We present an operator-algebraic approach to derive the low-lying quasidegenerate spectrum of weakly interacting trapped N bosons with total angular momentum $\ensuremath{\Elzxh}L$ for the case of $L/N\ensuremath{\ll}1.$ We demonstrate that the lowest-lying excitation spectrum is given by ${27gn}_{3}{(n}_{3}\ensuremath{-}1)/34,$ where g is the strength of the repulsive contact interaction and ${n}_{3}$ is the number of excited octupole quanta. Our method provides constraints for these quasidegenerate many-body states and gives higher excitation energies that depend linearly on N.We present an operator-algebraic approach to derive the low-lying quasidegenerate spectrum of weakly interacting trapped N bosons with total angular momentum $\ensuremath{\Elzxh}L$ for the case of $L/N\ensuremath{\ll}1.$ We demonstrate that the lowest-lying excitation spectrum is given by ${27gn}_{3}{(n}_{3}\ensuremath{-}1)/34,$ where g is the strength of the repulsive contact interaction and ${n}_{3}$ is the number of excited octupole quanta. Our method provides constraints for these quasidegenerate many-body states and gives higher excitation energies that depend linearly on N.

arXiv:cond-mat/0012458Physical Review ANov 15, 20016 citations

Elementary excitation spectrum of a trapped weakly interacting Bose-Einstein condensate

Mircea Marinescu, Anthony F. Starace

An analytic expression is presented for the elementary excitation spectrum of the Bose-Einstein condensate of a trapped boson system in the weakly interacting, low-density limit. Explicit analytic formulas for the elementary excitation spectrum are obtained for harmonic-oscillator traps. These formulas provide information about the behavior of the elementary excitation levels as a function of the number of atoms and their interaction strength for a given trap geometry. They also provide a low-density benchmark for results of fully numerical calculations.An analytic expression is presented for the elementary excitation spectrum of the Bose-Einstein condensate of a trapped boson system in the weakly interacting, low-density limit. Explicit analytic formulas for the elementary excitation spectrum are obtained for harmonic-oscillator traps. These formulas provide information about the behavior of the elementary excitation levels as a function of the number of atoms and their interaction strength for a given trap geometry. They also provide a low-density benchmark for results of fully numerical calculations.

Physical Review AJul 1, 19978 citations

Excitation spectrum for interacting bosons

Kapil M. Khanna, B.K. Das

PhysicaNov 1, 197314 citations

Perturbative spectrum of trapped weakly interacting bosons in two dimensions

Velimir Bardek, Larisa Jonke, Stjepan Meljanac

We study a trapped Bose-Einstein condensate under rotation in the limit of weak, translational and rotational invariant two-particle interactions. We use the perturbation-theory approach (the large- $N$ expansion) to calculate the ground-state energy and the excitation spectrum in the asymptotic limit where the total number of particles N goes to infinity while keeping the total angular momentum L finite. Calculating the probabilities of different configurations of angular momentum in the exact eigenstates gives us a clear view of the physical content of excitations. We briefly discuss the case of repulsive contact interaction.We study a trapped Bose-Einstein condensate under rotation in the limit of weak, translational and rotational invariant two-particle interactions. We use the perturbation-theory approach (the large-$N$ expansion) to calculate the ground-state energy and the excitation spectrum in the asymptotic limit where the total number of particles N goes to infinity while keeping the total angular momentum L finite. Calculating the probabilities of different configurations of angular momentum in the exact eigenstates gives us a clear view of the physical content of excitations. We briefly discuss the case of repulsive contact interaction.

arXiv:cond-mat/0012438Physical Review AJun 11, 20013 citations

Excitation spectrum and structure factor for interacting bosons

Kapil M. Khanna, S. Chauba Singh, O. P. Sinha

Physica B+CAug 1, 19820 citations

{n}_{3}

is the number of excited octupole quanta. Our method provides constraints for these quasidegenerate many-body states and gives higher excitation energies that depend linearly on N.

We study a trapped Bose-Einstein condensate under rotation in the limit of weak, translational and rotational invariant two-particle interactions. We use the perturbation-theory approach (the large-

N

expansion) to calculate the ground-state energy and the excitation spectrum in the asymptotic limit where the total number of particles N goes to infinity while keeping the total angular momentum L finite. Calculating the probabilities of different configurations of angular momentum in the exact eigenstates gives us a clear view of the physical content of excitations. We briefly discuss the case of repulsive contact interaction.