Related papers: Semirelativistic N-boson systems bound by attracti…
General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. A…
We study the lowest energy E of a relativistic system of N identical bosons bound by harmonic-oscillator pair potentials in three spatial dimensions. In natural units the system has the semirelativistic ``spinless-Salpeter'' Hamiltonian H =…
We study the lowest energy E of a relativistic system of N identical bosons bound by pair potentials of the form V(r_{ij}) = g(r_{ij}^2) in three spatial dimensions. In natural units hbar = c = 1 the system has the semirelativistic…
We study a bound system of N identical bosons interacting by model pair potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a variational trial function and the `equivalent 2-body method', we find explicit upper and…
General analytic energy bounds are derived for N-boson systems governed by ultrarelativistic Hamiltonians of the form H = sum_{i=1}^N||p_i|| + sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. It is proved that a…
We study the lowest energy E of a semirelativistic system of N identical massless bosons with Hamiltonian H= sum{i=1 to N} sqrt(p_i^2)+ sum{j>i=1 to N} g |r_i - r_j|^2, g > 0. We prove the inequalities A [g N^2 (N-1)^2]^{1/3} < E < B [g N^2…
For the class of attractive potentials V(r) <= 0 which vanish at infinity, we prove that the ground-state energy E of the semirelativistic Hamiltonian H = \sqrt{m^2 + p^2} + V(r) is bounded below by the ground-state energy e of the…
We consider a system of N nonrelativistic bosons in two dimensions, interacting weakly via a short-range attractive potential. We show that for N large, but below some critical value, the properties of the N-boson bound state are universal.…
We consider the nonrelativistic four-boson system in two dimensions interacting via a short-range attractive potential. For a weakly attractive potential with one shallow two-body bound state with binding energy B_2, the binding energies…
We establish that the ability of a localized trapping potential to bind weakly-interacting bosons is dramatically enhanced in the vicinity of the threshold of formation of the single-particle bound-state of the trap. Specifically, for…
New upper and lower limits are given for the number of S-wave bound states yielded by an attractive (monotonic) potential in the context of the Schrodinger or Klein-Gordon equation.
Consider an N-Boson system interacting via a two-body repulsive short-range potential $V$ in a three dimensional box $\Lambda$ of side length $L$. We take the limit $N, L \to \infty$ while keeping the density $\rho = N / L^3$ fixed and…
The lower bound masses of the ground-state relativistic three-boson system in 1+1, 2+1 and 3+1 space-time dimensions are obtained. We have considered a reduction of the ladder Bethe-Salpeter equation to the light-front in a model with…
We present a semiclassical study of the spectrum of a few-body system consisting of two short-range interacting bosonic particles in one dimension, a particular case of a general class of integrable many-body systems where the energy…
The problem of computing the effective nonrelativistic potential $U_{D}$ for the interaction of charged scalar bosons within the context of D-dimensional electromagnetism with a cutoff, is reduced to quadratures. It is shown that $U_3$…
We consider a system of N trapped bosons with repulsive interactions in a combined semiclassical mean-field limit at positive temperature. We show that the free energy is well approximated by the minimum of the Hartree free energy…
We calculate the energy and the condensate fraction of a system of trapped bosons interacting via a short-range two-body potential with positive scattering length. The potential is attractive and has a two-body bound state. When the…
We obtain lower bounds on the ground state energy, in one and three dimensions, for the spinless Salpeter equation (Schr\"odinger equation with a relativistic kinetic energy operator) applicable to potentials for which the attractive parts…
Problems posed by semirelativistic Hamiltonians of the form H = sqrt{m^2+p^2} + V(r) are studied. It is shown that energy upper bounds can be constructed in terms of certain related Schroedinger operators; these bounds include free…
We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations…