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1.
Miriam Lemanska 《Physica A》2008,387(12):2719-2735
A dynamical system of infinite volume and of infinite number of identical interacting particles occupying energy levels has been constructed as the limit of an infinite sequence of finite, equivalent systems of increasing size and particle number. Systems both in equilibrium and in non-equilibrium state (designated S=limSk, , respectively, k=1,2,…) were investigated. The main results are:(i) The values in the T-limit (thermodynamic limit) of the physical quantities characterizing these systems are determined.(ii) The time evolution process both in and in systems is governed by the non-linear rate equations with common initial conditions pi(t0), where pi(t)=ni(t)/N are the occupation probabilities at time t. The time evolution process in the and systems is the same. The asymptotic approach to the equilibrium state is proved.(iii) For the case of the equilibrium state, the Boltzmann probability distribution pi is given by the equation −lnpi+a+eib=0 common to Sk and S systems with the same value of a and b. The term a=β−1ae, where ae is the free energy per particle, and .(iv) The conditions for the equivalence of the systems being in equilibrium and also of the ones in non-equilibrium are stated.  相似文献   

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Robert K. Niven  Hiroki Suyari 《Physica A》2009,388(19):4045-4060
An axiomatic definition is given for the q-gamma function of Tsallis (non-extensive) statistical physics, the continuous analogue of the q-factorial of Suyari [H. Suyari, Physica A 368 (1) (2006) 63], and the q-analogue of the gamma function of Euler and Gauss. A working definition in closed form, based on the Hurwitz and Riemann zeta functions (including their analytic continuations), is shown to satisfy this definition. Several relations involving the q-gamma and other functions are obtained. The (q,q)-polygamma functions , defined by successive derivatives of , where lnqa=(1−q)−1(a1−q−1),a>0 is the q-logarithmic function, are also reported. The new functions are used to calculate the inferred probabilities and multipliers for Tsallis systems with finite numbers of particles N?.  相似文献   

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We construct the explicit formulation of the probabilistically perfect quantum cloning machine that perfectly duplicates the input states chosen from the special set consisting of the linearly independent and nonorthogonal quantum states with 〈φiφj〉 = r ∈ (0, 1)(i ≠ j). The success probabilities of cloning the input states are equal and maximal. As two examples, we present the explicit transformations of the optimal 1 → 2 probabilistically perfect quantum cloning of the real states in 2 and 3 dimensions. The success probabilities of each of two cloning machines are equal and maximal.  相似文献   

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Phase-singular solid solutions of La0.6Sr0.4Mn1−yZnyO3−δ(0≤y≤0.3) [LSMZO] perovskite of rhombohedral symmetry (space group: ) with y up to 30 at.% could be synthesized notwithstanding the differences in ionic radii of MnV I3+ (i.r.=0.645 Å) and ZnV I2+ (i.r.=0.74 Å). The LSMZO≤02 compositions are ferromagnetic metallic (FMM) at room temperature whereas LSMZO-02-08 are ferromagnetic insulators (FMI) and LSMZO>08 are paramagnetic insulators (PMI). Total obliteration of the FM transition is unique to Zn-doping at leading to PMI even at low temperatures, measured up to 8 K (presently). The FM to PM transition (Tc) and the peak (Tp) in resistivity-temperature curves decreases with the Zn-content. The charge-transport in p-type LSMZO is predictable by variable range hopping (VRH), which changes to nearest-neighbor hopping of small polarons (NNHP) at T>Tp. Non-stoichiometry (0.005≤δ≤0.21) evaluated chemically from redox titrations indicated the prevalence of excess oxygen vacancy rather than charge compensatively predictable values which, in turn, indicates the diminishing Mn4+ content in LSMZO. The ’s act as electron donors in p-LSMZO and this increases the resistivity (ρRT) associated with the shift in Tc to low temperatures. Increased ρRT on annealing in low is a clear evidence on the role of in LSMZO.  相似文献   

