initial conditions the exact time evolution for all three individuals of the SIR model is given analytically. Depending on the initial conditions and reaction rates $\beta$ and $\gamma$, the $I$-population may increase initially before decaying to zero. Due to fluctuations, isolated regions of susceptible individuals evolve and unlike in the standard mean-field SIR model one observes a finite stationary distribution of the $S$-type even for large population size. The exact results for the ensemble averaged population size are compared with simulations for single realizations of the process and also with standard mean field theory which is expected to be valid on large fully-connected graphs., Comment: 19 pages, 4 figures

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 detected for both spatial and temporal bond orientational correlation functions in an intermediate temperature regime, and it provides an explicit evidence for the existence of the hexatic phase. From the finite-size scaling analysis of the global bond orientational order parameter, the disclination unbinding temperature Ti is estimated. In addition, from dynamic Monte Carlo simulations of the positional order parameter, we extract the critical exponents at the dislocation unbinding temperature Tm. All the results are in agreement with those from experiments and support the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory., Comment: 23 pages, 12figures

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 voltage there is a master curve for concentration in terms of the initial concentration. Enhancing the voltage causes an increase of the ion concentration gradient and consequently the applicability of the NPP is violated for high voltages. The analytical finding is estimated by using experimental data from recent measurements (P. Kohn et al Phys. Rev. Left. 99, 086104 (2007)). As the result we find an upper bound for the validity of the NPP. Above this voltage higher order gradient terms become relevant., Comment: 12 pages, 4 figures

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 additional contribution within the spin Hall conductivity. A further contribution to the conductivity is originated from the averaged underlying crystal potential, the mean value of which depends significantly on the electric field. We derive an exact expression for the electrical conductivity. All corrections are estimated in lowest order of a relativistic approach and in the linear response regime., Comment: 12 pages, 1 figure

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 the charge transport. The corrections to the conventional Drude conductivity are determined by the configurational part of the partition function. The activation energy for the conductivity process is expressed by a combination of the free energy of the underlying equilibrium system. The electric current is calculated in the linear response regime by solving the Smoluchowski equation. The steady state solution differs significantly from the equilibrium distribution. In case of a tight binding potential the conductivity offers corrections depending on the amplitude of the potential. As a further application we discuss nanocontacts with piecewise constant potentials. The electric conductivity is corrected by the potential height., Comment: 12 pages, 3 figures

There is an increasing interest in the role of macroscopic environments to our understanding of the basics of quantum theory. The knowledge of the implications of the quantum theory to other theories, especially to the statistical mechanics and the domain of validity has captivated scientists from the beginning of quantum description. In such a context, the presence of an environment is commonly thought as entanglement, decohering and mixing properties of quantum system. Generically, an environment is assumed to be a noisy reservoir or a heat bath. Whereas in common interpretation of statistical mechanics the heat bath is unspecified, in quantum systems a heat bath can also provide an indirect interaction between otherwise totally decoupled subsystems and consequently a means to entangle them \cite{cdkl,dvclp,bfp}. In simple example for the entanglement between two qubits due to the interaction with a common heat bath has been explicitly shown in \cite{b}. Whereas in that paper the bath is described by a collection of harmonic oscillators, it seems to be more reasonable to specify the bath by stochastic forces represented by stochastic fields. From a more general point of view we expect the bath should be better described in a stochastic manner and not by deterministic forces. In the present paper we consider a two level system (qubits) which are able to perform flip processes by a coupling to classical stochastic fields. Thus we bridge the gap between quantum and classical probability theory. This problem is related to many other questions of quantum optics and quantum electronics where quantum statistical aspects arising from the intrinsic quantum character of the system while the possible time-dependence of system parameters may be interpreted as the influence of classical thermal fluctuations., Comment: 5 pages

We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the traps within a sphere of radius $R(t)= v t^{\alpha}$ around $\vec x$ will be activated and a particle is released with a rate $\mu$. Due to the competition between both reactions the system evolves three different time regimes. While in the initial time interval the diffusive process dominates the behavior of the system, there appears a transient regime, where the system shows a driveling wave solution which tends to a non-trivial stationary solution for $v \to 0$. In that regime one observes a very slow decay of the concentration. In the final long time regime a crossover to an exponentially decaying process is observed. In case of $\lambda = \mu$ the concentration is a conserved quantity whereas for $\mu > \lambda$ the total particle number tends to zero after a finite time. The mean square displacement offers an anomalous diffusive behavior where the dynamic exponent is determined by the exponent $\alpha $. In one dimension the model can be solved exactly. In higher dimension we find approximative analytical results in very good agreement with numerical solutions. The situation could be applied for the development of a bacterial colony or a gene-pool., Comment: 14 pages

