XXZ-like phase in the F-AF anisotropic Heisenberg chain

By means of the Density Matrix Renormalization Group technique, we have studied the region where XXZ-like behavior is most likely to emerge within the phase diagram of the F-AF anisotropic extended (J-J’) Heisenberg chain. We have analyzed, in great detail, the equal-time two-spin correlation functions, both in- and out-of- plane, as functions of the distance (and momentum). Then, we have extracted, through an accurate fitting procedure, the exponents of the asymptotic power-law decay of the spatial correlations. We have used the exact solution of XXZ model (J’ = 0) to benchmark our results, which clearly show the expected agreement. A critical value of J’ has been found where the relevant power-law decay exponent is independent of the in-plane nearest-neighbor coupling.     

Particle-particle correlation and fluctuations in non-equilibrium Fermi/Bose gases

A theory of fluctuations and correlations in non-equilibrium Fermi and Bose gases is developed. A specific quantum correlation is predicted in non-equilibrium collisional quasi-classical gases, created by collisions between particles. The expressions for correlation sources entering the equation for an equal-time two-particle correlation function are obtained and analyzed. The expressions are valid for arbitrary particle-particle interaction potentials. The possibility of display of the quantum correlation in the macroscopic characteristics of fluctuation phenomena in non-equilibrium gases (e.g., current fluctuations in semiconductors) is discussed. A comparison with correlations in a Lorentz gas is made.     

Density-Density Propagator of the Luttinger Model of Spin-Half Fermions after an Interaction Quench

Motivated by recent research achievement of quantum interacting systems in non-equilibrium, we consider a Luttinger model with a suddenly switched-on interaction proposed by Cazalilla [M.A. Cazalilla, Phys. Rev. Lett. 97 (2006) 156403]. In order to compare with real systems, we extend Cazalilla's scenario to the spinful system. To find the influence of initial states on the time evolution of some non-equilibrium systems, we mainly focus on the density-density propagator. By comparison and analysis, we discover the different behavior of this non-equilibrium system. Further, it is found that the propagator saves strong memory of initial state, and the effects of right-left interaction cancel out in total density-density propagator.     

Density-Density Propagator of the Luttinger Model of Spin-Half Fermions after an Interaction Quench

Motivated by recent research achievement of quantum interacting systems in non-equilibrium, we consider a Luttinger model with a suddenly switched-on interaction proposed by Cazalilla [M.A. Cazalilla, Phys. Rev. Lett. 97 (2006) 156403]. In order to compare with real systems, we extend Cazalilla's scenario to the spinful system. To find the influence of initial states on the time evolution of some non-equilibrium systems, we mainly focus on the density-density propagator. By comparison and analysis, we discover the different behavior of this non-equilibrium system. Further, it is found that the propagator saves strong memory of initial state, and the effects of right-left interaction cancel out in total density-density propagator.     

A lattice gas coupled to two thermal reservoirs: Monte Carlo and field theoretic studies

We investigate the collective behavior of an Ising lattice gas, driven to non-equilibrium steady states by being coupled to two thermal baths. Monte Carlo methods are applied to a two-dimensional system in which one of the baths is fixed at infinite temperature. Both generic long range correlations in the disordered state and critical properties near the second order transition are measured. Anisotropic scaling, a key feature near criticality, is used to extract and some critical exponents. On the theoretical front, a continuum theory, in the spirit of Landau-Ginzburg, is presented. Being a renormalizable theory, its predictions can be computed by standard methods of -expansions and found to be consistent with simulation data. In particular, the critical behavior of this system belongs to a universality class which is quite different from the uniformly driven Ising model. Received 4 October 2000     

The ballast resistor; An electro-thermal instability in a conducting wire II; Fluctuations around homogeneous stationary states

The correlation function of temperature fluctuations around homogeneous stationary states of the ballast resistor is evaluated by extending the theory of thermal fluctuations around equilibrium states to non-equilibrium situations. It is found that equal-time temperature fluctuations become correlated over large distances if one approaches the critical point. At the “critical point” of the ballast resistor the correlation length and the amplitude of the temperature fluctuations diverge. Furthermore the theory predicts a critical slowing down for the time-dependent temperature fluctuation correlation function. The electric noise of the system is also analyzed.     

Effect of Correlations on the Exponents for the Power-Law Distributions in Self-Organized Criticality

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is mapped to a first-return random-walk process in a one-dimensional lattice. In order to understand the reason of variant exponents for the power-law distributions in different self-organized critical systems, we introduce the correlations among evolution steps. Power-law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. It is found that the longer the correlation length, the smaller values of the exponents for the power-law distributions.     

Effect of Correlations on the Exponents for the Power-Law Distributions in Self-Organized Criticality

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is mapped to a first-return random-walk process in a one-dimensional lattice. In order to understand the reason of variant exponents for the power-law distributions in different self-organized critical systems, we introduce the correlations among evolution steps. Power-law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. It is found that the longer the correlation length, the smaller values of the exponents for the power-law distributions.     

Magnetic response of nonmagnetic impurities in cuprates

A theory of the local magnetic response of a nonmagnetic impurity in a doped antiferromagnet, as relevant to the normal-state in cuprates, is presented. It is based on the assumption of the overdamped collective mode in the bulk system and on the evidence that equal-time spin correlations are only weakly renormalized in the vicinity of the impurity. The theory relates the Kondo-like behavior of the local susceptibility to the anomalous temperature dependence of the bulk magnetic susceptibility.     

Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators

A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal entanglement is found in the high-temperature limit. In the weak coupling limit the system converges to an entangled non-equilibrium steady state. A critical temperature for the appearance of quantum correlations is found.     

