ScienceWeek

QUANTUM PHYSICS: ON NONEQUILIBRIA IN ONE DIMENSION

The following points are made by Henk T. Stoof (Nature 2006 440:877):

1) Through microscopic collisions that result in macroscopic processes such as the diffusion of particles and energy, nature's first tendency is to seek a state of thermodynamic equilibrium, in which all mechanical, chemical and thermal variables reach constant values. In an ultracold atomic gas, for example, a state of equilibrium has generally been reached by the time each atom has collided with just three others.

2) The speed with which relaxation occurs makes observing non-equilibrium phenomena difficult. We are all, for instance, familiar with the equilibrium state of condensation on our windows on a cold day. However, actually seeing the non-equilibrium process -- the formation and growth of the water droplets -- is not so common. But help may be at hand: New work [1] discloses that an atomic gas, when confined to an array of one-dimensional tubes by a web of laser beams, does not relax to equilibrium -- even after each atom has collided several thousand times.

3) Physics in one dimension is often strange and counter-intuitive. Two atoms brought very close to one another repel each other strongly, so, classically speaking, when an atomic gas is confined to a one-dimensional tube, every atom in the gas is restricted to oscillating back and forth between its two neighbors. This situation can be brought about quantum mechanically also [2,3], in which case a so-called Tonks gas forms. In quantum mechanics, however, atoms can generally also pass through each other, and so do not have to be reflected completely. Both the fully and partially reflecting regimes are considered by Kinoshita et al [1], with identical outcomes.

4) The results of their experiments are most easily understood by noting that, compared with the situation in three dimensions, a collision between two atoms in a one-dimensional tube is always very simple. In three dimensions, if two incoming atoms have a head-on collision, the outgoing atoms are located on a spherical shell that expands isotropically from the point of impact, as has been dramatically confirmed in experiment [4,5]. The collisions can change the velocities of the incoming atoms, allowing the velocity distribution of the gas to assume its equilibrium form -- a process known as thermalization. If the collision takes place in a one-dimensional tube, however, the outgoing spherical shell collapses to two points, and the velocities of the outgoing atoms are exactly the same as those of the incoming atoms. Collisions cannot, therefore, change the velocity distribution of the gas and so bring about thermalization.

References:

1. Kinoshita, T. , Wenger, T. & Weiss, D. S. Nature 440, 900-903 (2006)

2. Kinoshita, T. , Wenger, T. & Weiss, D. S. Science 305, 1125-1128 (2004)

3. Paredes, B. et al. Nature 429, 277-281 (2004)

4. Chikkatur, A. P. et al. Phys. Rev. Lett. 85, 483-486 (2000)

5. Buggle, Ch. et al. Phys. Rev. Lett. 93, 173202 (2004)

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