Nearest-Neighbor Distributions and Tunneling Splittings in Interacting Many-Body Two-Level Boson Systems

We study the nearest-neighbor distributions of the $k$-body embedded ensembles of random matrices for $n$ bosons distributed over two-degenerate single-particle states. This ensemble, as a function of $k$, displays a transition from harmonic oscillator behavior ($k=1$) to random matrix type behavior ($k=n$). We show that a large and robust quasi-degeneracy is present for a wide interval of values of $k$ when the ensemble is time-reversal invariant. These quasi-degenerate levels are Shnirelman doublets which appear due to the integrability and time-reversal invariance of the underlying classical systems. We present results related to the frequency in the spectrum of these degenerate levels in terms of $k$, and discuss the statistical properties of the splittings of these doublets.Comment: 13 pages (double column), 7 figures some in color. The movies can be obtained at http://link.aps.org/supplemental/10.1103/PhysRevE.81.03621

Fidelity decay in interacting two-level boson systems: Freezing and revivals

We study the fidelity decay in the $k$-body embedded ensembles of random matrices for bosons distributed in two single-particle states, considering the reference or unperturbed Hamiltonian as the one-body terms and the diagonal part of the $k$-body embedded ensemble of random matrices, and the perturbation as the residual off-diagonal part of the interaction. We calculate the ensemble-averaged fidelity with respect to an initial random state within linear response theory to second order on the perturbation strength, and demonstrate that it displays the freeze of the fidelity. During the freeze, the average fidelity exhibits periodic revivals at integer values of the Heisenberg time $t_H$. By selecting specific $k$-body terms of the residual interaction, we find that the periodicity of the revivals during the freeze of fidelity is an integer fraction of $t_H$, thus relating the period of the revivals with the range of the interaction $k$ of the perturbing terms. Numerical calculations confirm the analytical results

On the Long Time Behavior of Fluid Flows

AbstractThis work is devoted to the study of the long time asymptotics of solutions of the Euler equations in a bounded 2-dimensional domain. Experiments and numerical simulations indicate the presence of an attracting set in the space of incompressible velocity fields. In this work this attractor is described, and its attracting property is established in an extended dynamics where the time is replaced by the ‘long time’ taking values in the Alexandroff line. The attracting property in the usual sense remains a conjecture

Hyperborea: The Arctic Myth of Contemporary Russian Radical Nationalists

After the disintegration of the Soviet Union Russians had to search for a new identity. This was viewed as an urgent task by ethnic Russian nationalists, who were dreaming of a ‘pure Russian country’, or at least of the privileged status of ethnic Russians within the Russian state. To mobilise people they picked up the obsolete Aryan myth rooted in both occult teachings and Nazi ideology and practice. I will analyse the main features of the contemporary Russian Aryan myth developed by radical Russian intellectuals. While rejecting medieval and more recent Russian history as one of oppression implemented by ‘aliens’, the advocates of the Aryan myth are searching for a Golden Age in earlier epochs. They divide history into two periods: initially the great Aryan civilisation and civilising activity successfully developed throughout the world, after which a period of decline began. An agent of this decline is identified as the Jews, or ‘Semites’, who deprived the Aryans of their great achievements and pushed them northwards. The Aryans are identified as the Slavs or Russians, who suffer from alien treachery and misdeeds. The myth seeks to replace former Marxism with racism and contributes to contemporary xenophobia.&nbsp

Localized spectral asymptotics for boundary value problems and correlation effects in the free Fermi gas in general domains

We rigorously derive explicit formulae for the pair correlation function of the ground state of the free Fermi gas in the thermodynamic limit for general geometries of the macroscopic regions occupied by the particles and arbitrary dimension. As a consequence we also establish the asymptotic validity of the local density approximation for the corresponding exchange energy. At constant density these formulae are universal and do not depend on the geometry of the underlying macroscopic domain. In order to identify the correlation effects in the thermodynamic limit, we prove a local Weyl law for the spectral asymptotics of the Laplacian for certain quantum observables which are themselves dependent on a small parameter under very general boundary conditions

Double Dirichlet series and quantum unique ergodicity of weight 1/2 Eisenstein series

The problem of quantum unique ergodicity (QUE) of weight 1/2 Eisenstein series for {\Gamma}_0(4) leads to the study of certain double Dirichlet series involving GL2 automorphic forms and Dirichlet characters. We study the analytic properties of this family of double Dirichlet series (analytic continuation, convexity estimate) and prove that a subconvex estimate implies the QUE result.Comment: 45 pages, 4 figures. Several minor corrections. To appear in Algebra and Number theor

On admissibility criteria for weak solutions of the Euler equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.Comment: 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proof