Geometric phase effects for wavepacket revivals

The study of wavepacket revivals is extended to the case of Hamiltonians which are made time-dependent through the adiabatic cycling of some parameters. It is shown that the quantal geometric phase (Berry's phase) causes the revived packet to be displaced along the classical trajectory, by an amount equal to the classical geometric phase (Hannay's angle), in one degree of freedom. A physical example illustrating this effect in three degrees of freedom is mentioned.Comment: Revtex, 11 pages, no figures

Observing the spin of a free electron

Long ago, Bohr, Pauli, and Mott argued that it is not, in principle, possible to measure the spin components of a free electron. One can try to use a Stern-Gerlach type of device, but the finite size of the beam results in an uncertainty of the splitting force that is comparable with the gradient force. The result is that no definite spin measurement can be made. Recently there has been a revival of interest in this problem, and we will present our own analysis and quantum-mechanical wave-packet calculations which suggest that a spin measurement is possible for a careful choice of initial conditions

First Simultaneous Optical and EUV Observations of the Quasi-Coherent Oscillations of SS Cygni

Using EUV photometry obtained with the Extreme Ultraviolet Explorer (EUVE) satellite and UBVR optical photometry obtained with the 2.7-m telescope at McDonald Observatory, we have detected quasi-coherent oscillations (so-called ``dwarf nova oscillations'') in the EUV and optical flux of the dwarf nova SS Cygni during its 1996 October outburst. There are two new results from these observations. First, we have for the first time observed ``frequency doubling:'' during the rising branch of the outburst, the period of the EUV oscillation was observed to jump from 6.59 s to 2.91 s. Second, we have for the first time observed quasi-coherent oscillations simultaneously in the optical and EUV. We find that the period and phase of the oscillations are the same in the two wavebands, finally confirming the long-held assumption that the periods of the optical and EUV/soft X-ray oscillations of dwarf novae are equal. The UBV oscillations can be simply the Rayleigh-Jeans tail of the EUV oscillations if the boundary layer temperature kT_bb <~ 15 eV and hence the luminosity L_bb >~ 1.2e34 (d/75 pc)^2 erg/s (comparable to that of the accretion disk). Otherwise, the lack of a phase delay between the EUV and optical oscillations requires that the optical reprocessing site lies within the inner third of the accretion disk. This is strikingly different from other cataclysmic variables, where much or all of the disk contributes to the optical oscillations.Comment: 16 pages including 3 tables and 4 encapsulated postscript figures; LaTeX format, uses aastex.cls; accepted on 2001 August 2 for publication in The Astrophysical Journa

Run Scenarios for the Linear Collider

Scenarios are developed for runs at a Linear Collider, in the case that there is a rich program of new physics.Comment: 12 pages, 10 tables, Latex; Snowmass 2001 plenary repor

Radial Squeezed States and Rydberg Wave Packets

We outline an analytical framework for the treatment of radial Rydberg wave packets produced by short laser pulses in the absence of external electric and magnetic fields. Wave packets of this type are localized in the radial coordinates and have p-state angular distributions. We argue that they can be described by a particular analytical class of squeezed states, called radial squeezed states. For hydrogenic Rydberg atoms, we discuss the time evolution of the corresponding hydrogenic radial squeezed states. They are found to undergo decoherence and collapse, followed by fractional and full revivals. We also present their uncertainty product and uncertainty ratio as functions of time. Our results show that hydrogenic radial squeezed states provide a suitable analytical description of hydrogenic Rydberg atoms excited by short-pulsed laser fields.Comment: published in Physical Review

Compton Scattering of Fe K alpha Lines in Magnetic Cataclysmic Variables

Compton scattering of X-rays in the bulk flow of the accretion column in magnetic cataclysmic variables (mCVs) can significantly shift photon energies. We present Monte Carlo simulations based on a nonlinear algorithm demonstrating the effects of Compton scattering on the H-like, He-like and neutral Fe K alpha lines produced in the post-shock region of the accretion column. The peak line emissivities of the photons in the post-shock flow are taken into consideration and frequency shifts due to Doppler effects are also included. We find that line profiles are most distorted by Compton scattering effects in strongly magnetized mCVs with a low white dwarf mass and high mass accretion rate and which are viewed at an oblique angle with respect to the accretion column. The resulting line profiles are most sensitive to the inclination angle. We have also explored the effects of modifying the accretion column width and using a realistic emissivity profile. We find that these do not have a significant overall effect on the resulting line profiles. A comparison of our simulated line spectra with high resolution Chandra/HETGS observations of the mCV GK Per indicates that a wing feature redward of the 6.4 keV line may result from Compton recoil near the base of the accretion column.Comment: Accepted for publication in MNRAS, 10 pages with 8 figure

