Quasiperiodic Solutions for Dissipative Boussinesq Systems

In this paper we analyze the behavior of the solution of the dissipative Boussinesq systems

Maximum Speed of Quantum Gate Operation

We consider a quantum gate, driven by a general time-dependent Hamiltonian, that complements the state of a qubit and then adds to it an arbitrary phase shift. It is shown that the minimum operation time of the gate is

Gauge Theoretical Equivariant Gromov–Witten Invariants and the Full Seiberg–Witten Invariants¶of Ruled Surfaces

Let F be a differentiable manifold endowed with an almost K?hler structure (J,ω), α a J-holomorphic action of a compact Lie group on F, and K a closed normal subgroup of which leaves ω invariant. The purpose of this article is to introduce gauge theoretical invariants for such triples (F,α,K). The invariants are associated with moduli spaces of solutions of a certain vortex type equation on a Riemann surface Σ. Our main results concern the special case of the triple

On the Spectrum of the Generator of an Infinite System of Interacting Diffusions

We study the spectrum of the operator

Nodal Statistics for the Van Vleck Polynomials

 The Van Vleck polynomials naturally arise from the generalized Lamé equation

Construction of position and momentum operators and Hamiltonians by embedding and submersion

Extrinsic position and momentum operators are defined on a manifold M via an embedding i: M→(R _n , g _n ) and, via a submersion, π: R _n →M. A Hamiltonian , describing free dynamics on M, is constructed as an intrinsic property of M by the embedding i and an associated Riemannian geodesic submersion.     

Functors of White Noise Associated to Characters of the Infinite Symmetric Group

 The characters of the infinite symmetric group are extended to multiplicative positive definite functions on pair partitions by using an explicit representation due to Veršik and Kerov. The von Neumann algebra generated by the fields with f in an infinite dimensional real Hilbert space is infinite and the vacuum vector is not separating. For a family depending on an integer N< - 1 an ``exclusion principle' is found allowing at most ``identical particles' on the same state:

On the Absolutely Continuous Spectrum of Stark Operators

 The stability of the absolutely continuous spectrum of the one-dimensional Stark operator

The Hamiltonian formulation of general relativity: myths and reality

A conventional wisdom often perpetuated in the literature states that: (i) a 3 + 1 decomposition of spacetime into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation of General Relativity (GR); (ii) the canonical treatment unavoidably breaks the symmetry between space and time in GR and the resulting algebra of constraints is not the algebra of four-dimensional diffeomorphism; (iii) according to some authors this algebra allows one to derive only spatial diffeomorphism or, according to others, a specific field-dependent and non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac [21] and of ADM [22] of the canonical structure of GR are equivalent. We provide some general reasons why these statements should be questioned. Points (i–iii) have been shown to be incorrect in [45] and now we thoroughly re-examine all steps of the Dirac Hamiltonian formulation of GR. By direct calculation we show that Dirac’s references to space-like surfaces are inessential and that such surfaces do not enter his calculations. In addition, we show that his assumption g _0k = 0, used to simplify his calculation of different contributions to the secondary constraints, is unwarranted; yet, remarkably his total Hamiltonian is equivalent to the one computed without the assumption g _0k = 0. The secondary constraints resulting from the conservation of the primary constraints of Dirac are in fact different from the original constraints that Dirac called secondary (also known as the “Hamiltonian” and “diffeomorphism” constraints). The Dirac constraints are instead particular combinations of the constraints which follow directly from the primary constraints. Taking this difference into account we found, using two standard methods, that the generator of the gauge transformation gives diffeomorphism invariance in four-dimensional space-time; and this shows that points (i–iii) above cannot be attributed to the Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric _{g μν} to lapse and shift functions and the three-metric g _km , which is not canonical. This proves that point (iv) is incorrect. Points (i–iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein’s theory itself.     

Pure E 0-Semigroups and Absorbing States

An E ₀-semigroup acting on is called pure if its tail von Neumann algebra is trivial in the sense that

A Multiplicative Ergodic Theorem and Nonpositively Curved Spaces

We study integrable cocycles u(n,x) over an ergodic measure preserving transformation that take values in a semigroup of nonexpanding maps of a nonpositively curved space Y, e.g. a Cartan–Hadamard space or a uniformly convex Banach space. It is proved that for any y∈Y and almost all x, there exist A≥ 0 and a unique geodesic ray γ (t,x) in Y starting at y such that

