Interaction of a Two-Level Atom with the Morse Potential in the Framework of Jaynes-Cummings Model

A theoretical study of the dynamical behaviors of the interaction between a two-level atom with a Morse potential in the framework of the Jaynes Cummings model （JCM） is discussed. We show that this system is equivalent to an intensity-dependent coupling between the two-level atom and the non-deformed single-mode radiation field in the presence of an additional nonlinear interaction. We study the dynamical properties of the system such as, atomic population inversion, the probability distribution of cavity-field, the Mandel parameter and atomic dipole squeezing. It is shown how the depth of the Morse potential can be affected by non-classical properties of the system. Moreover, the temporal evolution of the Husimi-distribution function is explored.     

Analytical results for the cluster size distribution in controlled deposition processes

This paper proposes a controlled particle deposition model for cluster growth on the substrate surface and then presents exact results for the cluster (island) size distribution. In the system, at every time step a fixed number of particles are injected into the system and immediately deposited onto the substrate surface. It investigates the cluster size distribution by employing the generalized rate equation approach. The results exhibit that the evolution behaviour of the system depends crucially on the details of the adsorption rate kernel. The cluster size distribution can take the Poisson distribution or the conventional scaling form in some cases, while it is of a quite complex form in other cases.     

Structures and Dynamics of a Two-Dimensional Confined Dusty Plasma System

The influence of the confining potential strength and temperature on the structures and dynamics of a two-dimensional （2D） dusty plasma system is investigated through molecular dynamic （MD） simulation. The circular symmetric confining potential leads to the nonuniform packing of particles, that is, an inner core with a hexagon lattice surrounded by a few outer circular shells. Under the appropriate confining potential and temperature, the particle trajectories on middle shells form a series of concentric and nested hexagons due to tangential movements of particles. Mean square displacement, self-diffusion constant, pair correlation function, and the nearest bond are used to characterize the structural and dynamical properties of the system. With the increase of the confining potential, the radial and tangential movements of particles have different behaviors. With the increase of temperature, the radial and tangential motions strengthen, particle trajectories gradually become disordered, and the system gradually changes from a crystal or liquid state to a gas state.     

Kinetics of catalytically activated duplication in aggregation growth

We propose a catalytically activated duplication model to mimic the coagulation and duplication of the DNA polymer system under the catalysis of the primer RNA. In the model, two aggregates of the same species can coagulate themselves and a DNA aggregate of any size can yield a new monomer or double itself with the help of RNA aggregates. By employing the mean-field rate equation approach we analytically investigate the evolution behaviour of the system. For the system with catalysis-driven monomer duplications, the aggregate size distribution of DNA polymers a_k(t) always follows a power law in size in the long-time limit, and it decreases with time or approaches a time-independent steady-state form in the case of the duplication rate independent of the size of the mother aggregates, while it increases with time increasing in the case of the duplication rate proportional to the size of the mother aggregates. For the system with complete catalysis-driven duplications, the aggregate size distribution a_k(t) approaches a generalized or modified scaling form.     

Effect of a barrier potential on soliton dynamical characteristics in condensates

By using the multiple-scale method, this paper analytically studies the effect of a barrier potential on the dynamical characteristics of the soliton in Bose--Einstein condensates. It is shown that a stable soliton is exhibited at the top of the barrier potential and the region of the absence of the barrier potential. Meanwhile, it is found that the height of the barrier potential has an important effect on the dark soliton dynamical characteristics in the condensates. With the increase of height of the barrier potential, the amplitude of the dark soliton becomes smaller, its width is narrower, and the soliton propagates more slowly.     

