Thermodynamic approach to generating functions and nonequilibrium dynamics

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

The Route of Sir John Franklin's Third Arctic Expedition: An Evaluation and Test of an Alternative Hypothesis

An archaeological survey to aid in the determination of the exact route of the last Sir John Franklin expedition following its overwintering at Beechey Island in 1845-46 was conducted in June 1982. The survey was designed to test the hypothesis that the expedition sailed from Beechey Island south to King William Island via McClintock Channel, rather than through Peel Sound and Franklin Strait, as is generally accepted. Surveyed areas included Kilian, Stefansson, and northeast Victoria Islands in northwest McClintock Channel, and Russell and northern Prince of Wales Islands to the northeast of McClintock Channel. Although three cairns associated with Austin's searching expedition of 1850-51 were located, as well as several prehistoric and historic Inuit sites, no structures or materials associated with the Franklin expedition were identified. While inconclusive, the survey essentially completes the examination of coastlines along which the Franklin expedition may have sailed.Key words: Sir John Franklin, route of third arctic expedition, McClintock ChannelEn juin 1982, on a effectué une étude archéologique destinée à permettre de retracer la route empruntée par la dernière expédition de sir John Franklin après le long hivernage de 1845-46 à l'île Beechey. L'étude avait pour but de vérifier l'hypothèse selon laquelle l'expédition avait navigué de l'île Beechey en direction du sud vers l'île du Roi-Guillaume via le chenal McClintock, plutôt qu'à travers le détroit de Peel et celui de Franklin, comme on le pense habituellement. Les régions de l'étude comprenaient les îles Kilian et Stefansson et le nord-est de l'île Victoria dans la partie nord-ouest du chenal McClintock, ainsi que l'île Russell et la partie septentrionale de l'île du Prince-de-Galles au nord-est du chenal McClintock. Bien qu'on ait localisé trois cairns datant de l'expédition de recherche menée par Austin en 1850-51, ainsi que divers sites inuit préhistoriques et historiques, on n'a pu identifier ni structure ni matériaux remontant à l'expédition Franklin. Si l'étude n'a pas abouti à une conclusion définitive, elle a du moins permis de compléter l'examen du rivage côtier le long duquel l'expédition Franklin a pu naviguer.Mots clés: sir John Franklin, route de la troisième expédition arctique, chenal McClintoc