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The low-temperature magnetic ordering of the dimorphic DySi compound has been studied at 1.5 K by neutron diffraction on two polycrystalline samples. The samples comprise various amounts of the two orthorhombic modifications: CrB-type (Cmcm Nr. 63, all atoms at 4c site: (0, y, )) and FeB-type (Pnma Nr. 62, all atoms at 4c site: (x, , z)), both order antiferromagnetically (TN≈38 K). The CrB-type phase orders with a uniaxial structure with the wave vector q1=(0, 0, ) requiring a doubling of the c-axis. The Dy moments point along the linear chain with the shortest distance c. At 1.5 K, the ordered moment value is 8.57(1) μB/Dy atom.Two symmetry independent wave vectors describe the 1.5 K magnetic ordering of the FeB-type phase: q2=(0, , ) and q3=(0, 0.484(1), 0.0892(1)), coexisting in form of domains. In both structures the magnetic moments are confined to the (0 0 1) plane at an angle of 2(2)° and 22(3)° from the shortest axis b, respectively. Both structures correspond to sine wave modulations. The amplitude of the q2 wave is mo=7.5(1) μB/Dy atom and that of q3 8.2(1) μB/Dy atom. The wave vector q2 when referring to the (a, 2b, c) cell and the wave vector q=(0, 0, ) corresponds to a transversal modulation, which by a proper origin choice can be also described as an antiphase domain structure with two amplitudes. The moments point to the b-axis and are stacked in the sequence (+mo/2, −mo/2, −mo, −mo/2, +mo/2, +mo, …) along the c-direction, while tb acts as an antitranslation. For the q3 phase, the local moment value depends on the atom position in the wave. We also discuss the case where q3 and q2 act simultaneously in physical space.  相似文献   

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Starting with the relative entropy based on a previously proposed entropy function , we find the corresponding Fisher's information measure. After function redefinition we then maximize the Fisher information measure with respect to the new function and obtain a differential operator that reduces to a space coordinate second derivative in the q→1 limit. We then propose a simple differential equation for anomalous diffusion and show that its solutions are a generalization of the functions in the Barenblatt-Pattle solution. We find that the mean squared displacement, up to a q-dependent constant, has a time dependence according to 〈x2〉∼K1/qt1/q, where the parameter q takes values (superdiffusion) and (subdiffusion), ∀n?1.  相似文献   

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It is shown that the bound l-state solutions of the Klein-Gordon equation for the general scalar and vector Hulthén potentials obtained by Qiang et al. are valid only for q?1 and . We clarify the problem and give the correct solutions when 0<q<1 or q<0. In each case, we derive a transcendental quantization condition for the s-state energy levels.  相似文献   

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Possible short and semi-short representations for and superconformal symmetry in four dimensions are discussed. For the well known short supermultiplets whose lowest dimension conformal primary operators correspond to -BPS or -BPS states and are scalar fields belonging to the SU(4) R-symmetry representations [0,p,0] and [q,p,q] and having scale dimension Δ=p and Δ=2q+p, respectively, are recovered. The representation content of semi-short multiplets, which arise at the unitarity threshold for long multiplets, is discussed. It is shown how, at the unitarity threshold, a long multiplet can be decomposed into four semi-short multiplets. If the conformal primary state is spinless one of these becomes a short multiplet. For a -BPS multiplet need not have a protected dimension unless the primary state belongs to a [1,p,1] representation.  相似文献   

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We investigate the detailed dynamics of multi-dimensional Hamiltonian systems by studying the evolution of volume elements formed by unit deviation vectors about their orbits. The behavior of these volumes is strongly influenced by the regular or chaotic nature of the motion, the number of deviation vectors, their linear (in)dependence and the spectrum of Lyapunov exponents. The different time evolution of these volumes can be used to identify rapidly and efficiently the nature of the dynamics, leading to the introduction of quantities that clearly distinguish between chaotic behavior and quasiperiodic motion on N-dimensional tori. More specifically we introduce the Generalized Alignment Index of order k () as the volume of a generalized parallelepiped, whose edges are k initially linearly independent unit deviation vectors with respect to the orbit studied whose magnitude is normalized to unity at every time step. We show analytically and verify numerically on particular examples of N-degree-of-freedom Hamiltonian systems that, for chaotic orbits, tends exponentially to zero with exponents that involve the values of several Lyapunov exponents. In the case of regular orbits, fluctuates around non-zero values for 2≤kN and goes to zero for N<k≤2N following power laws that depend on the dimension of the torus and the number m of deviation vectors initially tangent to the torus: ∝t−2(kN)+m if 0≤m<kN, and ∝t−(kN) if mkN. The is a generalization of the Smaller Alignment Index (SALI) (). However, provides significantly more detailed information on the local dynamics, allows for a faster and clearer distinction between order and chaos than SALI and works even in cases where the SALI method is inconclusive.  相似文献   

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Sungmin Lee  Yup Kim 《Physica A》2008,387(12):3033-3038
Dynamical scalings for the end-to-end distance Ree and the number of distinct visited nodes Nv of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈Ree〉 shows the dynamical scaling behavior , where is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, in the limit t satisfies the relation , where d is the diameter of network with for γ≥3 or for γ<3. Based on the scaling relation 〈Ree〉, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.  相似文献   

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We present a simple two-dimensional model of a px + ipy superfluid in which the mass flow that gives rise to the intrinsic angular momentum is easily calculated by numerical diagonalization of the Bogoliubov-de Gennes operator. We find that, at zero temperature and for constant director l, the mass flow closely follows the Ishikawa-Mermin-Muzikar formula .  相似文献   

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