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260172 UE Quantum gases-collisions and statistics (2013S)
Continuous assessment of course work
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Vorbesprechung: 04.03.2013, 14:00 Uhr, Ernst-Mach-Hörsaal, Boltzmanng. 5, 2.StockTermine:
12.04., 19.04., 26.04., 03.05., 10.05., 17.05., 24.05., 31.05., 07.06., 14.06., 21.06. und 28.06.2013 jeweils von 13:00-14:30 Uhr im Josef-Stefan-Hörsaal, Boltzmanngasse 5, 2.Stock, 1090 Wien
12.04., 19.04., 26.04., 03.05., 10.05., 17.05., 24.05., 31.05., 07.06., 14.06., 21.06. und 28.06.2013 jeweils von 13:00-14:30 Uhr im Josef-Stefan-Hörsaal, Boltzmanngasse 5, 2.Stock, 1090 Wien
Details
Information
Aims, contents and method of the course
Assessment and permitted materials
Written, with homework problems
Minimum requirements and assessment criteria
These lectures give an introduction in the kinetic and energetic aspects of collisions in quantum gases of neutral atoms. Further we have a look at the quantum statistics with emphasis on inhomogeneous gases and confinement by external trapping potentials.
Examination topics
Oral (3/4) plus discussion of homework problems (1/4)
Reading list
Syllabus - will be given in the lectures
Association in the course directory
MaG 18, MaV 5, Dok 1.
Last modified: Fr 31.08.2018 08:55
Hamiltonian of trapped gas with binary interactions; ideal gas limit; quasi-classical behavior; canonical distribution; link to thermodynamics; phase-space distributions of trapped gases; density of states; power-law traps; adiabatic variations of trapping potentials – adiabatic cooling; evaporative cooling.
2. Quantum motion in an interaction potential
Radial Schrödinger equation for a simple model potential (3D square well); phase shift - the central quantity in quantum scattering. Characteristic length scales: range of the interaction, scattering length and effective range. Scattering resonances; energy of a gas with binary interactions. Generalization to arbitrary short-range potentials; Van der Waals interaction as an example.
3. Quantum collisions
Relation between phase shift and collisional properties; partial wave scattering amplitudes; differential and total cross section; scattering of identical atoms; scattering at low energy; Ramsauer-Townsend effect.
4. Kinetic phenomena in dilute quasi-classical gases
Boltzmann equation for a collisionless gas; Boltzmann equation in the presence of collisions; collision rates in equilibrium gases; Thermalization.
5. Quantum Statistics
Occupation number representation; grand canonical distribution; statistical operator; ideal quantum gases; Gibbs factor; Bose-Einstein statistics; Fermi-Dirac statistics; Semi-classical approximation – dependence on dimensionality; grand partition function; link to thermodynamics.
6. Ideal quantum gases in inhomogeneous traps
Onset of quantum degeneracy; Bose-Einstein condensation; quantum degeneracy without BEC; trapped Fermi gases.