Renormalization Group Theory And Variational Calculations For Propagating Fronts

We study the propagation of uniformly translating fronts into a linearly unstable state, both analytically and numerically. We introduce a perturbative renormalization group (RG) approach to compute the change in the propagation speed when the fronts are perturbed by structural modification of their governing equations. This approach is successful when the fronts are structurally stable, and allows us to select uniquely the (numerical) experimentally observable propagation speed. For convenience and completeness, the structural stability argument is also briefly described. We point out that the solvability condition widely used in studying dynamics of nonequilibrium systems is equivalent to the assumption of physical renormalizability. We also implement a variational principle, due to Hadeler and Rothe, which provides a very good upper bound and, in some cases, even exact results on the propagation speeds, and which identifies the transition from ` linear'- to ` nonlinear-marginal-stability' as parameters in the governing equation are varied.Comment: 34 pages, plain tex with uiucmac.tex. Also available by anonymous ftp to gijoe.mrl.uiuc.edu (128.174.119.153), file /pub/front_RG.tex (or .ps.Z

Keplerian Squeezed States and Rydberg Wave Packets

We construct minimum-uncertainty solutions of the three-dimensional Schr\"odinger equation with a Coulomb potential. These wave packets are localized in radial and angular coordinates and are squeezed states in three dimensions. They move on elliptical keplerian trajectories and are appropriate for the description of the corresponding Rydberg wave packets, the production of which is the focus of current experimental effort. We extend our analysis to incorporate the effects of quantum defects in alkali-metal atoms, which are used in experiments.Comment: accepted for publication in Physical Review

Classical Evolution of Quantum Elliptic States

The hydrogen atom in weak external fields is a very accurate model for the multiphoton excitation of ultrastable high angular momentum Rydberg states, a process which classical mechanics describes with astonishing precision. In this paper we show that the simplest treatment of the intramanifold dynamics of a hydrogenic electron in external fields is based on the elliptic states of the hydrogen atom, i.e., the coherent states of SO(4), which is the dynamical symmetry group of the Kepler problem. Moreover, we also show that classical perturbation theory yields the {\it exact} evolution in time of these quantum states, and so we explain the surprising match between purely classical perturbative calculations and experiments. Finally, as a first application, we propose a fast method for the excitation of circular states; these are ultrastable hydrogenic eigenstates which have maximum total angular momentum and also maximum projection of the angular momentum along a fixed direction. %Comment: 8 Pages, 2 Figures. Accepted for publication in Phys. Rev.

Long-Term Evolution and Revival Structure of Rydberg Wave Packets for Hydrogen and Alkali-Metal Atoms

This paper begins with an examination of the revival structure and long-term evolution of Rydberg wave packets for hydrogen. We show that after the initial cycle of collapse and fractional/full revivals, which occurs on the time scale $t_{\rm rev}$, a new sequence of revivals begins. We find that the structure of the new revivals is different from that of the fractional revivals. The new revivals are characterized by periodicities in the motion of the wave packet with periods that are fractions of the revival time scale $t_{\rm rev}$. These long-term periodicities result in the autocorrelation function at times greater than $t_{\rm rev}$ having a self-similar resemblance to its structure for times less than $t_{\rm rev}$. The new sequence of revivals culminates with the formation of a single wave packet that more closely resembles the initial wave packet than does the full revival at time $t_{\rm rev}$, i.e., a superrevival forms. Explicit examples of the superrevival structure for both circular and radial wave packets are given. We then study wave packets in alkali-metal atoms, which are typically used in experiments. The behavior of these packets is affected by the presence of quantum defects that modify the hydrogenic revival time scales and periodicities. Their behavior can be treated analytically using supersymmetry-based quantum-defect theory. We illustrate our results for alkali-metal atoms with explicit examples of the revival structure for radial wave packets in rubidium.Comment: To appear in Physical Review A, vol. 51, June 199