Deviations from Berry--Robnik Distribution Caused by Spectral Accumulation

By extending the Berry--Robnik approach for the nearly integrable quantum systems,\cite{[1]} we propose one possible scenario of the energy level spacing distribution that deviates from the Berry--Robnik distribution. The result described in this paper implies that deviations from the Berry--Robnik distribution would arise when energy level components show strong accumulation, and otherwise, the level spacing distribution agrees with the Berry--Robnik distribution.Comment: 4 page

Development of singularities for the compressible Euler equations with external force in several dimensions

We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singularity formation, "the best sufficient condition", in the sense that one can explicitly construct a global in time smooth solution for which this condition is not satisfied "arbitrary little". Also compactly supported perturbation of nontrivial constant state is considered. We generalize the known theorem by Sideris on initial data resulting in singularities. Finally, we investigate the influence of frictional damping and rotation on the singularity formation.Comment: 23 page

Level spacing statistics of classically integrable systems -Investigation along the line of the Berry-Robnik approach-

By extending the approach of Berry and Robnik, the limiting level spacing distribution of a system consisting of infinitely many independent components is investigated. The limiting level spacing distribution is characterized by a single monotonically increasing function $\bar{\mu}(S)$ of the level spacing $S$. Three cases are distinguished: (i) Poissonian if $\bar{\mu}(+\infty)=0$, (ii) Poissonian for large $S$, but possibly not for small $S$ if $0<\bar{\mu}(+\infty)< 1$, and (iii) sub-Poissonian if $\bar{\mu}(+\infty)=1$. This implies that, even when energy-level distributions of individual components are statistically independent, non-Poissonian level spacing distributions are possible.Comment: 19 pages, 4 figures. Accepted for publication in Phys. Rev.

Electronic structure of Ca1−x_{1-x}Srx_xVO3_3: a tale of two energy-scales

We investigate the electronic structure of Ca$_{1-x}$Sr$_x$VO$_3$ using photoemission spectroscopy. Core level spectra establish an electronic phase separation at the surface, leading to distinctly different surface electronic structure compared to the bulk. Analysis of the photoemission spectra of this system allowed us to separate the surface and bulk contributions. These results help us to understand properties related to two vastly differing energy-scales, namely the low energy-scale of thermal excitations (~$k_{B}T$) and the high-energy scale related to Coulomb and other electronic interactions.Comment: 4 pages and 3 figures. Europhysics Letters (appearing

Statistical properties of spectral fluctuations for a quantum system with infinitely many components

Extending the idea formulated in Makino {\it{et al}}[Phys.Rev.E {\bf{67}},066205], that is based on the Berry--Robnik approach [M.V. Berry and M. Robnik, J. Phys. A {\bf{17}}, 2413], we investigate the statistical properties of a two-point spectral correlation for a classically integrable quantum system. The eigenenergy sequence of this system is regarded as a superposition of infinitely many independent components in the semiclassical limit. We derive the level number variance (LNV) in the limit of infinitely many components and discuss its deviations from Poisson statistics. The slope of the limiting LNV is found to be larger than that of Poisson statistics when the individual components have a certain accumulation. This property agrees with the result from the semiclassical periodic-orbit theory that is applied to a system with degenerate torus actions[D. Biswas, M.Azam,and S.V.Lawande, Phys. Rev. A {\bf 43}, 5694].Comment: 6 figures, 10 page

The Cosmic No-Hair Theorem and the Nonlinear Stability of Homogeneous Newtonian Cosmological Models

The validity of the cosmic no-hair theorem is investigated in the context of Newtonian cosmology with a perfect fluid matter model and a positive cosmological constant. It is shown that if the initial data for an expanding cosmological model of this type is subjected to a small perturbation then the corresponding solution exists globally in the future and the perturbation decays in a way which can be described precisely. It is emphasized that no linearization of the equations or special symmetry assumptions are needed. The result can also be interpreted as a proof of the nonlinear stability of the homogeneous models. In order to prove the theorem we write the general solution as the sum of a homogeneous background and a perturbation. As a by-product of the analysis it is found that there is an invariant sense in which an inhomogeneous model can be regarded as a perturbation of a unique homogeneous model. A method is given for associating uniquely to each Newtonian cosmological model with compact spatial sections a spatially homogeneous model which incorporates its large-scale dynamics. This procedure appears very natural in the Newton-Cartan theory which we take as the starting point for Newtonian cosmology.Comment: 16 pages, MPA-AR-94-

Constraints on Resonant Particle Production during Inflation from the Matter and CMB Power Spectra

We analyze the limits on resonant particle production during inflation based upon the power spectrum of fluctuations in matter and the cosmic microwave background. We show that such a model is consistent with features observed in the matter power spectrum deduced from galaxy surveys and damped Lyman-alpha systems at high redshift. It also provides an alternative explanation for the excess power observed in the power spectrum of the cosmic microwave background fluctuations in the range of 1000 < l < 3500. For our best-fit models, epochs of resonant particle creation reenter the horizon at wave numbers ~ 0.4 and/or 0.2 (h/Mpc). The amplitude and location of these features correspond to the creation of fermion species of mass ~ 1-2 Mpl during inflation with a coupling constant between the inflaton field and the created fermion species of near unity. Although the evidence is marginal, if this interpretation is correct, this could be one of the first observational hints of new physics at the Planck scale.Comment: 9 pages, 6 figures, Phys. Rev. D15, in Press, Septermber 15 (2004) Issu

Hierarchical black hole triples in young star clusters: impact of Kozai-Lidov resonance on mergers

Mergers of compact-object binaries are one of the most powerful sources of gravitational waves (GWs) in the frequency range of second-generation ground-based GW detectors (advanced LIGO and Virgo). Dynamical simulations of young dense star clusters (SCs) indicate that ~27 per cent of all double compact-object binaries are members of hierarchical triple systems (HTs). In this paper, we consider 570 HTs composed of three compact objects (black holes or neutron stars) that formed dynamically in N-body simulations of young dense SCs. We simulate them for a Hubble time with a new code based on the Mikkola's algorithmic regularization scheme, including the 2.5 post-Newtonian term. We find that ~88 per cent of the simulated systems develop Kozai-Lidov (KL) oscillations. KL resonance triggers the merger of the inner binary in three systems (corresponding to 0.5 per cent of the simulated HTs), by increasing the eccentricity of the inner binary. Accounting for KL oscillations leads to an increase of the total expected merger rate by 4850 per cent. All binaries that merge because of KL oscillations were formed by dynamical exchanges (i.e. none is a primordial binary) and have chirp mass &gt;20 M 99. This result might be crucial to interpret the formation channel of the first recently detected GW events

Statistical Mechanics of maximal independent sets

The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and covering constraints. It is known that finding minimum and maximum-density maximal independent sets are hard optimization problems. In this paper, we use cavity method of statistical physics and Monte Carlo simulations to study the corresponding constraint satisfaction problem on random graphs. We obtain the entropy of maximal independent sets within the replica symmetric and one-step replica symmetry breaking frameworks, shedding light on the metric structure of the landscape of solutions and suggesting a class of possible algorithms. This is of particular relevance for the application to the study of strategic interactions in social and economic networks, where maximal independent sets correspond to pure Nash equilibria of a graphical game of public goods allocation