Shock waves in a one-dimensional Bose gas: from a Bose-Einstein condensate to a Tonks gas

We derive and analyze shock-wave solutions of hydrodynamic equations describing repulsively interacting one dimensional Bose gas. We also use the number-conserving Bogolubov approach to verify accuracy of the Gross-Pitaevskii equation in shock wave problems. We show that quantum corrections to dynamics of shocks (dark-shock-originated solitons) in a Bose-Einstein condensate are negligible (important) for a realistic set of system parameters. We point out possible signatures of a Bose-Einstein condensate -- Tonks crossover in shock dynamics. Our findings can be directly verified in different experimental setups.Comment: 10 pages, small corrections with respect to the last submission, version accepted in Phys. Rev.

Path Integral Quantization of the Symplectic Leaves of the SU(2)* Poisson-Lie Group

The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_q(su(2)). This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parametrizations and also compare the results with the path integral quantization of spin.Comment: 24 pages, LaTeX, no figures, full postscript available from http://phyweb.lbl.gov/theorygroup/papers/40890.p

Nonlinear Schr\"odinger Equation with Spatio-Temporal Perturbations

We investigate the dynamics of solitons of the cubic Nonlinear Schr\"odinger Equation (NLSE) with the following perturbations: non-parametric spatio-temporal driving of the form $f(x,t) = a \exp[i K(t) x]$, damping, and a linear term which serves to stabilize the driven soliton. Using the time evolution of norm, momentum and energy, or, alternatively, a Lagrangian approach, we develop a Collective-Coordinate-Theory which yields a set of ODEs for our four collective coordinates. These ODEs are solved analytically and numerically for the case of a constant, spatially periodic force $f(x)$. The soliton position exhibits oscillations around a mean trajectory with constant velocity. This means that the soliton performs, on the average, a unidirectional motion although the spatial average of the force vanishes. The amplitude of the oscillations is much smaller than the period of $f(x)$. In order to find out for which regions the above solutions are stable, we calculate the time evolution of the soliton momentum $P(t)$ and soliton velocity $V(t)$: This is a parameter representation of a curve $P(V)$ which is visited by the soliton while time evolves. Our conjecture is that the soliton becomes unstable, if this curve has a branch with negative slope. This conjecture is fully confirmed by our simulations for the perturbed NLSE. Moreover, this curve also yields a good estimate for the soliton lifetime: the soliton lives longer, the shorter the branch with negative slope is.Comment: 21 figure

THE TUROLIAN HIPPARIONS FROM CIOBURCIU SITE (REPUBLIC OF MOLDOVA): SYSTEMATICS AND PALEODIET

The Cioburciu hipparions, Republic of Moldova, are included in a Turolian assemblage, approximately dated between 9 and 7 million years. We assess herein their taxonomic position, systematics, biogeography and paleodietary habits. We have undertaken standard equid measurements as well as accessing the Vera Eisenmann website for measurements and images and analysed craniodental and postcranial elements. This assemblage has been determined to be of a medium-sized hipparion with an elongated muzzle, well developed preorbital fossa that is dorsoventrally extensive and placed close to the orbit, lacking a caninus fossa and having a prominent and deep buccinator fossa. As such, this assemblage is referable to Cremohipparion moldavicum Gromova 1952 common to the Western Ukraine, Balkans, Romania, Republic of Georgia, Turkey and Iran. We have employed a combination of gross cheek tooth wear morphology utilizing the mesowear method and a microscopic analysis of occlusal enamel scars utilizing the light microscope microwear technique. These complementary paleodietary methods indicate that these hipparions engaged in a mixed feeding dietary behavior and that the Cioburciu sample of C. moldavicum likely alternated its diet between browsing and grazing seasonally and/or regionally. A hierarchical cluster analysis based on average scratch and pit numbers positions this taxon among extant mixed feeding ungulates. Large pitting and gouging assessed through the microwear technique indicates occasional consumption of relatively coarser foods than typical mixed feeders or grazers or grit-laden food just prior to death while mesowear indicates that this was not a lifetime habit

