Table of contents

The evolution of quantum entanglement of a pair of non-interacting qubits is studied for the case where one of them is non-dissipatively but dephasingly coupled to the environment. The reduced non-Markovian dynamics of the qubits is exact for an arbitrary strength of coupling to the environment and the arbitrary frequency spectrum of environment fluctuations. While for the subohmic and ohmic environments the entanglement diminishes, for the superohmic zero-temperature environment it survives for a long time.

The unlimited energy growth (Fermi acceleration) of a classical particle moving in a billiard with a parameter-dependent boundary oscillating in time is numerically studied. The shape of the boundary is controlled by a parameter and the billiard can change from a focusing one to a billiard with dispersing pieces of the boundary. The complete and simplified versions of the model are considered in the investigation of the conjecture that Fermi acceleration will appear in the time-dependent case when the dynamics is chaotic for the static boundary. Although this conjecture holds for the simplified version, we have not found evidence of Fermi acceleration for the complete model with a breathing boundary. When the breathing symmetry is broken, Fermi acceleration appears in the complete model.

The Green function (GF) equation of motion technique for solving the effective two-band Hubbard model of high-T_c superconductivity in cuprates (Plakida et al 1995 Phys. Rev. B 51 16599, Plakida et al 2003 JETP97 331) rests on the Hubbard operator (HO) algebra. We show that, if we take into account the invariance to translations and spin reversal, the HO algebra results in invariance properties of several specific correlation functions. The use of these properties allows rigorous derivation and simplification of the expressions of the frequency matrix (FM) and of the generalized mean-field approximation (GMFA) Green functions (GFs) of the model. For the normal singlet-hopping and anomalous exchange pairing correlation functions which enter the FM and GMFA-GFs, an approximation procedure based on the identification and elimination of exponentially small quantities is described. It secures the reduction of the correlation order to GMFA-GF expressions.

We introduce a lattice gas model for the merging of two single-lane automobile highways. The merging rules for traffic on the two lanes are deterministic, but the inflow on both lanes is stochastic. Analysing the stationary distribution of this stochastic cellular automaton, we find a discontinuous phase transition from a free-flow phase which depends on the initial state of the road to a jammed phase where all memory of the initial state is lost. Inside the jammed phase we identify dynamical phase transitions in the approach to stationarity. Each dynamical phase is characterized by a fixed number of relaxation cycles which is decreasing as one moves deeper into the jammed phase. In each cycle step, the number of 'desperate' drivers who force their way onto the main road when they reach the end of the on-ramp increases until stationarity.

The thermostatistic problems of a q-deformed ideal Fermi gas in any dimensional space and with a general energy spectrum are studied, based on the q-deformed Fermi–Dirac distribution. The effects of the deformation parameter q on the properties of the system are revealed. It is shown that q-deformation results in some novel characteristics different from those of an ordinary system. Besides, it is found that the effects of the q-deformation on the properties of the Fermi systems are very different for different dimensional spaces and different energy spectrums.

We provide a combinatorial description of exclusion statistics in terms of minimal difference p partitions. We compute the probability distribution of the number of parts in a random minimal p partition. It is shown that the bosonic point p = 0 is a repulsive fixed point for which the limiting distribution has a Gumbel form. For all positive p, the distribution is shown to be Gaussian.

In many social, economical and biological systems, the evolution of the states of interacting units cannot be simply treated with a physical law in the realm of traditional statistical mechanics. We propose a simple binary-state model to discuss the effect of the inflexible units on the dynamical behavior of a social system, in which a unit may have a chance to keep its state with a probability 1 − q even though its state is different from those of the majority of its interacting neighbors. It is found that the effect of these inflexible units can lead to a nontrivial phase diagram.

The Abelian sandpile model (ASM) is a paradigm of self-organized criticality (SOC) which is related to c = −2 conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the first corrections to such fields, in a field theoretical approach, when the lattice parameter is non-vanishing, and consider them in the presence of a boundary.

We calculate analytically a statistical average of trajectories of an approximate expectation-maximization (EM) algorithm with generalized belief propagation (GBP) and a Gaussian graphical model for the estimation of hyperparameters from observable data in probabilistic image processing. A statistical average with respect to observed data corresponds to a configuration average for the random-field Ising model in spin glass theory. In the present paper, hyperparameters which correspond to interactions and external fields of spin systems are estimated by an approximate EM algorithm. A practical algorithm is described for gray-level image restoration based on a Gaussian graphical model and GBP. The GBP approach corresponds to the cluster variation method in statistical mechanics. Our main result in the present paper is to obtain the statistical average of the trajectory in the approximate EM algorithm by using loopy belief propagation and GBP with respect to degraded images generated from a probability density function with true values of hyperparameters. The statistical average of the trajectory can be expressed in terms of recursion formulas derived from some analytical calculations.