We analyze a simple spin-flip process 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 $T ^{\prime}$. The situation can be described by using a master equation approach in a second quantized Hamiltonian formulation. The stationary solution leads to a generalized Fermi-Dirac distribution with an effective temperature $T_e$. Likewise the relaxation time is given in terms of $T_e$. Introducing a spin-representation we perform a Landau expansion for the averaged spin $<\sigma>$ as order parameter and consequently, a free energy functional can be derived. Owing to the two reservoirs the model is invariant with respect to a simultaneous change $\sigma \leftrightarrow - \sigma $ and $ T \leftrightarrow T ^{\prime}$. This new symmetry generates a third order term in the free energy which gives rise a dynamically induced first order transition., Comment: 11 pages, no figure

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 parameter. As the consequence the deterministic part of the underlying Langevin equation is likewise determined by the noise strength of the stochastic part. This memory induced stochastic behavior is discussed for different initial distributions. The analytical calculations are supported by numerical results., Comment: 14 pages, 17 figures

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 single flip-process $w_i(\sigma_i)$ which is in accordance with the principle of detailed balance. The transition rate differs significantly from the conventional one due to Glauber in the low temperature regime. Here the behavior is controlled by the Ising energy and not by the microscopic time scale., Comment: 8 pages

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 be changed incessantly. Depending on the deepness of the social contacts, which will be characterized by a parameter $\alpha $, a stable distribution of party members emerges. At a critical $\alpha_c$ an abrupt depletion of almost all parties is observed and as the consequence all the peoples are assembled at a single party. The model is based on a hierarchical social network. The probability that a certain person is contacted to another one depends on the social distance introduced within the network and homophily parameter $\alpha $., Comment: 15 pages, 6 figures

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 scaling behavior almost immediately after the system starts to evolve while the correlation and response functions demonstrate scaling behavior which is typical for aging phenomena. The corresponding fluctuation-dissipation ratio is computed to first order in $\epsilon$ and the relation between transverse and longitudinal fluctuations is discussed., Comment: 5 pages, revtex4

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 $p_c^{(1)}=1/2$ where memory effects vanish there is a transition from a weakly localized regime (where the walker returns to its starting point) to an escape regime. Inside the escape regime there is a second critical value where the random walk becomes superdiffusive. The probability distribution is shown to be governed by a non-Markovian Fokker-Planck equation with hopping rates that depend both on time and on the starting position of the walk. On large scales the memory organizes itself into an effective harmonic oscillator potential for the random walker with a time-dependent spring constant $k = (2p-1)/t$. The solution of this problem is a Gaussian distribution with time-dependent mean and variance which both depend on the initiation of the process., Comment: 10 pages

The diffusion equation is extended by including spatial-temporal memory in such a manner that the conservation of the concentration is maintained. The additional memory term gives rise to the formation of non-trivial stationary solutions. The steady state pattern in an infinite domain is driven by a competition between conventional particle current and a feedback current. We give a general criteria for the existence of a non-trivial stationary state. The applicability of the model is tested in case of a strongly localized, time independent memory kernel. The resulting evolution equation is exactly solvable in arbitrary dimensions and the analytical solutions are compared with numerical simulations. When the memory term offers an spatially decaying behavior, we find also the exact stationary solution in form of a screened potential., Comment: 14 pages, 12 figures

We study the dynamics of a spin facilitated Ising model with long range kinetic constraints. To formulate those restrictions within an analytical approach we introduce the size of a kinetic active environment of a given spin. Based on a Master equation in second quantized form, the spin-autocorrelation function is calculated. It exhibits a pronounced slow dynamics, manifested by a logarithmic decay law of the spin-autocorrelation function. In case of an infinite kinetic interaction the mean field solution yields an asymptotic exact expression for the autocorrelation function which is in excellent agreement with Monte Carlo Simulations for finite interaction lengths. With increasing size of the active zone the cooperative processes, characterizing the facilitated model with short range kinetic interaction, become irrelevant. We demonstrate that the long range kinetic interaction dominates the actual spin configurations of the whole system and the mean field solution is the exact one., Comment: 18 pages, 5 figures

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 $p(\vec r, t)$ is generalized to include non-linear and non-local spatial-temporal memory effects. The realization of the memory kernels are restricted due the conservation of the basic quantity $p$. A general criteria is given for the existence of stationary solutions. In case the memory kernel depends on $p$ polynomially the transport is prevented. Owing to the delay effects a finite amount of particles remains localized and the further transport is terminated. For diffusion with non-linear memory effects we find an exact solution in the long-time limit. Although the mean square displacement shows diffusive behavior, higher order cumulants exhibits differences to diffusion and they depend on the memory strength.

