Integrable Systems and Conformal Invariance

Hector J. de Vega, M. Karowski

Michael N. Barber, Paul A. Pearce

Dalit Engelhardt

Abstract We present a framework for investigating the response of conformally invariant confined 1 + 1-dimensional systems to a quantum quench. While conformal invariance is generally destroyed in a global quantum quench, systems that can be described as or mapped to integrable deformations of a CFT may present special instances where a conformal field theory-based analysis could provide useful insight into the non-equilibrium dynamics. We investigate this possibility by considering a quench analogous to that of the quantum Newton’s Cradle experiment (Kinoshita et al 2006 Nature 440 900 ) and demonstrating qualitative agreement between observables derived in the CFT framework and those of the experimental system. We propose that this agreement may be a feature of the proximity of the experimental system to an integrable deformation of a c = 1 CFT.

M. Karowski

Willi-Hans Steeb

Autonomous systems of first order ordinary differential equations can be embedded into a Hilbert space description by using Bose operators and Glauber coherent states. The first integrals and conformal invariants of the autonomous system can be represented by states in a Hilbert space. Thus the embedding in a Hilbert space allows us to study entanglement of the states. We apply it here to first integrals and conformal invariants which are expressed as states.

M. Karowski