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Excited states of a static dilute spherical Bose condensate in a trap | Alexander L. Fetter
; | Date: |
4 Jun 1996 | Subject: | cond-mat atom-ph | Affiliation: | Physics Department, Stanford University | Abstract: | The Bogoliubov approximation is used to study the excited states of a dilute gas of $N$ atomic bosons trapped in an isotropic harmonic potential characterized by a frequency $omega_0$ and an oscillator length $d_0 = sqrt{hbar/momega_0}$. The self-consistent static Bose condensate has macroscopic occupation number $N_0 gg 1$, with nonuniform spherical condensate density $n_0(r)$; by assumption, the depletion of the condensate is small ($N’ equiv N - N_0ll N_0$). The linearized density fluctuation operator $hat
ho’$ and velocity potential operator $hatPhi’$ satisfy coupled equations that embody particle conservation and Bernoulli’s theorem. For each angular momentum $l$, introduction of quasiparticle operators yields coupled eigenvalue equations for the excited states; they can be expressed either in terms of Bogoliubov coherence amplitudes $u_l(r)$ and $v_l(r)$ that determine the appropriate linear combinations of particle operators, or in terms of hydrodynamic amplitudes $
ho_l’(r)$ and $Phi_l’(r)$. The hydrodynamic picture suggests a simple variational approximation for $l >0$ that provides an upper bound for the lowest eigenvalue $omega_l$ and an estimate for the corresponding zero-temperature occupation number $N_l’$; both expressions closely resemble those for a uniform bulk Bose condensate. | Source: | arXiv, cond-mat/9606016 | Services: | Forum | Review | PDF | Favorites |
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