We obtain exact moving and stationary, spatially periodic and localized solutions of a generalized discrete nonlinear Schrödinger equation. More specifically, we find two different moving periodic wave solutions and a localized moving pulse solution. We also address the problem of finding exact stationary solutions and, for a particular case of the model when stationary solutions can be expressed through the Jacobi elliptic functions, we present a two-point map from which all possible stationary solutions can be found. Numerically we demonstrate the generic stability of the stationary pulse solutions and also the robustness of moving pulses in long-term dynamics.

We present the results of our studies of various scattering properties of topological solitons on obstructions in the form of holes and barriers in 1+1 dimensions. Our results are based on two models involving a φ⁴ potential. The obstructions are characterized by a potential parameter, λ, which has a nonzero value in a certain region of space and zero elsewhere. In the first model the potential parameter is included in the potential and in the second model the potential parameter is included in the metric. Our results are based on numerical simulations and analytical considerations.

The aim of this paper is to provide a method for explicit computation of the Bures metric over the space of N-level quantum system, based on the coset parametrization of density matrices.

We show how to construct discrete-time quantum walks on directed, Eulerian graphs. These graphs have tails on which the particle making the walk propagates freely, and this makes it possible to analyze the walks in terms of scattering theory. The probability of entering a graph from one tail and leaving from another can be found from the scattering matrix of the graph. We show how the scattering matrix of a graph that is an automorphic image of the original is related to the scattering matrix of the original graph, and we show how the scattering matrix of the reverse graph is related to that of the original graph. Modifications of graphs and the effects of these modifications are then considered. In particular we show how the scattering matrix of a graph is changed if we remove two tails and replace them with an edge or cut an edge and add two tails. This allows us to combine graphs, that is if we connect two graphs we can construct the scattering matrix of the combined graph from those of its parts. Finally, using these techniques, we show how two graphs can be compared by constructing a larger graph in which the two original graphs are in parallel, and performing a quantum walk on the larger graph. This is a kind of quantum walk interferometry.

Quantum discord, as defined by Olliver and Zurek (2002 Phys. Rev. Lett.88 017901) as the difference of two natural quantum extensions of the classical mutual information, plays an interesting role in characterizing quantumness of correlations. Inspired by this idea, we will study quantumness of bipartite states arising from different quantum analogs of the classical conditional entropy. Our approach is intrinsic, in contrast to the Olliver–Zurek method that involves extrinsic local measurements. For this purpose, we introduce two alternative variants of quantum conditional entropies via conditional density operators, which in turn are intuitive quantum extensions of equivalent classical expressions for the conditional probability. The significance of these quantum conditional entropies in characterizing quantumness of bipartite states is illustrated through several examples.

In two-dimensional space, where the intermediate statistics between bosons and fermions are possible, we study a localization of some stationary coherent states on classical orbits in the potentials V(r) = −γ_ν/r^ν, γ_ν > 0 for the total energy E = 0. It is shown that excellent quantum-classical correspondence can be reached for two large classes of classical orbits with ν < −2 (open curves) and with ν > 2 (closed curves). To that purpose, it was necessary to introduce fractional angular momenta for some values of ν. They are a consequence of imposing special boundary conditions on the used wavefunctions.

We study the dynamic evolution of the entanglement in a spin channel with an XY-type interaction initially in an entangled state. We find that the phenomenon of entanglement sudden death (ESD) appears in the evolution of entanglement for some initial states. We calculate the entanglement and obtain the parameter regions of disentanglement for the chains with several numbers of sites. The influence of the presence of one common spin environment is also discussed.

The time-dependent Dirac–Maxwell's equations in the presence of electric and magnetic sources are reformulated in a chiral medium, and the solutions for the classical problem are obtained in a unique, simple and consistent manner. The quaternion reformulation of generalized electromagnetic fields in the chiral medium has also been discussed in a compact, simple and consistent manner.

Two different conformal field theories can be joined together along a defect line. We study such defects for the case where the conformal field theories on either side are single free bosons compactified on a circle. We concentrate on topological defects for which the left- and right-moving Virasoro algebras are separately preserved, but not necessarily any additional symmetries. For the case where both radii are rational multiples of the self-dual radius we classify these topological defects. We also show that the isomorphism between two T-dual free boson conformal field theories can be described by the action of a topological defect, and hence that T-duality can be understood as a special type of order–disorder duality.