111 research outputs found
A mechanism to derive multi-power law functions: an application in the econophysics framework
It is generally recognized that economical systems, and more in general
complex systems, are characterized by power law distributions. Sometime, these
distributions show a changing of the slope in the tail so that, more
appropriately, they show a multi-power law behavior. We present a method to
derive analytically a two-power law distribution starting from a single power
law function recently obtained, in the frameworks of the generalized
statistical mechanics based on the Sharma-Taneja-Mittal information measure. In
order to test the method, we fit the cumulative distribution of personal income
and gross domestic production of several countries, obtaining a good agreement
for a wide range of data.Comment: 10pages, 3 figures. Presented at Int. Conf. on Application of Physics
in Financial Analisys (APFA5), June 29 - July 1, 2006 Torino, Ital
A new one parameter deformation of the exponential function
Recently, in the ref. Physica A \bfm{296} 405 (2001), a new one parameter
deformation for the exponential function , which presents a power law
asymptotic behaviour, has been proposed. The statistical distribution
, has been obtained
both as stable stationary state of a proper non linear kinetics and as the
state which maximizes a new entropic form. In the present contribution,
starting from the -algebra and after introducing the -analysis,
we obtain the -exponential as
the eigenstate of the -derivative and study its main mathematical
properties.Comment: 5 pages including 2 figures. Paper presented in NEXT2001 Meetin
Legendre structure of the thermostatistics theory based on the Sharma-Taneja-Mittal entropy
The statistical proprieties of complex systems can differ deeply for those of
classical systems governed by Boltzmann-Gibbs entropy. In particular, the
probability distribution function observed in several complex systems shows a
power law behavior in the tail which disagrees with the standard exponential
behavior showed by Gibbs distribution. Recently, a two-parameter deformed
family of entropies, previously introduced by Sharma, Taneja and Mittal (STM),
has been reconsidered in the statistical mechanics framework. Any entropy
belonging to this family admits a probability distribution function with an
asymptotic power law behavior. In the present work we investigate the Legendre
structure of the thermostatistics theory based on this family of entropies. We
introduce some generalized thermodynamical potentials, study their
relationships with the entropy and discuss their main proprieties.
Specialization of the results to some one-parameter entropies belonging to the
STM family are presented.Comment: 11 pages, RevTex4; contribution to the international conference "Next
Sigma Phi" on News, EXpectations, and Trends in statistical physics, Crete
200
Intensive variables in the framework of the non-extensive thermostatistics
By assuming an appropriate energy composition law between two systems
governed by the same non-extensive entropy, we revisit the definitions of
temperature and pressure, arising from the zeroth principle of thermodynamics,
in a manner consistent with the thermostatistics structure of the theory. We
show that the definitions of these quantities are sensitive to the composition
law of entropy and internal energy governing the system. In this way, we can
clarify some questions raised about the possible introduction of intensive
variables in the context of non-extensive statistical mechanics.Comment: 14 pages, elsart style, version accepted on Physics Letters
Nonlinear gauge transformation for a class of Schroedinger equations containing complex nonlinearities
We consider a wide class of nonlinear canonical quantum systems described by
a one-particle Schroedinger equation containing a complex nonlinearity. We
introduce a nonlinear unitary transformation which permits us to linearize the
continuity equation. In this way we are able to obtain a new quantum system
obeying to a nonlinear Schroedinger equation with a real nonlinearity. As an
application of this theory we consider a few already studied Schroedinger
equations as that containing the nonlinearity introduced by the
exclusion-inclusion principle, the Doebner-Goldin equation and others.
PACS numbers: 03.65.-w, 11.15.-qComment: 3pages, two columns, RevTeX4, no figure
Wave Propagation And Landau-Type Damping In Liquids
Intermolecular forces are modeled by means of a modified Lennard-Jones
potential, introducing a distance of minimum approach, and the effect of
intermolecular interactions is accounted for with a self consistent field of
the Vlasov type. A Vlasov equation is then written and used to investigate the
propagation of perturbations in a liquid. A dispersion relation is obtained and
an effect of damping, analogous to what is known in plasmas as "Landau
damping", is found to take place.Comment: 13 pages, 3 figures, SigmaPhi 2011 conferenc
Kinetical Foundations of Non Conventional Statistics
After considering the kinetical interaction principle (KIP) introduced in
ref. Physica A {\bf296}, 405 (2001), we study in the Boltzmann picture, the
evolution equation and the H-theorem for non extensive systems. The
-kinetics and the -kinetics are studied in detail starting from the
most general non linear Boltzmann equation compatible with the KIP.Comment: 11 pages, no figures. Contribution paper to the proseedings of the
International School and Workshop on Nonextensive Thermodynamics and Physical
Applications, NEXT 2001, 23-30 May 2001, Cagliari Sardinia, Italy (Physica A
Generalized Kinetic Theory of Electrons and Phonons: Models, Equilibrium, Stability
In the present paper our aim is to introduce some models for the
generalization of the kinetic theory of electrons and phonons (KTEP), as well
as to study equilibrium solutions and their stability for the generalized KTEP
(GKTEP) equations. We consider a couple of models, relevant to non standard
quantum statistics, which give rise to inverse power law decays of the
distribution function with respect to energy. In the case of electrons in a
phonon background, equilibrium and stability are investigated by means of
Lyapounov theory. Connections with thermodynamics are pointed out.Comment: 10 pages, 2 figures, (RevTeX4), to appear in Physica B (2003
Nonlinear Transformation for a Class of Gauged Schroedinger Equations with Complex Nonlinearities
In the present contribution we consider a class of Schroedinger equations
containing complex nonlinearities, describing systems with conserved norm
and minimally coupled to an abelian gauge field. We introduce a
nonlinear transformation which permits the linearization of the source term in
the evolution equations for the gauge field, and transforms the nonlinear
Schroedinger equations in another one with real nonlinearities. We show that
this transformation can be performed either on the gauge field or,
equivalently, on the matter field . Since the transformation does not
change the quantities and , it can be considered a
generalization of the gauge transformation of third kind introduced some years
ago by other authors.
Pacs numbers: 03.65.-w, 11.15.-qComment: 4pages, two columns, RevTeX4, no figure
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