Search results for "Spectral gap"
showing 7 items of 7 documents
Correlation at low temperature I. Exponential decay
2003
Abstract The present paper generalizes the analysis in (Ann. H. Poincare 1 (2000) 59, Math. J. (AMS) 8 (1997) 123) of the correlations for a lattice system of real-valued spins at low temperature. The Gibbs measure is assumed to be generated by a fairly general Hamiltonian function with pair interaction. The novelty, as compared to [2,20], is that the single-site (self-) energies of the spins are not required to have only a single local minimum and no other extrema. Our derivation of exponential decay of correlations goes through the spectral analysis of a deformed Laplacian closely related to the Witten Laplacian studied in [2,20]. We prove that this Laplacian has a spectral gap above zero…
The spectrum of weakly coupled map lattices
1998
We consider weakly coupled analytic expanding circle maps on the lattice Zd (for d 2 l), with small coupling strength c and coupling between two sites decaying exponentially with the distance. We study the spectrum of the associated (Perron-Frobenius) transfer operators. We give a FrCchet space on which the operator associated to the full system has a simple eigenvalue at 1 (corresponding to the SRB measure p* previously obtained by Bricmont-Kupiainen (BKl)) and the rest of the spectrum, except maybe for continuous spectrum, is inside a disc of radius smaller than one. For d = 1 we also construct Banach spaces of densities with respect to pr on which perturbation theory, applied to the diff…
Solvability of nonlinear equations in spectral gaps of the linearization
1992
Keywords: strongle indefinite ; nonlinear Hill's equation Reference ANA-ARTICLE-1992-002doi:10.1016/0362-546X(92)90116-VView record in Web of Science Record created on 2008-12-10, modified on 2016-08-08
Fate of the false Mott-Hubbard transition in two dimensions
2014
We have studied the impact of non-local electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte-Carlo and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling -- irrespectively of the preformation of localized or short-ranged magnetic moments. This is the reason, why the two-dimensional Hubbard model is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed.
Entanglement amplification in the nonperturbative dynamics of modular quantum systems
2013
We analyze the conditions for entanglement amplification between distant and not directly interacting quantum objects by their common coupling to media with static modular structure and subject to a local (single-bond) quenched dynamics. We show that in the non-perturbative regime of the dynamics the initial end-to-end entanglement is strongly amplified and, moreover, can be distributed efficiently between distant objects. Due to its intrinsic local and non-perturbative nature the dynamics is fast and robust against thermal fluctuations, and its control is undemanding. We show that the origin of entanglement amplification lies in the interference of the ground state and at most one of the l…
Existence and gap-bifurcation of multiple solutions to certain nonlinear eigenvalue problems
1993
IN THIS PAPER we study: (i) a class of operator equations in an abstract Hilbert space; and (ii) the L2-theory of certain nonlinear Schrodinger equations which can be viewed as special cases of (i). In order to describe the type of abstract nonlinear eigenvalue problems to be discussed, consider a real Hilbert space H with scalar product (* , *) and norm II.11 and let S be a (not necessarily bounded) positive self-adjoint linear operator in li. We write S in the form
Poincare Inequalities and Spectral Gap, Concentration Phenomenon for G-Measures
2002
We produce a new approach based upon inequalities of Poincare’s type for giving constructive estimates of the mixing rate for a family of mixing stationary processes continuously depending on their past called g-measures. We establish also exponential inequalities of Hoeffding’s type leading to a concentration phenomenon for a large class of observables; this last property permits in particular to give the typical behaviour of the n-orbits of a g-measure.