BMQ

BMQ: Boston Medical Quarterly was published from 1950-1966 by the Boston University School of Medicine and the Massachusetts Memorial Hospitals

Radio-Frequency Spectroscopy

Contains reports on four research projects

Algebraic approach in the study of time-dependent nonlinear integrable systems: Case of the singular oscillator

The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability of this system is established by evaluating the exact invariant closely related to the Lewis and Riesenfeld invariant for the time-dependent harmonic oscillator. We study extensively the special and interesting case of a kicked quadratic potential from which we derive a new integrable, nonlinear, area preserving, two-dimensional map which may, for instance, be used in numerical algorithms that integrate the Calogero-Sutherland-Moser Hamiltonian. The dynamics, both classical and quantal, is studied via the time-evolution operator which we evaluate using a recent method of integrating the quantum Liouville-Bloch equations \cite{rau}. The results show the exact one-to-one correspondence between the classical and the quantal dynamics. Our analysis also sheds light on the connection between properties of the SU(1,1) algebra and that of simple dynamical systems.Comment: 17 pages, 4 figures, Accepted in PR

Radiation reaction for multipole moments

We propose a Poincare-invariant description for the effective dynamics of systems of charged particles by means of intrinsic multipole moments. To achieve this goal we study the effective dynamics of such systems within two frameworks -- the particle itself and hydrodynamical one. We give a relativistic-invariant definition for the intrinsic multipole moments both pointlike and extended relativistic objects. Within the hydrodynamical framework we suggest a covariant action functional for a perfect fluid with pressure. In the case of a relativistic charged dust we prove the equivalence of the particle approach to the hydrodynamical one to the problem of radiation reaction for multipoles. As the particular example of a general procedure we obtain the effective model for a neutral system of charged particles with dipole moment.Comment: 12 pages, 1 figure, RevTeX 4; references updated, minor textual correction

Classical limit in terms of symbolic dynamics for the quantum baker's map

We derive a simple closed form for the matrix elements of the quantum baker's map that shows that the map is an approximate shift in a symbolic representation based on discrete phase space. We use this result to give a formal proof that the quantum baker's map approaches a classical Bernoulli shift in the limit of a small effective Plank's constant.Comment: 12 pages, LaTex, typos correcte

Computational Study of Baryon Number Violation in High Energy Electroweak Collisions

We use semiclassical methods to study processes which give rise to change of topology and therefore to baryon number violation in the standard model. We consider classically allowed processes, i.e.~energies above the sphaleron barrier. We develop a computational procedure that allows us to solve the Yang Mills equations of motion for spherically symmetric configurations and to identify the particle numbers of the in- and out-states. A stochastic sampling technique is then used to map the region spanned by the topology changing solutions in the energy versus incoming particle number plane and, in particular, to determine its lower boundary. A lower boundary which approaches small particle number would be a strong indication that baryon number violation would occur in high energy collisions, whereas a lower asymptote at large particle number would be evidence of the contrary. With our method and the computational resources we have had at our disposal, we have been able to determine the lower boundary up to energies approximately equal to one and a half time times the sphaleron energy and observed a 40\% decrease in particle number with no sign of the particle number leveling off. However encouraging this may be, the decrease in incoming particle number is only from particles 50 down to approximately 30. Nevertheless, the formalism we have established will make it possible to extend the scope of this investigation and also to study processes in the classically forbidden region, which we plan to do in the future.Comment: 57 pages, LaTeX, 14 figues. Four of these figures are gray scale 3D surface plots too large to distribute in color. The full color figures can be viewed or downloaded from http://cthulu.bu.edu/~bobs/bviolate.htm

Wigner function for twisted photons

A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented, with special emphasis in the implications of rotational periodicity and angular-momentum discreteness.Comment: 6 pages, 4 figure

Femtometer Toroidal Structures in Nuclei

The two-nucleon density distributions in states with isospin $T=0$, spin $S$=1 and projection $M_S$=0 and $\pm$1 are studied in $^2$H, $^{3,4}$He, $^{6,7}$Li and $^{16}$O. The equidensity surfaces for $M_S$=0 distributions are found to be toroidal in shape, while those of $M_S$=$\pm$1 have dumbbell shapes at large density. The dumbbell shapes are generated by rotating tori. The toroidal shapes indicate that the tensor correlations have near maximal strength at $r<2$ fm in all these nuclei. They provide new insights and simple explanations of the structure and electromagnetic form factors of the deuteron, the quasi-deuteron model, and the $dp$, $dd$ and $\alpha d$ $L$=2 ($D$-wave) components in $^3$He, $^4$He and $^6$Li. The toroidal distribution has a maximum-density diameter of $\sim$1 fm and a half-maximum density thickness of $\sim$0.9 fm. Many realistic models of nuclear forces predict these values, which are supported by the observed electromagnetic form factors of the deuteron, and also predicted by classical Skyrme effective Lagrangians, related to QCD in the limit of infinite colors. Due to the rather small size of this structure, it could have a revealing relation to certain aspects of QCD.Comment: 35 pages in REVTeX, 25 PostScript figure