TY - JOUR

T1 - Instanton calculus without equations of motion

T2 - Semiclassics from monodromies of a Riemann surface

AU - Gulden, Tobias

AU - Janas, Michael

AU - Kamenev, Alex

N1 - Publisher Copyright:
© 2015 IOP Publishing Ltd.

PY - 2015/2/20

Y1 - 2015/2/20

N2 - 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. As an example, we consider quenching of tunneling processes in SMM by an applied magnetic field.

AB - 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. As an example, we consider quenching of tunneling processes in SMM by an applied magnetic field.

KW - Algebraic topology

KW - Riemann surface calculations

KW - Semiclassical theories and applications

KW - Single-molecule magnets

UR - http://www.scopus.com/inward/record.url?scp=84921770221&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921770221&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/48/7/075304

DO - 10.1088/1751-8113/48/7/075304

M3 - Article

AN - SCOPUS:84921770221

SN - 1751-8113

VL - 48

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 7

M1 - 075304

ER -