1,025 research outputs found
Multidimensional integrable Schrodinger operators with matrix potential
The Schrodinger operators with matrix rational potential, which are D-integrable, i.e., can be intertwined with the pure Laplacian, are investigated. Corresponding potentials are uniquely determined by their singular data which are a configuration of the hyperplanes in C-n with prescribed matrices. We describe some algebraic conditions (matrix locus equations) on these data, which are sufficient for D-integrability. As the examples some matrix generalizations of the Calogero-Moser operators are considered
Flavour SU(3) Symmetry in Charmless B Decays
QCD sum rules are used to estimate the flavour SU(3)-symmetry violation in
two-body B decays to pions and kaons. In the factorizable amplitudes the
SU(3)-violation manifests itself in the ratio of the decay constants f_K/f_pi
and in the differences between the B->K, B_s->K and B->pi form factors. These
effects are calculated from the QCD two-point and light-cone sum rules,
respectively, in terms of the strange quark mass and the ratio of the strange
and nonstrange quark-condensate densities. Importantly, QCD sum rules predict
that SU(3) breaking in the heavy-to-light form factors can be substantial and
does not vanish in the heavy-quark mass limit. Furthermore, we investigate the
strange-quark mass dependence of nonfactorizable effects in the B->K pi decay
amplitudes. Taking into account these effects we estimate the accuracy of
several SU(3)-symmetry relations between charmless B-decay amplitudes.Comment: Two references added, version to be published in Phys.Rev.D, 21
pages, 12 postscript figure
Combinatorial Alexander Duality -- a Short and Elementary Proof
Let X be a simplicial complex with the ground set V. Define its Alexander
dual as a simplicial complex X* = {A \subset V: V \setminus A \notin X}. The
combinatorial Alexander duality states that the i-th reduced homology group of
X is isomorphic to the (|V|-i-3)-th reduced cohomology group of X* (over a
given commutative ring R). We give a self-contained proof.Comment: 7 pages, 2 figure; v3: the sign function was simplifie
On one integrable system with a cubic first integral
Recently one integrable model with a cubic first integral of motion has been
studied by Valent using some special coordinate system. We describe the
bi-Hamiltonian structures and variables of separation for this system.Comment: LaTeX with AMS fonts, 9 page
Small-amplitude normal modes of a vortex in a trapped Bose-Einstein condensate
We consider a cylindrically symmetric trap containing a small Bose-Einstein
condensate with a singly quantized vortex on the axis of symmetry. A
time-dependent variational Lagrangian analysis yields the small-amplitude
dynamics of the vortex and the condensate, directly determining the equations
of motion of the coupled normal modes. As found previously from the Bogoliubov
equations, there are two rigid dipole modes and one anomalous mode with a
negative frequency when seen in the laboratory frame.Comment: 4 pages, no figures, Revte
Giant vortex state in perforated aluminum microsquares
We investigate the nucleation of superconductivity in a uniform perpendicular
magnetic field H in aluminum microsquares containing a few (2 and 4) submicron
holes (antidots). The normal/superconducting phase boundary T_c(H) of these
structures shows a quite different behavior in low and high fields. In the low
magnetic field regime fluxoid quantization around each antidot leads to
oscillations in T_c(H), expected from the specific sample geometry, and
reminiscent of the network behavior. In high magnetic fields, the T_c(H)
boundaries of the perforated and a reference non-perforated microsquare reveal
cusps at the same values of Phi/Phi_0 (where Phi is the applied flux threading
the total square area and Phi_0 is the superconducting flux quantum), while the
background on T_c(H) becomes quasi-linear, indicating that a giant vortex state
is established. The influence of the actual geometries on T_c(H) is analyzed in
the framework of the linearized Ginzburg-Landau theory.Comment: 14 pages, 6 PS figures, RevTex, accepted for publication in Phys.
Rev.
Critical temperature oscillations in magnetically coupled superconducting mesoscopic loops
We study the magnetic interaction between two superconducting concentric
mesoscopic Al loops, close to the superconducting/normal phase transition. The
phase boundary is measured resistively for the two-loop structure as well as
for a reference single loop. In both systems Little-Parks oscillations,
periodic in field are observed in the critical temperature Tc versus applied
magnetic field H. In the Fourier spectrum of the Tc(H) oscillations, a weak
'low frequency' response shows up, which can be attributed to the inner loop
supercurrent magnetic coupling to the flux of the outer loop. The amplitude of
this effect can be tuned by varying the applied transport current.Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev.
Oscillations of a rapidly rotating annular Bose-Einstein condensate
A time-dependent variational Lagrangian analysis based on the
Gross-Pitaevskii energy functional serves to study the dynamics of a metastable
giant vortex in a rapidly rotating Bose-Einstein condensate. The resulting
oscillation frequencies of the core radius reproduce the trends seen in recent
experiments [Engels et al., Phys. Rev. Lett. 90, 170405 (2003)], but the
theoretical values are smaller by a factor approximately 0.6-0.8.Comment: 7 pages, revtex
CLES, Code Liegeois d'Evolution Stellaire
Cles is an evolution code recently developed to produce stellar models
meeting the specific requirements of studies in asteroseismology. It offers the
users a lot of choices in the input physics they want in their models and its
versatility allows them to tailor the code to their needs and implement easily
new features. We describe the features implemented in the current version of
the code and the techniques used to solve the equations of stellar structure
and evolution. A brief account is given of the use of the program and of a
solar calibration realized with it.Comment: Comments: 8 pages, Astrophys. Space Sci. CoRoT-ESTA Volume, in the
pres
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