Summary: Adiabatic Swimming in an Ideal Quantum Gas
J. E. Avron, B. Gutkin, and D. H. Oaknin
Department of Physics, Technion, Haifa 32000, Israel
(Received 31 August 2005; published 6 April 2006)
Interference effects are important for swimming of mesoscopic systems that are small relative to the
coherence length of the surrounding quantum medium. Swimming is geometric for slow swimmers and
the distance covered in each stroke is determined, explicitly, in terms of the on-shell scattering matrix.
Remarkably, for a one-dimensional Fermi gas at zero temperature we find that slow swimming is
topological: the swimming distance covered in one stroke is quantized in half integer multiples of the
Fermi wavelength. In addition, a careful choice of the swimming stroke can eliminate dissipation.
DOI: 10.1103/PhysRevLett.96.130602 PACS numbers: 05.70.Ln, 02.40.ÿk, 05.40.ÿa, 73.23.ÿb
The theory of classical swimming studies how a cyclic
change in the shape of a swimmer immersed in a fluid leads
to a change in its location. The theory is both elegant and
practical [1,2] and has been applied to the swimming and
flying of organisms, robots , and microbots [4,5].
A classical medium may be viewed as a limiting case of
quantum medium when the quantum coherence length is
small compared to the size of the swimmer and interfer-
ence is negligible. Quantum mechanics takes over once the