Population and Asset Distributions in Economically Competitive Activities： a Rate-Equation Approach

We introduce a simple asset migration model for the wealth redistribution in economical activities, in which a unit of asset migrates from one individual to another whenever they interact. By means of the mean-field rate equation, we have analysed the dynamic behaviour of the system. In the random migration case, the asset distribution of individuals takes the standard Caussian form and consistently decreases to zero at the end. As for the system in which only the richer can gain assets from the poorer, it is found that the individual asset distribution is discontinuous at a critical point and only the individuals with asset absolute value less than a cutoff value have a uniform and non-zero distribution. Moreover, the result shows that for the system with migration bias the assets of the individuals may have a cutoff value at each given time, which is different from the system without migration bias.     

Tsallis holographic dark energy under complex form of quintessence model

In this paper, we use a Tsallis holographic dark energy model in two forms, interacting and noninteracting cases, to acquire some parameters as the equation of state for the energy density of the Tsallis model in the FRW Universe concerning the complex form of quintessence model. We will study the cosmology of complex quintessence by revamping the potential and investigating the scalar field dynamics. Then we analyze(w-w’) and stability in two cases, i.e. noninteracting and interacting. We will ...     

Traffic of indistinguishable particles in complex networks

In this paper, we apply a simple walk mechanism to the study of the traffic of many indistinguishable particles in complex networks. The network with particles stands for a particle system, and every vertex in the network stands for a quantum state with the corresponding energy determined by the vertex degree. Although the particles are indistinguishable, the quantum states can be distinguished. When the many indistinguishable particles walk randomly in the system for a long enough time and the system reaches dynamic equilibrium, we find that under different restrictive conditions the particle distributions satisfy different forms, including the Bose--Einstein distribution, the Fermi--Dirac distribution and the non-Fermi distribution (as we temporarily call it). As for the Bose--Einstein distribution, we find that only if the particle density is larger than zero, with increasing particle density, do more and more particles condense in the lowest energy level. While the particle density is very low, the particle distribution transforms from the quantum statistical form to the classically statistical form, i.e., transforms from the Bose distribution or the Fermi distribution to the Boltzmann distribution. The numerical results fit well with the analytical predictions.     

On the fractal dimension of orbits compatible with Tsallis statistics

In a previous paper [A. Carati, Physica A 348 (2005) 110-120] it was shown how, for a dynamical system, the probability distribution function of sojourn-times in phase-space, defined in terms of the dynamical orbits (up to a given observation time), induces unambiguously a statistical ensemble in phase-space. In the present paper, the p.d.f. of the sojourn-times corresponding to a Tsallis ensemble is obtained (this, by the way, requires the solution of a problem of a general character, disregarded in paper [A. Carati, Physica A 348 (2005) 110-120]). In particular some qualitative properties, such as the fractal dimension, of the dynamical orbits compatible with the Tsallis ensembles are indicated.     

Extensive Rényi statistics from non-extensive entropy

We show that starting with either the non-extensive Tsallis entropy in Wang's formalism or the extensive Rényi entropy, it is possible to construct equilibrium non-Gibbs canonical distribution functions which satisfy the fundamental equations of thermodynamics. The statistical mechanics with Tsallis entropy does not satisfy the zeroth law of thermodynamics at dynamical and statistical independence request, whereas the extensive Rényi statistics fulfills all requirements of equilibrium thermodynamics in the microcanonical ensemble. Transformation formulas between Tsallis statistics in Wang representation and Rényi statistics are presented. The one-particle distribution function in Rényi statistics for a classical ideal gas at finite particle number has a power-law tail for large momenta.     

On the construction of complex networks with optimal Tsallis entropy

In this work, we first formulate the Tsallis entropy in the context of complex networks. We then propose a network construction whose topology maximizes the Tsallis entropy. The growing network model has two main ingredients: copy process and random attachment mechanism (C-R model). We show that the resulting degree distribution exactly agrees with the required degree distribution that maximizes the Tsallis entropy. We also provide another example of network model using a combination of preferential and random attachment mechanisms (P-R model) and compare it with the distribution of the Tsallis entropy. In this case, we show that by adequately identifying the exponent factor q, the degree distribution can also be written in the q-exponential form. Taken together, our findings suggest that both mechanisms, copy process and preferential attachment, play a key role for the realization of networks with maximum Tsallis entropy. Finally, we discuss the interpretation of q parameter of the Tsallis entropy in the context of complex networks.     

