arXiv subjects

Steffen Trimper

Publications and source records attributed to Steffen Trimper.

At least 19 recordsLinked to original sources

arXiv2012

Nonlocal feedback in ferromagnetic resonance

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.

cond-mat.mes-hall↗

arXiv2011

Temperature gradient assisted magnetodynamics in a ferromagnetic nanowire

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.

cond-mat.mes-hall↗

arXiv2011

Noise-assisted tumor-immune cells interaction

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 $τ$ 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 $τ$. 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.

q-bio.TO↗

arXiv2011

Influence of randomness and retardation on the FMR-linewidth

The theory predicts that the spin-wave lifetime $τ_L$ and the linewidth of ferromagnetic resonance $ΔB$ 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 $ξ$. 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 $τ_c$ as well as the retardation strength $Γ_0$ and the size $ξ$. Whereas $τ_L$ decreases with increasing $D$, retardation strength $Γ_0$ and $τ_c$, the lifetime is enhanced for growing width $ξ$ of the spatial retardation kernel. In the same manner we calculate the experimentally measurable linewidth $ΔB$ is increased strongly when the correlation time $τ_c$ ranges in the nanosecond interval.

cond-mat.mes-hall↗

arXiv2011

Lagrangian approach and dissipative magnetic systems

A Lagrangian is introduced which includes the coupling between magnetic moments $\mathbf{m}$ and the degrees of freedom $\boldsymbolσ$ 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.

cond-mat.stat-mech↗

arXiv2010

Correlation Effects in the Stochastic Landau-Lifshitz-Gilbert Equation

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 $τ$. 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 $α$, the strength of the stochastic forces $D$ and its temporal range $τ$. 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 $α-D$ plane for different values of $τ$ 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 $τ$ leads to an increase of the oscillations of the correlation function.

cond-mat.mes-hall↗

arXiv2008

A stochastic model for tumor growth with immunization

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.

q-bio.CB↗

arXiv2008

Modified Jarzynski Relation for non-Markovian noise

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.

cond-mat.stat-mech↗

arXiv2008

Exact solution of a stochastic SIR model

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 $β$ by an infectious $I$- type provided that both are in contact. The $I$- type may recover with a rate $γ$ 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 $β$ and $γ$, 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.

cond-mat.stat-mech↗

arXiv2008

Computer simulations of two-dimensional melting with dipole-dipole interactions

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.

cond-mat.soft↗

arXiv2008

Non-linear effects in electrolytes at large applied voltage

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.

cond-mat.soft↗

arXiv2008

Thermally Assisted Spin Hall Effect

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.

cond-mat.stat-mech↗

arXiv2008

Exact expression for Drude conductivity in one-dimension with an arbitrary potential

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.

cond-mat.stat-mech↗

arXiv2006

Persistence of Quantum Information

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.

quant-ph↗

arXiv2006

Spatiotemporal Memory in a Diffusion-Reaction System

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 $λ$ at a certain point $\vec x$. In that case the traps within a sphere of radius $R(t)= v t^α$ around $\vec x$ will be activated and a particle is released with a rate $μ$. 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 $λ= μ$ the concentration is a conserved quantity whereas for $μ> λ$ 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 $α$. 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.

cond-mat.stat-mech↗

arXiv2006

Master Equation and Two Heat Reservoirs

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 $<σ>$ 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 $σ\leftrightarrow - σ$ 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.

cond-mat.stat-mech↗

arXiv2006

Relationship between a Non-Markovian Process and Fokker-Planck Equation

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.

cond-mat.stat-mech↗

arXiv2006

On the Glauber model in a quantum representation

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 $w_i(σ_i)$ 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.

cond-mat.stat-mech↗