Shock waves in ultracold Fermi (Tonks) gases

It is shown that a broad density perturbation in a Fermi (Tonks) cloud takes a shock wave form in the course of time evolution. A very accurate analytical description of shock formation is provided. A simple experimental setup for the observation of shocks is discussed.Comment: approx. 4 pages&figures, minor corrections^2, to be published as a Letter in Journal of Physics

Acoustic attenuation rate in the Fermi-Bose model with a finite-range fermion-fermion interaction

We study the acoustic attenuation rate in the Fermi-Bose model describing a mixtures of bosonic and fermionic atom gases. We demonstrate the dramatic change of the acoustic attenuation rate as the fermionic component is evolved through the BEC-BCS crossover, in the context of a mean-field model applied to a finite-range fermion-fermion interaction at zero temperature, such as discussed previously by M.M. Parish et al. [Phys. Rev. B 71, 064513 (2005)] and B. Mihaila et al. [Phys. Rev. Lett. 95, 090402 (2005)]. The shape of the acoustic attenuation rate as a function of the boson energy represents a signature for superfluidity in the fermionic component

On the forward cone quantization of the Dirac field in "longitudinal boost-invariant" coordinates with cylindrical symmetry

We obtain a complete set of free-field solutions of the Dirac equation in a (longitudinal) boost-invariant geometry with azimuthal symmetry and use these solutions to perform the canonical quantization of a free Dirac field of mass $M$. This coordinate system which uses the 1+1 dimensional fluid rapidity $\eta = 1/2 \ln [(t-z)/(t+z)]$ and the fluid proper time $\tau = (t^2-z^2)^{1/2}$ is relevant for understanding particle production of quarks and antiquarks following an ultrarelativistic collision of heavy ions, as it incorporates the (approximate) longitudinal "boost invariance" of the distribution of outgoing particles. We compare two approaches to solving the Dirac equation in curvilinear coordinates, one directly using Vierbeins, and one using a "diagonal" Vierbein representation

Auxiliary field formalism for dilute fermionic atom gases with tunable interactions

We develop the auxiliary field formalism corresponding to a dilute system of spin-1/2 fermions. This theory represents the Fermi counterpart of the BEC theory developed recently by F. Cooper et al. [Phys. Rev. Lett. 105, 240402 (2010)] to describe a dilute gas of Bose particles. Assuming tunable interactions, this formalism is appropriate for the study of the crossover from the regime of Bardeen-Cooper-Schriffer (BCS) pairing to the regime of Bose-Einstein condensation (BEC) in ultracold fermionic atom gases. We show that when applied to the Fermi case at zero temperature, the leading-order auxiliary field (LOAF) approximation gives the same equations as those obtained in the standard BCS variational picture. At finite temperature, LOAF leads to the theory discussed by by Sa de Melo, Randeria, and Engelbrecht [Phys. Rev. Lett. 71, 3202(1993); Phys. Rev. B 55, 15153(1997)]. As such, LOAF provides a unified framework to study the interacting Fermi gas. The mean-field results discussed here can be systematically improved upon by calculating the one-particle irreducible (1-PI) action corrections, order by order.Comment: 12 pages, 5 figure

Z-prime Gauge Bosons at the Tevatron

We study the discovery potential of the Tevatron for a Z-prime gauge boson. We introduce a parametrization of the Z-prime signal which provides a convenient bridge between collider searches and specific Z-prime models. The cross section for p pbar -> Z-prime X -> l^+ l^- X depends primarily on the Z-prime mass and the Z-prime decay branching fraction into leptons times the average square coupling to up and down quarks. If the quark and lepton masses are generated as in the standard model, then the Z-prime bosons accessible at the Tevatron must couple to fermions proportionally to a linear combination of baryon and lepton numbers in order to avoid the limits on Z--Z-prime mixing. More generally, we present several families of U(1) extensions of the standard model that include as special cases many of the Z-prime models discussed in the literature. Typically, the CDF and D0 experiments are expected to probe Z-prime-fermion couplings down to 0.1 for Z-prime masses in the 500--800 GeV range, which in various models would substantially improve the limits set by the LEP experiments.Comment: 34 pages, 13 figure