Bogoliubov Excitations of Inhomogeneous Bose-Einstein ...
Bogoliubov Excitations of Inhomogeneous Bose-Einstein ...
Bogoliubov Excitations of Inhomogeneous Bose-Einstein ...
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uν(r) <strong>Bogoliubov</strong> eigenstate, normal component<br />
V External potential<br />
˜V (n) n-th order <strong>of</strong> the smoothed potential (2.24)<br />
�V Scattering amplitude (4.5) in the hydrodynamic regime<br />
vν(r) <strong>Bogoliubov</strong> eigenstate, anomalous component<br />
vk Coefficient for <strong>Bogoliubov</strong> transformation uk = (ɛk − ɛk)/(2 √ ɛkɛk)<br />
W Normal coupling element<br />
ξ Healing length<br />
Y Anomalous coupling element<br />
Z Partition function<br />
Bloch part<br />
Ã(z, t) Envelope function (6.7)<br />
b Collective coordinates (section 6.5): conjugate momentum <strong>of</strong> the<br />
width degree <strong>of</strong> freedom w<br />
d Lattice spacing<br />
dk Phase modulation with wavenumber k (section 6.6)<br />
F Force<br />
η Bounded time variable<br />
∆k Quantity related to the Lyapunov exponent, equation (6.27)<br />
J Tunneling amplitude (6.4)<br />
λ Lyapunov exponent<br />
M Monodromy matrix<br />
p Momentum <strong>of</strong> the wave packet, equation (6.7)<br />
sk Density modulation with wavenumber k (section 6.6)<br />
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