Universal far-from-equilibrium Dynamics of a Holographic Superconductor

Symmetry breaking phase transitions are an example of non-equilibrium processes that require real time treatment, a major challenge in strongly coupled systems without long-lived quasiparticles. Holographic duality provides such an approach by mapping strongly coupled field theories in D dimensions into weakly coupled quantum gravity in D+1 anti-de Sitter spacetime. Here, we use holographic duality to study formation of topological defects -- winding numbers -- in the course of a superconducting transition in a strongly coupled theory in a 1D ring. When the system undergoes the transition on a given quench time, the condensate builds up with a delay that can be deduced using the Kibble-Zurek mechanism from the quench time and the universality class of the theory, as determined from the quasinormal mode spectrum of the dual model. Typical winding numbers deposited in the ring exhibit a universal fractional power law dependence on the quench time, also predicted by the Kibble-Zurek Mechanism.Comment: 33 pages; 8 figure

Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model

The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of the critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point that allows one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter. The method is illustrated in the one-dimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.Comment: 2 figures, 5 page

R^2-corrections to Chaotic Inflation

Scalar density cosmological perturbations, spectral indices and reheating in a chaotic inflationary universe model, in which a higher derivative term is added, are investigated. This term is supposed to play an important role in the early evolution of the Universe, specifically at times closer to the Planck era.Comment: 14 pages, accepted for publication in MPL

Atom cooling by non-adiabatic expansion

Motivated by the recent discovery that a reflecting wall moving with a square-root in time trajectory behaves as a universal stopper of classical particles regardless of their initial velocities, we compare linear in time and square-root in time expansions of a box to achieve efficient atom cooling. For the quantum single-atom wavefunctions studied the square-root in time expansion presents important advantages: asymptotically it leads to zero average energy whereas any linear in time (constant box-wall velocity) expansion leaves a non-zero residual energy, except in the limit of an infinitely slow expansion. For finite final times and box lengths we set a number of bounds and cooling principles which again confirm the superior performance of the square-root in time expansion, even more clearly for increasing excitation of the initial state. Breakdown of adiabaticity is generally fatal for cooling with the linear expansion but not so with the square-root expansion.Comment: 4 pages, 4 figure

Fluxoid formation: size effects and non-equilibrium universality

Simple causal arguments put forward by Kibble and Zurek suggest that the scaling behaviour of condensed matter at continuous transitions is related to the familiar universality classes of the systems at quasi-equilibrium. Although proposed 25 years ago or more, it is only in the last few years that it has been possible to devise experiments from which scaling exponents can be determined and in which this scenario can be tested. In previous work, an unusually high Kibble-Zurek scaling exponent was reported for spontaneous fluxoid production in a single isolated superconducting Nb loop, albeit with low density. Using analytic approximations backed up by Langevin simulations, we argue that densities as small as these are too low to be attributable to scaling, and are conditioned by the small size of the loop. We also reflect on the physical differences between slow quenches and small rings, and derive some criteria for these differences, noting that recent work on slow quenches does not adequately explain the anomalous behaviour seen here.Comment: 7 pages, 4 figures, presentation given at CMMP 201

False vacuum decay in a brane world cosmological model

The false vacuum decay in a brane world model is studied in this work. We investigate the vacuum decay via the Coleman-de Luccia instanton, derive explicit approximative expressions for the Coleman-de Luccia instanton which is close to a Hawking-Moss instanton and compare the results with those already obtained within Einstein's theory of relativity.Comment: minor changes done, references added, version to appear in GR