A New Expansion for Nucleon-Nucleon Interactions

We introduce a new and well defined power counting for the effective field theory describing nucleon-nucleon interactions. Because of the large NN scattering lengths it differs from other applications of chiral perturbation theory and is facilitated by introducing an unusual subtraction scheme and renormalization group analysis. Calculation to subleading order in the expansion can be done analytically, and we present the results for both the 1S0 and 3S1-3D1 channels.Comment: 10 pages, 3 figures, latex. Corrected typo, small change to tex

Semiclassical Accuracy in Phase Space for Regular and Chaotic Dynamics

A phase-space semiclassical approximation valid to $O(\hbar)$ at short times is used to compare semiclassical accuracy for long-time and stationary observables in chaotic, stable, and mixed systems. Given the same level of semiclassical accuracy for the short time behavior, the squared semiclassical error in the chaotic system grows linearly in time, in contrast with quadratic growth in the classically stable system. In the chaotic system, the relative squared error at the Heisenberg time scales linearly with $\hbar_{\rm eff}$, allowing for unambiguous semiclassical determination of the eigenvalues and wave functions in the high-energy limit, while in the stable case the eigenvalue error always remains of the order of a mean level spacing. For a mixed classical phase space, eigenvalues associated with the chaotic sea can be semiclassically computed with greater accuracy than the ones associated with stable islands.Comment: 9 pages, 6 figures; to appear in Physical Review

Comment on "The Phenomenology of a Nonstandard Higgs Boson in W_L W_L Scattering"

We show that in Composite Higgs models, the coupling of the Higgs resonance to a pair of $W$ bosons is weaker than the corresponding Standard Model coupling, provided the Higgs arises from electroweak doublets only. This is partly due to the effects of the nonlinear realization of the chiral symmetries at the compositeness scale.Comment: 6 pages, BU-HEP 94-2

Localization of Eigenfunctions in the Stadium Billiard

We present a systematic survey of scarring and symmetry effects in the stadium billiard. The localization of individual eigenfunctions in Husimi phase space is studied first, and it is demonstrated that on average there is more localization than can be accounted for on the basis of random-matrix theory, even after removal of bouncing-ball states and visible scars. A major point of the paper is that symmetry considerations, including parity and time-reversal symmetries, enter to influence the total amount of localization. The properties of the local density of states spectrum are also investigated, as a function of phase space location. Aside from the bouncing-ball region of phase space, excess localization of the spectrum is found on short periodic orbits and along certain symmetry-related lines; the origin of all these sources of localization is discussed quantitatively and comparison is made with analytical predictions. Scarring is observed to be present in all the energy ranges considered. In light of these results the excess localization in individual eigenstates is interpreted as being primarily due to symmetry effects; another source of excess localization, scarring by multiple unstable periodic orbits, is smaller by a factor of $\sqrt{\hbar}$.Comment: 31 pages, including 10 figure

The Long and Short of Nuclear Effective Field Theory Expansions

Nonperturbative effective field theory calculations for NN scattering seem to break down at rather low momenta. By examining several toy models, we clarify how effective field theory expansions can in general be used to properly separate long- and short-range effects. We find that one-pion exchange has a large effect on the scattering phase shift near poles in the amplitude, but otherwise can be treated perturbatively. Analysis of a toy model that reproduces 1S0 NN scattering data rather well suggests that failures of effective field theories for momenta above the pion mass can be due to short-range physics rather than the treatment of pion exchange. We discuss the implications this has for extending the applicability of effective field theories.Comment: 22 pages, 9 figures, references corrected, minor modification

Electron-phonon bound states in graphene in a perpendicular magnetic field

The spectrum of electron-phonon complexes in a monolayer graphene is investigated in the presence of a perpendicular quantizing magnetic field. Despite the small electron-phonon coupling, usual perturbation theory is inapplicable for calculation of the scattering amplitude near the threshold of the optical phonon emission. Our findings beyond perturbation theory show that the true spectrum near the phonon emission threshold is completely governed by new branches, corresponding to bound states of an electron and an optical phonon with a binding energy of the order of $\alpha \omega_{0}$ where $\alpha$ is the electron-phonon coupling and $\omega_{0}$ the phonon energy.Comment: To be published in Phys. Rev. Lett., 5 pages, 3 figures, 1 tabl

New Experimental Constraints on Non-Newtonian Forces below 100 microns

We have searched for large deviations from Newtonian gravity by means of a microcantilever-based Cavendish-style experiment. Our data eliminate from consideration mechanisms of deviation that posit strengths ~10^4 times Newtonian gravity at length scales of 20 microns. This measurement is 3 orders of magnitude more sensitive than others that provide constraints at similar length scales.Comment: 4 pages, 4 figure

The path-coalescence transition and its applications

We analyse the motion of a system of particles subjected a random force fluctuating in both space and time, and experiencing viscous damping. When the damping exceeds a certain threshold, the system undergoes a phase transition: the particle trajectories coalesce. We analyse this transition by mapping it to a Kramers problem which we solve exactly. In the limit of weak random force we characterise the dynamics by computing the rate at which caustics are crossed, and the statistics of the particle density in the coalescing phase. Last but not least we describe possible realisations of the effect, ranging from trajectories of raindrops on glass surfaces to animal migration patterns.Comment: 4 pages, 3 figures; revised version, as publishe

Mass corrections in string theory and lattice field theory

Kaluza-Klein compactifications of higher dimensional Yang-Mills theories contain a number of four dimensional scalars corresponding to the internal components of the gauge field. While at tree-level the scalar zero modes are massless, it is well known that quantum corrections make them massive. We compute these radiative corrections at 1-loop in an effective field theory framework, using the background field method and proper Schwinger-time regularization. In order to clarify the proper treatment of the sum over KK--modes in the effective field theory approach, we consider the same problem in two different UV completions of Yang-Mills: string theory and lattice field theory. In both cases, when the compactification radius $R$ is much bigger than the scale of the UV completion ($R \gg \sqrt{\alpha'},a$), we recover a mass renormalization that is independent of the UV scale and agrees with the one derived in the effective field theory approach. These results support the idea that the value of the mass corrections is, in this regime, universal for any UV completion that respects locality and gauge invariance. The string analysis suggests that this property holds also at higher loops. The lattice analysis suggests that the mass of the adjoint scalars appearing in $\mathcal N=2,4$ Super Yang-Mills is highly suppressed due to an interplay between the higher-dimensional gauge invariance and the degeneracy of bosonic and fermionic degrees of freedom.Comment: 27 page

Lattice formulation of (2,2) supersymmetric gauge theories with matter fields

We construct lattice actions for a variety of (2,2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.Comment: 13 pages, 2 figures. Appendix added, references updated, typos fixe