A quantum-group-like structure on noncommutative 2-tori

In this paper we show that in the case of noncommutative two-tori one gets in a natural way simple structures which have analogous formal properties as Hopf algebra structures but with a deformed multiplication on the tensor product

On the Thermodynamic Limit in Random Resistors Networks

We study a random resistors network model on a euclidean geometry \bt{Z}^d. We formulate the model in terms of a variational principle and show that, under appropriate boundary conditions, the thermodynamic limit of the dissipation per unit volume is finite almost surely and in the mean. Moreover, we show that for a particular thermodynamic limit the result is also independent of the boundary conditions.Comment: 14 pages, LaTeX IOP journal preprint style file `ioplppt.sty', revised version to appear in Journal of Physics

Density Wave -Supersolid and Mott Insulator-Superfluid transition in presence of an artificial gauge field : a strong coupling perturbation approach

We study the effect of an artificial gauge field on the zero temperature phase diagram of extended Bose Hubbard model, that describes ultra cold atoms in optical lattices with long range interaction using strong coupling perturbation theory . We determine analytically the effect of the artificial gauge field on the density wave - supersolid (DW-SS) and the the Mott insulator-superfluid (MI -SF) transition boundary . The momentum distribution at these two transition boundaries is also calculated in this approach. It is shown that such momentum distribution which can be observed in time of flight measurement, reveals the symmetry of the gauge potential through the formation of magnetic Brillouin zone and clearly distinguishes between the DW-SS and MI-SF boundary. We also point out that in symmetric gauge the momentum distribution structure at these transition boundaries bears distinctive signatures of vortices in supersolid and superfluid phases.Comment: 18 latexed two column pages including appendix, 9 .eps figures Figure positioning readjusted and one reference adde

Hofstadter butterfly for a finite correlated system

We investigate a finite two-dimensional system in the presence of external magnetic field. We discuss how the energy spectrum depends on the system size, boundary conditions and Coulomb repulsion. On one hand, using these results we present the field dependence of the transport properties of a nanosystem. In particular, we demonstrate that these properties depend on whether the system consists of even or odd number of sites. On the other hand, on the basis of exact results obtained for a finite system we investigate whether the Hofstadter butterfly is robust against strong electronic correlations. We show that for sufficiently strong Coulomb repulsion the Hubbard gap decreases when the magnetic field increases.Comment: 7 pages, 5 figures, revte

Physical nature of critical wave functions in Fibonacci systems

We report on a new class of critical states in the energy spectrum of general Fibonacci systems. By introducing a transfer matrix renormalization technique, we prove that the charge distribution of these states spreads over the whole system, showing transport properties characteristic of electronic extended states. Our analytical method is a first step to find out the link between the spatial structure of these critical wave functions and the quasiperiodic order of the underlying lattice.Comment: REVTEX 3.0, 11 pages, 2 figures available upon request. To appear in Phys. Rev. Let

Statistics of resonances and of delay times in quasiperiodic Schr"odinger equations

We study the statistical distributions of the resonance widths ${\cal P} (\Gamma)$, and of delay times ${\cal P} (\tau)$ in one dimensional quasi-periodic tight-binding systems with one open channel. Both quantities are found to decay algebraically as $\Gamma^{-\alpha}$, and $\tau^{-\gamma}$ on small and large scales respectively. The exponents $\alpha$, and $\gamma$ are related to the fractal dimension $D_0^E$ of the spectrum of the closed system as $\alpha=1+D_0^E$ and $\gamma=2-D_0^E$. Our results are verified for the Harper model at the metal-insulator transition and for Fibonacci lattices.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Coherent States of the SU(N) groups

Coherent states $(CS)$ of the $SU(N)$ groups are constructed explicitly and their properties are investigated. They represent a nontrivial generalization of the spining $CS$ of the $SU(2)$ group. The $CS$ are parametrized by the points of the coset space, which is, in that particular case, the projective space $CP^{N-1}$ and plays the role of the phase space of a corresponding classical mechanics. The $CS$ possess of a minimum uncertainty, they minimize an invariant dispersion of the quadratic Casimir operator. The classical limit is ivestigated in terms of symbols of operators. The role of the Planck constant playes $h=P^{-1}$, where $P$ is the signature of the representation. The classical limit of the so called star commutator generates the Poisson bracket in the $CP^{N-1}$ phase space. The logarithm of the modulus of the $CS$ overlapping, being interpreted as a symmetric in the space, gives the Fubini-Study metric in $CP^{N-1}$. The $CS$ constructed are useful for the quasi-classical analysis of the quantum equations of the $SU(N)$ gauge symmetric theories.Comment: 19pg, IFUSP/P-974 March/199

Spin-charge gauge approach to metal-insulator crossover and transport properties in High-Tc_c cuprates

The spin-charge gauge approach to consider the metal-insulator crossover (MIC) and other anomalous transport properties in High-T$_c$ cuprates is briefly reviewed. A U(1) field gauging the global charge symmetry and an SU(2) field gauging the global spin-rotational symmetry are introduced to study the two-dimensional $t-J$ model in the limit $t\gg J$. The MIC as a clue to the understanding of the ``pseudogap'' (PG) phase, is attributed to the competition between the short-range antiferromagnetic order and dissipative motion of charge carriers coupled to the slave-particle gauge field. The composite particle formed by binding the charge carrier (holon) and spin excitation (spinon) via the slave particle gauge field exhibits a number of peculiar properties, and the calculated results are in good agreement with experimental data for both PG and ``strange metal'' phases. Connections to other gauge field approaches in studying the strong correlation problem are also briefly outlined.Comment: 32 pages, to appear in the special issue on "Correlated Electrons" of J. Phys.: Condens. Mat

The Aharonov-Bohm effect for massless Dirac fermions and the spectral flow of Dirac type operators with classical boundary conditions

We compute, in topological terms, the spectral flow of an arbitrary family of self-adjoint Dirac type operators with classical (local) boundary conditions on a compact Riemannian manifold with boundary under the assumption that the initial and terminal operators of the family are conjugate by a bundle automorphism. This result is used to study conditions for the existence of nonzero spectral flow of a family of self-adjoint Dirac type operators with local boundary conditions in a two-dimensional domain with nontrivial topology. Possible physical realizations of nonzero spectral flow are discussed.Comment: 15 pages, 6 figures. Submitted to Theoretical and Mathematical Physics. v2: A change has been made to the paragraph describing the previous work of M. Prokhorov

Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms

The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and phenomena. They have been derived in deterministic and, later, in stochastic frameworks. Other results first obtained for stochastic processes, and later considered in deterministic dynamics, describe the temporal evolution of fluctuations. The field has grown beyond expectation: research works and different perspectives are proposed at an ever faster pace. Indeed, understanding fluctuations is important for the emerging theory of nonequilibrium phenomena, as well as for applications, such as those of nanotechnological and biophysical interest. However, the links among the different approaches and the limitations of these approaches are not fully understood. We focus on these issues, providing: a) analysis of the theoretical models; b) discussion of the rigorous mathematical results; c) identification of the physical mechanisms underlying the validity of the theoretical predictions, for a wide range of phenomena.Comment: 44 pages, 2 figures. To appear in Nonlinearity (2007