## View abstract

### Session S30 - Mathematical Methods in Quantum Mechanics

Monday, July 19, 17:00 ~ 17:25 UTC-3

## Some generic properties of a uniformly bounded family of discrete one-dimensional Schrödinger operators

### Silas Luiz Carvalho

#### Universidade Federal de Minas Gerais, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak84171642a8639a26468b6fc7e8838b0c').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy84171642a8639a26468b6fc7e8838b0c = 's&#105;l&#97;s' + '&#64;'; addy84171642a8639a26468b6fc7e8838b0c = addy84171642a8639a26468b6fc7e8838b0c + 'm&#97;t' + '&#46;' + '&#117;fmg' + '&#46;' + 'br'; var addy_text84171642a8639a26468b6fc7e8838b0c = 's&#105;l&#97;s' + '&#64;' + 'm&#97;t' + '&#46;' + '&#117;fmg' + '&#46;' + 'br';document.getElementById('cloak84171642a8639a26468b6fc7e8838b0c').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy84171642a8639a26468b6fc7e8838b0c + '\'>'+addy_text84171642a8639a26468b6fc7e8838b0c+'<\/a>';

We present some generic spectral and dynamical properties of a uniformly bounded family of discrete one-dimensional Schrödinger operators, such as: Hausdorff, packing, upper and lower $q$-generalized fractal dimensions of a typical spectral measure, typical transport exponents, etc. We also discuss the application of the main techniques to limit-periodic Schrödinger operators.

Joint work with Moacir Aloisio (Universidade Federal do Amazonas) and César R. de Oliveira (Universidade Federal de São Carlos).