Spin-charge separation in cold Fermi-gases: a real time analysis

Using the adaptive time-dependent density-matrix renormalization group method for the 1D Hubbard model, the splitting of local perturbations into separate wave packets carrying charge and spin is observed in real-time. We show the robustness of this separation beyond the low-energy Luttinger liquid theory by studying the time-evolution of single particle excitations and density wave packets. A striking signature of spin-charge separation is found in 1D cold Fermi gases in a harmonic trap at the boundary between liquid and Mott-insulating phases. We give quantitative estimates for an experimental observation of spin-charge separation in an array of atomic wires

Phases of Bosons or Fermions in confined optical lattices

Phases of Bose or Fermi atoms in optical lattices confined in harmonic traps are studied within the Thomas-Fermi approximation. Critical radii and particle number for onset of Mott insulator states are calculated and phase diagrams shown in 1D, and estimated for 2 and 3D. Methods to observe these and novel phases such as d-wave superconductivity is discussed. Specifically the collective modes are calculated.Comment: Revised and extended. To appear in PR

Magnetic Braking and Viscous Damping of Differential Rotation in Cylindrical Stars

Differential rotation in stars generates toroidal magnetic fields whenever an initial seed poloidal field is present. The resulting magnetic stresses, along with viscosity, drive the star toward uniform rotation. This magnetic braking has important dynamical consequences in many astrophysical contexts. For example, merging binary neutron stars can form "hypermassive" remnants supported against collapse by differential rotation. The removal of this support by magnetic braking induces radial fluid motion, which can lead to delayed collapse of the remnant to a black hole. We explore the effects of magnetic braking and viscosity on the structure of a differentially rotating, compressible star, generalizing our earlier calculations for incompressible configurations. The star is idealized as a differentially rotating, infinite cylinder supported initially by a polytropic equation of state. The gas is assumed to be infinitely conducting and our calculations are performed in Newtonian gravitation. Though highly idealized, our model allows for the incorporation of magnetic fields, viscosity, compressibility, and shocks with minimal computational resources in a 1+1 dimensional Lagrangian MHD code. Our evolution calculations show that magnetic braking can lead to significant structural changes in a star, including quasistatic contraction of the core and ejection of matter in the outermost regions to form a wind or an ambient disk. These calculations serve as a prelude and a guide to more realistic MHD simulations in full 3+1 general relativity.Comment: 20 pages, 19 figures, 3 tables, AASTeX, accepted by Ap

Polaron to molecule transition in a strongly imbalanced Fermi gas

A single down spin Fermion with an attractive, zero range interaction with a Fermi sea of up-spin Fermions forms a polaronic quasiparticle. The associated quasiparticle weight vanishes beyond a critical strength of the attractive interaction, where a many-body bound state is formed. From a variational wavefunction in the molecular limit, we determine the critical value for the polaron to molecule transition. The value agrees well with the diagrammatic Monte Carlo results of Prokof'ev and Svistunov and is consistent with recent rf-spectroscopy measurements of the quasiparticle weight by Schirotzek et. al. In addition, we calculate the contact coefficient of the strongly imbalanced gas, using the adiabatic theorem of Tan and discuss the implications of the polaron to molecule transition for the phase diagram of the attractive Fermi gas at finite imbalance.Comment: 10 pages, 4 figures, RevTex4, minor changes, references adde

Gravitational waves from relativistic rotational core collapse

We present results from simulations of axisymmetric relativistic rotational core collapse. The general relativistic hydrodynamic equations are formulated in flux-conservative form and solved using a high-resolution shock-capturing scheme. The Einstein equations are approximated with a conformally flat 3-metric. We use the quadrupole formula to extract waveforms of the gravitational radiation emitted during the collapse. A comparison of our results with those of Newtonian simulations shows that the wave amplitudes agree within 30%. Surprisingly, in some cases, relativistic effects actually diminish the amplitude of the gravitational wave signal. We further find that the parameter range of models suffering multiple coherent bounces due to centrifugal forces is considerably smaller than in Newtonian simulations.Comment: 4 pages, 3 figure

