A note on the analogy between superfluids and cosmology

A new analogy between superfluid systems and cosmology is here presented, which relies strongly on the following ingredient: the back-reaction of the vacuum to the quanta of sound waves. We show how the presence of thermal phonons, the excitations above the quantum vacuum for $T> 0$, enable us to deduce an hydrodynamical equation formally similar to the one obtained for a perfect fluid in a Universe obeying the Friedmann-Robertson-Walker metric.Comment: Accepted for publication in Modern Physics Letters

Unified approach to structure factors and neutrino processes in nucleon matter

We present a unified approach to neutrino processes in nucleon matter based on Landau's theory of Fermi liquids that includes one- and two-quasiparticle-quasihole pair states as well as mean-field effects. We show how rates of neutrino processes involving two nucleons may be calculated in terms of the collision integral in the Landau transport equation for quasiparticles. Using a relaxation time approximation, we solve the transport equation for density and spin-density fluctuations and derive a general form for the response functions. We apply our approach to neutral-current processes in neutron matter, where the spin response function is crucial for calculations of neutrino elastic and inelastic scattering, neutrino-pair bremsstrahlung and absorption from strongly-interacting nucleons. We calculate the relaxation rates using modern nuclear interactions and including many-body contributions, and find that rates of neutrino processes are reduced compared with estimates based on the one-pion exchange interaction, which is used in current simulations of core-collapse supernovae.Comment: 16 pages, 4 figures; NORDITA-2008-30; published versio

Decay of polarons and molecules in a strongly polarized Fermi gas

The ground state of an impurity immersed in a Fermi sea changes from a polaron to a molecule as the interaction strength is increased. We show here that the coupling between these two states is strongly suppressed due to a combination of phase space effects and Fermi statistics, and that it vanishes much faster than the energy difference between the two states, thereby confirming the first order nature of the polaron-molecule transition. In the regime where each state is metastable, we find quasiparticle lifetimes which are much longer than what is expected for a usual Fermi liquid. Our analysis indicates that the decay rates are sufficiently slow to be experimentally observable.Comment: Version accepted in PRL. Added discussion of three-body losses to deeply bound molecular state

Symmetry protected fractional Chern insulators and fractional topological insulators

In this paper we construct fully symmetric wavefunctions for the spin-polarized fractional Chern insulators (FCI) and time-reversal-invariant fractional topological insulators (FTI) in two dimensions using the parton approach. We show that the lattice symmetry gives rise to many different FCI and FTI phases even with the same filling fraction $\nu$ (and the same quantized Hall conductance $\sigma_{xy}$ in FCI case). They have different symmetry-protected topological orders, which are characterized by different projective symmetry groups. We mainly focus on FCI phases which are realized in a partially filled band with Chern number one. The low-energy gauge groups of a generic $\sigma_{xy}=1/m\cdot e^2/h$ FCI wavefunctions can be either $SU(m)$ or the discrete group $Z_m$, and in the latter case the associated low-energy physics are described by Chern-Simons-Higgs theories. We use our construction to compute the ground state degeneracy. Examples of FCI/FTI wavefunctions on honeycomb lattice and checkerboard lattice are explicitly given. Possible non-Abelian FCI phases which may be realized in a partially filled band with Chern number two are discussed. Generic FTI wavefunctions in the absence of spin conservation are also presented whose low-energy gauge groups can be either $SU(m)\times SU(m)$ or $Z_m\times Z_m$. The constructed wavefunctions also set up the framework for future variational Monte Carlo simulations.Comment: 24 pages, 13 figures, published versio

Landau Damping in a Turbulent Setting

To address the problem of Landau damping in kinetic turbulence, the forcing of the linearized Vlasov equation by a stationary random source is considered. It is found that the time-asymptotic density response is dominated by resonant particle interactions that are synchronized with the source. The energy consumption of this response is calculated, implying an effective damping rate, which is the main result of this paper. Evaluating several cases, it is found that the effective damping rate can differ from the Landau damping rate in magnitude and also, remarkably, in sign. A limit is demonstrated in which the density and current become phase-locked, which causes the effective damping to be negligible; this potentially resolves an energy paradox that arises in the application of critical balance to a kinetic turbulence cascade.Comment: Introduction significantly expanded to help contextualize results. Calculations unchange

