Course 1: Bose-Einstein Condensates in Atomic Gases: Simple Theoretical Results

By Y. Castin. 2001

155 citations recorded by the source corpus.

1.1 1925: Einstein’s prediction for the ideal Bose gas Einstein considered N non-interacting bosonic and non-relativistic particles in a cubic box of volume L3 with periodic boundary conditions. In the thermodynamic limit, defined as $$ N,L \to \infty {\text{ }}with{\text{ }}\frac{N} {{L^3 }} = \rho = constant, $$ (1.1) a phase transition occurs at a temperature Tc defined by: $$ \rho \lambda _{{\text{dB}}}^3 (T_c ) = \zeta (3/2) = 2.612... $$ (1.2) > where we have defined the thermal de Broglie wavelength of the gas as function of the temperature T: $$ \lambda _{{\text{dB}}} (T) = \left( {\frac{{2\pi \hbar ^2 }} {{mk_B T}}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $$ (1.3) and where $ \zeta (\alpha ) = \sum\nolimits_{k = 1}^\infty {1/k^\alpha } $ is the Riemann Zeta function.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/429a4a4db2f1145c8db05224d8e22ad1cfbd2424

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum trajectories and open many-body quantum systems (2014, background): “Moreover, because the collision energies of atoms are very small, the scattering (which typically involves complicated interatomic potentials with many bound states) reduces to a universal regime where the behaviour can be described by a single parameter, the s-wave scattering length ascatt [271,272”
Probing semiclassical analog gravity in Bose-Einstein condensates with widely tunable interactions (2003, background): “(These quantum fluctuations are present even at zero temperature owing to the so-called quantum depletion phenomenon, see for example [23].”