Regensburg 2016 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 1: Tutorial: Correlations in Integrable Quantum Many-Body Systems

TT 1.3: Tutorium

Sonntag, 6. März 2016, 17:45–18:30, H20

Quantum quenches and equilibration of lattice and continuum systems — •Michael Brockmann — Max Planck Institute for the Physics of Complex Systems, Dresden, Germany

In this tutorial we will discuss the problem of relaxation and equilibration in closed quantum systems which are prepared in an off-equilibrium initial state. Quantum quenches are examples of such out of equilibrium situations. The focus will be on one-dimensional integrable theories where additional conservation laws heavily restrict the dynamics of the system.

I will briefly present two examples for which the steady state can be investigated by means of exact methods. The first example is a quench protocol where the ground state of a free many-particle bosonic theory unitarily evolves in time under the Lieb-Liniger Hamiltonian of δ-interacting repulsive bosons. In the second example the anti-ferromagnetic Néel state, the ground state of the spin-1/2 Ising chain, is released into the anisotropic Heisenberg spin chain. Using a variational method, the so-called quench action approach (QAA), one obtains the exact non-thermal steady state of the system in the thermodynamic limit, which correctly reproduces expectation values of local observables. Besides being rare cases of exact solutions of quench situations in truly interacting theories, those two quench protocols represent examples where a naive implementation of the generalized Gibbs ensemble (GGE) fails.