Covariant statistical mechanics and the stress-energy tensor

After recapitulating the covariant formalism of equilibrium statistical mechanics in special relativity and extending it to the case of a non-vanishing spin tensor, we show that the relativistic stress-energy tensor at thermodynamical equilibrium can be obtained from a functional derivative of the partition function with respect to the inverse temperature four-vector \beta. For usual thermodynamical equilibrium, the stress-energy tensor turns out to be the derivative of the relativistic thermodynamic potential current with respect to the four-vector \beta, i.e. T^{\mu \nu} = - \partial \Phi^\mu/\partial \beta_\nu. This formula establishes a relation between stress-energy tensor and entropy current at equilibrium possibly extendable to non-equilibrium hydrodynamics.Comment: 4 pages. Final version accepted for publication in Phys. Rev. Let

Quantum thermodynamics: thermodynamics at the nanoscale

A short introduction on quantum thermodynamics is given and three new topics are discussed: 1) Maximal work extraction from a finite quantum system. The thermodynamic prediction fails and a new, general result is derived, the ``ergotropy''. 2) In work extraction from two-temperature setups, the presence of correlations can push the effective efficiency beyond the Carnot bound. 3) In the presence of level crossing, non-slow changes may be more optimal than slow ones.Comment: 5 pages. Talk given at Physics of Quantum Electronics (PQE2004), Snowbird, by Th.M. Nieuwenhuize

Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula

We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index as an orbit is traversed. Results are given for isolated periodic orbits and rotationally invariant families of periodic orbits in axially symmetric billiard systems. A practical method for determining the stability matrix and the Maslov index is described.Comment: LaTeX, 19 page

Bias and Hierarchical Clustering

It is now well established that galaxies are biased tracers of the distribution of matter, although it is still not known what form this bias takes. In local bias models the propensity for a galaxy to form at a point depends only on the overall density of matter at that point. Hierarchical scaling arguments allow one to build a fully-specified model of the underlying distribution of matter and to explore the effects of local bias in the regime of strong clustering. Using a generating-function method developed by Bernardeau & Schaeffer (1992), we show that hierarchical models lead one directly to the conclusion that a local bias does not alter the shape of the galaxy correlation function relative to the matter correlation function on large scales. This provides an elegant extension of a result first obtained by Coles (1993) for Gaussian underlying fields and confirms the conclusions of Scherrer & Weinberg (1998) obtained using a different approach. We also argue that particularly dense regions in a hierarchical density field display a form of bias that is different from that obtained by selecting such peaks in Gaussian fields: they are themselves hierarchically distributed with scaling parameters $S_p=p^{(p-2)}$. This kind of bias is also factorizable, thus in principle furnishing a simple test of this class of models.Comment: Latex, accepted for publication in ApJL; moderate revision

Obstructive Sleep Apnea Syndrome (OSAS) treated with orthodontic appliances in children : a new feasible approach

Obstructive Sleep Apnea Syndrome (OSAS) affects up to 4% of the paediatric population and, due to the high risk of cardio-vascular and neurological complications and negative outcomes on the developmental process associated, represents the most serious type of Sleep Disordered Breathing (SDB) and the most challenging for public health.Although the most common treatment for OSAS in childhood is Adenotonsillectomy (AT), this approach is limited by its surgical risks and by a high prevalence of recurrence or partial success, with persistence of signs and symptoms of obstructive apnea.The presence of cranio-facial abnormalities and malocclusion is considered an important risk factor for paediatric OSAS and its recurrence after AT. Children affected by OSAS often present specific oro-facial features such asnarrow maxilla, mandibular retrusion, anterior openbite, bilateral/ monolateral cross bite, that are frequently associated with dysfunctions such as oral breathing and atypical swallowing. Those alterations can represent an anatomical base which can contribute to the development of paediatric OSAS, especially in preschool child aged 3-6 years, when the hyperplasia of adenoids and tonsils is reported to be at its peak with a higher risk for obstruction. The purpose of the present research is to evaluate the possibility that an orthodontic treatment, primary aiming to the treatment of malocclusion and the related dysfunctions, can induce improvement or relief of respiratory nighttime distress, as a secondary effect. The sample consisted of 5 children affected by OSAS, 3 female and 2 male, average aged 4.5 years, who have never undergone AT or have had a recurrence of sign and symptoms 1 year after AT.All patients presented narrow maxilla, associated with monolateral/ bilateral crossbite and or anterior openbite. The patients underwent orthodontic treatment performed with an elastodontic appliance, which is a removable oral device made of PVC and widely used in children aged less than 6 years. The following variables were evaluated in each patient at the beginning (T0) and after 1 year (T2) of orthodontic treatment:occlusal parameters; Sleep Clinical Score (SCS); Night time poligraphic parameters: Snoring, Apnea/Hypopnea Index (AHI) andOswestry Disability Index (ODI).Four out of 5 patients showed high compliance to the orthodontic treatment and improved their occlusal relationship. In those patients also AHI and ODI index improved as well as the SCS score, revealing a reduction of sign and symptoms of OSAS. The only patient who did not improve his occlusal and respiratory findings also showed poor compliance to the orthodontic treatment. The study suggest that the treatment of malocclusion might produce improvements in sign and symptoms of OSAS in children aged 3-6 years and that preformed elastodontc appliances are a feasible therapeutic tool for this purpose

