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

Magnetic order in the Ising model with parallel dynamics

It is discussed how the equilibrium properties of the Ising model are described by an Hamiltonian with an antiferromagnetic low temperature behavior if only an heat bath dynamics, with the characteristics of a Probabilistic Cellular Automaton, is assumed to determine the temporal evolution of the system.Comment: 9 pages, 3 figure

Multi-interaction mean-field renormalization group

We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of different sublattices of the given lattice and it generates as many flow equations as coupling constants without arbitrary truncations on the renormalized Hamiltonian. We obtain good results for the test case of Ising systems with an additional second-neighbor coupling in two and three dimensions. An application of the method is also done to a morphological model of interacting surfaces introduced recenlty by Likos, Mecke and Wagner [J. Chem. Phys. {\bf{102}}, 9350 (1995)]. PACS: 64.60.Ak, 64.60.Fr, 05.70.JkComment: Tex file and three macros appended at the end. Five figures available upon request to: [email protected], Fax: [+]39-40-224-60

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.

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

Quantum Particle-Trajectories and Geometric Phase

"Particle"-trajectories are defined as integrable $dx_\mu dp^\mu = 0$ paths in projective space. Quantum states evolving on such trajectories, open or closed, do not delocalise in $(x, p)$ projection, the phase associated with the trajectories being related to the geometric (Berry) phase and the Classical Mechanics action. High Energy Physics properties of states evolving on "particle"-trajectories are discussed.Comment: 4 page

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

Optical identification of X-ray source 1RXS J180431.1-273932 as a magnetic cataclysmic variable

The X-ray source 1RXS J180431.1-273932 has been proposed as a new member of the symbiotic X-ray binary (SyXB) class of systems, which are composed of a late-type giant that loses matter to an extremely compact object, most likely a neutron star. In this paper, we present an optical campaign of imaging plus spectroscopy on selected candidate counterparts of this object. We also reanalyzed the available archival X-ray data collected with XMM-Newton. We find that the brightest optical source inside the 90% X-ray positional error circle is spectroscopically identified as a magnetic cataclysmic variable (CV), most likely of intermediate polar type, through the detection of prominent Balmer, He I, He II, and Bowen blend emissions. On either spectroscopic or statistical grounds, we discard as counterparts of the X-ray source the other optical objects in the XMM-Newton error circle. A red giant star of spectral type M5 III is found lying just outside the X-ray position: we consider this latter object as a fore-/background one and likewise rule it out as a counterpart of 1RXS J180431.1-273932. The description of the X-ray spectrum of the source using a bremsstrahlung plus black-body model gives temperatures of around 40 keV and around 0.1 keV for these two components, respectively. We estimate a distance of about 450 pc and a 0.2-10 keV X-ray luminosity of about 1.7e32 erg/s for this system and, using the information obtained from the X-ray spectral analysis, a mass of about 0.8 solar masses for the accreting white dwarf (WD). We also confirm an X-ray periodicity of 494 s for this source, which we interpret as the spin period of the WD. In summary, 1RXS J180431.1-273932 is identified as a magnetic CV and its SyXB nature is excluded.Comment: 9 pages, 7 figures, 3 tables, accepted for publication on Astronomy & Astrophysics, main journal. Version 2 includes the A&A Language Editor's correction

Geometry, thermodynamics, and finite-size corrections in the critical Potts model

We establish an intriguing connection between geometry and thermodynamics in the critical q-state Potts model on two-dimensional lattices, using the q-state bond-correlated percolation model (QBCPM) representation. We find that the number of clusters of the QBCPM has an energy-like singularity for q different from 1, which is reached and supported by exact results, numerical simulation, and scaling arguments. We also establish that the finite-size correction to the number of bonds, has no constant term and explains the divergence of related quantities as q --> 4, the multicritical point. Similar analyses are applicable to a variety of other systems.Comment: 12 pages, 6 figure

Physical Consequences of Complex Dimensions of Fractals

It has recently been realized that fractals may be characterized by complex dimensions, arising from complex poles of the corresponding zeta function, and we show here that these lead to oscillatory behavior in various physical quantities. We identify the physical origin of these complex poles as the exponentially large degeneracy of the iterated eigenvalues of the Laplacian, and discuss applications in quantum mesoscopic systems such as oscillations in the fluctuation $\Sigma^2 (E)$ of the number of levels, as a correction to results obtained in Random Matrix Theory. We present explicit expressions for these oscillations for families of diamond fractals, also studied as hierarchical lattices.Comment: 4 pages, 3 figures; v2: references added, as published in Europhysics Letter