arXiv subjects
Publications and source records attributed to Uwe R. Fischer.
We propose an experimental scheme to observe the Gibbons-Hawking effect in the acoustic analog of a 1+1-dimensional de Sitter universe, produced in an expanding, cigar-shaped Bose-Einstein condensate. It is shown that a two-level system created at the center of the trap, an atomic quantum dot interacting with phonons, observes a thermal Bose distribution at the de Sitter temperature.
We investigate vortex-antivortex pair creation in a supersonically expanding and contracting quasi-2D Bose-Einstein condensate at zero temperature. For sufficiently large amplitude condensate oscillations, pair production provides the leading dissipation mechanism. The condensate oscillations decay in a nonexponential fashion, and the dissipation rate depends strongly on the oscillation amplitude. These features allow to distinguish the decay due to pair creation from other possible damping mechanisms. Experimental observation of the predicted oscillation behavior of the superfluid gas provides a direct confirmation of the hydrodynamical analogy of quantum electrodynamics and quantum vortex dynamics in two spatial dimensions.
We show that, in the Thomas-Fermi regime, the cores of vortices in rotating dilute Bose-Einstein condensates adjust in radius as the rotation velocity, $Ω$, grows, thus precluding a phase transition associated with core overlap at high vortex density. In both a harmonic trap and a rotating hard-walled bucket, the core size approaches a limiting fraction of the intervortex spacing. At large rotation speeds, a system confined in a bucket develops, within Thomas-Fermi, a hole along the rotation axis, and eventually makes a transition to a giant vortex state with all the vorticity contained in the hole.
We construct a kinematical analogue of superluminal travel in the ``warped'' space-times curved by gravitation, in the form of ``super-phononic'' travel in the effective space-times of perfect nonrelativistic fluids. These warp-field space-times are most easily generated by considering a solid object that is placed as an obstruction in an otherwise uniform flow. No violation of any condition on the positivity of energy is necessary, because the effective curved space-times for the phonons are ruled by the Euler and continuity equations, and not by the Einstein field equations.
We consider quasiparticle propagation in constant-speed-of-sound (iso-tachic) and almost incompressible (iso-pycnal) hydrodynamic flows, using the technical machinery of general relativity to investigate the ``effective space-time geometry'' that is probed by the quasiparticles. This effective geometry, described for the quasiparticles of condensed matter systems by the Painleve-Gullstrand metric, generally exhibits curvature (in the sense of Riemann), and many features of quasiparticle propagation can be re-phrased in terms of null geodesics, Killing vectors, and Jacobi fields. As particular examples of hydrodynamic flow we consider shear flow, a constant-circulation vortex, flow past an impenetrable cylinder, and rigid rotation.
We derive an inequality governing ``long range'' order for a localized Bose-condensed state, relating the condensate fraction at a given temperature with effective curvature radius of the condensate and total particle number. For the specific example of a one-dimensional, harmonically trapped dilute Bose condensate, it is shown that the inequality gives an explicit upper bound for the Thomas-Fermi condensate size which may be tested in current experiments.
We consider acoustic propagation in an irrotational vortex, using the technical machinery of differential geometry to investigate the ``acoustic geometry'' that is probed by the sound waves. The acoustic space-time curvature of a constant circulation hydrodynamical vortex leads to deflection of phonons at appreciable distances from the vortex core. The scattering angle for phonon rays is shown to be quadratic in the small quantity $Γ/(2πcb)$, where $Γ$ is the vortex circulation, $c$ the speed of sound, and $b$ the impact parameter.
We compare dynamical and energetical stability criteria for vortex rings. It is argued that vortex rings will be intrinsically unstable against perturbations with short wavelengths below a critical wavelength, because the canonical vortex Hamiltonian is unbounded from below for these modes. To explicitly demonstrate this behaviour, we derive the oscillation spectrum of vortex rings in incompressible, inviscid fluids, within a geometrical cutoff procedure for the core. The spectrum develops an anomalous branch of negative group velocity, and approaches the zero of energy for wavelengths which are about six times the core diameter. We show the consequences of this dispersion relation for the thermodynamics of vortex rings in superfluid $^4$He at low temperatures.
We derive electromagnetomotive force fields for charged particles moving in a rotating Hall sample, satisfying a twofold U(1) gauge invariance principle. It is then argued that the phase coherence property of quantization of the line integral of total collective particle momentum into multiples of Planck's quantum of action is solely responsible for quantization in the Hall state. As a consequence, the height of the Hall quantization steps should remain invariant in a rapidly rotating Hall probe. Quantum Hall particle conductivities do not depend on charge and mass of the electron, and are quantized in units of the inverse of Planck's action quantum.
