1,584 research outputs found
Fermi-Bose transformation for the time-dependent Lieb-Liniger gas
Exact solutions of the Schrodinger equation describing a freely expanding
Lieb-Liniger (LL) gas of delta-interacting bosons in one spatial dimension are
constructed. The many-body wave function is obtained by transforming a fully
antisymmetric (fermionic) time-dependent wave function which obeys the
Schrodinger equation for a free gas. This transformation employs a differential
Fermi-Bose mapping operator which depends on the strength of the interaction
and the number of particles.Comment: 4+ pages, 1 figure; added reference
Momentum distribution of a freely expanding Lieb-Liniger gas
We numerically study free expansion of a few Lieb-Liniger bosons, which are
initially in the ground state of an infinitely deep hard-wall trap. Numerical
calculation is carried out by employing a standard Fourier transform, as
follows from the Fermi-Bose transformation for a time-dependent Lieb-Liniger
gas. We study the evolution of the momentum distribution, the real-space
single-particle density, and the occupancies of natural orbitals. Our numerical
calculation allows us to explore the behavior of these observables in the
transient regime of the expansion, where they are non-trivially affected by the
particle interactions. We derive analytically (by using the stationary phase
approximation) the formula which connects the asymptotic shape of the momentum
distribution and the initial state. For sufficiently large times the momentum
distribution coincides (up to a simple scaling transformation) with the shape
of the real-space single-particle density (the expansion is asymptotically
ballistic). Our analytical and numerical results are in good agreement.Comment: small changes; references 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
The BCS model and the off shell Bethe ansatz for vertex models
We study the connection between the BCS pairing model and the inhomogeneous
vertex model. The two spectral problems coincide in the quasi-classical limit
of the off-shell Bethe Ansatz of the disordered six vertex model. The latter
problem is transformed into an auxiliary spectral problem which corresponds to
the diagonalization of the integrals of motion of the BCS model. A generating
functional whose quasi classical expansion leads to the constants of motion of
the BCS model and in particular the Hamiltonian, is identified.Comment: 10 pages, 1 figure. To be published in J. Phys.
Exact solution of the spin-isospin proton-neutron pairing Hamiltonian
The exact solution of proton-neutron isoscalar-isovector (T=0,1) pairing
Hamiltonian with non-degenerate single-particle orbits and equal pairing
strengths (g_{T=1}= g_{T=0}) is presented for the first time. The Hamiltonian
is a particular case of a family of integrable SO(8) Richardson-Gaudin (RG)
models. The exact solution of the T=0,1 pairing Hamiltonian is reduced to a
problem of 4 sets of coupled non linear equations that determine the spectral
parameters of the complete set of eigenstates. The microscopic structure of
individual eigenstates is analyzed in terms of evolution of the spectral
parameters in the complex plane for system of A=80 nucleons. The spectroscopic
trends of the exact solutions are discussed in terms of generalized rotations
in isospace.Comment: 4 pages, 2 figure
Diagonalization of infinite transfer matrix of boundary face model
We study infinitely many commuting operators , which we call infinite
transfer matrix of boundary face model. We diagonalize
infinite transfer matrix by using free field realizations of the
vertex operators of the elliptic quantum group .Comment: 36 pages, Dedicated to Professor Etsuro Date on the occassion of the
60th birthda
Exact Results for Three-Body Correlations in a Degenerate One-Dimensional Bose Gas
Motivated by recent experiments we derive an exact expression for the
correlation function entering the three-body recombination rate for a
one-dimensional gas of interacting bosons. The answer, given in terms of two
thermodynamic parameters of the Lieb-Liniger model, is valid for all values of
the dimensionless coupling and contains the previously known results
for the Bogoliubov and Tonks-Girardeau regimes as limiting cases. We also
investigate finite-size effects by calculating the correlation function for
small systems of 3, 4, 5 and 6 particles.Comment: 4 pages, 2 figure
On the exactly solvable pairing models for bosons
We propose the new exactly solvable model for bosons corresponding to the
attractive pairing interaction. Using the electrostatic analogy, the solution
of this model in thermodynamic limit is found. The transition from the
superfluid phase with the Bose condensate and the Bogoliubov - type spectrum of
excitations in the weak coupling regime to the incompressible phase with the
gap in the excitation spectrum in the strong coupling regime is observed.Comment: 19 page
Correlation functions of the one-dimensional attractive Bose gas
The zero-temperature correlation functions of the one-dimensional attractive
Bose gas with delta-function interaction are calculated analytically for any
value of the interaction parameter and number of particles, directly from the
integrability of the model. We point out a number of interesting features,
including zero recoil energy for large number of particles, analogous to a
M\"ossbauer effect.Comment: 4 pages, 2 figure
Emergence of Wigner molecules in one-dimensional systems of repulsive fermions under harmonic confinement
A Bethe-Ansatz spin-density functional approach is developed to evaluate the
ground-state density profile in a system of repulsively interacting spin-1/2
fermions inside a quasi-one-dimensional harmonic well. The approach allows for
the formation of antiferromagnetic quasi-order with increasing coupling
strength and reproduces with high accuracy the exact solution that is available
for the two-fermion system.Comment: 3 pages, 2 figures, submitte
- …