Quantum gases: dynamical versus statistical interaction
Tutorial talk exploring the thermodynamic properties of quantum
gases.
Effects of spatial dimensionality:
- dimensionality as continuous parameter,
- disk-shaped atomic trap (quasi-two-dimensional),
- cigar-shaped atomic trap (quasi-one-dimensional).
Effects of containment:
- atomic traps with walls of various degrees of softness,
- existence of Bose condensate depends on dimensionality and
wall softness.
Effects of fractional exclusion statistics:
- generalized Pauli principle,
- interpolation between fermions and bosons,
- semions, Fibonacci numbers, and the golden section,
- counting rules and placement rules,
- Calogero-Sutherland model,
- thermodynamics of ideal semion gas,
- concept of statistical interaction.
Effects of dynamical interaction:
- nonlinear Schrödinger model,
- thermodynamic Bethe ansatz,
- equivalence between dynamical and statistical interaction.