The geometric theory of vortex tunnelling in superfluid liquids is developed. Geometry rules the tunnelling process in the approximation of an incompressible superfluid, which yields the identity of phase and configuration space in the vortex collective co-ordinate. To exemplify the implications of this approach to tunnelling, we solve explicitly for the two-dimensional motion of a point vortex in the presence of an ellipse, showing that the hydrodynamic collective co-ordinate description limits the constant energy paths allowed for the vortex in configuration space. We outline the experimental procedure used in helium II to observe tunnelling events, and compare the conclusions we draw to the experimental results obtained so far. Tunnelling in Fermi superfluids is discussed, where it is assumed that the low energy quasiparticle excitations localised in the vortex core govern the vortex dynamical equations. The tunnelling process can be dominated by Hall or dissipative terms, respectively be under the influence of both, with a possible realization of this last intermediate case in unconventional, high-temperature superconductors.
We give an account of the physical behaviour of a quasiparticle horizon due to non-Lorentz invariant modifications of the effective space-time experienced by the quasiparticles (``matter'') for high momenta. By introducing a ``relativistic'' conserved energy-momentum tensor, we derive quasi-equilibrium states of the fluid across the ``Landau'' quasiparticle horizon at temperatures well above the quantum Hawking temperature. Nonlinear dispersion of the quasiparticle energy spectrum is instrumental for quasiparticle communication and exchange across the horizon. It is responsible for the establishment of the local thermal equilibrium across the horizon with the Tolman temperature being inhomogeneous behind the horizon. The inhomogeneity causes relaxation of the quasi-equilibrium states due to scattering of thermal quasiparticles, which finally leads to a shrinking black hole horizon. This process serves as the classical thermal counterpart of the quantum effect of Hawking radiation and will allow for an observation of the properties of the horizon at temperatures well above the Hawking temperature. We discuss the thermal entropy related to the horizon. We find that only the first nonlinear correction to the energy spectrum is important for the thermal properties of the horizon. They are fully determined by an energy of order $E_{\rm Planck}(T/E_{\rm Planck})^{1/3}$, which is well below the Planck energy scale $E_{\rm Planck}$, so that Planck scale physics is not involved in determining thermal quantities related to the horizon.
It is pointed out that the specific heat of helical vortex line excitations, in low temperature superfluid turbulence experiments carried out in helium II, can be of the same order as the specific heat of the phononic quasiparticles. The ratio of Kelvin mode and phonon specific heats scales with L_0 T^{-5/2}, where L_0 represents the smoothed line length per volume within the vortex tangle, such that the contribution of the vortex mode specific heat should be observable for L_0 = 10^6-10^8 cm^{-2}, and at temperatures which are of order 1-10 mK.
The general local, nondissipative equations of motion for a quantized vortex moving in an uncharged laboratory superfluid are derived from a relativistic, co-ordinate invariant framework, having vortices as its elementary objects in the form of stable topological excitations. This derivation is carried out for a pure superfluid with isotropic gap at the absolute zero of temperature, on the level of a hydrodynamic, collective co-ordinate description. In the formalism, we use as fundamental ingredients that particle number as well as vorticity are conserved, and that the fluid is perfect. No assumptions are involved as regards the dynamical behaviour of the order parameter. The interaction of the vortex with the background fluid, representing the Magnus force, and with itself via phonons, giving rise to the hydrodynamic vortex mass, are separated. For a description of the motion of the vortex in a dense laboratory superfluid like helium II, two limits have to be considered: The nonrelativistic limit for the superfluid background is taken, and the motion of the vortex is restricted to velocities much less than the speed of sound. The canonical structure of vortex motion in terms of the collective co-ordinate is used for the quantization of this motion.
The quantum tunnelling and nucleation theory of vortices in helium II is reviewed. Arguments are given that the only reliable method to calculate tunnelling probabilities in this highly correlated, strongly interacting many-body system is the semiclassical, large scale approach for evaluation of the tunnelling exponent, which does not make any assumptions about the unknown dynamical behaviour of the fluid on microscopic scales. The geometric implications of this semiclassical theory are represented in some detail and its relevance for the interpretation of experimental data is discussed.
In the semiclassical domain the exponent of vortex quantum tunneling is dominated by a volume which is associated with the path the vortex line traces out during its escape from the metastable well. We explicitly show the influence of geometrical quantities on this volume by describing point vortex motion in the presence of an ellipse. It is argued that for the semiclassical description to hold the introduction of an additional geometric constraint, the distance of closest approach, is required. This constraint implies that the semiclassical description of vortex nucleation by tunneling at a boundary is in general not possible. Geometry dependence of the tunneling volume provides a means to verify experimental observation of vortex quantum tunneling in the superfluid Helium II.
We demonstrate the way in which vortex rings in neutral superfluids are equivalent to massive, charged, elastic strings in an electromagnetic field defined locally on the string from a Kalb-Ramond gauge field. We argue that the action thus obtained describes an intermediate scale of vortex motion with phonon fluctuations of the line between the incompressible hydrodynamic régime and the microscopic one dominated by roton emission and absorption. The formalism gives an accurate semiclassical picture of vortex string motion and is of relevance for the description of vortex ring quantum nucleation in a perturbation theory of the purely incompressible case.