arXiv subjects

Alexander L. Fetter

Publications and source records attributed to Alexander L. Fetter.

39 records · Page 3Linked to original sources

arXiv1996

Variational study of a dilute Bose condensate in a harmonic trap

A two-parameter trial condensate wave function is used to find an approximate variational solution to the Gross-Pitaevskii equation for $N_0$ condensed bosons in an isotropic harmonic trap with oscillator length $d_0$ and interacting through a repulsive two-body scattering length $a>0$. The dimensionless parameter ${\cal N}_0 \equiv N_0a/d_0$ characterizes the effect of the interparticle interactions, with ${\cal N}_0 \ll 1$ for an ideal gas and ${\cal N}_0 \gg 1$ for a strongly interacting system (the Thomas-Fermi limit). The trial function interpolates smoothly between these two limits, and the three separate contributions (kinetic energy, trap potential energy, and two-body interaction energy) to the variational condensate energy and the condensate chemical potential are determined parametrically for any value of ${\cal N}_0$, along with illustrative numerical values. The straightforward generalization to an anisotropic harmonic trap is considered briefly.

cond-mat↗

arXiv1996

Excited states of a static dilute spherical Bose condensate in a trap

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 $ω_0$ and an oscillator length $d_0 = \sqrt{\hbar/mω_0}$. 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 ($N' \equiv N - N_0\ll N_0$). The linearized density fluctuation operator $\hat ρ'$ and velocity potential operator $\hatΦ'$ 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 $ρ_l'(r)$ and $Φ_l'(r)$. The hydrodynamic picture suggests a simple variational approximation for $l >0$ that provides an upper bound for the lowest eigenvalue $ω_l$ and an estimate for the corresponding zero-temperature occupation number $N_l'$; both expressions closely resemble those for a uniform bulk Bose condensate.

cond-mat↗

arXiv1995

Ground State and Excited States of a Confined Bose Gas

The Bogoliubov approximation is used to study the ground state and low-lying excited states of a dilute gas of $N$ atomic bosons held in an isotropic harmonic potential characterized by frequency $ω$ and oscillator length $d_0$. By assumption, the self-consistent condensate has a macroscopic occupation number $N_0 >> 1$, with $N-N_0 << N_0$. For negative scattering length $ -|a|$, a simple variational trial function yields an estimate for the critical condensate number $N_{0\,c} = \big({8π/25\sqrt{5}}\,\big)^{1/2}\,(d_0/|a|) \approx 0.671\,(d_0/|a|)$ at the onset of collapse. For positive scattering length and large $N_0 >>d_0/a$, the spherical condensate has a well-defined radius $R >> d_0$, and the low-lying excited states are compressional waves localized near the surface. The frequencies of the lowest radial modes ($n = 0$) for successive values of orbital angular momentum $l$ form a rotational band $ω_{0l} \approx ω_{00} + {1\over 2} l(l+1)\,ω\,(d_0/R)^2$, with $ω_{00} $ somewhat larger than $ω$.

cond-mat↗