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  • 1
    Electronic Resource
    Electronic Resource
    Explicit calculation of a model for diffusion in nonconstant temperature (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1220-1224 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: As a model for diffusion in a nonhomogeneous medium, Landauer [Phys. Lett. A 68, 15 (1978)] proposed a pipe filled with a Knudsen gas. The wall temperature varies along the pipe, and the gas molecules, on colliding with the wall, assume its temperature. Here, by explicit calculation, in the limit of small diameter, an equation is derived for the flow of the gas through the pipe. The derivation is possible because the transverse motion of the gas particles rapidly establishes thermal equilibrium. It can therefore be eliminated using the method of eliminating fast variables. The surviving equation for the slow longitudinal flow has the form of a diffusion equation with nonconstant coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527963
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  • 2
    Electronic Resource
    Electronic Resource
    Book review (1981)
    Springer
    Journal of statistical physics 26 (1981), S. 847-848 
    Details
    ISSN: 1572-9613
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01010946
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  • 3
    Electronic Resource
    Electronic Resource
    Langevin-like equation with colored noise (1989)
    Springer
    Journal of statistical physics 54 (1989), S. 1289-1308 
    Details
    ISSN: 1572-9613
    Keywords: Colored noise ; stochastic differential equations ; elimination of fast variables
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Consider a stochastic differential equation of the form of a Langevin equation, but in which the noise source is not white. If it is nearly white, i.e., its autocorrelation time is short, a systematic approximation method is known. It leads to a Fokker-Planck equation with successive higher order corrections. To obtain the coefficients more explicitly, a secondary expansion may be employed. The validity of the resulting double series approximation is discussed and confronted with the various results given in the literature. In addition, an alternative approximation method is obtained using the technique for eliminating fast variables. It produces the same terms in a different sequence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01044716
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  • 4
    Electronic Resource
    Electronic Resource
    The validity of nonlinear Langevin equations (1981)
    Springer
    Journal of statistical physics 25 (1981), S. 431-442 
    Details
    ISSN: 1572-9613
    Keywords: Langevin equation ; nonlinear noise
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In the presence of internal noise the variables describing a system are intrinsically stochastic. If they constitute a Markov process the Ω expansion enables one to extract a deterministic macroscopic equation and to compute the fluctuations in successive approximations. In the lowest or linear noise approximation the fluctuations can be represented by a Langevin equation, provided it is handled appropriately. Higher orders cannot be described by any white noise Langevin equation. The question whether the equation has to be interpreted according to Itô or Stratonovich concerns these higher orders, for which the equation is not valid anyway.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01010798
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  • 5
    Electronic Resource
    Electronic Resource
    A soluble model for quantum mechanical dissipation (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 299-310 
    Details
    ISSN: 1572-9613
    Keywords: Dissipation ; noise ; quantum master equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In order to derive the equations for dissipation and noise in a quantum mechanical system it is necessary to include the equations of motion of a suitably chosen bath interacting with the system. In this way the standard treatment arrives at an approximate master equation for the density matrix of the system, at the expense of a number ofad hoc assumptions. These assumptions are here scrutinized on the basis of an exactly soluble model. The conclusion is: the bath must obey certain specifications; the interaction must be weak; and the temperature must be so high that the interaction energy is within the classical domain rather than occurring in quanta. Some additional comments concerning dissipation in quantum mechanics are relegated to an appendix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02183350
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  • 6
    Electronic Resource
    Electronic Resource
    Langevin and master equation in quantum mechanics (1997)
    Springer
    Journal of statistical physics 87 (1997), S. 1325-1334 
    Details
    ISSN: 1572-9613
    Keywords: Quantum Langevin equation ; quantum master equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The behavior of a system in contact with a heat bath can be described either by a Langevin equation or by an equation for its density matrix. As both descriptions inevitably involve approximations, it is not evident that their results coincide. It is shown here by explicit calculation that they do. The main complication is that in the Langevin equation the random force is multiplied by a nonconstant factor, which itself feels the fluctuations. In an alternative formulation of the Langevin approach this complication is avoided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02181287
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  • 7
    Electronic Resource
    Electronic Resource
    Determinism and predictability (1991)
    Springer
    Synthese 〈Dordrecht〉 89 (1991), S. 273-281 
    Details
    ISSN: 1573-0964
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General , Philosophy
    Notes: Abstract Theoretical determinism, as it is usually ascribed to Laplace, is neither verifiable nor falsifiable and has therefore no real content. It is not the same as predictability of actually observable phenomena. On the other hand, predictability is not an abstract principle; rather it is true to a certain degree, depending on the phenomena considered. It can be discussed only by examining the scientific state of affairs. This is done in some detail for classical statistical mechanics. Much of a recently published debate on determinism (Amsterdamski et al. 1990) is thereby obviated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00413908
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  • 8
    Electronic Resource
    Electronic Resource
    Statistical mechanics of trimers (1981)
    Springer
    Flow, turbulence and combustion 37 (1981), S. 67-75 
    Details
    ISSN: 1573-1987
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The statistical mechanics of polymers in solution has given rise to a paradox, which has only recently been fully explained. The paradox is demonstrated for the trimer. An even simpler model is constructed to elucidate the state of affairs. It also serves to describe the quantum mechanical treatment of systems with constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00382618
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  • 9
    Electronic Resource
    Electronic Resource
    Diffusion in inhomogeneous media (1987)
    Springer
    The European physical journal 68 (1987), S. 135-138 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The problem is to establish the correct diffusion equation in a medium that is inhomogeneous and whose temperature also varies in space. As a special model we study particles whose phase space distribution obeys Kramers' equation with a generalized collision operator. In the usual limit of strong collisions a diffusion equation is obtained. This equation contains additional drift terms, which depend on the form of the collision operator. They cannot be expressed as a mobility and a diffusion coefficient, unless the decay law of the velocity happens to be linear. Conclusion: no universal form of the diffusion equation exists, but each system has to be studied individually.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01304217
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  • 10
    Electronic Resource
    Electronic Resource
    Book reviews (1974)
    Springer
    Space science reviews 15 (1974), S. 541-543 
    Details
    ISSN: 1572-9672
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00178218
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