Epidemiological processes are studied within a recently proposed hierarchical network model using the susceptible-infected-refractory dynamics of an epidemic. Within the network model, a population may be characterized by $H$ independent hierarchies or dimensions, each of which consists of groupings of individuals into layers of subgroups. Detailed numerical simulations reveal that for $H>1$, global spreading results regardless of the degree of homophily of the individuals forming a social circle. For H=1, a transition from global to local spread occurs as the population becomes decomposed into increasingly homophilous groups. Multiple dimensions in classifying individuals (nodes) thus make a society (computer network) highly susceptible to large scale outbreaks of infectious diseases (viruses)., Comment: 10 pages, Revtex, 4 figures, corrected references

We consider a diffusion-limited reaction in case the reacting entities are not available simultaneously. Due to the fact that the reaction takes place after a spatiotemporal accumulation of reactants, the underlying rate equation has to be modified by additional non-local terms. Owing to the delay effects a finite amount of reactants remains localized, preventing a further reaction and the asymptotic decay is terminated at a finite density. The resulting inhomogeneous non-zero stationary concentration is stable against long wave length fluctuations. Below a critical wave vector $k_c$ the system becomes inert, whereas a complete decay is realized above $k_c$. The phase diagram for the one species-annihilation process $A + A \to 0$ exhibits a behavior comparable to a second order phase transition. Obviously the memory effects are equivalent to long range interaction and the non-local kinetics is basically independent on space dimensions., Comment: 12 pages, 2 figures

When the entities undergoing a chemical reaction are not available simultaneously, the classical rate equation of a reaction or, alternatively for the evolution of a population, should be extended by including non-Markovian memory effects. We consider the two cases of an external feedback, realized by fixed functions and an internal feedback originated in a self-organized manner by the relevant concentration itself. Whereas in the first case the fixed points are not changed, although the dynamical process is altered, the second case offers a complete new behaviour, characterized by the existence of a time persistent solution. Due to the feedback the reaction may lead to a finite concentration in the stationary limit even in case of a single-species pair annihilation $A + A \to 0$ process. We argue that the different cases are similar to a coupling of additive or multiplicative noises in stochastic processes., Comment: 18 pages, 3 figures

We propose and study a model of weighted scale-free networks incorporating a stochastic scheme for weight assignments to the links, taking into account both the popularity and fitness of a node. As the network grows the weights of links are driven either by the connectivity with probability $p$ or by the fitness with probability $1-p$. Results of numerical simulations show that the total weight associated with a selected node exhibits a power law distribution with an exponent $\sigma$, the value of which depends on the probability $p$. The exponent $\sigma$ decreases continuously as $p$ increases. For $p=0$, the total weight distribution displays the same scaling behavior as that of the connectivity distribution with $\sigma= \gamma = 3$, where $\gamma$ is the exponent characterizing the connectivity distribution. An analytical expression for the total weight is derived so as to explain the features observed in the numerical results. Numerical results are also presented for a generalized model with a fitness-dependent link formation mechanism., Comment: 13 pages, Revtex, 4 figures

Starting from a master equation in a quantum Hamiltonian form and a coupling to a heat bath we derive an evolution equation for a collective hopping process under the influence of a stochastic energy landscape. There results different equations in case of an arbitrary occupation number per lattice site or in a system under exclusion. Based on scaling arguments it will be demonstrated that both systems belong below the critical dimension $d_c$ to the same universality class leading to anomalous diffusion in the long time limit. The dynamical exponent $z$ can be calculated by an $\epsilon = d_c-d$ expansion. Above the critical dimension we discuss the differences in the diffusion constant for sufficient high temperatures. For a random potential we find a higher mobility for systems with exclusion., Comment: 15 pages, no figures

An Ising model with local Glauber dynamics is studied under the influence of additional kinetic restrictions for the spin-flip rates depending on the orientation of neighboring spins. Even when the static interaction between the spins is completely eliminated and only an external field is taken into account the system offers a phase transition at a finite value of the applied field. The transition is realized due to a competition between the activation processes driven by the field and the dynamical rules for the spin-flips. The result is based on a master equation approach in a quantum formulation., Comment: 13 pages

Starting from a master equation in a quantum Hamilton form we study analytically a nonequilibrium system which is coupled locally to two heat bathes at different temperatures. Based on a lattice gas description an evolution equation for the averaged density in the presence of a temperature gradient is derived. Firstly, the case is analysed where a particle is removed from a heat bath at a fixed temperature and is traced back to the bath at another temperature. The stationary solution and the relaxation time is discussed. Secondly, a collective hopping process between different heat bathes is studied leading to an evolution equation which offers a bilinear coupling between density and temperature gradient contrary to the conventional approach. Whereas in case of a linear decreasing static temperature field the relaxtion time offers a continuous spectrum it results a discrete spectrum for a quadratically decreasing temperature profile., Comment: 9 pages, Revtex, to be published in Int. J. of Mod. Phys. B

The ionic conductivity of mixed alkali glasses exhibits a deep minimum as a function of the relative concentrations of the two alkali ions. To study this behaviour we consider a simple one-dimensional model for asymmetric diffusion of two kinds of particles. Different particles are assumed to repulse each other. We consider two versions of the model: with or without overtaking of particles. For the case of perfect repulsion we find exact expressions for the stationary current. The model with weaker repulsion is studied by means of numerical simulations. The stationary current as a function of the ratio of particle concentrations is found to exhibit a minimum, related to correlations existing in this system., Comment: revised version (Some minor errors were corrected and some changes made.), 16 pages RevTeX and 3 postscript figures