Energy flow and fluctuations in non-equilibrium conformal field theory on star graphs

TL;DR

This paper derives an exact cumulant generating function for energy flows in non-equilibrium conformal field theory on star graphs, extending fluctuation relations and providing a Virasoro algebra-based approach.

Contribution

It introduces a Virasoro algebraic method to analyze non-equilibrium steady states in CFT on star graphs, generalizing previous two-leg results to multiple legs.

Findings

Exact long-time cumulant generating function derived

Generalized non-equilibrium fluctuation relations established

Viraroso algebra approach confirms universality of results

Abstract

We consider non-equilibrium quantum steady states in conformal field theory (CFT) on star-graph configurations, with a particular, simple connection condition at the vertex of the graph. These steady states occur after a large time as a result of initially thermalizing the legs of the graph at different temperatures, and carry energy flows. Using purely Virasoro algebraic calculations we evaluate the exact long-time cumulant generating function for these flows. We show that this function satisfies a generalization of the usual non-equilibrium fluctuation relations. This extends the results by two of the authors (J. Phys. A 45: 362001, 2012; arXiv:1302.3125) to the cases of more than two legs. It also provides an alternative derivation centered on Virasoro algebra operators rather than local fields, hence an alternative regularization scheme, thus confirming the validity and universality of the long-time cumulant generating function. Our derivation shows how the usual Virasoro algebra leads, in large volumes, to a continuous-index Virasoro algebra for which we develop diagramatic principles, which may be of interest in other non-equilibrium contexts as well. Finally, our results shed light on the Poisson process interpretation of the long-time energy transfer in CFT.