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

Intertwining technique for a system of difference Schroedinger equations and new exactly solvable multichannel potentials

The intertwining operator technique is applied to difference Schroedinger equations with operator-valued coefficients. It is shown that these equations appear naturally when a discrete basis is used for solving a multichannel Schroedinger equation. New families of exactly solvable multichannel Hamiltonians are found

Shifting Bordering and Rescue Practices in the Central Mediterranean Sea, October 2013–October 2015

This counter‐mapping project illustrates the areas of intervention of different operations geared toward rescue and enforcement between 2013 and 2015, including the Italian Navy's “Mare Nostrum” search and rescue mission, the EU border agency Frontex's “Triton” enforcement operation, the humanitarian interventions of commercial vessels, and the action of civil‐society rescue vessels such as those operated by Médecins Sans Frontières (MSF—Doctors Without Borders). The project offers a spatial understanding of the Mediterranean border‐scape, the practices of rescue and enforcement that occur within it, and the risk of sea‐crossing at this particular moment. Through these maps, the Central Mediterranean Sea emerges as a striking laboratory from which novel legal arrangements, surveillance technologies, and institutional assemblages converge

Shifting Bordering and Rescue Practices in the Central Mediterranean Sea, October 2013-October 2015

This counter‐mapping project illustrates the areas of intervention of different operations geared toward rescue and enforcement between 2013 and 2015, including the Italian Navy's “Mare Nostrum” search and rescue mission, the EU border agency Frontex's “Triton” enforcement operation, the humanitarian interventions of commercial vessels, and the action of civil‐society rescue vessels such as those operated by Médecins Sans Frontières (MSF—Doctors Without Borders). The project offers a spatial understanding of the Mediterranean border‐scape, the practices of rescue and enforcement that occur within it, and the risk of sea‐crossing at this particular moment. Through these maps, the Central Mediterranean Sea emerges as a striking laboratory from which novel legal arrangements, surveillance technologies, and institutional assemblages converge

Beyond the First Recurrence in Scar Phenomena

The scarring effect of short unstable periodic orbits up to times of the order of the first recurrence is well understood. Much less is known, however, about what happens past this short-time limit. By considering the evolution of a dynamically averaged wave packet, we show that the dynamics for longer times is controlled by only a few related short periodic orbits and their interplay.Comment: 4 pages, 4 Postscript figures, submitted to Phys. Rev. Let

Influence of diffraction on the spectrum and wavefunctions of an open system

In this paper, we demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off of a sharp edge of the system are found to have a strong influence on the transmission spectrum of the system, especially in the regime where there are no stable classical orbits. On resonance, the wavefunctions are influenced by both classical and diffractive orbits. Off resonance, the wavefunctions are determined by the constructive interference of multiple transient, nonperiodic orbits. Experimental, numerical, and semiclassical results are presented.Comment: 27 pages, 29 figures, and 3 tables. Submitted to Physical Review E. A copy with higher resolution figures is available at http://monsoon.harvard.edu/~hersch/papers.htm

Vortices and confinement at weak coupling

We discuss the physical picture of thick vortices as the mechanism responsible for confinement at arbitrarily weak coupling in SU(2) gauge theory. By introducing appropriate variables on the lattice we distinguish between thin, thick and `hybrid' vortices, the latter involving Z(2) monopole loop boundaries. We present numerical lattice simulation results that demonstrate that the full SU(2) string tension at weak coupling arises from the presence of vortices linked to the Wilson loop. Conversely, excluding linked vortices eliminates the confining potential. The numerical results are stable under alternate choice of lattice action as well as a smoothing procedure which removes short distance fluctuations while preserving long distance physics.Comment: 21 pages, LaTe

Probing the Region of Massless Quarks in Quenched Lattice QCD using Wilson Fermions

We study the spectrum of $H(m)=\gamma_5 W(-m)$ with $W(m)$ being the Wilson-Dirac operator on the lattice with bare mass equal to $m$. The background gauge fields are generated using the SU(3) Wilson action at $\beta=5.7$ on an $8^3\times 16$ lattice. We find evidence that the spectrum of $H(m)$ is gapless for $1.02 < m < 2.0$, implying that the physical quark is massless in this whole region.Comment: 22 pages, LaTeX file, uses elsart.sty, includes 11 figures A typographical error in one reference has been fixe