Sharp Bounds on the Critical Stability Radius for Relativistic Charged Spheres

In a recent paper by Giuliani and Rothman [17], the problem of finding a lower bound on the radius R of a charged sphere with mass M and charge Q < M is addressed. Such a bound is referred to as the critical stability radius. Equivalently, it can be formulated as the problem of finding an upper bound on M for given radius and charge. This problem has resulted in a number of papers in recent years but neither a transparent nor a general inequality similar to the case without charge, i.e., M ≤ 4R/9, has been found. In this paper we derive the surprisingly transparent inequality

Semiclassical Dynamics¶with Exponentially Small Error Estimates

We construct approximate solutions to the time–dependent Schr?dinger?equation

Rotational bands and signature inversion phenomena in πh9/2⊗νi13/2 and πi13/2⊗νi13/2 structures in odd-odd 176Ir

The ^109,111,113Rh nuclei have been produced as fission fragments in the fusion reaction ¹⁸O + ²⁰⁸Pb at 85 MeV. Their level schemes have been built from gamma-rays detected using the Euroball IV array. High-spin states of the neutron-rich ^111,113Rh nuclei have been identified for the first time. Several rotational bands with the odd proton occupying the πg _9/2, πp _1/2 and π(g _7/2/d _5/2) sub-shells have been observed. A band of low-energy transitions has been identified at excitation energy around 2 MeV in ^109,111Rh, which can be interpreted in terms of three-quasiparticle excitation, πg _9/2νh _11/2νg _7/2/d _5/2. In addition another structure built on states located at low excitation energy (608 keV in ¹¹¹Rh, 570 keV in ¹¹³Rh) points out that, as already observed in the lighter isotopes ^107,109Rh, triaxial deformation plays a role in the neutron-rich Rh isotopes well beyond the mid-shell. Received: 15 July 2002 / Accepted: 9 October 2002 / Published online: 3 December 2002 RID="a" ID="a"e-mail: porquet@csnsm.in2p3.fr RID="b" ID="b"Present address: CSNSM IN2P3-CNRS and Université Paris-Sud 91405 Orsay, France. RID="c" ID="c"Present address: CEA/Saclay, DSM/DAPNIA/SPhN, 91191 Gif-sur-Yvette Cedex, France. Communicated by D. Schwalm     

On the Rate of Convergence to Equilibrium of the Andersen Thermostat in Molecular Dynamics

It has been shown in E and Li (Comm. Pure. Appl. Math., 2007, in press) that the Andersen dynamics is uniformly ergodic. Exponential convergence to the invariant measure is established with an error bound of the form

Anderson Localization for Schrödinger Operators on ℤ with Strongly Mixing Potentials

In this paper we show that for a.e. x∈[ 0,2 π) the operators defined on as

Maximally aligned states in 99Ag

Excited states of ⁹⁹Ag were populated via the ⁵⁰Cr + ⁵⁸Ni (261 MeV) reaction using the NORDBALL detector array equipped with charged-particle and neutron detector systems for reaction channel separation. On the basis of the measured γγ-coincidence relations and angular distribution ratios a significantly extended level scheme has been constructed up to E _x ∼ 7.8 MeV and I = 35/2. The experimental results were described within the framework of the shell model. Candidates for states fully aligned in the πg _9/2 ^-3ν(d _5/2, g _7/2)² valence configuration space were found at 4109 and 6265 keV. Received: 18 June 2002 / Accepted: 11 October 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: sohler@atomki.hu Communicated by J. ?yst?     

Maximum Solutions of Normalized Ricci Flow on 4-Manifolds

We consider the maximum solution g(t), t ∈ [0,  + ∞), to the normalized Ricci flow. Among other things, we prove that, if (M, ω) is a smooth compact symplectic 4-manifold such that and let g(t), t ∈ [0, ∞), be a solution to (1.3) on M whose Ricci curvature satisfies that |Ric(g(t))| ≤ 3 and additionally χ(M) = 3τ (M) > 0, then there exists an , and a sequence of points {x _j,k ∈ M}, j = 1, . . . , m, satisfying that, by passing to a subsequence,

Scattering Below Critical Energy for the Radial 4D Yang-Mills Equation and for the 2D Corotational Wave Map System

Given g and f  =  gg′, we consider solutions to the following non linear wave equation :

Stochastic Dissipative PDE's and Gibbs Measures

We study a class of dissipative nonlinear PDE's forced by a random force η^{omega( t} , ^x ), with the space variable x varying in a bounded domain. The class contains the 2D Navier–Stokes equations (under periodic or Dirichlet boundary conditions), and the forces we consider are those common in statistical hydrodynamics: they are random fields smooth in t and stationary, short-correlated in time t. In this paper, we confine ourselves to “kick forces” of the form