Andre M. C. Souza

Constructing a statistical mechanics for Beck-Cohen superstatistics.

The basic aspects of both Boltzmann-Gibbs (BG) and nonextensive statistical mechanics can be seen through three different stages. First, the proposal of an entropic functional (S(BG)=-k Sigma(i)p(i)ln p(i) for the BG formalism) with the appropriate constraints (Sigma(i)p(i)=1 and Sigma(i)p(i)E(i)=U for the BG canonical ensemble). Second, through optimization, the equilibrium or stationary-state distribution (p(i)=e(-betaE(i))/Z(BG) with Z(BG)= Sigma(j)e(-betaE(j)) for BG). Third, the connection to thermodynamics (e.g., F(BG)=-(1/beta)ln Z(BG) and U(BG)=-(partial differential/partial differential beta)ln Z(BG)). Assuming temperature fluctuations, Beck and Cohen recently proposed a generalized Boltzmann factor B(E)= integral (infinity)(0)dbetaf(beta)e(-betaE). This corresponds to the second stage described above. In this paper, we solve the corresponding first stage, i.e., we present an entropic functional and its associated constraints which lead precisely to B(E). We illustrate with all six admissible examples given by Beck and Cohen.

Quantum-state transfer in staggered coupled-cavity arrays

We consider a coupled-cavity array, where each cavity interacts with an atom under the rotating-wave approximation. For a staggered pattern of intercavity couplings, a pair of field normal modes, each bilocalized at the two array ends, arises. A rich structure of dynamical regimes can hence be addressed, depending on which resonance condition is set between the atom and the field modes. We show that this can be harnessed to carry out high-fidelity quantum-state transfer (QST) of photonic, atomic, or polaritonic states. Moreover, by partitioning the array into coupled modules of shorter length, the QST time can be substantially shortened without significantly affecting the fidelity.

Localization properties of a tight-binding electronic model on the Apollonian network

An investigation on the properties of electronic states of a tight-binding Hamiltonian on the Apollonian network is presented. This structure, which is defined based on the Apollonian packing problem, has been explored both as a complex network, and as a substrate, on the top of which physical models can defined. The Schrodinger equation of the model, which includes only nearest neighbor interactions, is written in a matrix formulation. In the uniform case, the resulting Hamiltonian is proportional to the adjacency matrix of the Apollonian network. The characterization of the electronic eigenstates is based on the properties of the spectrum, which is characterized by a very large degeneracy. The

Thermal entanglement witness for materials with variable local spin lengths

2\pi /3

Enhancement of thermal entanglement in two-qubit XY models

rotation symmetry of the network and large number of equivalent sites are reflected in all eigenstates, which are classified according to their parity. Extended and localized states are identified by evaluating the participation rate. Results for other two non-uniform models on the Apollonian network are also presented. In one case, interaction is considered to be dependent of the node degree, while in the other one, random on-site energies are considered.

Quantum transport with coupled cavities on the Apollonian network

We show that the thermal entanglement in a spin system using only magnetic-susceptibility measurements is restricted to the insulator materials. We develop a generalization of the thermal entanglement witness that allows us to get information about the system entanglement with variable local spin lengths that can be used experimentally in conductor or insulator materials. As an application, we study thermal entanglement for the half-filled Hubbard model for linear, square, and cubic clusters. We note that it is the itinerancy of electrons that favors the entanglement. Our results suggest a weak dependence between entanglement and external spin freedom degrees.

Correlated electron systems on the Apollonian network

We analyse conditions leading to enhancement of thermal entanglement in two-qubit XY models. The effect of including cross-product terms, besides the standard XY exchange interactions, in the presence of an external magnetic field, is investigated. We show that entanglement can be yielded at elevated temperatures by tuning the orientation of the external magnetic field. The details of the intrinsic exchange interactions determine the optimal orientation.

Thermodynamic properties of samarium hexaboride

We study the dynamics of atomic and photonic excitations in the Jaynes-Cummings-Hubbard (JCH) model when each cavity occupies the nodes of an Apollonian network (AN). Such structure shows small-world and scale-free properties, and has been investigated within many physical models. By numerically diagonalizing the system Hamiltonian in the single-excitation subspace, we evaluate the time evolution of an initial state prepared as an even superposition of both atomic and photonic modes fully localized at a specific node. For the large hopping regime we provide a detailed description of the quantum transport properties of the AN and show that the complex interplay between the many cavity-cavity degrees of freedom induces both extended and localized states varying periodically. The excitation is most likely to be found in the initial node and its propagation strongly depends on the initial conditions. We also discuss the strong atom-cavity coupling regime, where atomic and photonic modes propagates identically, and the JCH regime, where the system is allowed to roam between atomic and photonic degrees of freedom, since the hopping parameter and the atom-cavity coupling strength are of the same order. In this regime, different cavities contribute either to the atomic or photonic component mostly, depending on the initial conditions.

GENERALIZING THE PLANCK DISTRIBUTION

Strongly correlated electrons on an Apollonian network are studied using the Hubbard model. Ground-state and thermodynamic properties, including specific heat, magnetic susceptibility, spin-spin correlation function, double occupancy, and one-electron transfer, are evaluated applying direct diagonalization and quantum Monte Carlo techniques. In the strong-coupling limit, the quantum anisotropic spin-1/2 Heisenberg model is used and the phase diagram is discussed using the renormalization group method. The results support an antiferromagnetic order with a metal-insulator transition for U/t=11.1 at temperature T=0 and a tendency toward a nonordered phase in the half-filled Hubbard model for any U/t. We also indicate that the spectral dimension must control the magnetic behavior on the Apollonian network.

Discrete time quantum walk on the Apollonian network

Summary form only given. The heavy fermion semiconductor samarium hexaboride is the first compound in which the phenomenon of intermediate valence has been seen directly by X-ray absorption, but the theory which explains all properties of this compound within a unified physical model remains elusive in spite of unceasing efforts of theoreticians and experimentalists. SmB/sub 6/ may be modeled as an indirect hybridization gap semiconductor, in which gap features are identified as spin exciton excitations, which are induced by residual anti-ferro magnetic interaction between the renormalized quasi-particles. In this work we consider the Falicov-Kimball model to study the thermodynamic properties of SmB/sub 6/. We study the temperature dependence of the specific heat, entropy, susceptibility, and of the correlation functions of the one-dimensional half-filled-band Falicov-Kimball model.