Global study of quadrupole correlation effects

We discuss the systematics of ground-state quadrupole correlations of binding energies and mean-square charge radii for all even-even nuclei, from O16 up to the superheavies, for which data are available. To that aim we calculate their correlated J=0 ground state by means of the angular-momentum and particle-number projected generator coordinate method, using the axial mass quadrupole moment as the generator coordinate and self-consistent mean-field states only restricted by axial, parity, and time-reversal symmetries. The calculation is performed within the framework of a non-relativistic self-consistent mean-field model using the same non-relativistic Skyrme interaction SLy4 and a density-dependent pairing force to generate the mean-field configurations and mix them. (See the paper for the rest of the abstract).Comment: 28 pages revtex, 29 eps figures (2 of which in color), 10 tables. submitted to Phys. Rev.

Semiclassical Casimir Energies at Finite Temperature

We study the dependence on the temperature T of Casimir effects for a range of systems, and in particular for a pair of ideal parallel conducting plates, separated by a vacuum. We study the Helmholtz free energy, combining Matsubara's formalism, in which the temperature appears as a periodic Euclidean fourth dimension of circumference 1/T, with the semiclassical periodic orbital approximation of Gutzwiller. By inspecting the known results for the Casimir energy at T=0 for a rectangular parallelepiped, one is led to guess at the expression for the free energy of two ideal parallel conductors without performing any calculation. The result is a new form for the free energy in terms of the lengths of periodic classical paths on a two-dimensional cylinder section. This expression for the free energy is equivalent to others that have been obtained in the literature. Slightly extending the domain of applicability of Gutzwiller's semiclassical periodic orbit approach, we evaluate the free energy at T>0 in terms of periodic classical paths in a four-dimensional cavity that is the tensor product of the original cavity and a circle. The validity of this approach is at present restricted to particular systems. We also discuss the origin of the classical form of the free energy at high temperatures.Comment: 17 pages, no figures, Late

Coagulation by Random Velocity Fields as a Kramers Problem

We analyse the motion of a system of particles suspended in a fluid which has a random velocity field. There are coagulating and non-coagulating phases. We show that the phase transition is related to a Kramers problem, and use this to determine the phase diagram, as a function of the dimensionless inertia of the particles, epsilon, and a measure of the relative intensities of potential and solenoidal components of the velocity field, Gamma. We find that the phase line is described by a function which is non-analytic at epsilon=0, and which is related to escape over a barrier in the Kramers problem. We discuss the physical realisations of this phase transition.Comment: 4 pages, 3 figure

Tunneling and the Band Structure of Chaotic Systems

We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex orbits. These turn out to be fundamental for a proper description of the band structure since they incorporate conduction processes through tunneling mechanisms. The results obtained, illustrated with the kicked-Harper model, are in excellent agreement with numerical simulations, even in the extreme quantum regime.Comment: 11 pages, Latex, figures on request to the author (to be sent by fax