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

Probabilistic Hysteresis in an Isolated Quantum System: The Microscopic Onset of Irreversibility from a Quantum Perspective

Recently probabilistic hysteresis in isolated Hamiltonian systems of ultracold atoms has been studied in the limit of large particle numbers, where a semiclassical treatment is adequate. The origin of irreversibility in these sweep experiments, where a control parameter is slowly (adiabatically) tuned back and forth, turned out to be a passage blue back and forth across a separatrix (integrable case) or a passage in and out of a chaotic sea in phase space (chaotic case). Here we focus on the full quantum mechanical description of the integrable system and show how the semiclassical results emerge in the limit of large particle numbers. Instead of the crossing of a separatrix in phase space, where classical adiabaticity fails, the origin of irreversibility in the quantum system is a series of avoided crossings of the adiabatic energy levels: they become so close that already for modest particle numbers the change of the external parameter has to be unrealistically slow to reach the quantum adiabatic limit of perfectly reversible evolution. For a slow but finite sweep rate we find a broad regime where the quantum results agree with the semiclassical results, but only if besides the limit $N\to \infty$ an initial ensemble of states is considered, with sufficient initial energy width. For a single initial energy eigenstate we find in contrast that the backward sweep reveals strong quantum effects even for very large particle numbers

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

Threshold coupling strength for equilibration between small systems

In this paper we study the thermal equilibration of small bipartite Bose-Hubbard systems, both quantum mechanically and in mean-field approximation. In particular we consider small systems composed of a single-mode "thermometer" coupled to a three-mode "bath", with no additional environment acting on the four-mode system, and test the hypothesis that the thermometer will thermalize if and only if the bath is chaotic. We find that chaos in the bath alone is neither necessary nor sufficient for equilibration in these isolated four-mode systems. The two subsystems can thermalize if the combined system is chaotic even when neither subsystem is chaotic in isolation, and under full quantum dynamics there is a minimum coupling strength between the thermometer and the bath below which the system does not thermalize even if the bath itself is chaotic. We show that the quantum coupling threshold scales like $1/N$ (where $N$ is the total particle number), so that the classical results are obtained in the limit $N\rightarrow \infty$

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

Post-adiabatic Hamiltonian for low-energy excitations in a slowly time-dependent BCS-BEC crossover

We develop a Hamiltonian that describes the time-dependent formation of a molecular Bose-Einstein condensate (BEC) from a Bardeen-Cooper-Schrieffer (BCS) state of fermionic atoms as a result of slowly sweeping through a Feshbach resonance. In contrast to many other calculations in the field (see e.g. [1-4]), our Hamiltonian includes the leading post-adiabatic effects that arise because the crossover proceeds at a non-zero sweep rate. We apply a path integral approach and a stationary phase approximation for the molecular zero momentum background, which is a good approximation for narrow resonances (see e.g. [5, 6]). We use two-body adiabatic approximations to solve the atomic evolution within this background. The dynamics of the non-zero momentum molecular modes is solved within a dilute gas approximation and by mapping it onto a purely bosonic Hamiltonian. Our main result is a post-adiabatic effective Hamiltonian in terms of the instantaneous bosonic (Anderson-)Bogoliubov modes, which holds throughout the whole resonance, as long as the Feshbach sweep is slow enough to avoid breaking Cooper pairs