Diffraction of wave packets in space and time

The phenomenon of wave packet diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wave packet quantum scattering off an attractive or repulsive time independent potential. An analytical formula for the pattern at $t\to\infty$ is derived both in one dimension and in three dimensions. The condition for the pattern to exist is developed. The phenomenon is shown numerically and analytically for the Dirac equation in one dimension also. An experiment for the verification of the phenomenon is described and simulated numerically.Comment: replaces quant-ph 0008077, 0008107, Journal of physics, A, in pres

Entanglement Generation in the Scattering of One-Dimensional Particles

This article provides a convenient framework for quantitative evaluation of the entanglement generated when two structureless, distinguishable particles scatter non-relativistically in one dimension. It explores how three factors determine the amount of entanglement generated: the momentum distributions of the incoming particles, their masses, and the interaction potential. Two important scales emerge, one set by the kinematics and one set by the dynamics. This method also provides two approximate analytic formulas useful for numerical evaluation of entanglement and reveals an interesting connection between purity, linear coordinate transformations, and momentum uncertainties.Comment: 11 pages, submitted to PR

Multifractality and scale invariance in human heartbeat dynamics

Human heart rate is known to display complex fluctuations. Evidence of multifractality in heart rate fluctuations in healthy state has been reported [Ivanov et al., Nature {\bf 399}, 461 (1999)]. This multifractal character could be manifested as a dependence on scale or beat number of the probability density functions (PDFs) of the heart rate increments. On the other hand, scale invariance has been recently reported in a detrended analysis of healthy heart rate increments [Kiyono et al., Phys. Rev. Lett. {\bf 93}, 178103 (2004)]. In this paper, we resolve this paradox by clarifying that the scale invariance reported is actually exhibited by the PDFs of the sum of detrended healthy heartbeat intervals taken over different number of beats, and demonstrating that the PDFs of detrended healthy heart rate increments are scale dependent. Our work also establishes that this scale invariance is a general feature of human heartbeat dynamics, which is shared by heart rate fluctuations in both healthy and pathological states

Sensitivity of exclusive proton knockout spin observables to different Lorentz invariant representations of the NN interaction

Within the framework of the relativistic plane wave impulse approximation, we study the observable consequences of employing a complete Lorentz invariant representation of the NN scattering matrix in terms of 44 independent amplitudes, as opposed to the previously-employed, but ambiguous, five-term Lorentz invariant parametrization of the NN scattering matrix, for the prediction of complete sets of exclusive ($\vec{p},2 \vec{p}$) polarization transfer observables. Two kinematic conditions are considered, namely proton knockout from the $3s_{1/2}$ state of $^{208}$Pb at an incident energy of 202 MeV for coplanar scattering angles ($28.0^{\circ}, -54.6^{\circ}$), as well as an incident energy of 392 MeV for the angle pair ($32.5^{\circ}, -80.0^{\circ}$). The results indicate that certain spin observables are ideal for discriminating between the two representations.Comment: 19 pages, 5 figures, Revtex, To be published in Phys. Rev.

Phenomenological analysis of the double pion production in nucleon-nucleon collisions up to 2.2 GeV

With an effective Lagrangian approach, we analyze several NN \to NN\pi\pi channels by including various resonances with mass up to 1.72 GeV. For the channels with the pion pair of isospin zero, we confirm the dominance of N*(1440)\to N\sigma in the near threshold region. At higher energies and for channels with the final pion pair of isospin one, we find large contributions from N*(1440)\to \Delta\pi, double-Delta, \Delta(1600) \to N*(1440)\pi, \Delta(1600) \to \Delta\pi and \Delta(1620) \to \Delta\pi. There are also sizeable contributions from \Delta \to \Delta\pi, \Delta \to N\pi, N \to \Delta\pi and nucleon pole at energies close to the threshold. We well reproduce the total cross sections up to beam energies of 2.2 GeV except for the pp\to pp\pi^0\pi^0 channel at energies around 1.1 GeV and our results agree with the existing data of differential cross sections of pp \to pp\pi^+\pi^-, pp \to nn\pi^+\pi^+ and pp \to pp\pi^0\pi^0 which are measured at CELSIUS and COSY.Comment: 36 pages, 18 figure

Renormalization of One-Pion Exchange and Power Counting

The renormalization of the chiral nuclear interactions is studied. In leading order, the cutoff dependence is related to the singular tensor interaction of the one-pion exchange potential. In S waves and in higher partial waves where the tensor force is repulsive this cutoff dependence can be absorbed by counterterms expected at that order. In the other partial waves additional contact interactions are necessary. The implications of this finding for the effective-field-theory program in nuclear physics are discussed.Comment: 19 pages, 18 figure

Violations of Bjorken scaling in inclusive e+e- annihilation

We discuss the application of renormalization-group techniques to inclusive e+e- annihilation. It is shown by a modest extension of Mueller's techniques that annihilation structure functions have a behavior completely analogous to electroproduction structure functions: Their moments scale for large virtual photon mass, and this scaling is described by "anomalous dimensions" which have a singularity structure and general form very similar to the usual anomalous dimension, though there is no simple relation between the two. We show how information about the structure functions can be deduced from the moments and how, in appropriate limits, deviations from Bjorken scaling can be interpreted in terms of an underlying field theory

Stress-energy tensor for a quantised bulk scalar field in the Randall-Sundrum brane model

We calculate the vacuum expectation value of the stress-energy tensor for a quantised bulk scalar field in the Randall-Sundrum model, and discuss the consequences of its local behaviour for the self-consistency of the model. We find that, in general, the stress-energy tensor diverges in the vicinity of the branes. Our main conclusion is that the stress-energy tensor is sufficiently complicated that it has implications for the effective potential, or radion stabilisation, methods that have so far been used.Comment: 16 pages, 3 figures. Minor changes made and references added. To appear in Phys. Rev.