Macroscopic Determinism in Noninteracting Systems Using Large Deviation Theory

We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the particle microstates is then examined in the large-n limit. Using the theory of large deviations, we show that if the initial macroscopic average is constrained to be near a given value, y, then the macroscopic average at time t converges in probability as n to a value _t(y) given explicitly in terms of a canonical expectation. Some general features of the graph of _t(y) versus t are examined, particularly in regard to continuity, symmetry, and convergence.     

The Dilute Potts Model on Random Surfaces

We present a new solution of the asymmetric two-matrix model in the large-N limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with the topology of the sphere (resp. the disk) for closed (resp. open) surfaces; we elaborate on the resulting phase diagram. The method can be equally well applied to a more general (Q+1)-matrix model which represents the dilute Potts model on random dynamical lattices. We discuss in particular duality of boundary conditions for open random surfaces.     

Variational approach to spin fluctuations in the Hubbard model

We study a one parameter variational wave function to improve the spin density wave ground state of the Hubbard model by inclusion of quantum spin fluctuations. Using a perturbative approach and novel lattice summation techniques we present analytical as well as numerical results for the correlation energies and the staggered magnetizations in one and two dimensions. We find ground state energies which are satisfyingly close to known exact results and are significantly lower than those of existing Gutzwiller and numerical treatments.     

Dynamical linked cluster expansions with applications to disordered systems

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. We discuss physical applications to systems with annealed and quenched disorder. Examples are the bond-diluted Ising model and the Sherrington-Kirkpatrick spin glass. We derive the rules and identify the full set of graphs that contribute to the series in the quenched case. This way it becomes possible to avoid the vague extrapolation from positive integer n to n = 0, that usually goes along with an application of the replica trick. Received 13 December 2001 Published online 25 June 2002     

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t = - 0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder. Received 23 January 2002     

Generalized algebraic transformations and exactly solvable classical-quantum models

The rigorous approach aimed at providing exact analytical results for hybrid classical-quantum models is elaborated on the grounds of generalized algebraic mapping transformations. This conceptually simple method allows one to obtain novel interesting exact results for the hybrid classical-quantum models, which may for instance describe interacting many-particle systems composed of the classical Ising spins and quantum Heisenberg spins, the localized Ising spins and delocalized electrons, or many other hybrid systems of a mixed classical-quantum nature.     

A nonextensive approach to the dynamics of financial observables

We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy . More precisely, we present stochastic dynamical mechanisms which mimic probability density functions empirically observed. These mechanisms provide possible interpretations for the emergence of the entropic indices q in the time evolution of the corresponding observables. In addition to this, through multi-fractal analysis of return time series, we verify that the dual relation q_stat+q_sens=2 is numerically satisfied, q_stat and q_sens being associated to the probability density function and to the sensitivity to initial conditions respectively. This type of simple relation, whose understanding remains ellusive, has been empirically verified in various other systems.     

Phase diagram of frustrated mixed-spin ladders in the strong-coupling limit

We study the ground-state properties of frustrated Heisenberg ferrimagnetic ladders with antiferromagnetic exchange interactions and two types of alternating sublattice spins. In the limit of strong rung couplings, we show that the mixed spin-1/2 and spin-1 ladders can be systematically mapped onto a spin-1/2 Heisenberg model with additional next-nearest-neighbor exchanges. The system is either in a ferrimagnetic state or in a critical spin-liquid state depending on the competition between the spin exchanges along the legs and the diagonal exchanges.     

Decentralized delayed-feedback control of an optimal velocity traffic model

The jam phenomenon in traffic flow wastes not only considerable traffic-transportation time but also great amounts of fuel due to many accelerate-decelerate actions. From traffic-economic and traffic-pollution viewpoints, the suppression of traffic jam is an important issue we have to solve. The present paper shows that -norm, which has been used in the field of control theory, can reveal the traffic jam phenomenon in an optimal velocity traffic model under an open boundary condition. Furthermore, we suppress the traffic jam in the model by the decentralized delayed-feedback control method. Some numerical simulations are shown to verify our theoretical results. Received 27 October 1999