1,860 research outputs found
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
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
BCS-to-BEC crossover from the exact BCS solution
The BCS-to-BEC crossover, as well as the nature of Cooper pairs, in a
superconducting and Fermi superfluid medium is studied from the exact ground
state wavefunction of the reduced BCS Hamiltonian. As the strength of the
interaction increases, the ground state continuously evolves from a
mixed-system of quasifree fermions and pair resonances (BCS), to pair
resonances and quasibound molecules (pseudogap), and finally to a system of
quasibound molecules (BEC). A single unified scenario arises where the
Cooper-pair wavefunction has a unique functional form. Several exact analytic
expressions, such as the binding energy and condensate fraction, are derived.
We compare our results with recent experiments in ultracold atomic Fermi gases.Comment: 5 pages, 4 figures. Revised version with one figure adde
Attractive Fermi gases with unequal spin populations in highly elongated traps
We investigate two-component attractive Fermi gases with imbalanced spin
populations in trapped one dimensional configurations. The ground state
properties are determined within local density approximation, starting from the
exact Bethe-ansatz equations for the homogeneous case. We predict that the
atoms are distributed according to a two-shell structure: a partially polarized
phase in the center of the trap and either a fully paired or a fully polarized
phase in the wings. The partially polarized core is expected to be a superfluid
of the FFLO type. The size of the cloud as well as the critical spin
polarization needed to suppress the fully paired shell, are calculated as a
function of the coupling strength.Comment: Final accepted versio
Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle
We introduce an integrable lattice discretization of the quantum system of n
bosonic particles on a ring interacting pairwise via repulsive delta
potentials. The corresponding (finite-dimensional) spectral problem of the
integrable lattice model is solved by means of the Bethe Ansatz method. The
resulting eigenfunctions turn out to be given by specializations of the
Hall-Littlewood polynomials. In the continuum limit the solution of the
repulsive delta Bose gas due to Lieb and Liniger is recovered, including the
orthogonality of the Bethe wave functions first proved by Dorlas (extending
previous work of C.N. Yang and C.P. Yang).Comment: 25 pages, LaTe
Attempted Bethe ansatz solution for one-dimensional directed polymers in random media
We study the statistical properties of one-dimensional directed polymers in a
short-range random potential by mapping the replicated problem to a many body
quantum boson system with attractive interactions. We find the full set of
eigenvalues and eigenfunctions of the many-body system and perform the
summation over the entire spectrum of excited states. The analytic continuation
of the obtained exact expression for the replica partition function from
integer to non-integer replica parameter N turns out to be ambiguous.
Performing the analytic continuation simply by assuming that the parameter N
can take arbitrary complex values, and going to the thermodynamic limit of the
original directed polymer problem, we obtain the explicit universal expression
for the probability distribution function of free energy fluctuations.Comment: 32 pages, 1 figur
Long-lived memory for electronic spin in a quantum dot: Numerical analysis
Techniques for coherent control of electron spin-nuclear spin interactions in
quantum dots can be directly applied in spintronics and in quantum information
processing. In this work we study numerically the interaction of electron and
nuclear spins in the context of storing the spin-state of an electron in a
collective state of nuclear spins. We take into account the errors inherent in
a realistic system: the incomplete polarization of the bath of nuclear spins
and the different hyperfine interactions between the electron and individual
nuclei in the quantum dot. Although these imperfections deteriorate the
fidelity of the quantum information retrieval, we find reasonable fidelities
are achievable for modest bath polarizations.Comment: RevTex, 10 pages, 9 EPS figure
New challenges for agricultural research: climate change, food security, rural development, agricultural knowledge systems. 2nd SCAR Foresight exercise
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
Plasmon channels in the electronic relaxation of diamond under high-order harmonics femtosecond irradiation
We used high order harmonics of a femtosecond titanium-doped sapphire system
(pulse duration 25 fs) to realise Ultraviolet Photoelectron Spectroscopy (UPS)
measurements on diamond. The UPS spectra were measured for harmonics in the
range 13 to 27. We also made ab initio calculations of the electronic lifetime
of conduction electrons in the energy range produced in the UPS experiment.
Such calculations show that the lifetime suddenly diminishes when the
conduction electron energy reaches the plasmon energy, whereas the UPS spectra
show evidence in this range of a strong relaxation mechanism with an increased
production of low energy secondary electrons. We propose that in this case the
electronic relaxation proceeds in two steps : excitation of a plasmon by the
high energy electron, the latter decaying into individual electron-hole pairs,
as in the case of metals. This process is observed for the first time in an
insulator and, on account of its high efficiency, should be introduced in the
models of laser breakdown under high intensity
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