Harry L. Morrison

On the dynamics of quantum vortices

Abstract We consider the functional integral representation of the interacting Bose system. Within the steepest descents approximation, the evolution equations of quantum vortices are obtained.

Robust L Estimation of Scale with an Application in Astronomy

Abstract In this article, we investigate the robustness properties of a class of L estimators of scale and then develop robust procedures for making inferences about scale. We pay particular attention to trimmed estimators that should perform well when the underlying model is Gaussian. We find that trimmed versions of the efficient linear L estimator for the Gaussian distribution perform better than trimmed standard deviation estimators. We then apply a trimmed version of the efficient linear L estimator for the Gaussian distribution to astronomical data.

Absence of Long‐Range Order in Thin Films

Thin films are described as idealized systems having finite extent in one direction but infinite extent in the other two. For systems of particles interacting through smooth potentials (e.g., no hard cores), it is shown that an equilibrium state for a homogeneous thin film is necessarily invariant under any continuous internal symmetry group generated by a conserved density. For short‐range interactions it is also shown that equilibrium states are necessarily translation invariant. The absence of long‐range order follows from its relation to broken symmetry. The only properties of the state required for the proof are local normality, spatial translation invariance, and the Kubo‐Martin‐Schwinger boundary condition. The argument employs the Bogoliubov inequality and the techniques of the algebraic approach to statistical mechanics. For inhomogeneous systems, the same argument shows that all order parameters defined by anomalous averages must vanish. Identical results can be obtained for systems with infinit...

Quantum theory of the two-dimensional Bose liquid

Abstract The local matter density and current density have proven natural coordinates for the study of the elementary excitation spectrum in the Bose liquid. A fundamental decomposition of the current density into algebraic and topological parts is shown to yield both quasiparticle and pseudoparticle excitations.

GALILEAN RELATIVITY, LOCALITY, AND QUANTUM HYDRODYNAMICS.

In this work we study the consequences of locality and Galilean covariance for the operators that occur in Landaus quantum hydrodynamics. We specifically consider the following requirements: (1) Galilean covariance of the velocity field, (2) locality of the velocity field, and (3) Landaus assumption that the momentum density is a symmetrized product of the velocity and density operators. It is demonstrated that the density‐velocity commutation relation of the Landau theory is essentially a direct consequence of (1) and (2). The addition of (3) is sufficient to determine the velocity‐velocity commutation relation, also in agreement with Laudau. We further show that the density‐velocity commutation relation, independent of (3) or any specific form for the velocity field, is inconsistent with the nonnegative character of the local density.

Derivation of the Landau quantum hydrodynamics for interacting bose systems

In this work we demonstrate that the basic equations of the Landau hydrodynamics may be derived directly from the quantum-mechanical microscopic N-body Hamiltonian, which is expressed as a functional of the local observables, namely, particle and current densities. The Landau quantum hydrodynamic equations are then the Heisenberg equations of motion of these quantities.

ON THE KOSTERLITZ–THOULESS TRANSITION ON COMPACT RIEMANN SURFACES

A Lagrangian for the two-dimensional vortex gas is derived from a general microscopic Lagrangian for 4He atoms on an arbitrary compact Riemann Surface without boundary. In the constant density limit the vortex Hamiltonian obtained from this Lagrangian is found to be the same as the Kosterlitz and Thouless Coulombic interaction Hamiltonian. The partition function for the Kosterlitz–Thouless ensemble on the general compact is formulated and mapped into the sine–Gordon field theory.

Observations on the dynamics of the two-dimensional vortex gas on compact Riemann surfaces

The dynamics and symmetries of the two-dimensional vortex gas on compact Riemann surfaces are analysed using Lagrangian dynamics. As the vortex Lagrangian is linear in the canonical momenta, Diracs theory of constraints is then used to form the Hamiltonian dynamics for the system.

On the theory of superfluidity in two dimensions

The superfluid phase transition ofthe general vortex gas, in which the circulatims may be any non-zero integer, is studied. When the net circulation of the system is not zero the absence ofasuperfluid phase is shown. When the net circulation ofthevortices vanishes. the presence of off-diagonal long range order is demonstrated and the existence of an order parameter is proposed. The transition temperature for the general vortex gas is shown to be the Koaterlitz-Thouless temperature. An upper bound for the average vortex number density is established for the general vonex gas and an exact expression is derived for the Kosterlitz-Thouleas ensemble.

Representations of the diffeomorphism group describing an infinite Bose gas in the presence of ideal vortex filaments

A number of representations of the group of volume preserving diffeomorphisms of M=S3 in the finite‐volume case and M=R3 in the infinite‐volume case that describe a Bose gas in the presence of a vortex filament are examined. The core of the vortex is taken to lie along a curve γ. Let Difu2009u2009fu2009γμ(M) be the group of volume preserving diffeomorphisms that map γ onto itself, Mγ the manifold M with γ removed, and Map(Mγ,T) the space of smooth maps of Mγ into the complex numbers of modulus unity. It is shown, using the formalism of Klauder [J. Math. Phys. 11, 233 (1970)], that an infinite number of inequivalent representations of Difu2009u2009fu2009γμ(M) exist in the infinite‐volume limit using cyclic vectors, which are coherent states based on elements in Map(Mγ,T). It is found, however, that these states have questionable physical significance since they appear to violate the continuity equation for quantum probability flow. This leads to the postulation that Difu2009u2009fu2009γμ(M) acts as gauge group. The representations of Difu2009u2009fu2009...