Some Properties of Weighted Tsallis and Kaniadakis Divergences

We are concerned with the weighted Tsallis and Kaniadakis divergences between two measures. More precisely, we find inequalities between these divergences and Tsallis and Kaniadakis logarithms, prove that they are limited by similar bounds with those that limit Kullback–Leibler divergence and show that are pseudo-additive.     

Spin Statistics and CPT for Solitons

Conditions are analysed under which the statistics of soliton sectors of massive two-dimensional field theories can be properly defined. A soliton field algebra is defined as a crossed product with the group of soliton sectors. In this algebra, the nonlocal commutation relations are determined and weak locality, spin statistics and CPT theorems are proven. These theorems depart from their usual appearance due to the broken symmetry connecting the inequivalent vacua. An interpretation of these results in terms of modular theory is given. For the neutral subalgebra of the soliton algebra, the theorems hold in a familiar form, and twisted duality is derived.     

Activation-Like Processes at Zero Temperature

We examine the possibility that a metastable quantum state could experiment a phenomenon similar to thermal activation but at zero temperature. To do that we study the real-time dynamics of the reduced Wigner function in a simple open quantum system: an anharmonic oscillator with a cubic potential linearly interacting with an environment of harmonic oscillators. Our results suggest that this activation-like phenomenon exists indeed as a consequence of the fluctuations induced by the environment and that its associated decay rate is comparable to the tunneling rate as computed by the instanton method, at least for the particular potential of the system and the distribution of frequencies for the environment considered in this paper. However, we are not able to properly deal with the term which leads to tunneling in closed quantum systems, and a definite conclusion cannot be reached until tunneling and activation-like effects are considered simultaneously.     

Resonant tunneling and quantum fluctuation in a driven triple-well system

The influence of parameters such as the strength and frequency of a periodic driving force on the tunneling dynamics is investigated in a symmetric triple-well potential. It is shown that for some special values of the parameters, tunneling could be enhanced considerably or suppressed completely. Quantum fluctuation during the tunneling is discussed as well and the numerical results are presented and analysed by virtue of Floquet formalism.     

Energy distribution and energy fluctuation in Tsallis statistics

The energy distribution and the energy fluctuation in the Tsallis canonical ensemble are studied with the OLM formalism but following a new way. The resulting formula for the energy fluctuation is not the same as that in previous work [L.Y. Liu, J.L. Du, Physica A 387 (2008) 5417]. In discussing the application of an ideal gas, we find that the energy fluctuation can not be negligible in the thermodynamic limit, showing the ensemble nonequivalence for this case in Tsallis statistics. We investigate the energy fluctuation with a Tsallis generalized canonical distribution studied by Plastino and Plastino [A.R. Plastino, A. Plastino, Phys. Lett. A 193 (1994) 140] for describing a system in contact with a finite heat bath. For this situation, the two formulae for the energy fluctuation are shown to be equivalent, while the nonextensive parameter q$q$ plays a very important role.     

On Asymptotic Behavior of Multilinear Eigenvalue Statistics of Random Matrices

We prove the Law of Large Numbers and the Central Limit Theorem for analogs of U- and V- (von Mises) statistics of eigenvalues of random matrices as their size tends to infinity. We show first that for a certain class of test functions (kernels), determining the statistics, the validity of these limiting laws reduces to the validity of analogous facts for certain linear eigenvalue statistics. We then check the conditions of the reduction statements for several most known ensembles of random matrices. The reduction phenomenon is well known in statistics, dealing with i.i.d. random variables. It is of interest that an analogous phenomenon is also the case for random matrices, whose eigenvalues are strongly dependent even if the entries of matrices are independent.     

Computing activation energies of non-thermal reactions

The chemistry in bulk gases involves reactions of nascent radicals that are almost invariably non-thermal. The energy requirements of reactions involving radicals depend on the reactions that produce them and the intra- and inter-molecular energy transfer they may undergo. Here, we extend the generalised Tolman activation energy (GTEa) method to non-thermal reactions in molecular dynamics (MD) simulations. We compute the energy requirements, which we refer to as chemical-activation energies (CE _a), of reactions of radicals formed by the decomposition of hydrogen peroxide. The equipartition theorem is adapted to compute average energies of small isolated systems with internal degrees of freedom in MD simulations with periodic boundary conditions, which is necessary for application of the GTEa method to non-thermal reactions. To illustrate the applicability of the GTEa method to non-thermal reactions, we present CE _a results for H₂O₂?+?OH → H₂O?+?HO₂, a key reaction in hydrogen combustion, as described by the ReaxFF force field. The OH radicals are the products of the self-dissociation of H₂O₂ and subsequent reactions. We define the chemical-activation energy for a back reaction (BCE _a) as the difference between the energy of the products and the average energy of the system. We show that the BCE _a and CEa are linearly correlated.     

