Triatomic continuum resonances for large negative scattering lengths

We study triatomic systems in the regime of large negative scattering lengths which may be more favorable for the formation of condensed trimers in trapped ultracold monoatomic gases as the competition with the weakly bound dimers is absent. The manipulation of the scattering length can turn an excited weakly bound Efimov trimer into a continuum resonance. Its energy and width are described by universal scaling functions written in terms of the scattering length and the binding energy, $B_3$, of the shallowest triatomic molecule. For $a^{-1}<-0.0297 \sqrt{m B_3/\hbar^2}$ the excited Efimov state turns into a continuum resonance.Comment: 4 pages, 4 figure

Fermion mixing in quasi-free states

Quantum field theoretic treatments of fermion oscillations are typically restricted to calculations in Fock space. In this letter we extend the oscillation formulae to include more general quasi-free states, and also consider the case when the mixing is not unitary.Comment: 10 pages, Plain Te

Quantizing the damped harmonic oscillator

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.Comment: 4 pages, no figure

Engineered nonlinear lattices

We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term a quasilattice, which interpolates between a lattice system and a continuous system.Peer ReviewedPostprint (published version

Spatially valid proprioceptive cues improve the detection of a visual stimulus

Vision and proprioception are the main sensory modalities that convey hand location and direction of movement. Fusion of these sensory signals into a single robust percept is now well documented. However, it is not known whether these modalities also interact in the spatial allocation of attention, which has been demonstrated for other modality pairings. The aim of this study was to test whether proprioceptive signals can spatially cue a visual target to improve its detection. Participants were instructed to use a planar manipulandum in a forward reaching action and determine during this movement whether a near-threshold visual target appeared at either of two lateral positions. The target presentation was followed by a masking stimulus, which made its possible location unambiguous, but not its presence. Proprioceptive cues were given by applying a brief lateral force to the participant’s arm, either in the same direction (validly cued) or in the opposite direction (invalidly cued) to the on-screen location of the mask. The d′ detection rate of the target increased when the direction of proprioceptive stimulus was compatible with the location of the visual target compared to when it was incompatible. These results suggest that proprioception influences the allocation of attention in visual spac

Resonances Width in Crossed Electric and Magnetic Fields

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.Comment: 3 figure

Localization of shadow poles by complex scaling

Through numerical examples we show that the complex scaling method is suited to explore the pole structure in multichannel scattering problems. All poles lying on the multisheeted Riemann energy surface, including shadow poles, can be revealed and the Riemann sheets on which they reside can be identified.Comment: 6 pages, Latex with Revtex, 3 figures (not included) available on reques

Stable directions for small nonlinear Dirac standing waves

We prove that for a Dirac operator with no resonance at thresholds nor eigenvalue at thresholds the propagator satisfies propagation and dispersive estimates. When this linear operator has only two simple eigenvalues close enough, we study an associated class of nonlinear Dirac equations which have stationary solutions. As an application of our decay estimates, we show that these solutions have stable directions which are tangent to the subspaces associated with the continuous spectrum of the Dirac operator. This result is the analogue, in the Dirac case, of a theorem by Tsai and Yau about the Schr\"{o}dinger equation. To our knowledge, the present work is the first mathematical study of the stability problem for a nonlinear Dirac equation.Comment: 62 page