Thermodynamic approach to generating functions and nonequilibrium dynamics - Hickey, James M. (2014)
This thesis investigates the dynamical properties of equilibrium and nonequilibrium systems, both quantum and classical, under the guise of a thermodynamic formalism. Large deviation functions associated with the generating functions of time-integrated observables play the role of dynamical free energies and thus determine the trajectory phase structure of a system. The 1d Glauber-Ising chain is studied using the time-integrated energy as the dynamical order parameter and a whole curve of second order trajectory transitions are uncovered in the complex counting field plane. The leading dynamical Lee-Yang zeros of the associated generating function are extracted directly from the time dependent high order cumulants. Resolving the cumulants into constituent contributions the motion of each contribution’s leading Lee-Yang zeros pair allows one to infer the positions of the trajectory transition points. Contrastingly if one uses the full cumulants only the positions of those closest to the origin, in the limit of low temperatures, can be inferred. Motivated by homodyne detection schemes this thermodynamic approach to trajectories is extended to the quadrature trajectories of light emitted from open quantum systems. Using this dynamical observable the trajectory phases of a simple “blinking” 3-level system, two weakly coupled 2-level systems and the micromaser are studied. The trajectory phases of this observable are found to either carry as much information as the photon emission trajectories or in some cases capture extra dynamically features of the system (the second example). Finally, the statistics of the time-integrated longitudinal and transverse magnetization in the 1d transverse field quantum Ising model are explored. In both cases no large deviation function exists but the generating functions are still calculable. From the singularities of these generating functions new transition lines emerge. These were shown to be linked to: (a) the survival probability of an associated open system, (b) PT-symmetry, (c) the temporal scaling of the cumulants and (d) the topology of an associated set of states.