Bose-Einstein Condensation Temperature of a Homogeneous Weakly Interacting Bose Gas : PIMC study

Using a finite-temperature Path Integral Monte Carlo simulation (PIMC) method and finite-size scaling, we have investigated the interaction-induced shift of the phase transition temperature for Bose-Einstein condensation of homogeneous weakly interacting Bose gases in three dimensions, which is given by a proposed analytical expression $T_{c} = T_{c}^{0}\{1 + c_{1}an^{1/3}+[c'_{2}\ln(an^{1/3})+c''_{2}]a^{2}n^{2/3} +O(a^{3}n)\}$, where $T_{c}^{0}$ is the critical temperature for an ideal gas, $a$ is the s-wave scattering length, and $n$ is the number density. We have used smaller number densities and more time slices than in the previous PIMC simulations [Gruter {\it et al.}, Phys. Rev. Lett. {\bf 79}, 3549 (1997)] in order to understand the difference in the value of the coefficient $c_{1}$ between their results and the (apparently) other reliable results in the literature. Our results show that $\{(T_{c}-T_{c}^{0})/T_{c}^{0}\}/(an^{1/3})$ depends strongly on the interaction strength $an^{1/3}$ while the previous PIMC results are considerably flatter and smaller than our results. We obtain $c_{1}$ = 1.32 $\pm$ 0.14, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar $\phi^{4}$ field theory and variational perturbation theory

Quantum ether: photons and electrons from a rotor model

We give an example of a purely bosonic model -- a rotor model on the 3D cubic lattice -- whose low energy excitations behave like massless U(1) gauge bosons and massless Dirac fermions. This model can be viewed as a ``quantum ether'': a medium that gives rise to both photons and electrons. It illustrates a general mechanism for the emergence of gauge bosons and fermions known as ``string-net condensation.'' Other, more complex, string-net condensed models can have excitations that behave like gluons, quarks and other particles in the standard model. This suggests that photons, electrons and other elementary particles may have a unified origin: string-net condensation in our vacuum.Comment: 10 pages, 6 figures, RevTeX4. Home page http://dao.mit.edu/~we

High-energy gluon bremsstrahlung in a finite medium: harmonic oscillator versus single scattering approximation

A particle produced in a hard collision can lose energy through bremsstrahlung. It has long been of interest to calculate the effect on bremsstrahlung if the particle is produced inside a finite-size QCD medium such as a quark-gluon plasma. For the case of very high-energy particles traveling through the background of a weakly-coupled quark-gluon plasma, it is known how to reduce this problem to an equivalent problem in non-relativistic two-dimensional quantum mechanics. Analytic solutions, however, have always resorted to further approximations. One is a harmonic oscillator approximation to the corresponding quantum mechanics problem, which is appropriate for sufficiently thick media. Another is to formally treat the particle as having only a single significant scattering from the plasma (known as the N=1 term of the opacity expansion), which is appropriate for sufficiently thin media. In a broad range of intermediate cases, these two very different approximations give surprisingly similar but slightly differing results if one works to leading logarithmic order in the particle energy, and there has been confusion about the range of validity of each approximation. In this paper, I sort out in detail the parametric range of validity of these two approximations at leading logarithmic order. For simplicity, I study the problem for small alpha_s and large logarithms but alpha_s log << 1.Comment: 40 pages, 23 figures [Primary change since v1: addition of new appendix reviewing transverse momentum distribution from multiple scattering

On an exact hydrodynamic solution for the elliptic flow

Looking for the underlying hydrodynamic mechanisms determining the elliptic flow we show that for an expanding relativistic perfect fluid the transverse flow may derive from a solvable hydrodynamic potential, if the entropy is transversally conserved and the corresponding expansion "quasi-stationary", that is mainly governed by the temperature cooling. Exact solutions for the velocity flow coefficients $v_2$ and the temperature dependence of the spatial and momentum anisotropy are obtained and shown to be in agreement with the elliptic flow features of heavy-ion collisions.Comment: 10 pages, 4 figure

A new modelling framework for statistical cumulus dynamics

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits