Quantum fluctuations in the spiral phase of the Hubbard model

We study the magnetic excitations in the spiral phase of the two--dimensional Hubbard model using a functional integral method. Spin waves are strongly renormalized and a line of near--zeros is observed in the spectrum around the spiral pitch $\pm{\bf Q}$. The possibility of disordered spiral states is examined by studying the one--loop corrections to the spiral order parameter. We also show that the spiral phase presents an intrinsic instability towards an inhomogeneous state (phase separation, CDW, ...) at weak doping. Though phase separation is suppressed by weak long--range Coulomb interactions, the CDW instability only disappears for sufficiently strong Coulomb interaction.Comment: Figures are NOW appended via uuencoded postscript fil

Upflows in the upper transition region of the quiet Sun

We investigate the physical meaning of the prominent blue shifts of Ne VIII, which is observed to be associated with quiet-Sun network junctions (boundary intersections), through data analyses combining force-free-field extrapolations with EUV spectroscopic observations. For a middle-latitude region, we reconstruct the magnetic funnel structure in a sub-region showing faint emission in EIT-Fe 195. This funnel appears to consist of several smaller funnels that originate from network lanes, expand with height and finally merge into a single wide open-field region. However, the large blue shifts of Ne VIII are generally not associated with open fields, but seem to be associated with the legs of closed magnetic loops. Moreover, in most cases significant upflows are found in both of the funnel-shaped loop legs. These quasi-steady upflows are regarded as signatures of mass supply to the coronal loops rather than the solar wind. Our observational result also reveals that in many cases the upflows in the upper transition region (TR) and the downflows in the middle TR are not fully cospatial. Based on these new observational results, we suggest different TR structures in coronal holes and in the quiet Sun.Comment: 4 pages, 4 figures, will appear in the Proceedings of the Solar wind 12 conferenc

Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in 2+1 dimensions

Riemann theta functions are used to construct one-periodic and two-periodic wave solutions to a class of (2+1)-dimensional Hirota bilinear equations. The basis for the involved solution analysis is the Hirota bilinear formulation, and the particular dependence of the equations on independent variables guarantees the existence of one-periodic and two-periodic wave solutions involving an arbitrary purely imaginary Riemann matrix. The resulting theory is applied to two nonlinear equations possessing Hirota bilinear forms: $u_t+u_{xxy}-3uu_y-3u_xv=0$ and $u_t+u_{xxxxy}-(5u_{xx}v+10u_{xy}u-15u^2v)_x=0$ where $v_x=u_y$, thereby yielding their one-periodic and two-periodic wave solutions describing one dimensional propagation of waves

On the thermalization of a Luttinger liquid after a sequence of sudden interaction quenches

We present a comprehensive analysis of the relaxation dynamics of a Luttinger liquid subject to a sequence of sudden interaction quenches. We express the critical exponent $\beta$ governing the decay of the steady-state propagator as an explicit functional of the switching protocol. At long distances $\beta$ depends only on the initial state while at short distances it is also history dependent. Continuous protocols of arbitrary complexity can be realized with infinitely long sequences. For quenches of finite duration we prove that there exist no protocol to bring the initial non-interacting system in the ground state of the Luttinger liquid. Nevertheless memory effects are washed out at short-distances. The adiabatic theorem is then investigated with ramp-switchings of increasing duration, and several analytic results for both the propagator and the excitation energy are derived.Comment: 7 pages, 4 figure

Magic Wavelengths for Terahertz Clock Transitions

Magic wavelengths for laser trapping of boson isotopes of alkaline-earth Sr, Ca and Mg atoms are investigated while considering terahertz clock transitions between the $^{3}P_{0}, ^{3}P_{1}, ^{3}P_{2}$ metastable triplet states. Our calculation shows that magic wavelengths of trapping laser do exist. This result is important because those metastable states have already been used to realize accurate clocks in the terahertz frequency domain. Detailed discussions for magic wavelength for terahertz clock transitions are given in this paper.Comment: 7 page

False discovery rate regression: an application to neural synchrony detection in primary visual cortex

