Construction of the dynamics of quantum lattice systems

Bruno Nachtergaele, Benjamin Schlein, Robert Sims +2 more

We construct a W*-dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved Lieb–Robinson bounds for such systems on finite lattices [19].

T.R. KOEHLER

D. Goderis, André F. Verbeure, P. Vets

Zachary Smith

Ultracold atomic gases are often used as quantum simulators, where the ability to precisely control and modulate the potential landscape allows many model Hamiltonians to be realized. Recently, dynamic control over these potentials has been leveraged to extend the kinds of systems that can be explored. Our lab has constructed an optical lattice generator capable of dynamically altering the spacing, phase, and amplitude of an optical lattice at RF timescales. The rapid timescales allows the construction of a time-averaged disordered potential from individual flashes of optical lattice, producing layered system exhibiting a Griffiths phase. A future experiment where the optical lattice is periodically expanded and contracted is proposed, and a numerical treatment is presented suggesting interesting structure in the tunneling dynamics.

Rei Inoue, Kazuhiro Hikami

We construct the quantum integrable dynamical system on a (2+1)-dimensional lattice. We consider the q -commuting operators on 2-D lattice as a discretization of the current algebra, and two evolution operators are explicitly defined in terms of the quantum dilogarithm function.

Mario Pulvirenti, Brunello Tirozzi