Bogoliubov Excitations of Inhomogeneous Bose-Einstein ...
Bogoliubov Excitations of Inhomogeneous Bose-Einstein ...
Bogoliubov Excitations of Inhomogeneous Bose-Einstein ...
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A. List <strong>of</strong> Symbols and Abbreviations<br />
ˆH Hamiltonian<br />
η Diagonal matrix diag(1, −1), (section 2.5, subsection 3.3.2)<br />
η(r) Random field on rough surface (only section 3.1)<br />
i Imaginary unit i 2 = −1<br />
k Wave vector<br />
L Distance in speckle geometry (only section 3.1)<br />
Λ Relative correction <strong>of</strong> the dispersion relation [in units <strong>of</strong> V 2 /µ 2 ]<br />
λ Wave length<br />
µ Chemical potential<br />
n Condensate density<br />
P Cauchy principal value<br />
Φ(r) Gross-Pitaevskii ground-state<br />
ˆϕ Phase operator<br />
ˆΨ(r) Field operator<br />
R Diffusor radius in speckle geometry (only section 3.1)<br />
ρ(ω) Density <strong>of</strong> states<br />
Sd Surface <strong>of</strong> the d-dimensional unit sphere<br />
S(k, ω) Spectral function subsection 3.4.1<br />
Σ Self-energy<br />
σ Disorder correlation length<br />
T Transmission coefficient (subsection 2.4.5)<br />
TF Thomas-Fermi (page 26)<br />
138<br />
t Time<br />
uk Coefficient for <strong>Bogoliubov</strong> transformation uk = (ɛk + ɛk)/(2 √ ɛkɛk)