Exact Scaling in the Expansion-Modification System

This work is devoted to the study of the scaling, and the consequent power-law behavior, of the correlation function in a mutation-replication model known as the expansion-modification system. The latter is a biology inspired random substitution model for the genome evolution, which is defined on a binary alphabet and depends on a parameter interpreted as a mutation probability. We prove that the time-evolution of this system is such that any initial measure converges towards a unique stationary one exhibiting decay of correlations not slower than a power-law. We then prove, for a significant range of mutation probabilities, that the decay of correlations indeed follows a power-law with scaling exponent smoothly depending on the mutation probability. Finally we put forward an argument which allows us to give a closed expression for the corresponding scaling exponent for all the values of the mutation probability. Such a scaling exponent turns out to be a piecewise smooth function of the parameter.     

Auto- and cross-correlations in the spinful topological Kondo model

The correlations in charge transport in multiple Majorana fermions systems contain much richer physics and carry more information than the conventional transport coefficients. We calculate the auto- and cross-correlations in the spinful topological Kondo model (SKTM) and point out the frequencies dependencies of the correlations that may serve as a proof of the existence of the Majorana fermions in our system, particularly the change of the cross-correlation from positive to negative at higher frequency.     

Correlated flares in models of a magnetized “canopy”

A model of the Lu-Hamilton kind is applied to the study of critical behavior of the magnetized solar atmosphere. The main novelty is that its driving is done via sources undergoing a diffusion. This mimics the effect of a virtual turbulent substrate forcing the system. The system exhibits power-law statistics not only in the size of the flares, but also in the distribution of the waiting times.     

Energy fluctuations in vibrated and driven granular gases

We investigate the behavior of energy fluctuations in several models of granular gases maintained in a non-equilibrium steady state. In the case of a gas heated from a boundary, the inhomogeneities of the system play a predominant role. Interpreting the total kinetic energy as a sum of independent but not identically distributed random variables, it is possible to compute the probability density function (pdf) of the total energy. Neglecting correlations and using the analytical expression for the inhomogeneous temperature profile obtained from the granular hydrodynamic equations, we recover results that have previously been observed numerically and that had been attributed to the presence of correlations. In order to separate the effects of spatial inhomogeneities from those ascribable to velocity correlations, we have also considered two models of homogeneously thermostated gases: in this framework it is possible to reveal the presence of non-trivial effects due to velocity correlations between particles. Such correlations stem from the inelasticity of collisions. Moreover, the observation that the pdf of the total energy tends to a Gaussian in the large system limit suggests that they are also due to the finite size of the system.     

A correlation measure in non-equilibrium phase transitions

Bit-number cumulants of a probability distribution give ordered measures of correlations between subsystems. Especially the second one, the bit-number variance (which in equilibrium is connected with specific heat) is discussed with respect to its critical behaviour for special non-equilibrium phase transitions in chemical reaction systems. Also in non-equilibrium the critical behaviour indicates critical correlations.     

RELATIVISTIC EQUAL-TIME EQUATION OF BOSE-FERMI SYSTEM

The relativistic equal-time equation of Bose-Fermi system and its conjugate equation are found.The hermiticity of equal-time potential and equal-time scattering amplitude is discussed. The result shows that if the Feynman Green function is replaced by the retarded Green function, the hermiticity of equal-time potential and equal-time-scattering am-plitude will be confirmed.     

Non-equilibrium scaling properties of a double quantum dot system: Comparison between perturbative renormalization group and flow equation approach

Since the experimental realization of Kondo physics in quantum dots, its far-from-equilibrium properties have generated considerable theoretical interest. This is due to the interesting interplay of non-equilibrium physics and correlation effects in this model, which has now been analyzed using several new theoretical methods that generalize renormalization techniques to non-equilibrium situations. While very good agreement between these methods has been found for the spin-1/2 Kondo model, it is desirable to have a better understanding of their applicability for more complicated impurity models. In this paper the differences and commons between two such approaches, namely the flow equation method out of equilibrium and the frequency-dependent poor man's scaling approach are presented for the non-equilibrium double quantum dot system. This will turn out to be a particularly suitable testing ground while being experimentally interesting in its own right. An outlook is given on the quantum critical behavior of the double quantum dot system and its accessibility with the two methods.     

Searching for the QCD critical point in AA collisions at CERN SPS

We investigate the transverse momentum correlations of pairs of opposite charged pions near their production threshold. Through intermittency analysis, we search for power-law dependence on observation scale, as dictated by critical QCD. We analyze the data on the most central collisions in four A systems (A = p, C, Si, Pb) at maximum SPS energy. We find a significant effect for the SiSi system approaching in size the critical QCD predictions as measured by the intermittency index ? ₂. Absence of this effect in the (?? ^?, ?? ^?) sector of the SiSi system gives further support that the observed behavior in the isoscalar mode is of critical origin.     

Critical behavior of a three-state Potts model on a Voronoi lattice

We use the single-histogram technique to study the critical behavior of the three-state Potts model on a (random) Voronoi-Delaunay lattice with size ranging from 250 to 8 000 sites. We consider the effect of an exponential decay of the interactions with the distance, , with a>0, and observe that this system seems to have critical exponents and which are different from the respective exponents of the three-state Potts model on a regular square lattice. However, the ratio remains essentially the same. We find numerical evidences (although not conclusive, due to the small range of system size) that the specific heat on this random system behaves as a power-law for a=0 and as a logarithmic divergence for a=0.5 and a=1.0 Received 5 April 2000