35,001 research outputs found
Diffeomorphism, kappa transformations and the theory of non-linear realisations
We will show how the theory of non-linear realisations can be used to
naturally incorporate world line diffeomorphisms and kappa transformations for
the point particle and superpoint particle respectively. Similar results also
hold for a general p-brane and super p-brane, however, we must in these cases
include an additional Lorentz transformation.Comment: 19pages, no figure. References are added and typos are correcte
Canonical and non-canonical equilibrium distribution
We address the problem of the dynamical foundation of non-canonical
equilibrium. We consider, as a source of divergence from ordinary statistical
mechanics, the breakdown of the condition of time scale separation between
microscopic and macroscopic dynamics. We show that this breakdown has the
effect of producing a significant deviation from the canonical prescription. We
also show that, while the canonical equilibrium can be reached with no apparent
dependence on dynamics, the specific form of non-canonical equilibrium is, in
fact, determined by dynamics. We consider the special case where the thermal
reservoir driving the system of interest to equilibrium is a generator of
intermittent fluctuations. We assess the form of the non-canonical equilibrium
reached by the system in this case. Using both theoretical and numerical
arguments we demonstrate that Levy statistics are the best description of the
dynamics and that the Levy distribution is the correct basin of attraction. We
also show that the correct path to non-canonical equilibrium by means of
strictly thermodynamic arguments has not yet been found, and that further
research has to be done to establish a connection between dynamics and
thermodynamics.Comment: 13 pages, 6 figure
Non-Poisson dichotomous noise: higher-order correlation functions and aging
We study a two-state symmetric noise, with a given waiting time distribution
, and focus our attention on the connection between the four-time
and the two-time correlation functions. The transition of from
the exponential to the non-exponential condition yields the breakdown of the
usual factorization condition of high-order correlation functions, as well as
the birth of aging effects. We discuss the subtle connections between these two
properties, and establish the condition that the Liouville-like approach has to
satisfy in order to produce a correct description of the resulting diffusion
process
Non-Poisson dichotomous noise: higher-order correlation functions and aging
We study a two-state symmetric noise, with a given waiting time distribution
, and focus our attention on the connection between the four-time
and the two-time correlation functions. The transition of from
the exponential to the non-exponential condition yields the breakdown of the
usual factorization condition of high-order correlation functions, as well as
the birth of aging effects. We discuss the subtle connections between these two
properties, and establish the condition that the Liouville-like approach has to
satisfy in order to produce a correct description of the resulting diffusion
process
Fractional Calculus as a Macroscopic Manifestation of Randomness
We generalize the method of Van Hove so as to deal with the case of
non-ordinary statistical mechanics, that being phenomena with no time-scale
separation. We show that in the case of ordinary statistical mechanics, even if
the adoption of the Van Hove method imposes randomness upon Hamiltonian
dynamics, the resulting statistical process is described using normal calculus
techniques. On the other hand, in the case where there is no time-scale
separation, this generalized version of Van Hove's method not only imposes
randomness upon the microscopic dynamics, but it also transmits randomness to
the macroscopic level. As a result, the correct description of macroscopic
dynamics has to be expressed in terms of the fractional calculus.Comment: 20 pages, 1 figur
Probability flux as a method for detecting scaling
We introduce a new method for detecting scaling in time series. The method
uses the properties of the probability flux for stochastic self-affine
processes and is called the probability flux analysis (PFA). The advantages of
this method are: 1) it is independent of the finiteness of the moments of the
self-affine process; 2) it does not require a binning procedure for numerical
evaluation of the the probability density function. These properties make the
method particularly efficient for heavy tailed distributions in which the
variance is not finite, for example, in Levy alpha-stable processes. This
utility is established using a comparison with the diffusion entropy (DE)
method
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