1,248 research outputs found
Extended trigonometric Cherednik algebras and nonstationary Schr\"odinger equations with delta-potentials
We realize an extended version of the trigonometric Cherednik algebra as
affine Dunkl operators involving Heaviside functions. We use the quadratic
Casimir element of the extended trigonometric Cherednik algebra to define an
explicit nonstationary Schr\"odinger equation with delta-potential. We use
coordinate Bethe ansatz methods to construct solutions of the nonstationary
Schr\"odinger equation in terms of generalized Bethe wave functions. It is
shown that the generalized Bethe wave functions satisfy affine difference
Knizhnik-Zamolodchikov equations in their spectral parameter. The relation to
the vector valued root system analogs of the quantum Bose gas on the circle
with pairwise delta-function interactions is indicated.Comment: 23 pages; Version 2: expanded introduction and misprints correcte
Spectra and Symmetry in Nuclear Pairing
We apply the algebraic Bethe ansatz technique to the nuclear pairing problem
with orbit dependent coupling constants and degenerate single particle energy
levels. We find the exact energies and eigenstates. We show that for a given
shell, there are degeneracies between the states corresponding to less and more
than half full shell. We also provide a technique to solve the equations of
Bethe ansatz.Comment: 15 pages of REVTEX with 2 eps figure
Noise correlations of the ultra-cold Fermi gas in an optical lattice
In this paper we study the density noise correlations of the two component
Fermi gas in optical lattices. Three different type of phases, the BCS-state
(Bardeen, Cooper, and Schieffer), the FFLO-state (Fulde, Ferrel, Larkin, and
Ovchinnikov), and BP (breach pair) state, are considered. We show how these
states differ in their noise correlations. The noise correlations are
calculated not only at zero temperature, but also at non-zero temperatures
paying particular attention to how much the finite temperature effects might
complicate the detection of different phases. Since one-dimensional systems
have been shown to be very promising candidates to observe FFLO states, we
apply our results also to the computation of correlation signals in a
one-dimensional lattice. We find that the density noise correlations reveal
important information about the structure of the underlying order parameter as
well as about the quasiparticle dispersions.Comment: 25 pages, 11 figures. Some figures are updated and text has been
modifie
Spin waves in a one-dimensional spinor Bose gas
We study a one-dimensional (iso)spin 1/2 Bose gas with repulsive
delta-function interaction by the Bethe Ansatz method and discuss the
excitations above the polarized ground state. In addition to phonons the system
features spin waves with a quadratic dispersion. We compute analytically and
numerically the effective mass of the spin wave and show that the spin
transport is greatly suppressed in the strong coupling regime, where the
isospin-density (or ``spin-charge'') separation is maximal. Using a
hydrodynamic approach, we study spin excitations in a harmonically trapped
system and discuss prospects for future studies of two-component ultracold
atomic gases.Comment: 4 pages, 1 figur
Exactly Solvable Interacting Spin-Ice Vertex Model
A special family of solvable five-vertex model is introduced on a square
lattice. In addition to the usual nearest neighbor interactions, the vertices
defining the model also interact alongone of the diagonals of the lattice. Such
family of models includes in a special limit the standard six-vertex model. The
exact solution of these models gives the first application of the matrix
product ansatz introduced recently and applied successfully in the solution of
quantum chains. The phase diagram and the free energy of the models are
calculated in the thermodynamic limit. The models exhibit massless phases and
our analyticaland numerical analysis indicate that such phases are governed by
a conformal field theory with central charge and continuosly varying
critical exponents.Comment: 14 pages, 11 figure
High domain wall velocities induced by current in ultrathin Pt/Co/AlOx wires with perpendicular magnetic anisotropy
Current-induced domain wall (DW) displacements in an array of ultrathin
Pt/Co/AlOx wires with perpendicular magnetic anisotropy have been directly
observed by wide field Kerr microscopy. DWs in all wires in the array were
driven simultaneously and their displacement on the micrometer-scale was
controlled by the current pulse amplitude and duration. At the lower current
densities where DW displacements were observed (j less than or equal to 1.5 x
10^12 A/m^2), the DW motion obeys a creep law. At higher current density (j =
1.8 x 10^12 A/m^2), zero-field average DW velocities up to 130 +/- 10 m/s were
recorded.Comment: Minor changes to Fig. 1(b) and text, correcting for the fact that
domain walls were subsequently found to move counter to the electron flow.
References update
Exact Solution of the Quantum Calogero-Gaudin System and of its q-Deformation
A complete set of commuting observables for the Calogero-Gaudin system is
diagonalized, and the explicit form of the corresponding eigenvalues and
eigenfunctions is derived. We use a purely algebraic procedure exploiting the
co-algebra invariance of the model; with the proper technical modifications
this procedure can be applied to the deformed version of the model, which
is then also exactly solved.Comment: 20 pages Late
Exactly Solvable Pairing Model Using an Extension of Richardson-Gaudin Approach
We introduce a new class of exactly solvable boson pairing models using the
technique of Richardson and Gaudin. Analytical expressions for all energy
eigenvalues and first few energy eigenstates are given. In addition, another
solution to Gaudin's equation is also mentioned. A relation with the
Calogero-Sutherland model is suggested.Comment: 9 pages of Latex. In the proceedings of Blueprints for the Nucleus:
From First Principles to Collective Motion: A Festschrift in Honor of
Professor Bruce Barrett, Istanbul, Turkey, 17-23 May 200
Mesoscopic BCS pairing in the repulsive 1d-Hubbard model
We study mesoscopic pairing in the one dimensional repulsive Hubbard model
and its interplay with the BCS model in the canonical ensemble. The key tool is
comparing the Bethe ansatz equations of the two models in the limit of small
Coulomb repulsion. For the ordinary Hubbard interaction the BCS Bethe equations
with infinite pairing coupling are recovered; a finite pairing is obtained by
considering a further density-dependent phase-correlation in the hopping
amplitude of the Hubbard model. We find that spin degrees of freedom in the
Hubbard ground state are arranged in a state of the BCS type, where the
Cooper-pairs form an un-condensed liquid on a ``lattice'' of single particle
energies provided by the Hubbard charge degrees of freedom; the condensation in
the BCS ground state corresponds to Hubbard excitations constituted by a sea of
spin singlets.Comment: 15 pages, 6 figures. To be published on Physical Review
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