Many approaches for multiple testing begin with the assumption that all tests in a given study should be combined into a global false-discovery-rate analysis. But this may be inappropriate for many of today's large-scale screening problems, where auxiliary information about each test is often available, and where a combined analysis can lead to poorly calibrated error rates within different subsets of the experiment. To address this issue, we introduce an approach called false-discovery-rate regression that directly uses this auxiliary information to inform the outcome of each test. The method can be motivated by a two-groups model in which covariates are allowed to influence the local false discovery rate, or equivalently, the posterior probability that a given observation is a signal. This poses many subtle issues at the interface between inference and computation, and we investigate several variations of the overall approach. Simulation evidence suggests that: (1) when covariate effects are present, FDR regression improves power for a fixed false-discovery rate; and (2) when covariate effects are absent, the method is robust, in the sense that it does not lead to inflated error rates. We apply the method to neural recordings from primary visual cortex. The goal is to detect pairs of neurons that exhibit fine-time-scale interactions, in the sense that they fire together more often than expected due to chance. Our method detects roughly 50% more synchronous pairs versus a standard FDR-controlling analysis. The companion R package FDRreg implements all methods described in the paper

Validity of the scattering length approximation in strongly interacting Fermi systems

We investigate the energy spectrum of systems of two, three and four spin-1/2 fermions with short range attractive interactions both exactly, and within the scattering length approximation. The formation of molecular bound states and the ferromagnetic transition of the excited scattering state are examined systematically as a function of the 2-body scattering length. Identification of the upper branch (scattering states) is discussed and a general approach valid for systems with many particles is given. We show that an adiabatic ferromagnetic transition occurs, but at a critical transition point kF a much higher than predicted from previous calculations, almost all of which use the scattering length approximation. In the 4-particle system the discrepancy is a factor of 2. The exact critical interaction strength calculated in the 4-particle system is consistent with that reported by experiment. To make comparisons with the adiabatic transition, we study the quench dynamics of the pairing instability using the eigenstate wavefunctions.Comment: 7 pages, 7 figure

Linear spaces with a line-transitive point-imprimitive automorphism group and Fang-Li parameter gcd(k,r) at most eight

In 1991, Weidong Fang and Huiling Li proved that there are only finitely many non-trivial linear spaces that admit a line-transitive, point-imprimitive group action, for a given value of gcd(k,r), where k is the line size and r is the number of lines on a point. The aim of this paper is to make that result effective. We obtain a classification of all linear spaces with this property having gcd(k,r) at most 8. To achieve this we collect together existing theory, and prove additional theoretical restrictions of both a combinatorial and group theoretic nature. These are organised into a series of algorithms that, for gcd(k,r) up to a given maximum value, return a list of candidate parameter values and candidate groups. We examine in detail each of the possibilities returned by these algorithms for gcd(k,r) at most 8, and complete the classification in this case.Comment: 47 pages Version 1 had bbl file omitted. Apologie

Fermionic R-operator approach for the small-polaron model with open boundary condition

Exact integrability and algebraic Bethe ansatz of the small-polaron model with the open boundary condition are discussed in the framework of the quantum inverse scattering method (QISM). We employ a new approach where the fermionic R-operator which consists of fermion operators is a key object. It satisfies the Yang-Baxter equation and the reflection equation with its corresponding K-operator. Two kinds of 'super-transposition' for the fermion operators are defined and the dual reflection equation is obtained. These equations prove the integrability and the Bethe ansatz equation which agrees with the one obtained from the graded Yang-Baxter equation and the graded reflection equations.Comment: 10 page

A Field Effect Transitor based on the Mott Transition in a Molecular Layer

Here we propose and analyze the behavior of a FET--like switching device, the Mott transition field effect transistor, operating on a novel principle, the Mott metal--insulator transition. The device has FET-like characteristics with a low ``ON'' impedance and high ``OFF'' impedance. Function of the device is feasible down to nanoscale dimensions. Implementation with a class of organic charge transfer complexes is proposed.Comment: Revtex 11pages, Figures available upon reques