On the theory of point vortices in two-dimensional Bose liquids

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1991

OSTI ID:5589188

Speliotopoulos, A D

The physics and structure of the Kosterlitz-Thouless phase transition, as it is applied to superfluidity in two dimensions, will be studied by looking at the origins and properties of point vortices in a Bose Liquid. A lagrangian for the two-dimensional vortex gas is derived from a general microscopic lagrangian for {sup 4}He atoms on an arbitrary compact Riemann Surface without boundary. In the contrast density limit the vortex hamiltonian obtained from this lagrangian is found to be the same as the Kosterlitz and Thouless coulombic interaction hamiltonian. The dynamics and symmetries of the vortex gas on compact Riemann Surfaces are analyzed using lagrangian dynamics and Dirac's theory of constraints is used to formulate the hamiltonian dynamics for the system. The superfluid phase transition of the general vortex gas, in which the circulations may be any non-zero integer, is studied. When the net circulation of the system is not zero the absence of a superfluid phase is shown. When the net circulation of the vortices vanishes, presence of off-diagonal long range order is demonstrated and the existence of an order parameter is proposed. The transition temperature for general vortex gas is shown to be the Kosterlitz-Thouless temperature. An upper bound for the average vortex number density is established for the general vortex gas and an exact expression is derived for the Kosterlitz-Thouless ensemble.

• Research Organization: California Univ., Berkeley, CA (United States)
• OSTI ID: 5589188
• Country of Publication: United States
• Language: English

Related Subjects

665420* -- Superfluidity-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOSE-EINSTEIN GAS
DYNAMICS
EVEN-EVEN NUCLEI
FUNCTIONS
HELIUM 4
HELIUM ISOTOPES
ISOTOPES
KOSTERLITZ-THOULESS THEORY
LAGRANGIAN FUNCTION
LIGHT NUCLEI
MATHEMATICAL SPACE
MECHANICS
NUCLEI
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
RIEMANN SPACE
SPACE
STABLE ISOTOPES
SUPERFLUIDITY
SYMMETRY
THERMODYNAMIC PROPERTIES
TRANSITION TEMPERATURE
VORTICES