Local distortion techniques and unitarity of the S-matrix for the 2-body problem

AbstractThe two-body S-matrix for an interaction with exponential decay at infinity is defined in a time-independent way and its unitarity is proved directly by local distortion techniques. Complete sets of incoming and outgoing states, or delicate resolvent estimates are not needed for the proof

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

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

Quasiperiodic Envelope Solitons

We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally.Comment: Submitted to PRL. 4 pages with 5 figure

Calculation of the Characteristic Functions of Anharmonic Oscillators

The energy levels of quantum systems are determined by quantization conditions. For one-dimensional anharmonic oscillators, one can transform the Schrodinger equation into a Riccati form, i.e., in terms of the logarithmic derivative of the wave function. A perturbative expansion of the logarithmic derivative of the wave function can easily be obtained. The Bohr-Sommerfeld quantization condition can be expressed in terms of a contour integral around the poles of the logarithmic derivative. Its functional form is B_m(E,g) = n + 1/2, where B is a characteristic function of the anharmonic oscillator of degree m, E is the resonance energy, and g is the coupling constant. A recursive scheme can be devised which facilitates the evaluation of higher-order Wentzel-Kramers-Brioullin (WKB) approximants. The WKB expansion of the logarithmic derivative of the wave function has a cut in the tunneling region. The contour integral about the tunneling region yields the instanton action plus corrections, summarized in a second characteristic function A_m(E,g). The evaluation of A_m(E,g) by the method of asymptotic matching is discussed for the case of the cubic oscillator of degree m=3.Comment: 11 pages, LaTeX; three further typographical errors correcte

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

Upper bound on the density of Ruelle resonances for Anosov flows

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real axis and for large real parts.Comment: 57 page

Calculation of the Density of States Using Discrete Variable Representation and Toeplitz Matrices

A direct and exact method for calculating the density of states for systems with localized potentials is presented. The method is based on explicit inversion of the operator $E-H$. The operator is written in the discrete variable representation of the Hamiltonian, and the Toeplitz property of the asymptotic part of the obtained {\it infinite} matrix is used. Thus, the problem is reduced to the inversion of a {\it finite} matrix