Influence functionals and black body radiation

The Feynman-Vernon formalism is used to obtain a microscopic, quantum mechanical derivation of black body radiation, for a massless scalar field in 1+1 dimensions, weakly coupled to an environment of finite size. The model exhibits the absorption, thermal equilibrium, and emission properties of a canonical black body, but shows that the thermal radiation propagates outwards from the body, with the Planckian spectrum applying inside a wavefront region of finite thickness. The black body environment used in the derivation can be considered to represent a very fine, granular medium, such as lampblack. In the course of developing the model for black body radiation, thermalization of a single harmonic oscillator by a heat bath with slowly varying spectral density is demonstrated. Bargmann-Fock coherent state variables, being convenient for problems involving harmonic oscillators and free fields, are reviewed and then used throughout the paper. An appendix reviews the justification for using baths of independent harmonic oscillators to model generic quantum environments.Comment: 46 pages, Te

Vortices near surfaces of Bose-Einstein condensates

The theory of vortex motion in a dilute superfluid of inhomogeneous density demands a boundary layer approach, in which different approximation schemes are employed close to and far from the vortex, and their results matched smoothly together. The most difficult part of this procedure is the hydrodynamic problem of the velocity field many healing lengths away from the vortex core. This paper derives and exploits an exact solution of this problem in the two-dimensional case of a linear trapping potential, which is an idealization of the surface region of a large condensate. It thereby shows that vortices in inhomogeneous clouds are effectively 'dressed' by a non-trivial distortion of their flow fields; that image vortices are not relevant to Thomas-Fermi surfaces; and that for condensates large compared to their surface depths, the energetic barrier to vortex penetration disappears at the Landau critical velocity for surface modes.Comment: 14 pages, 4 figures. Error in review section corrected, notation simplified, typos corrected. No changes to any results, but a significantly clearer presentatio

How to be master of your domains

Prepare a two-species BEC in a perfectly phase-mixed state. By applying Rabi drives, one can tune the range of wavelengths of phase-separating excitations that are dynamically unstable. Yada yada yada, this determines the characteristic sizes of the eventual spin domains. The trapping potential is neglected because it makes life hard, but of course this is a terrible approximation, and the results are of only inspirational value. Since this is thus a rather trivial calculation, the very modest increase in kudos that might accrue from journal publication does not seem to outweigh the grief of having to change the title.Comment: 2 pages, not submitte

Thermal Equilibrium from the Hu-Paz-Zhang Master Equation

The exact master equation for a harmonic oscillator coupled to a heat bath, derived recently by Hu, Paz and Zhang, is simplified by taking the weak-coupling, late-time limit. The unique time-independent solution to this simplified master equation is the canonical ensemble at the temperature of the bath. The frequency of the oscillator is effectively lowered by the interaction with the bath.Comment: 10 pages, McGill/92--4

Inhomogeneous vortex matter

We present a generalization of the continuum theory of vortex matter for non-uniform superfluid density. This theory explains the striking regularity of vortex lattices observed in Bose-Einstein condensates, and predicts the frequencies of long-wavelength lattice excitations.Comment: 4 page

Mossbauer effect for dark solitons in Bose-Einstein condensates

We show that the energetic instability of dark solitons is associated with particle-like motion, and present a simple equation of motion, based on the M\"ossbauer effect, for dark solitons propagating in inhomogeneous Thomas-Fermi clouds. Numerical simulations support our theory. We discuss some experimental approaches.Comment: 4 pages, three figure

Turbulent Steady States in Two-Dimensional Sonic Black Holes: Superfluid Vortices and Emission of Sound

Simulation of a sonic black-hole/white-hole pair in a (2+1)-dimensional Bose-Einstein condensate shows formation of superfluid vortices through dynamical instabilities seeded by initial quantum noise. The instabilities saturate in a quasi-steady state of superfluid turbulence within the supersonic region, from which sound waves are emitted in qualitative resemblance to Hawking radiance. The power spectrum of the radiation from the slowly decaying two-dimensional sonic black hole is strongly non-thermal, however.Comment: 5 pages, 6 figure

An extension of Bogoliubov theory for a many-body system with a time scale hierarchy: the quantum mechanics of second Josephson oscillations

Adiabatic approximations are a powerful tool for simplifying nonlinear quantum dynamics, and are applicable whenever a system exhibits a hierarchy of time scales. Current interest in small nonlinear quantum systems, such as few-mode Bose-Hubbard models, warrants further development of adiabatic methods in the particular context of these models. Here we extend our recent work on a simple four-mode Bose-Hubbard model with two distinct dynamical time scales, in which we showed that among the perturbations around excited stationary states of the system is a slow collective excitation that is not present in the Bogoliubov spectrum. We characterized this mode as a resonant energy exchange with its frequency shifted by nonlinear effects, and referred to it as a second Josephson oscillation, in analogy with the second sound mode of liquid helium II. We now generalize our previous theory beyond the mean field regime, and construct a general Bogoliubov free quasiparticle theory that explicitly respects the system's adiabatic invariant as well the exact conservation of particles. We compare this theory to the numerically exact quantum energy spectrum with up to forty particles, and find good agreement over a significant range of parameter space

A precision test of decoherence

The motion of a charged particle over a conducting plate is damped by Ohmic resistance to image currents. This interaction between the particle and the plate must also produce decoherence, which can be detected by examining interference patterns made by diffracted particle beams which have passed over the plate. Because the current densities within the plate decay rapidly with the height of the particle beam above it, the strength of decoherence should be adjustable across a wide range, allowing one to probe the full range of quantum through classical behaviour.Comment: 4 pages, PlainTex, 1 embedded figure (needs epsf.tex). To appear in proceedings of the 31st Rencontres de Moriond, 20-27 Jan 199

Probing quantum statistical mechanics with Bose gases: Non-trivial order parameter topology from a Bose-Einstein quench

This is a less technical presentation of the ideas in quant-ph/9804035 [Phys Rev Lett 83 (1999), 1707-1710]. A second order phase transition induced by a rapid quench can lock out topological defects with densities far exceeding their equilibrium expectation values. This phenomenon is a generic prediction of nonequilibrium statistical mechanics, and can appear in a wide range of physical systems. We discuss it qualitatively in the context of trapped dilute Bose-Einstein condensates, outline a simple quantitative theory based on the time-dependent Ginzburg-Landau equation, and briefly compare the results of quantum kinetic theory.Comment: 6 pages, 3 figures, to appear in the proceedings of ISQM Tokyo 9