Ehrenfest Dynamics and Frictionless Cooling Methods

Recently introduced methods which result in shortcuts to adiabaticity, particularly in the context of frictionless cooling, are rederived and discussed in the framework of an approach based on Ehrenfest dynamics. This construction provides physical insights into the emergence of the Ermakov equation, the choice of its boundary conditions, and the use of minimum uncertainty states as indicators of the efficiency of the procedure. Additionally, it facilitates the extension of frictionless cooling to more general situations of physical relevance, such as optical dipole trapping schemes. In this context, we discuss frictionless cooling in the short-time limit, a complementary case to the one considered in the literature, making explicit the limitations intrinsic to the technique when the full three-dimensional case is analyzed.Comment: 9 pages, 4 figures, v2: To appear in Physical Review A. (some minor typos corrected and some references added

Consistency and heterogeneity of individual behavior under uncertainty

By using graphical representations of simple portfolio choice problems, we generate a very rich data set to study behavior under uncertainty at the level of the individual subject. We test the data for consistency with the maximization hypothesis, and we estimate preferences using a two-parameter utility function based on Faruk Gul (1991). This specification provides a good interpretation of the data at the individual level and can account for the highly heterogeneous behaviors observed in the laboratory. The parameter estimates jointly describe attitudes toward risk and allow us to characterize the distribution of risk preferences in the population

Squeezing and robustness of frictionless cooling strategies

Quantum control strategies that provide shortcuts to adiabaticity are increasingly considered in various contexts including atomic cooling. Recent studies have emphasized practical issues in order to reduce the gap between the idealized models and actual ongoing implementations. We rephrase here the cooling features in terms of a peculiar squeezing effect, and use it to parametrize the robustness of frictionless cooling techniques with respect to noise-induced deviations from the ideal time-dependent trajectory for the trapping frequency. We finally discuss qualitative issues for the experimental implementation of this scheme using bichromatic optical traps and lattices, which seem especially suitable for cooling Fermi-Bose mixtures and for investigating equilibration of negative temperature states, respectively.Comment: 9 pages, 7 figures; To appear in Physical Review

Time-dependent coupled oscillator model for charged particle motion in the presence of a time varyingmagnetic field

The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the system, whereas unitary transformation approach is used when managing the system in the framework of quantum mechanics. For both approaches, the original system is transformed to a much more simple system that is the sum of two independent harmonic oscillators which have time-dependent frequencies. We therefore easily identified the wave functions in the transformed system with the help of invariant operator of the system. The full wave functions in the original system is derived from the inverse unitary transformation of the wave functions associated to the transformed system.Comment: 16 page

Anti-correlated time lags in the Z source GX 5-1: Possible evidence for a truncated accretion disk

We investigate the nature of the inner accretion disk in the neutron star source GX 5-1 by making a detailed study of time lags between X-rays of different energies. Using the cross-correlation analysis, we found anti-correlated hard and soft time lags of the order of a few tens to a few hundred seconds and the corresponding intensity states were mostly the horizontal branch (HB) and upper normal branch (NB). The model independent and dependent spectral analysis showed that during these time lags the structure of accretion disk significantly varied. Both eastern and western approaches were used to unfold the X-ray continuum and systematic changes were observed in soft and hard spectral components. These changes along with a systematic shift in the frequency of quasi-periodic oscillations (QPOs) made it substantially evident that the geometry of the accretion disk is truncated. Simultaneous energy spectral and power density spectral study shows that the production of the horizontal branch oscillations (HBOs) are closely related to the Comptonizing region rather than the disk component in the accretion disk. We found that as the HBO frequency decreases from the hard apex to upper HB, the disk temperature increases along with an increase in the coronal temperature which is in sharp contrast with the changes found in black hole binaries where the decrease in QPO frequency is accompanied by a decrease in the disk temperature and a simultaneous increase in the coronal temperature. We discuss the results in the context of re-condensation of coronal material in the inner region of the disk.Comment: 40 pages, 7 figures, accepted for publication in The Astrophysical Journal Supplement (ApJS

The definability criterions for convex projective polyhedral reflection groups

Following Vinberg, we find the criterions for a subgroup generated by reflections \Gamma \subset \SL^{\pm}(n+1,\mathbb{R}) and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in the field $\mathbb{R}$. We apply the criterions for groups generated by reflections that act cocompactly on irreducible properly convex open subdomains of the $n$-dimensional projective sphere. This gives a method for constructing injective group homomorphisms from such Coxeter groups to \SL^{\pm}(n+1,\mathbb{Z}). Finally we provide some examples of \SL^{\pm}(n+1,\mathbb{Z})-representations of such Coxeter groups. In particular, we consider simplicial reflection groups that are isomorphic to hyperbolic simplicial groups and classify all the conjugacy classes of the reflection subgroups in \SL^{\pm}(n+1,\mathbb{R}) that are definable over $\mathbb{Z}$. These were known by Goldman, Benoist, and so on previously.Comment: 31 pages, 8 figure

On sums of three squares

Let $r_3(n)$ be the number of representations of a positive integer $n$ as a sum of three squares of integers. We give two distinct proofs of a conjecture of Wagon concerning the asymptotic value of the mean square of $r_3(n)$.Comment: 11 pages, minor revisions made; to appear in Internat. J. Number Theor

Intersecting Brane World from Type I Compactification

We elaborate that general intersecting brane models on orbifolds are obtained from type I string compactifications and their T-duals. Symmetry breaking and restoration occur via recombination and parallel separation of branes, preserving supersymmetry. The Ramond-Ramond tadpole cancelation and the toron quantization constrain the spectrum as a branching of the adjoints of SO(32), up to orbifold projections. Since the recombination changes the gauge coupling, the single gauge coupling of type I could give rise to different coupling below the unification scale. This is due to the nonlocal properties of the Dirac-Born-Infeld action. The weak mixing angle sin^2 theta_W = 3/8 is naturally explained by embedding the quantum numbers to those of SO(10).Comment: 31 pages, 5 figure