Oscillating Casimir force between impurities in one-dimensional Fermi liquids

We study the interaction of two localized impurities in a repulsive one-dimensional Fermi liquid via bosonization. In a previous paper [Phys. Rev. A 72, 023616 (2005)], it was shown that at distances much larger than the interparticle spacing the impurities interact through a Casimir-type force mediated by the zero sound phonons of the underlying quantum liquid. Here we extend these results and show that the strength and sign of this Casimir interaction depend sensitively on the impurities separation. These oscillations in the Casimir interaction have the same period as Friedel oscillations. Their maxima correspond to tunneling resonances tuned by the impurities separation.Comment: This paper is a continuation of Phys. Rev. A 72, 023616 (2005). v2: two appendix adde

Scanning gate experiments: from strongly to weakly invasive probes

An open resonator fabricated in a two-dimensional electron gas is used to explore the transition from strongly invasive scanning gate microscopy to the perturbative regime of weak tip-induced potentials. With the help of numerical simulations that faithfully reproduce the main experimental findings, we quantify the extent of the perturbative regime in which the tip-induced conductance change is unambiguously determined by properties of the unperturbed system. The correspondence between the experimental and numerical results is established by analyzing the characteristic length scale and the amplitude modulation of the conductance change. In the perturbative regime, the former is shown to assume a disorder-dependent maximum value, while the latter linearly increases with the strength of a weak tip potential.Comment: 11 pages, 7 figure

The Spin Periods and Rotational Profiles of Neutron Stars at Birth

We present results from an extensive set of one- and two-dimensional radiation-hydrodynamic simulations of the supernova core collapse, bounce, and postbounce phases, and focus on the protoneutron star (PNS) spin periods and rotational profiles as a function of initial iron core angular velocity, degree of differential rotation, and progenitor mass. For the models considered, we find a roughly linear mapping between initial iron core rotation rate and PNS spin. The results indicate that the magnitude of the precollapse iron core angular velocities is the single most important factor in determining the PNS spin. Differences in progenitor mass and degree of differential rotation lead only to small variations in the PNS rotational period and profile. Based on our calculated PNS spins, at ~ 200-300 milliseconds after bounce, and assuming angular momentum conservation, we estimate final neutron star rotation periods. We find periods of one millisecond and shorter for initial central iron core periods of below ~ 10 s. This is appreciably shorter than what previous studies have predicted and is in disagreement with current observational data from pulsar astronomy. After considering possible spindown mechanisms that could lead to longer periods we conclude that there is no mechanism that can robustly spin down a neutron star from ~ 1 ms periods to the "injection" periods of tens to hundreds of milliseconds observed for young pulsars. Our results indicate that, given current knowledge of the limitations of neutron star spindown mechanisms, precollapse iron cores must rotate with periods around 50-100 seconds to form neutron stars with periods generically near those inferred for the radio pulsar population.Comment: 31 pages, including 20 color figures. High-resolution figures available from the authors upon request. Accepted to Ap

General-Relativistic MHD for the Numerical Construction of Dynamical Spacetimes

We assemble the equations of general relativistic magnetohydrodynamics (MHD) in 3+1 form. These consist of the complete coupled set of Maxwell equations for the electromagnetic field, Einstein's equations for the gravitational field, and the equations of relativistic MHD for a perfectly conducting ideal gas. The adopted form of the equations is suitable for evolving numerically a relativistic MHD fluid in a dynamical spacetime characterized by a strong gravitational field.Comment: 8 pages; scheduled for March 10 issue of Ap

Commensurate-incommensurate transition of cold atoms in an optical lattice

An atomic gas subject to a commensurate periodic potential generated by an optical lattice undergoes a superfluid--Mott insulator transition. Confining a strongly interacting gas to one dimension generates an instability where an arbitrary weak potential is sufficient to pin the atoms into the Mott state; here, we derive the corresponding phase diagram. The commensurate pinned state may be detected via its finite excitation gap and the Bragg peaks in the static structure factor.Comment: 4 pages, 2 figure