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  • 1
    Electronic Resource
    Electronic Resource
    Statistical mechanics Brownian motion and microscopic chaos (1998)
    [s.l.] : Macmillan Magazines Ltd.
    Nature 394 (1998), S. 831-833 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Einstein's 1905 paper on Brownian motion is his most cited article, and one of the most cited physics papers ever. But nearly a century later, we are still learning from this phenomenon. On page 865 of this issue, Gaspard et al. report a high-precision measurement of the position of a ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/29650
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  • 2
    Electronic Resource
    Electronic Resource
    Asymptotic motion of a classical particle in a random potential in two dimensions: Landau model (1987)
    Springer
    Communications in mathematical physics 113 (1987), S. 209-230 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the motion of a classical particle in a random isotropic potential arising from uniformly distributed scatterers in two dimensions. We prove that in the weak coupling limit the velocity process of the particle converges in distribution to Brownian motion on a surface of constant speed, i.e. on the circle. The resulting equation for the probability density of the particle is related to the Landau equation in plasmas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01223512
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  • 3
    Electronic Resource
    Electronic Resource
    The Onsager-Machlup function as Lagrangian for the most probable path of a diffusion process (1978)
    Springer
    Communications in mathematical physics 60 (1978), S. 153-170 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract By application of the Girsanov formula for measures induced by diffusion processes with constant diffusion coefficients it is possible to define the Onsager-Machlup function as the Lagrangian for the most probable tube around a differentiable function. The absolute continuity of a measure induced by a process with process depending diffusion w.r.t. a quasi translation invariant measure is investigated. The orthogonality of these measures w.r.t. quasi translation invariant measures is shown. It is concluded that the Onsager-Machlup function cannot be defined as a Lagrangian for processes with process depending diffusion coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609446
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  • 4
    Electronic Resource
    Electronic Resource
    Self-diffusion in a non-uniform one dimensional system of point particles with collisions (1987)
    Springer
    Probability theory and related fields 75 (1987), S. 279-290 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We generalize the results of Spitzer, Jepsen and others [1–4] on the motion of a tagged particle in a uniform one dimensional system of point particles undergoing elastic collisions to the case where there is also an external potential U(x). When U(x) is periodic or random (bounded and statistically translation invariant) then the scaled trajectory of a tagged particle $${{y_A (t) = y(At)} \mathord{\left/ {\vphantom {{y_A (t) = y(At)} {\sqrt A }}} \right. \kern-\nulldelimiterspace} {\sqrt A }}$$ converges, as A → ∞, to a Brownian motion W D (t) with diffusion constant $${{D = \rho _{\min } \left\langle {|v|} \right\rangle } \mathord{\left/ {\vphantom {{D = \rho _{\min } \left\langle {|v|} \right\rangle } {\hat \rho ^2 }}} \right. \kern-\nulldelimiterspace} {\hat \rho ^2 }}$$ , where $$\hat \rho $$ is the average density, $$\left\langle {|v|} \right\rangle = \sqrt {{2 \mathord{\left/ {\vphantom {2 {\pi \beta m}}} \right. \kern-\nulldelimiterspace} {\pi \beta m}}} $$ is the mean absolute velocity and β−1 the temperature of the system. When U(x) is itself changing on a macroscopic scale, i.e. $$U_A (x) = U({x \mathord{\left/ {\vphantom {x {\sqrt A }}} \right. \kern-\nulldelimiterspace} {\sqrt A }})$$ , then the limiting process is a spatially dependent diffusion. The stochastic differential equation describing this process is now non-linear, and is particularly simple in Stratonovich form. This lends weight to the belief that heuristics are best done in that form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00354038
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  • 5
    Electronic Resource
    Electronic Resource
    A global equilibrium as the foundation of quantum randomness (1993)
    Springer
    Foundations of physics 23 (1993), S. 721-738 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We analyze the origin of quantum randomness within the framework of a completely deterministic theory of particle motion—Bohmian mechanics. We show that a universe governed by this mechanics evolves in such a way as to give rise to the appearance of randomness, with empirical distributions in agreement with the predictions of the quantum formalism. Crucial ingredients in our analysis are the concept of the effective wave function of a subsystem and that of a random system. The latter is a notion of interest in its own right and is relevant to any discussion of the role of probability in a deterministic universe.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01883806
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  • 6
    Electronic Resource
    Electronic Resource
    David Joseph Bohm: 1917–1992 (1993)
    Springer
    Foundations of physics 6 (1993), S. 1-4 
    Details
    ISSN: 1572-9524
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00683105
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  • 7
    Electronic Resource
    Electronic Resource
    Naive realism about operators (1996)
    Springer
    Erkenntnis 45 (1996), S. 379-397 
    Details
    ISSN: 1572-8420
    Source: Springer Online Journal Archives 1860-2000
    Topics: Philosophy
    Notes: Abstract A source of much difficulty and confusion in the interpretation of quantum mechanics is a “naive realism about operators.” By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about “measuring operators” that occurs when the subject is quantum mechanics. Without a specification of what should be meant by “measuring” a quantum observable, such an expression can have no clear meaning. A definite specification is provided by Bohmian mechanics, a theory that emerges from Schrödinger's equation for a system of particles when we merely insist that “particles” means particles. Bohmian mechanics clarifies the status and the role of operators as observables in quantum mechanics by providing the operational details absent from standard quantum mechanics. It thereby allows us to readily dismiss all the radical claims traditionally enveloping the transition from the classical to the quantum realm — for example, that we must abandon classical logic or classical probability. The moral is rather simple: Beware naive realism, especially about operators!
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276801
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  • 8
    Electronic Resource
    Electronic Resource
    Stochastic processes originating in deterministic microscopic dynamics (1983)
    Springer
    Journal of statistical physics 30 (1983), S. 519-526 
    Details
    ISSN: 1572-9613
    Keywords: Central limit theorem ; Brownian motion ; test particle ; deterministic dynamics ; stochastic processes ; invariance principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the probability distribution of the scaled trajectory of a test particle moving in an equilibrium fluid according to the laws of classical mechanics, i.e., ifQ(t) is the displacement of the test particle we letQ A(t) =Q(At)/√A and consider the distribution of the trajectory QA(t) in the limit A→∞. The randomness of the motion is due entirely to the randomness of the initial state of the fluid, test particle, or both, and the process is generally non-Markovian. Nevertheless, it can be proven in some cases and we expect it to be true in many more that QA (t) looks like Brownian motion in the limit A→∞. Some results for simple model systems are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01012325
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  • 9
    Electronic Resource
    Electronic Resource
    Quantum equilibrium and the origin of absolute uncertainty (1992)
    Springer
    Journal of statistical physics 67 (1992), S. 843-907 
    Details
    ISSN: 1572-9613
    Keywords: Quantum randomness ; quantum uncertainty ; hidden variables ; effective wave function ; collapse of the wave function ; the measurement problem ; Bohm's causal interpretation of quantum theory ; pilot wave ; foundations of quantum mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The quantum formalism is a “measurement” formalism-a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schrödinger's equation for a system of particles when we merely insist that “particles” means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that anappearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by “ρ = ¦ψ¦ 2”. A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01049004
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  • 10
    Electronic Resource
    Electronic Resource
    Book review: Quantum theory of collective phenomena (1987)
    Springer
    Journal of statistical physics 47 (1987), S. 603-604 
    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/BF01007529
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