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  • 1975-1979  (8)
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Material
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Exact solutions of discrete master equations in terms of continued fractions (1979)
    Springer
    The European physical journal 34 (1979), S. 411-417 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present the continued fraction solution for the stationary probability of discrete master equations of one-variable processes. After we elucidate the method for simple birth and death processes we focus the study on processes which introduce at least two-particle jumps. Consequently, these processes do in general not obey a detailed balance condition. The outlined method applies as well to solutions of eigenmodes of the stochastic operator. Further we derive explicit continued fraction solutions for the Laplace transform of conditional probabilities. All the various continued fraction coefficients are given directly in terms of the transition rates and they obey recursion relations. The method is illustrated for the stationary solution of a simple nonlinear chemical reaction scheme originated by Nicolis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01325207
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Time evolution, correlations, and linear response of non-Markov processes (1977)
    Springer
    The European physical journal 26 (1977), S. 85-92 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the time evolution of stochastic non-Markov processes as they occur in the coarse-grained description of open and closed systems. We show that semigroups of propagators exist for all multivariate probability distributions, the generators of which yield a set of time-convolutionless master equations. We discuss the calculation of averages and time-correlation functions. Further, linear response theory is developed for such a system. We find that the response function cannot be expressed as an ordinary time-correlation function. Some aspects of the theory are illustrated for the two-state process and the Gauss process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01313376
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Microdynamics and time-evolution of macroscopic non-Markovian systems (1977)
    Springer
    The European physical journal 26 (1977), S. 389-395 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The time evolution of the single event probability of macroscopic variables is studied from a microscopic point of view. The explicit consideration of the preparation of the initial microdistribution leads to a unique decomposition of the macrodynamics into two parts, a local and instantaneous one and a nonlocal and retarded one. In this retarded, i.e., non-Markovian master equation no inhomogeneity occurs in contrast to previous approaches. It is shown that the retarded master equation can exactly be transformed into a time-convolutionless and homogeneous form $$\dot p(t) = \Gamma (t)p(t)$$ , which generates a substitutive Markov process with the same single event behaviour as the process in question.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01570749
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Microdynamics and time-evolution of macroscopic non-Markovian systems. II (1978)
    Springer
    The European physical journal 29 (1978), S. 273-280 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the time-evolution of the joint and the conditional probability of macroscopic variables of a closed system from a microscopic point of view. We derive an exact generalized master equation for their time rate of change which consists of two parts, one instantaneous and local in state space, the other retarded and nonlocal in state space. It is represented by stochastic operators depending both on the initial preparation and on the initial macrodistribution, which reflects the non-Markovian character of the process. The connection with the time-evolution of the single-event probability is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01321192
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    On derivations and solutions of master equations and asymptotic representations (1978)
    Springer
    The European physical journal 30 (1978), S. 85-95 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A linear semi-group for both: Markov processes and non-Markov processes as they occur in the description of macroscopic systems is introduced. The elegance of the semigroup approach is demonstrated by the derivation of the master equation for a Markov process which undergoes continuous and discontinuous jumps. By use of nonlinear transformations of stochastic processes a class of processes is found for which the whole stochastic kinetics reduces mainly to the kinetics of a general Gauss-Markov process. Further the convergence of sequences of Markov processes to a limiting Markov process is studied. In this context, a semi-group formulation for the validity of various expansion methods of master equations developed recently is given and the convergence of functionals of the original process to a limiting transformed process is investigated. Some results are illustrated for the behaviour of the stochastics in a bistable tunnel diode. A model for macroscopic irreversibility is introduced using a sequence of non-Markov processes which converges to a Fokker-Planck process. Finally a few accomplishments on some recent related works are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01323672
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Note on the evaluation of the memory-kernel occuring in generalized master equations (1979)
    Springer
    The European physical journal 34 (1979), S. 409-410 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this communication we comment on a recent work [12] on the evaluation of the memory-kernel of the generalized master equation. We derive in a transparent and straightforward way the basic expression for the memory kernel. We demonstrate that the evaluation of this expression in [12] is carried out by use of the exact Laplace transform of the Greens function solution of the master equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01325206
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Correlation functions and masterequations of generalized (non-Markovian) Langevin equations (1978)
    Springer
    The European physical journal 31 (1978), S. 407-416 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For the statistical behavior of macrovariables described in terms of Langevin equations with a in general colored random force we deduce useful formulas which simplify the calculation of correlation functions. Utilizing these results and the stochastic properties of the random force we derive an exact time-convolutionless masterequation for the probability hereby showing the mathematical equivalence of the formally different approaches of a Langevin description and a masterequation description. We study in detail the class of time-instantaneous Langevin equations and the important class of retarded (Mori-type) Langevin equations with both, Gaussian and general colored random forces. Using the generalization of the nonlinear Langevin equation for continuous Markov processes with white Gaussian noise and white generalized Poisson noise we show that the resulting masterequation can be recast in the Kramers-Moyal form. Interpreting this Langevin equation in the Stratonovitch sense we deduce the fluctuation induced drift (spurious drift) which can be divided up into two parts, the well known part induced by white Gaussian noise and the one induced by white generalized Poisson noise.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01351552
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Linear response and fluctuation theorems for nonstationary stochastic processes (1975)
    Springer
    The European physical journal 22 (1975), S. 295-300 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Linear response theory is developed for nonstationary Markov processes. A generalized fluctuation theorem is derived which relates the response function to a correlation of fluctuations of the unperturbed nonstationary process. It is shown that it reduces to an ordinary fluctuation theorem relating the response function to the two-point correlation between fluctuations of state variables in the case of a Gaussian distribution function. The results are illustrated by explicit calculation for the class of nonstationary linear Fokker-Planck processes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01362253
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    Paper (German National Licenses)
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