Mathematical inequalities for some divergences

Some natural phenomena are deviating from standard statistical behavior and their study has increased interest in obtaining new definitions of information measures. But the steps for deriving the best definition of the entropy of a given dynamical system remain unknown. In this paper, we introduce some parametric extended divergences combining Jeffreys divergence and Tsallis entropy defined by generalized logarithmic functions, which lead to new inequalities. In addition, we give lower bounds for one-parameter extended Fermi–Dirac and Bose–Einstein divergences. Finally, we establish some inequalities for the Tsallis entropy, the Tsallis relative entropy and some divergences by the use of the Young’s inequality.     

On the dynamics of the q-deformed logistic map

We analyze the q-deformed logistic map, where the q-deformation follows the scheme inspired in the Tsallis q-exponential function. We compute the topological entropy of the dynamical system, obtaining the parametric region in which the topological entropy is positive and hence the region in which chaos in the sense of Li and Yorke exists. In addition, it is shown the existence of the so-called Parrondo's paradox where two simple maps are combined to give a complicated dynamical behavior.     

Dynamical stability of systems with long-range interactions: application of the Nyquist method to the HMF model

We apply the Nyquist method to the Hamiltonian mean field (HMF) model in order to settle the linear dynamical stability of a spatially homogeneous distribution function with respect to the Vlasov equation. We consider the case of Maxwell (isothermal) and Tsallis (polytropic) distributions and show that the system is stable above a critical kinetic temperature T_c and unstable below it. Then, we consider a symmetric double-humped distribution, made of the superposition of two decentered Maxwellians, and show the existence of a re-entrant phase in the stability diagram. When we consider an asymmetric double-humped distribution, the re-entrant phase disappears above a critical value of the asymmetry factor Δ > 1.09. We also consider the HMF model with a repulsive interaction. In that case, single-humped distributions are always stable. For asymmetric double-humped distributions, there is a re-entrant phase for 1 ≤ Δ < 25.6, a double re-entrant phase for 25.6 < Δ < 43.9 and no re-entrant phase for Δ > 43.9. Finally, we extend our results to arbitrary potentials of interaction and mention the connexion between the HMF model, Coulombian plasmas and gravitational systems. We discuss the relation between linear dynamical stability and formal nonlinear dynamical stability and show their equivalence for spatially homogeneous distributions. We also provide a criterion of dynamical stability for spatially inhomogeneous systems.     

Test of h1(1830) made of $$K^* \bar K^*$$ with the $$\eta _c \to \varphi K^* \bar K^*$$ decay

The transverse momentum distributions of final-state particles produced in collisions at energies available at the Large Hadron Collider (LHC) are studied by using the two-Boltzmann distribution and Tsallis statistics. Experimental distributions described by the two-Boltzmann distribution can be described by the Tsallis statistics. The two-temperature emission described by the two-Boltzmann distribution reflects temperature fluctuation of interacting system. The Tsallis statistics can describe the temperature fluctuation and the degree of non-equilibrium. The results calculated by the two-Boltzmann distribution and the Tsallis statistics are in agreement with the experimental data available at the LHC energies. In some cases, the two-Boltzmann distribution degenerates to (single) Boltzmann distribution.

     

Tunable Tsallis distributions in dissipative optical lattices

We demonstrated experimentally that the momentum distribution of cold atoms in dissipative optical lattices is a Tsallis distribution. The parameters of the distribution can be continuously varied by changing the parameters of the optical potential. In particular, by changing the depth of the optical lattice, it is possible to change the momentum distribution from Gaussian, at deep potentials, to a power-law tail distribution at shallow optical potentials.