广义测不准关系与三维BTZ黑洞熵

通过应用在量子引力中,由广义测不准关系得出的新的态密度方程,研究三维BTZ背景下黑洞的熵.当取广义测不准关系中引入的,具有Planck量级与空间维数有关的常数λ为特定值时,得到BTZ黑洞Bekenstein-Hawking 熵和修正项.由于利用新的态密度方程,在计算中不存在用brick-wall模型计算黑洞熵时出现的发散项和小质量近似.所得结论,从量子统计力学角度给出了黑洞Bekenstein-Hawking 熵的修正值,使人们对黑洞熵的修正值有更深入的认识. 关键词： 广义测不准关系 量子统计 BTZ黑洞熵     

Temperature Dependence of Abnormal Fano Resonance in Photon-Assisted Transport Through a Side-Coupled Quantum Dot

We investigate transport through a perfect quantum wire with a side-coupled quantum dot under an ac field. Time-averaged complex conductance is formulated by using the nonequilibrium Green function (NGF) method. We find that the electron-photon interaction together with the quantum interference of electron wave function can lead to anti-resonance in the conductance, which is then useful for tuning coherence and phases of electrons. Meanwhile, we study the temperature dependence of the conductance. Interestingly, a peak-structure can be developed at the Fano resonance levels with increasing temperatures.     

Critique of multinomial coefficients method for evaluating Tsallis and Rényi entropies

Oikonomou [Th. Oikonomou, Physica A 386 (2007) 119] has published a calculation which purports to show that the Tsallis and Rényi entropies can be obtained from the generalized multinomial coefficients. In this paper, we prove that the method of generalized multinomial coefficients failed to determine the Tsallis entropy at equilibrium. Moreover, it is shown that Oikonomou’s analysis contains mistakes which led to misleading statements related to the Jaynes principle of maximum entropy, the Tsallis and the Rényi statistics.     

Tsallis statistics and magnetospheric self-organization

In this study we use Tsallis non-extensive statistics for a new understanding the magnetospheric dynamics and the magnetospheric self-organization during quiet and intensive superstorm periods. The _qsens$q_{sens}$, _qstat$q_{stat}$, and _qrel$q_{rel}$ indices set known as the Tsallis q$q$-triplet was estimated during both quiet and strongly active periods, as well as the correlation dimensions and Lyapunov exponents spectrum for magnetospheric bulk plasma flows data. The results obtained by our analysis clearly indicate the magnetospheric phase transition process from a high-dimensional quiet SOC state to a low-dimensional global chaotic state when superstorm events are developed. During such a phase transition process the non-extensive statistical character of the magnetospheric plasma is strengthened as the values of the q$q$-triplet indices changes obtaining higher values than their values during the quiet periods.     

Kaluza—Klein Black-Hole Entropy by Quantum Statistics

By using the method of quantum statistics, we directly derive the partition functions of bosonic and fermionic field in Kaluza—Klein black hole with axial symmetry. Then via the improved brick-wall method, membrane model, we obtain that the entropy of bosonic and fermionic field in black hole is proportional to the area of horizon. In our result, the stripped term and the divergent logarithmic term no longer exist. The problem that the state density is divergent around the horizon doesn't exist either. We also give the influence of the spining degeneracy of particles on the entropy of black hole. We offer a new, simple, and direct way of calculating the entropy of different complicated black holes.     

The Tsallis statistical distribution in a completely open system

We derive the statistical distributions, partition functions and thermodynamic formulas for a completely open system on the basis of Tsallis entropy. These results are derived for two types of constraints, using the method of maximum entropy.     

Energy and Heat Fluctuations in a Temperature Quench

Fluctuations of energy and heat are investigated during the relaxation following the instantaneous temperature quench of an extended system. Results are obtained analytically for the Gaussian model and for the large N model quenched below the critical temperature T_C. The main finding is that fluctuations exceeding a critical threshold do condense. Though driven by a mechanism similar to that of Bose-Einstein condensation, this phenomenon is an out-of-equilibrium feature produced by the breaking of energy equipartition occurring in the transient regime. The dynamical nature of the transition is illustrated by phase diagrams extending in the time direction.     

Tsallis Mapping in Growing Complex Networks with Fitness

We introduce Tsallis mapping in Bianconi-Barab'asi (B-B) fitness model of growing networks.This mapping addresses the dynamical behavior of the fitness model within the framework of nonextensive statistics mechanics,which is characterized by a dimensionless nonextensivity parameter q.It is found that this new phenomenological parameter plays an important role in the evolution of networks:the underlying evolving networks may undergo a different phases depending on the q exponents,comparing to the original B-B fitness model,and the corresponding critical transition temperature T C is also identified.     

The Fractional Statistics of Generalized Haldane Wave Function in 4D Quantum Hall Effect

Recently, a generalization of Laughlin‘s wave function expressed in Haldane‘s spherical geometry is con-structed in 4D quantum Hall effect. In fact, it is a membrane wave function in CP3 space. In this article, we usenon-Abelian Berry phase to analyze the statistics of this membrane wave function. Our results show that the membranewave function obeys fractional statistics. It is the rare example to realize fractional statistics in higher-dimensional spacethan 2D. And, it will help to make clear the unresolved problems in 4D quantum Hall effect.     

Controllable dissipative tunneling in an external electric field

We have studied the problem of controllable dissipative tunneling in the system of tunnel-binding quantum dots (quantum molecules) and in the “AFM/STM cantilever tip-quantum dot” system, which was simulated by a double-well oscillator potential interacting with a heat-bath in an external electric field. We show that theoretical results qualitatively describe some experimental I–V curves for “the AFM/STM cantilever tip-zirconium quantum dot” system. These experimental curves were obtained in the Research Institute of Physics and Technologies at the State University of Nizhniy Novgorod.