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Ultra-cold dilute-gas systems

A Bose-Einstein condensate forming as Rb87 is evaporatively cooled (Otago University).

Bose-Einstein condensation of dilute Rubidium gas was observed in 1995, sparking intense experimental and theoretical effort on Bose and Fermi gases. For an ultra-cold, nearly pure BEC, the system is well described by treating it as a single highly occupied quantum state, leading to the Gross-Pitaevskii theory of superfluid BECs. The theory resembles the ordinary single-particle Schroedinger equation, with a modified effective potential that describes two-body scattering between the atoms in the cold collision regime. The Gross-Pitaevskii equation and its semi-classical generalizations have provided an adequate description of a wide range of low-temperature phenomena in dilute gas BECs.

Stochastic Projected Gross-Pitaevskii theory

Relying as it does on the assumption that almost all of the atoms are in a single U(1) symmetry breaking ground state, the GP-theory struggles to give a reasonable description as the system approaches the critical temperature. A powerful generalization of the GPE, namely the Stochastic Projected GPE, has been developed. The theory is a grand canonical finite temperature theory; it uses methods pioneered in quantum optics for treating open quantum systems, and achieves a consistent and practical treatment of reservoir interactions and UV-divergences in the field theory.

The SPGPE theory has the advantage that chemical potential and temperature are control parameters of the theory, which greatly simplifies many practical calculations.

We are generalizing and applying the SPGPE to a range of high temperature BEC phenomena, including vortex formation and decay, critical phenomena, topological defect formation during the transition, spinor BECs, dipolar BECs, and persistent current formation and stability.

Two dimensional quantum turbulence

Quantized vortices were observed in the degenerate Bose gas in 1998. With increasing control and scope for manipulation, experiments are now able to probe a wide new range of vortex physics, and address long standing questions from condensed matter physics regarding the nature of vortices, their interactions, statistics, and mechanisms of formation and decay. The SPGPE forms an important tool in this work, offering a description of two important physical effects that vortices are sensitive to: dissipation, and fluctuations.

Three dimensional turbulence

In forced three dimensional turbulence, energy is transported from large to smaller scales through the decay of eddies via bending instability, as seen in this footage of a dragon fly. This process is known as a Richardson cascade, and an ideal cascade has an energy spectrum that takes a power law form, identified by Kolmogorov (and independently Onsager and Heisenberg) as E(k)~k-5/3.

Air flow past a dragon fly from the Japanese Society of Fluid Mechanics

Two dimensional turbulence

When the fluid is confined to two dimensions the bending instability is suppressed. The flow of energy reverses, and small eddies accumulate to form giant coherent structures, such as the Great Red Spot in the Jovian atmosphere.

Voyager 1 approach to Jupiter, 1979

Apparently low entropy states can thus emerge from chaotic motion. Maarten Rutgers developed some very clear experimental demonstrations of this phenomenon using soap films

Soap film turbulence image from Maarten Rutgers website

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