Efficient path sampling for trajectory ensembles with applications to non-equilibrium systems

This thesis utilises large deviation methods to study nonequilibrium phenomena in both quantum and classical systems. The dynamical analogues of the ensembles of statistical mechanics are used to explore dynamical phase spaces of systems, quantifying atypical fluctuations that can play a critical role in long term behaviour. A dynamical ensemble based on fixed numbers of dynamical events, allowing trajectory observation time to fluctuate, is introduced. This ensemble, denoted the x-ensemble, is found to be well suited to numerically simulate atypical fluctuations using transition path sampling (TPS). x-ensemble TPS schemes are analysed with reference to existing methods in both quantum and classical stochastic systems, and are found to offer more flexibility and efficiency in a variety of situations. The potential to develop this scheme into a self-optimizing algorithm is discussed with examples. The x-ensemble is then used in three non-equilibrium scenarios. Firstly in plaquette models of glass formers, in an effort to provide insight into the nature of the glass transition. It is shown that a two-dimensional triangular plaquette model (TPM) exhibits both a trajectory phase-transition between dynamical active and inactive phases, and when two replicas are coupled, a thermal phase transition between states of low and high overlap between the replicas. These two transitions are similar to those seen to occur in more realistic glass formers. When the TPM is generalised to a three-dimensional square pyramid plaquette model (SPyM) these dynamical and thermodynamic features of interest remain. It is argued that these models therefore provide an ideal test-bed for competing theories of the glass transition. Secondly the x-ensemble is used to define and analyse the dynamical analogue of the Jarzynski equality, allowing for the computation of dynamical free energy differences with, in principle, arbitrarily fast protocols linking two dynamical states. This relation is tested and found to hold in open quantum systems. Finally the partition sum zeros method of Lee and Yang is used to extract the location of dynamical phase transitions from the high-order, short-time cumulants of the x-ensemble. Results in both classical and open quantum systems are compared with previously studied dynamical ensembles, providing insight into the nature in which dynamical behaviours are encoded by these ensembles

Efficient path sampling for trajectory ensembles with applications to non-equilibrium systems

This thesis utilises large deviation methods to study nonequilibrium phenomena in both quantum and classical systems. The dynamical analogues of the ensembles of statistical mechanics are used to explore dynamical phase spaces of systems, quantifying atypical fluctuations that can play a critical role in long term behaviour. A dynamical ensemble based on fixed numbers of dynamical events, allowing trajectory observation time to fluctuate, is introduced. This ensemble, denoted the x-ensemble, is found to be well suited to numerically simulate atypical fluctuations using transition path sampling (TPS). x-ensemble TPS schemes are analysed with reference to existing methods in both quantum and classical stochastic systems, and are found to offer more flexibility and efficiency in a variety of situations. The potential to develop this scheme into a self-optimizing algorithm is discussed with examples. The x-ensemble is then used in three non-equilibrium scenarios. Firstly in plaquette models of glass formers, in an effort to provide insight into the nature of the glass transition. It is shown that a two-dimensional triangular plaquette model (TPM) exhibits both a trajectory phase-transition between dynamical active and inactive phases, and when two replicas are coupled, a thermal phase transition between states of low and high overlap between the replicas. These two transitions are similar to those seen to occur in more realistic glass formers. When the TPM is generalised to a three-dimensional square pyramid plaquette model (SPyM) these dynamical and thermodynamic features of interest remain. It is argued that these models therefore provide an ideal test-bed for competing theories of the glass transition. Secondly the x-ensemble is used to define and analyse the dynamical analogue of the Jarzynski equality, allowing for the computation of dynamical free energy differences with, in principle, arbitrarily fast protocols linking two dynamical states. This relation is tested and found to hold in open quantum systems. Finally the partition sum zeros method of Lee and Yang is used to extract the location of dynamical phase transitions from the high-order, short-time cumulants of the x-ensemble. Results in both classical and open quantum systems are compared with previously studied dynamical ensembles, providing insight into the nature in which dynamical behaviours are encoded by these ensembles

Exponential-Potential Scalar Field Universes I: The Bianchi I Models

We obtain a general exact solution of the Einstein field equations for the anisotropic Bianchi type I universes filled with an exponential-potential scalar field and study their dynamics. It is shown, in agreement with previous studies, that for a wide range of initial conditions the late-time behaviour of the models is that of a power-law inflating FRW universe. This property, does not hold, in contrast, when some degree of inhomogeneity is introduced, as discussed in our following paper II.Comment: 16 pages, Plain LaTeX, 1 Figure to be sent on request, to appear in Phys. Rev.

Protogalactic Extension of the Parker Bound

We extend the Parker bound on the galactic flux $\cal F$ of magnetic monopoles. By requiring that a small initial seed field must survive the collapse of the protogalaxy, before any regenerative dynamo effects become significant, we develop a stronger bound. The survival and continued growth of an initial galactic seed field $\leq 10^{-9}$G demand that ${\cal F} \leq 5 \times 10^{-21} (m/10^{17} {GeV}) {cm}^{-2} {sec}^{-1} {sr}^{-1}$. For a given monopole mass, this bound is four and a half orders of magnitude more stringent than the previous `extended Parker bound', but is more speculative as it depends on assumptions about the behavior of magnetic fields during protogalactic collapse. For monopoles which do not overclose the Universe ($\Omega_m <1$), the maximum flux allowed is now $8 \times 10^{-19}$ cm^{-2} s^{-1} sr^{-1}, a factor of 150 lower than the maximum flux allowed by the extended Parker bound.Comment: 9 pages, 1 eps figur

The KMOS Deep Survey (KDS) – I. Dynamical measurements of typical star-forming galaxies at z ≃ 3.5

We present dynamical measurements from the KMOS (K-band Multi-Object Spectrograph) Deep Survey (KDS), which is comprised of 77 typical star-forming galaxies at z z ≃ 3.5 in the mass range 9.0 1), with the sample average VC/σint value much smaller than at lower redshift. After carefully selecting comparable star-forming samples at multiple epochs, we find that the rotation-dominated fraction evolves with redshift with a z−0.2 dependence. The rotation-dominated KDS galaxies show no clear offset from the local rotation velocity-stellar mass (i.e. VC − M⋆) relation, although a smaller fraction of the galaxies are on the relation due to the increase in the dispersion-dominated fraction. These observations are consistent with a simple equilibrium model picture, in which random motions are boosted in high-redshift galaxies by a combination of the increasing gas fractions, accretion efficiency, specific star-formation rate and stellar feedback and which may provide significant pressure support against gravity on the galactic disk scale

Evaluation and histological examination of a Campylobacter fetus subsp. venerealis small animal infection model

Bovine genital campylobacteriosis (BGC), caused by Campylobacter fetus subsp. venerealis, is associated with production losses in cattle worldwide. This study aimed to develop a reliable BGC guinea pig model to facilitate future studies of pathogenicity, abortion mechanisms and vaccine efficacy. Seven groups of five pregnant guinea pigs (1 control per group) were inoculated with one of three strains via intra-peritoneal (IP) or intra-vaginal routes. Samples were examined using culture, PCR and histology. Abortions ranged from 0% to 100% and re-isolation of causative bacteria from sampled sites varied with strain, dose of bacteria and time to abortion. Histology indicated metritis and placentitis, suggesting that the bacteria induce inflammation, placental detachment and subsequent abortion. Variation of virulence between strains was observed and determined by culture and abortion rates. IP administration of C. fetus subsp. venerealis to pregnant guinea pigs is a promising small animal model for the investigation of BGC abortion