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

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

Repulsive Casimir Pistons

Casimir pistons are models in which finite Casimir forces can be calculated without any suspect renormalizations. It has been suggested that such forces are always attractive. We present three scenarios in which that is not true. Two of these depend on mixing two types of boundary conditions. The other, however, is a simple type of quantum graph in which the sign of the force depends upon the number of edges.Comment: 4 pages, 2 figures; RevTeX. Minor additions and correction

Bandwidth in bolometric interferometry

Bolometric Interferometry is a technology currently under development that will be first dedicated to the detection of B-mode polarization fluctuations in the Cosmic Microwave Background. A bolometric interferometer will have to take advantage of the wide spectral detection band of its bolometers in order to be competitive with imaging experiments. A crucial concern is that interferometers are presumed to be importantly affected by a spoiling effect known as bandwidth smearing. In this paper, we investigate how the bandwidth modifies the work principle of a bolometric interferometer and how it affects its sensitivity to the CMB angular power spectra. We obtain analytical expressions for the broadband visibilities measured by broadband heterodyne and bolometric interferometers. We investigate how the visibilities must be reconstructed in a broadband bolometric interferometer and show that this critically depends on hardware properties of the modulation phase shifters. Using an angular power spectrum estimator accounting for the bandwidth, we finally calculate the sensitivity of a broadband bolometric interferometer. A numerical simulation has been performed and confirms the analytical results. We conclude (i) that broadband bolometric interferometers allow broadband visibilities to be reconstructed whatever the kind of phase shifters used and (ii) that for dedicated B-mode bolometric interferometers, the sensitivity loss due to bandwidth smearing is quite acceptable, even for wideband instruments (a factor 2 loss for a typical 20% bandwidth experiment).Comment: 13 pages, 14 figures, submitted to A&

Scarring Effects on Tunneling in Chaotic Double-Well Potentials

The connection between scarring and tunneling in chaotic double-well potentials is studied in detail through the distribution of level splittings. The mean level splitting is found to have oscillations as a function of energy, as expected if scarring plays a role in determining the size of the splittings, and the spacing between peaks is observed to be periodic of period {$2\pi\hbar$} in action. Moreover, the size of the oscillations is directly correlated with the strength of scarring. These results are interpreted within the theoretical framework of Creagh and Whelan. The semiclassical limit and finite-{$\hbar$} effects are discussed, and connections are made with reaction rates and resonance widths in metastable wells.Comment: 22 pages, including 11 figure

Wess-Zumino model with exact supersymmetry on the lattice

A lattice formulation of the four dimensional Wess-Zumino model that uses Ginsparg-Wilson fermions and keeps exact supersymmetry is presented. The supersymmetry transformation that leaves invariant the action at finite lattice spacing is determined by performing an iterative procedure in the coupling constant. The closure of the algebra, generated by this transformation is also showed.Comment: 13 pages. Few references added. New appendix on Ward identity added. Version to be published in JHE

A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry

We construct super Yang-Mills theories with extended supersymmetry on hypercubic lattices of various dimensions keeping one or two supercharges exactly. Gauge fields are represented by ordinary unitary link variables, and the exact supercharges are nilpotent up to gauge transformations. Among the models, we show that the desired continuum theories are obtained without any fine tuning of parameters for the cases ${\cal N}=2, 4, 8$ in two-dimensions.Comment: 29 pages, 1 figure, LaTeX, (v2) problem on degenerate vacua discussed, renormalization arguments modified, (v3) explanations and references added, published version in JHE

Nanostratification of optical excitation in self-interacting 1D arrays

The major assumption of the Lorentz-Lorenz theory about uniformity of local fields and atomic polarization in dense material does not hold in finite groups of atoms, as we reported earlier [A. E. Kaplan and S. N. Volkov, Phys. Rev. Lett., v. 101, 133902 (2008)]. The uniformity is broken at sub-wavelength scale, where the system may exhibit strong stratification of local field and dipole polarization, with the strata period being much shorter than the incident wavelength. In this paper, we further develop and advance that theory for the most fundamental case of one-dimensional arrays, and study nanoscale excitation of so called "locsitons" and their standing waves (strata) that result in size-related resonances and related large field enhancement in finite arrays of atoms. The locsitons may have a whole spectrum of spatial frequencies, ranging from long waves, to an extent reminiscent of ferromagnetic domains, -- to super-short waves, with neighboring atoms alternating their polarizations, which are reminiscent of antiferromagnetic spin patterns. Of great interest is the new kind of "hybrid" modes of excitation, greatly departing from any magnetic analogies. We also study differences between Ising-like near-neighbor approximation and the case where each atom interacts with all other atoms in the array. We find an infinite number of "exponential eigenmodes" in the lossless system in the latter case. At certain "magic" numbers of atoms in the array, the system may exhibit self-induced (but linear in the field) cancellation of resonant local-field suppression. We also studied nonlinear modes of locsitons and found optical bistability and hysteresis in an infinite array for the simplest modes.Comment: 39 pages, 5 figures; v2: Added the Conclusions section, corrected a typo in Eq. (5.3), corrected minor stylistic and grammatical imperfection