Dynamics of spin-coherent states and instanton calculus on a Riemann surface

Seminar über Theoretische Festkörperphysik

Vortragender:

Tobias Gulden

Datum:

27.04.2015 14:00

Ort:

Raum 10.01, Geb. 30.23 (Physikhochhaus), Campus Süd

Zugehörigkeit:

University of Minnesota

Gastgeber:

Prof. J. Schmalian

Abstract

Instanton calculations in semiclassical quantum mechanics rely on integration along trajectories which solve classical equations of motion. However in systems with higher dimensionality or complexified phase space these are rarely attainable. A prime example are spin-coherent states which are used e.g. to describe single molecule magnets (SMM). We use this example to develop instanton calculus which does not rely on explicit solutions of the classical equations of motion. Energy conservation restricts the complex phase space to a Riemann surface of complex dimension one, allowing to deform integration paths according to Cauchy's integral theorem. As a result, the semiclassical actions can be evaluated without knowing actual classical paths. Furthermore we show that in many cases such actions may be solely derived from monodromy properties of the corresponding Riemann surface and residue values at its singular points. Among other results, we prove that the period of quenched tunneling in SMM in an external magnetic field is semiclassically exact.