Squeezing in the weakly interacting uniform Bose condensate

We investigate the presence of squeezing in the weakly repulsive uniform Bose gas, in both the condensate mode and in the nonzero opposite-momenta mode pairs, using two different variational formulations. We explore the U(1) symmetry breaking and Goldstone's theorem in the context of a squeezed coherent variational wavefunction, and present the associated Ward identity. We show that squeezing of the condensate mode is absent at the mean field Hartree-Fock-Bogoliubov level and emerges as a result of fluctuations about mean field as a finite volume effect, which vanishes in the thermodynamic limit. On the other hand, the squeezing of the excitations about the condensate survives the thermodynamic limit and is interpreted in terms of density-phase variables using a number-conserving formulation of the interacting Bose gas.Comment: 8 pages, 3 figures. Version 2 (Sept'06): expanded discussion

Transverse Spin Diffusion in a Dilute Spin-Polarized Degenerate Fermi Gas

We re-examine the calculation of the transverse spin-diffusion coefficient in a dilute degenerate spin-polarized Fermi gas, for the case of s-wave scattering. The special feature of this limit is that the dependence of the spin diffusion coefficient on temperature and field can be calculated explicitly with no further approximations. This exact solution uncovers a novel intermediate behavior between the high field spin-rotation dominated regime in which $D_{\bot} \propto H^{-2}$, $D_{\parallel} \propto T^{-2}$, and the low-field isotropic, collision dominated regime with $D_{\bot} = D_{\parallel} \propto T^{-2}$. In this intermediate regime, $D_{\bot ,\parallel} \propto T^{-2}$ but $D_{\bot} \neq D_{\parallel}$. We also present an analytical calculation of the self-energy in the s-wave approximation for a dilute spin-polarized Fermi gas, at zero temperature. This emphasizes the failure of the conventional Fermi-liquid phase space arguments for processes involving spin flips. We close by reviewing the evidence for the existence of the intermediate regime in experiments on weakly spin-polarized $^3{\rm He}$ and $^3{\rm He} - ^4{\rm He}$ mixtures.Comment: 38 pages, Latex-Revtex, 9 PostScript figures. Minor revisions, misprints corrected, references adde

Spin-Flavor Separation and Non-Fermi Liquid Behavior in the Multichannel Kondo Problem: A Large N Approach

We consider a $SU(N)\times SU(M)$ generalization of the multichannel single-impurity Kondo model which we solve analytically in the limit $N\rightarrow \infty$, $M\rightarrow\infty$, with $\gamma=M/N$ fixed. Non-Fermi liquid behavior of the single electron Green function and of the local spin and flavor susceptibilities occurs in both regimes, $N\le M$ and $N > M$, with leading critical exponents {\em identical} to those found in the conformal field theory solution for {\em all} $N$ and $M$ (with $M\ge 2$). We explain this remarkable agreement and connect it to ``spin-flavor separation", the essential feature of the non-Fermi-liquid fixed point of the multichannel Kondo problem.Comment: 14 pages, 1 Figure (Poscript file attached), Revte

Transition Temperature of Dilute, Weakly Repulsive Bose Gas

Within a quasiparticle framework, we reconsider the issue of computing the Bose-Einstein condensation temperature ($T_c$) in a weakly non-ideal Bose gas. The main result of this and previous investigations is that $T_c$ increases with the scattering length $a$, with the leading dependence being either linear or log-linear in $a$. The calculation of $T_c$ reduces to that of computing the excitation spectrum near the transition. We report two approaches to regularizing the infrared divergence at the transition point. One leads to a $a\sqrt{|\ln{a}|}$-like shift in $T_c$, and the other allows numerical calculations for the shift.Comment: 8 pages, 3 figures, revtex

Fast counting with tensor networks

We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of satisfying assignments of that formula, and use graph theoretical methods to determine favorable orders of contraction. We employ our heuristics for the solution of #P-hard counting boolean satisfiability (#SAT) problems, namely monotone #1-in-3SAT and #Cubic-Vertex-Cover, and find that they outperform state-of-the-art solvers by a significant margin.Comment: v2: added results for monotone #1-in-3SAT; published versio

Charge and Spin Gap Formation in Exactly Solvable Hubbard Chains with Long-Rang Hopping

We discuss the transition from a metal to charge or spin insulating phases characterized by the opening of a gap in the charge or spin excitation spectra, respectively. These transitions are addressed within the context of two exactly solvable Hubbard and tJ chains with long range, $1/r$ hopping. We discuss the specific heat, compressibility, and magnetic susceptibility of these models as a function of temperature, band filling, and interaction strength. We then use conformal field theory techniques to extract ground state correlation functions. Finally, by employing the $g$-ology analysis we show that the charge insulator transition is accompanied by an infinite discontinuity in the Drude weight of the electrical conductivity. While the magnetic properties of these models reflect the genuine features of strongly correlated electron systems, the charge transport properties, especially near the Mott-Hubbard transition, display a non-generic behavior.Comment: 47 pages, REVTEX 3.0, 14 postscript figures available form [email protected] (submitted using the figures-command

Optimal Path to Epigenetic Switching

We use large deviation methods to calculate rates of noise-induced transitions between states in multistable genetic networks. We analyze a synthetic biochemical circuit, the toggle switch, and compare the results to those obtained from a numerical solution of the master equation.Comment: 5 pages. 2 figures, uses revtex 4. PR-E reviewed for publicatio