Zobrazeno 1 - 10
of 164
pro vyhledávání: '"Jitomirskaya, Svetlana"'
We develop a sharp palindromic argument for general 1D operators, that proves absence of semi-uniform localization in the regime of exponential symmetry-based resonances. This provides the first examples of operators with dynamical localization but n
Externí odkaz:
http://arxiv.org/abs/2410.21700
We obtain the sharp arithmetic Gordon's theorem: that is, absence of eigenvalues on the set of energies with Lyapunov exponent bounded by the exponential rate of approximation of frequency by the rationals, for a large class of one-dimensional quasip
Externí odkaz:
http://arxiv.org/abs/2408.16935
Autor:
Ge, Lingrui, Jitomirskaya, Svetlana
We exploit the structure of dual cocycles to develop several new concepts and tools for the study of one-frequency quasiperiodic operators with analytic potentials. As applications we solve two long-standing arithmetic conjectures: universality of sh
Externí odkaz:
http://arxiv.org/abs/2407.08866
We prove the universality of sharp arithmetic localization for all one-dimensional quasiperiodic Schr\"odinger operators with anti-Lipschitz monotone potentials.
Comment: 36 pages, 1 figure
Comment: 36 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2407.00703
We solve the ten martini problem (Cantor spectrum with no condition on irrational frequencies, previously only established for the almost Mathieu) for a large class of one-frequency quasiperiodic operators, including nonperturbative analytic neighbor
Externí odkaz:
http://arxiv.org/abs/2308.09321
We introduce the concept of dual Lyapunov exponents, leading to a multiplicative version of the classical Jensen's formula for one-frequency analytic Schr\"odinger cocycles. This formula, in particular, gives a new proof and a quantitative version of
Externí odkaz:
http://arxiv.org/abs/2306.16387
We develop the technique to prove localization through the analysis of eigenfunctions in presence of both exponential frequency resonances and exponential phase barriers (anti-resonances) and use it to prove localization for the Maryland model for al
Externí odkaz:
http://arxiv.org/abs/2205.04021
We prove absolute continuity of the integrated density of states for frequency-independent analytic perturbations of the non-critical almost Mathieu operator under arithmetic conditions on frequency.
Comment: 17 pages
Comment: 17 pages
Externí odkaz:
http://arxiv.org/abs/2204.11000
We present a method for obtaining power-logarithmic bounds on the growth of the moments of the position operator for one-dimensional ergodic Schr\"odinger operators. We use Bourgain's semi-algebraic method to obtain such bounds for operators with mul
Externí odkaz:
http://arxiv.org/abs/2110.11883
Autor:
Jitomirskaya, Svetlana, Liu, Wencai
We present a simple method, not based on the transfer matrices, to prove vanishing of dynamical transport exponents. The method is applied to long range quasiperiodic operators.
Externí odkaz:
http://arxiv.org/abs/2104.13145