Weak Integrability Breaking: Chaos with Integrability Signature in Coherent Diffusion

Prethermalization and Thermalization in Models with Weak Integrability Breaking.

We study the effects of integrability-breaking perturbations on the nonequilibrium evolution of many-particle quantum systems. We focus on a class of spinless fermion models with weak interactions. We employ equation of motion techniques that can be viewed as generalizations of quantum Boltzmann equations. We benchmark our method against time-dependent density matrix renormalization group compu...

On Integrability and Chaos in Discrete Systems

The scalar nonlinear Schrödinger (NLS) equation and a suitable discretization are well known integrable systems which exhibit the phenomena of “effective” chaos. Vector generalizations of both the continuous and discrete system are discussed. Some attention is directed upon the issue of the integrability of a discrete version of the vector NLS equation.

Weak localization and integrability in ballistic cavities.

We demonstrate the existence of an interference contribution to the average magnetoconductance, G(B), of ballistic cavities and use it to test the semiclassical theory of quantum billiards. G(B) is qualitatively different for chaotic and regular cavities, an effect explained semiclassically by the differing classical distribution of areas. The magnitude of G(B) is poorly explained by the semicl...

Integrability and Chaos – algebraic and geometric approach

Nonlinear Physics: Integrability, Chaos and Beyond

Integrability and chaos are two of the main concepts associated with nonlinear physical systems which have revolutionized our understanding of them. Highly stable exponentially localized solitons are often associated with many of the important integrable nonlinear systems while motions which are sensitively dependent on initial conditions are associated with chaotic systems. Besides dramaticall...