Identical Phase Shifts Research Articles

Clash of Kinks: Phase Shifts in Colliding Nonintegrable Solitons

We derive a closed-form expression for the phase shift experienced by (1+1)-dimensional kinks colliding at ultrarelativistic velocities (γv>>1), valid for arbitrary periodic potentials. Our closed-form expression is the leading-order result of a more general scattering theory of solitary waves described in a related paper [Phys. Rev. D 88, 105024 (2013)]. This theory relies on a small kinematic parameter 1/(γv)<<1 rather than a small parameter in the Lagrangian. Our analytic results can be directly extracted from the Lagrangian without solving the equation of motion. Based on our closed-form expression, we prove that kink-kink and kink-antikink collisions have identical phase shifts at leading order.

All-Optical Format Conversion for Multichannel QPSK Signals

All-optical format conversion is a key function in providing flexible management and interface for optical networks with different formats. In this paper, we propose and demonstrate multichannel mutual format conversions between the nonreturn-to-zero quadrature phase-shift keying (NRZ-QPSK) and the return-to-zero QPSK (RZ-QPSK) signals using a single semiconductor optical amplifier and/or a delay interferometer (DI). The conversion from the NRZ-QPSK to RZ-QPSK is based on the cross phase modulation (XPM) effect, which is introduced by a synchronous optical clock signal with high input power, and subsequent detuned filtering. The amplitude of the NRZ-QPSK signal is converted to the RZ-QPSK signal with identical phase shift onto every input bit by the XPM effect. The conversion from the RZ-QPSK to NRZ-QPSK is based on the constructive interference in a single DI with a half-bit delay. The principle for the mutual conversions is analyzed theoretically, and simulations validate the feasibility of the proposed schemes. Parallel 4 channels format conversions between the NRZ-QPSK and the RZ-QPSK signals are experimentally achieved well with small Q penalty less than 2 dB.

All-optical parallel NRZ-DPSK to RZ-DPSK format conversion at 40 Gb/s based on XPM effect in a single SOA

We propose and demonstrate multi-channel parallel format conversions from the non return-to-zero differential phase shift keying (NRZ-DPSK) to the return-to-zero DPSK (RZ-DPSK) using a single semiconductor optical amplifier (SOA). The simultaneous conversions are based on the cross phase modulation (XPM) effect, which is induced by a synchronous optical clock signal with high input power. The XPM adds an identical phase shift onto every input bit, resulting in the phase difference unchanged. The input spectra are broadened and a subsequent filter is utilized to extract the specific part to form a RZ pulse. 6-channel NRZ-DPSK signals at 40 Gb/s can be converted to the corresponding RZ-DPSK signals with ~-0.8 to -1 dB power penalty for all the channels.

Adaptation to Natural Binocular Disparities in Primate V1 Explained by a Generalized Energy Model

Sensory processing in the brain is thought to have evolved to encode naturally occurring stimuli efficiently. We report an adaptation in binocular cortical neurons that reflects the tight constraints imposed by the geometry of 3D vision. We show that the widely used binocular energy model predicts that neurons dedicate part of their dynamic range to impossible combinations of left and right images. Approximately 42% of the neurons we record from V1 of awake monkeys behave in this way (a powerful confirmation of the model), while about 58% deviate from the model in a manner that concentrates more of their dynamic range on stimuli that obey the constraints of binocular geometry. We propose a simple extension of the energy model, using multiple subunits, that explains the adaptation we observe, as well as other properties of binocular neurons that have been hard to account for, such as the response to anti-correlated stereograms.

Stable identification of piecewise-constant potentials from fixed-energy phase shifts

Abstract - An identification of a spherically symmetric potential by its phase shifts is an important physical problem. Recent theoretical results assure that such a potential is uniquely defined by a sufficiently large subset of its phase shifts at any one fixed energy level. However, two different potentials can produce almost identical phase shifts. That is, the inverse problem of the identification of a potential from its phase shifts at one energy level k2 is ill-posed, and the reconstruction is unstable. In this paper we introduce a quantitative measure D(k) of this instability. The diameters of minimizing sets D(k) are used to study the change in the stability with the change of k, and the influence of noise on the identification. They are also used in the stopping criterion for the nonlinear minimization method IRRS (Iterative Random Reduced Search). IRRS combines probabilistic global and deterministic local search methods and it is used for the numerical recovery of the potential by the set of its phase shifts. The results of the identification for noiseless as well as noise corrupted data are presented.

Piecewise constant positive potentials with practically the same fixed energy phase shifts

It has recently been shown that spherically symmetric potentials of finite range are uniquely determined by the part of their phase shifts at a fixed energy level k2 > 0. However, numerical experiments show that two quite different potentials can produce almost identical phase shifts. It has been guessed by physicists that such examples are possible only for “less physical” oscillating and changing sign potentials. In this note it is shown that the above guess is incorrect: we give examples of four positive spherically symmetric compactly supported quite different potentials having practically identical phase shifts. The note also describes a hybrid stochastic deterministic method for global minimization for the construction of these potentials.

Identification of Piecewise-Constant Potentials by Fixed-Energy Phase Shifts

The identification of a spherically symmetric potential by its phase shifts is an important physical problem. Recent theoretical results assure that such a potential is uniquely defined by a sufficiently large subset of its phase shifts at any one fixed energy level. However, two different potentials can produce almost identical phase shifts. To resolve this difficulty we suggest the use of phase shifts corresponding to several energy levels. The identification is done by a nonlinear minimization of the appropriate objective function. It is based on a combination of probabilistic global and deterministic local minimization methods. The Multilevel Single-Linkage Method (MSLM) is used for the global minimization. A specially designed Local Minimization Method (LMM) with a Reduction Procedure is used for the local searches. Numerical results show the effectiveness of this procedure for potentials composed of a small number of spherical layers.

Flavor oscillations from a spatially localized source: A simple general treatment

A unique description avoiding confusion is presented for all flavor oscillation experiments in which particles of a definite flavor are emitted from a localized source. The probability for finding a particle with the wrong flavor must vanish at the position of the source for all times. This condition requires flavor-time and flavor-energy factorizations which determine uniquely the flavor mixture observed at a detector in the oscillation region, i.e., where the overlaps between the wave packets for different mass eigenstates are almost complete. Oscillation periods calculated for ``gedanken'' time-measurement experiments are shown to give the correct measured oscillation wavelength in space when multiplied by the group velocity. Examples of neutrino propagation in a weak field and in a gravitational field are given. In these cases the relative phase is modified differently for measurements in space and time. Energy-momentum (frequency-wave number) and space-time descriptions are complementary, equally valid, and give the same results. The two identical phase shifts obtained describe the same physics; adding them together to get a factor of 2 is double counting.

Distortion-free imaging through inhomogeneities by selective spatial filtering

Distortion-free imaging through a system with aberrations is possible for a certain class of input. The input spatial spectrum must be restricted to spatial frequencies which are equally affected by the aberrations (i.e., which experience identical phase shifts mod2pi). We demonstrate experimentally that if the aberrations can be localized in the pupil plane, an arbitrary input can be prefiltered to produce a distribution which is imaged without distortion by an aberrant system. Equivalently, the output of the system can be postfiltered to select the information which was imaged without distortion.

Nucleon-nucleon potential and minimal relativity

The effects of relativistic elastic unitarity on low-energy nucleon-nucleon scattering and the binding energy of nuclear matter are investigated. Relativistic unitarity is found to increase the nuclear matter binding by approximately 0.5 MeV per particle over the value obtained for a non-relativistic potential having a similar shape and identical phase shifts.