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S Trimper

Publications and source records attributed to S Trimper.

6 recordsLinked to original sources
PubMed2001

Variations of the asset prices.

The empirical established non-Gaussian behavior of asset price fluctuations is studied using an analytical approach. The analysis is based on a nonlinear Fokker-Planck equation with a self-organized feedback-coupling term, devised as a fundamental model for price dynamics. The evidence, and the analytical form of the memory term, are discussed in the context of statistical physics. It will be suggested that the memory term in leading order offers a power law dependence with an exponent straight theta. The stationary solution of the probability density leads asymptotically to a truncated Lévy distribution, the characteristic exponent beta of which is related to the exponent straight theta by beta=3/theta-1. The empirical data can be reproduced by theta approximately 5/4.

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PubMed2001

Corrections to scaling for the two-dimensional dynamic XY model.

With large-scale Monte Carlo simulations, we confirm that for the two-dimensional XY model, there is a logarithmic correction to scaling in the dynamic relaxation starting from a completely disordered state, while only an inverse power law correction in the case of starting from an ordered state. The dynamic exponent z is z=2.04(1).

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PubMed2000

Collective diffusion and a random energy landscape

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. Different equations result for 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.

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PubMed2000

Reaction-controlled diffusion

The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of different type B are present in their environment. Species B is subject to diffusion-limited reactions. If the density of B particles attains a finite asymptotic value (active state), the A species displays normal diffusion. On the other hand, if the B density decays algebraically approximately t(-alpha) at long times (inactive state), the effective attractive A-B interaction is weakened. The combination of B decay and activated A hopping processes gives rise to anomalous diffusion, with mean-square displacement (A)(t)(2)> approximately t(1-alpha) for alpha<1. Such algebraic subdiffusive behavior ensues for nth-order B annihilation reactions (nB-->) with n>/=3, and n=2 for d<2. The mean-square displacement of the A particles grows only logarithmically with time in the case of B pair annihilation (n=2) and d>/=2 dimensions. For radioactive B decay (n=1), the A particles remain localized. If the A particles may hop spontaneously as well, or if additional random forces are present, the A-B coupling becomes irrelevant, and conventional diffusion is recovered in the long-time limit.

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