arXiv subjects

A. M. Scarfone

Publications and source records attributed to A. M. Scarfone.

49 records · Page 3Linked to original sources

arXiv2004

Deformed logarithms and entropies

By solving a differential-functional equation inposed by the MaxEnt principle we obtain a class of two-parameter deformed logarithms and construct the corresponding two-parameter generalized trace-form entropies. Generalized distributions follow from these generalized entropies in the same fashion as the Gaussian distribution follows from the Shannon entropy, which is a special limiting case of the family. We determine the region of parameters where the deformed logarithm conserves the most important properties of the logarithm, and show that important existing generalizations of the entropy are included as special cases in this two-parameter class.

cond-mat.stat-mech↗

arXiv2004

Lesche Stability of $κ$-Entropy

The Lesche stability condition for the Shannon entropy [B. Lesche, J. Stat. Phys. 27, 419 (1982)], represents a fundamental test, for its experimental robustness, for systems obeying the Maxwell-Boltzmann statistical mechanics. Of course, this stability condition must be satisfied by any entropic functional candidate to generate non-conventional statistical mechanics. In the present effort we show that the $κ$-entropy, recently introduced in literature [G. Kaniadakis, Phys. Rev. E 66, 056125 (2002)], satisfies the Lesche stability condition.

cond-mat.stat-mech↗

arXiv2004

Stabilities of generalized entropies

The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its Lesche stability property (that is different from thermodynamic stability) is examined. A general condition, under which the generalized entropy becomes stable, is derived. Examples known in the literature, including the entropy for the stretched-exponential distribution, the quantum-group entropy, and the kappa-entropy are discussed.

cond-mat.stat-mech↗

arXiv2003

Travelling waves in a mixture of gases with bimolecular reversible reactions

Starting from the kinetic approach for a mixture of reacting gases whose particles interact through elastic scattering and a bimolecular reversible chemical reaction, the equations that govern the dynamics of the system are obtained by means of the relevant Boltzmann-like equation. Conservation laws are considered. Fluid dynamic approximations are used at the Euler level to obtain a close set of PDEs for six unknown macroscopic fields. The dispersion relation of the mixture of reacting gases is explicitly derived in the homogeneous equilibrium state. A set of ODE that governs the propagation of a plane travelling wave is obtained using the Galilei invariance. After numerical integration some solutions, including the well-known Maxwellian and the hard spheres cases, are found for various meaningful interaction laws. The main macroscopic observables for the gas mixture such as the drift velocity, temperature, total density, pressure and its chemical composition are shown.

cond-mat.soft↗

arXiv2003

Nonlinear Schroedinger Equations within the Nelson Quantization Picture

We present a class of nonlinear Schroedinger equations (NLSEs) describing, in the mean field approximation, systems of interacting particles. This class of NLSEs is obtained generalizing expediently the approach proposed in Ref. [G.K. Phys. Rev. A 55, 941 (1997)], where a classical system obeying to an exclusion-inclusion principle is quantized using the Nelson stochastic quantization. The new class of NLSEs is obtained starting from the most general nonlinear classical kinetics compatible with a constant diffusion coefficient D=\hbar/2m. Finally, in the case of s-stationary states, we propose a transformation which linearizes the NLSEs here proposed.

cond-mat.soft↗

arXiv2003

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.

cond-mat.soft↗

arXiv2002

Cole-Hopf Like Transformation for a Class of Coupled Nonlinear Schroedinger Equations

In this paper we consider a class of coupled nonlinear Schroedinger equations for the fields $ψ_i$ containing complex nonlinearities, that has been obtained by requiring that the norms $|ψ_i|^2$ are conserved densities. For this class of equations we introduce a Cole-Hopf like transformation, whose effect is to reduce the complex nonlinearities into real ones, this way reducing the continuity equations of the system to the standard bilinear form. Some examples are presented to illustrate the applicability of the method. Pacs numbers: 03.50.-z, 03.65.-w, 11.30.Na, 11.40.Dw Keywords: Coupled nonlinear Schroedinger equations, Cole-Hopf transformation, Nonlinear transformations.

quant-ph↗

arXiv2002

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 $|ψ|^2$ 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 $A_μ$ or, equivalently, on the matter field $ψ$. Since the transformation does not change the quantities $|ψ|^2$ and $F_{μν}$, 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.-q

quant-ph↗

arXiv2002

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.-q

quant-ph↗

arXiv2002

Quantum vortices in systems obeying a generalized exclusion principle

The paper deals with a planar particle system obeying a generalized exclusion principle (EP) and governed, in the mean field approximation, by a nonlinear Schroedinger equation. We show that the EP involves a mathematically simple and physically transparent mechanism, which allows the genesis of quantum vortices in the system. We obtain in a closed form the shape of the vortices and investigate its main physical properties. PACS numbers: 03.65.-w, 03.65.Ge, 05.45.Yv

cond-mat.soft↗

arXiv2002

Cole-Hopf Like Transformation for Schrödinger Equations Containing Complex Nonlinearities

We consider systems, which conserve the particle number and are described by Schrödinger equations containing complex nonlinearities. In the case of canonical systems, we study their main symmetries and conservation laws. We introduce a Cole-Hopf like transformation both for canonical and noncanonical systems, which changes the evolution equation into another one containing purely real nonlinearities, and reduces the continuity equation to the standard form of the linear theory. This approach allows us to treat, in a unifying scheme, a wide variety of canonical and noncanonical nonlinear systems, some of them already known in the literature. pacs{PACS number(s): 02.30.Jr, 03.50.-z, 03.65.-w, 05.45.-a, 11.30.Na, 11.40.Dw

quant-ph↗

arXiv2001

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 $q$-kinetics and the $κ$-kinetics are studied in detail starting from the most general non linear Boltzmann equation compatible with the KIP.

cond-mat.stat-mech↗

arXiv2001

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 $\exp_{_{\{{\scriptstyle κ}\}}}(x)= (\sqrt{1+κ^2x^2}+κx)^{1/κ}; \exp_{_{\{{\scriptstyle 0}\}}}(x)=\exp (x)$, which presents a power law asymptotic behaviour, has been proposed. The statistical distribution $f=Z^{-1}\exp_{_{\{{\scriptstyle κ}\}}}[-β(E-μ)]$, 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 $κ$-algebra and after introducing the $κ$-analysis, we obtain the $κ$-exponential $\exp_{_{\{{\scriptstyle κ}\}}}(x)$ as the eigenstate of the $κ$-derivative and study its main mathematical properties.

cond-mat.stat-mech↗