Related papers: A dynamical Thouless formula
The scaling of the Thouless time with system size is of fundamental importance to characterize dynamical properties in quantum systems. In this work, we study the scaling of the Thouless time in the Anderson model on random regular graphs…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…
The formalism for exactly calculating the retarded and advanced Green's functions of strongly correlated lattice models in a uniform electric field is derived within dynamical mean-field theory. To illustrate the method, we solve for the…
An adiabatic cycle around a degeneracy point in the parameter space of a one-dimensional band insulator is known to result in an integer valued noiseless particle transport in the thermodynamic limit. Recently, it was shown that in the case…
Localization of wave functions in disordered systems can be characterized by the Lyapunov exponent, which is zero in the extended phase and nonzero in the localized phase. Previous studies have shown that this exponent is an analytic…
In this paper, we study the non-self-dual extended Harper's model with a Liouville frequency. Based on the work of \cite{SY}, we show that the integrated density of states (IDS for short) of the model is $\frac{1}{2}$-H$\ddot{\text{o}}$lder…
We consider the out-of-equilibrium dynamics of the Heisenberg anisotropic quantum spin--$1/2$ chain threaded by a time-dependent magnetic flux. In the spirit of the recently developed generalized hydrodynamics (GHD), we exploit the…
We apply the theory of random Schr\"odinger operators to the analysis of multi-users communication channels similar to the Wyner model, that are characterized by short-range intra-cell broadcasting. With $H$ the channel transfer matrix,…
We investigate the nonlinear dynamics of turbulent shear flows, with and without rotation, in the context of a simple but physically motivated closure of the equation governing the evolution of the Reynolds stress tensor. We show that the…
We describe the relation between the dynamical properties of a quasiperiodically forced orientation-preserving circle homeomorphism and the behavior of the fibered rotation number with respect to strictly monotone perturbations. Despite the…
We consider products of a i.i.d. sequence in a set $\{f_1,\ldots,f_m\}$ of preserving orientation diffeomorphisms of the circle. we can naturally associate a Lyapunov exponent $\lambda$. Under few assumptions, it is known that $\lambda\leq…
We consider Holder continuous cocycles over hyperbolic dynamical systems with values in the group of invertible bounded linear operators on a Banach space. We show that two fiber bunched cocycles are Holder continuously cohomologous if and…
We study a classical integrable (Neumann) model describing the motion of a particle on the sphere, subject to harmonic forces. We tackle the problem in the infinite dimensional limit by introducing a soft version in which the spherical…
We show that a one-frequency analytic SL(2,R) cocycle with Diophantine rotation vector is analytically linearizable if and only if the Lyapunov exponent is zero through a complex neighborhood of the circle. More generally, we show (without…
We show that a $\mathrm{GL}(d,\mathbb{R})$ cocycle over a hyperbolic system with constant periodic data has a dominated splitting whenever the periodic data indicates it should. This implies global periodic data rigidity of generic Anosov…
Using an analogy between the conductivity tensor of electronic systems and the spin stiffness tensor of spin systems, we introduce the concept of the Thouless number $g_0$ and the dimensionless frequency dependent conductance $g( \omega )$…
We develop a mixed formulation for incompressible hyper-elastodynamics based on a continuum modeling framework recently developed and smooth generalizations of the Taylor-Hood element based on non-uniform rational B-splines (NURBS). This…
In this paper, we present a class of random Schr\"odinger cocycles showing that, for random cocycles with non-compact support, the presence of certain finite moment conditions is essential for establishing a specific modulus of continuity…
We show the following geometric generalization of a classical theorem of W.H. Gottschalk and G.A. Hedlund: a skew action induced by a cocycle of (affine) isometries of a Hilbert space over a minimal dynamics has a continuous invariant…
The purpose of this paper is first to give an asymptotic formula for the holomorphic analytic torsion forms of a fibration associated with increasing powers of a given line bundle. Secondly, we generalize this formula, thanks to the theory…