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 Uq,p(AN−1(1))U_{q,p}(A_{N-1}^{(1)}) face model

We study infinitely many commuting operators $T_B(z)$, which we call infinite transfer matrix of boundary $U_{q,p}(A_{N-1}^{(1)})$ face model. We diagonalize infinite transfer matrix $T_B(z)$ by using free field realizations of the vertex operators of the elliptic quantum group $U_{q,p}(A_{N-1}^{(1)})$.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 $\gamma$ 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