Quantization of the Nonlinear Sigma Model Revisited

We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The symmetries we consider are twofold: (i) diffeomorphism covariance for a general target manifold; (ii) a transitive group of isometries when the target manifold is a homogeneous space. We show that there are no anomalies in case (i) and that (ii) is also anomaly-free under additional assumptions on the target homogeneous space, in agreement with the work of Friedan. We carry out some explicit computations for the $O(N)$-model. Finally, we show how a suitable notion of the renormalization group establishes the Ricci flow as the one loop renormalization group flow of the nonlinear sigma model.Comment: 51 page

Gate voltage tuned quantum superconductor to insulator transition in an ultrathin bismuth film revisited

We explore the implications of Berezinskii-Kosterlitz-Thouless (BKT) critical behavior and variable-range hopping on the two dimensional (2D) quantum superconductor-insulator (QSI) transition driven by tuning the gate voltage. To illustrate the potential and the implications of this scenario we analyze sheet resistance data of Parendo et al. taken on a gate voltage tuned ultrathin amorphous bismuth film. The finite size scaling analysis of the BKT-transition uncovers a limiting length preventing the correlation length to diverge and to enter the critical regime deeply. Nevertheless the attained BKT critical regime reveals consistency with two parameter quantum scaling and an explicit quantum scaling function determined by the BKT correlation length. The two parameter scaling yields for the zero temperature critical exponents of the QSI-transition the estimates zn = 3/2, z = 3, and n = 1/2, revealing that hyperscaling is violated and in contrast to finite temperature disorder is relevant at zero temperature. Furthermore, zn = 3/2 is also consistent with the two variable quantum scaling form associated with a variable-range hopping controlled insulating ground state

Scaling Invariance in a Time-Dependent Elliptical Billiard

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although the static elliptical billiard is an integrable system, after to introduce time-dependent perturbation on the boundary the unlimited energy growth is observed. The behaviour of the average velocity is described using scaling arguments

Casimir force between two ideal-conductor walls revisited

The high-temperature aspects of the Casimir force between two neutral conducting walls are studied. The mathematical model of "inert" ideal-conductor walls, considered in the original formulations of the Casimir effect, is based on the universal properties of the electromagnetic radiation in the vacuum between the conductors, with zero boundary conditions for the tangential components of the electric field on the walls. This formulation seems to be in agreement with experiments on metallic conductors at room temperature. At high temperatures or large distances, at least, fluctuations of the electric field are present in the bulk and at the surface of a particle system forming the walls, even in the high-density limit: "living" ideal conductors. This makes the enforcement of the inert boundary conditions inadequate. Within a hierarchy of length scales, the high-temperature Casimir force is shown to be entirely determined by the thermal fluctuations in the conducting walls, modelled microscopically by classical Coulomb fluids in the Debye-H\"{u}ckel regime. The semi-classical regime, in the framework of quantum electrodynamics, is studied in the companion letter by P.R.Buenzli and Ph.A.Martin, cond-mat/0506363, Europhys.Lett.72, 42 (2005).Comment: 7 pages.One reference updated. Domain of validity of eq.(11) correcte

The Bosma effect revisited - I. HI and stellar disc scaling models

The observed proportionality between the centripetal contribution of the dynamically insignificant HI gas in the discs of spiral galaxies and the dominant contribution of DM - the "Bosma effect" - has been repeatedly mentioned in the literature but largely ignored. We have re-examined the evidence for the Bosma effect by fitting Bosma effect models for 17 galaxies in the THINGS data set, either by scaling the contribution of the HI gas alone or by using both the observed stellar disc and HI gas as proxies. The results are compared with two models for exotic cold DM: internally consistent cosmological NFW models with constrained compactness parameters, and URC models using fully unconstrained Burkert density profiles. The Bosma models that use the stellar discs as additional proxies are statistically nearly as good as the URC models and clearly better than the NFW ones. We thus confirm the correlation between the centripetal effects of DM and that of the interstellar medium of spiral galaxies. The edificacy of "maximal disc" models is explained as the natural consequence of "classic" Bosma models which include the stellar disc as a proxy in regions of reduced atomic gas. The standard explanation - that the effect reflects a statistical correlation between the visible and exotic DM - seems highly unlikely, given that the geometric forms and hence centripetal signatures of spherical halo and disc components are so different. A literal interpretation of the Bosma effect as being due to the presence of significant amounts of disc DM requires a median visible baryon to disc DM ratio of about 40%.Comment: Accepted by A&A (Paper I

Semigroup approach to birth-and-death stochastic dynamics in continuum

We describe a general approach to the construction of a state evolution corresponding to the Markov generator of a spatial birth-and-death dynamics in $\mathbb{R}^d$. We present conditions on the birth-and-death intensities which are sufficient for the existence of an evolution as a strongly continuous semigroup in a proper Banach space of correlation functions satisfying the Ruelle bound. The convergence of a Vlasov-type scaling for the corresponding stochastic dynamics is considered.Comment: 35 page

Fermi acceleration and suppression of Fermi acceleration in a time-dependent Lorentz Gas

We study some dynamical properties of a Lorentz gas. We have considered both the static and time dependent boundary. For the static case we have shown that the system has a chaotic component characterized with a positive Lyapunov Exponent. For the time-dependent perturbation we describe the model using a four-dimensional nonlinear map. The behaviour of the average velocity is considered in two situations (i) non-dissipative and (ii) dissipative. Our results show that the unlimited energy growth is observed for the non-dissipative case. However, when dissipation, via damping coefficients, is introduced the senary changes and the unlimited engergy growth is suppressed. The behaviour of the average velocity is described using scaling approach

The Central Charge of the Warped AdS^3 Black Hole

The AdS/CFT conjecture offers the possibility of a quantum description for a black hole in terms of a CFT. This has led to the study of general AdS^3 type black holes with a view to constructing an explicit toy quantum black hole model. Such a CFT description would be characterized by its central charge and the dimensions of its primary fields. Recently the expression for the central charges (C_L, C_R) of the CFT dual to the warped AdS^3 have been determined using asymptotic symmetry arguments. The central charges depend, as expected, on the warping factor. We show that topological arguments, used by Witten to constrain central charges for the BTZ black hole, can be generalized to deal with the warped AdS^3 case. Topology constrains the warped factor to be rational numbers while quasinormal modes are conjectured to give the dimensions of primary fields. We find that in the limit when warping is large or when it takes special rational values the system tends to Witten's conjectured unique CFT's with central charges that are multiples of 24.Comment: 6 pages, Latex fil