Parity-Time Symmetry Breaking beyond One Dimension: The Role of Degeneracy

We consider the role of degeneracy in Parity-Time (PT) symmetry breaking for non-hermitian wave equations beyond one dimension. We show that if the spectrum is degenerate in the absence of T-breaking, and T is broken in a generic manner (without preserving other discrete symmetries), then the standard PT-symmetry breaking transition does not occur, meaning that the spectrum is complex even for infinitesimal strength of gain and loss. However the realness of the entire spectrum can be preserved over a finite interval if additional discrete symmetries X are imposed when T is broken, if X decouple all degenerate modes. When this is true only for a subset of the degenerate spectrum, there can be a partial PT transition in which this subset remains real over a finite interval of T-breaking. If the spectrum has odd-degeneracy, a fraction of the degenerate spectrum can remain in the symmetric phase even without imposing additional discrete symmetries, and they are analogous to dark states in atomic physics. These results are illustrated by the example of different T-breaking perturbations of a uniform dielectric disk and sphere, and a group theoretical analysis is given in the disk case. Finally, we show that multimode coupling is capable of restoring the T-symmetric phase at finite T-breaking. We also analyze these questions when the parity operator is replaced by another spatial symmetry operator and find that the behavior can be qualitatively different.Comment: 8 pages, 6 figure

PT-symmetry breaking and laser-absorber modes in optical scattering systems

Using a scattering matrix formalism, we derive the general scattering properties of optical structures that are symmetric under a combination of parity and time-reversal (PT). We demonstrate the existence of a transition beween PT-symmetric scattering eigenstates, which are norm-preserving, and symmetry-broken pairs of eigenstates exhibiting net amplification and loss. The system proposed by Longhi, which can act simultaneously as a laser and coherent perfect absorber, occurs at discrete points in the broken symmetry phase, when a pole and zero of the S-matrix coincide.Comment: 4 pages, 4 figure

Quantification of three-dimensional folding using fluvial terraces: A case study from the Mushi anticline, northern margin of the Chinese Pamir

Fold deformation in three dimensions involves shortening, uplift, and lateral growth. Fluvial terraces represent strain markers that have been widely applied to constrain a fold's shortening and uplift. For the lateral growth, however, the utility of fluvial terraces has been commonly ignored. Situated along northern margin of Chinese Pamir, the Mushi anticline preserves, along its northern flank, flights of passively deformed fluvial terraces that can be used to constrain three-dimensional folding history, especially lateral growth. The Mushi anticline is a geometrically simple fault-tip fold with a total shortening of 740?±?110?m and rock uplift of ~1300?m. Geologic and geomorphic mapping and dGPS surveys reveal that terrace surfaces perpendicular to the fold's strike display increased rotation with age, implying the fold grows by progressive limb rotation. We use a pure-shear fault-tip fold model to estimate a uniform shortening rate of 1.5?+?1.3/?0.5?mm/a and a rock-uplift rate of 2.3?+?2.1/?0.8?mm/a. Parallel to the fold's strike, longitudinal profiles of terrace surfaces also display age-dependent increases in slopes. We present a new model to distinguish lateral growth mechanisms (lateral lengthening and/or rotation above a fixed tip). This model indicates that eastward lengthening of the Mushi anticline ceased by at least ~134?ka and its lateral growth has been dominated by rotation. Our study confirms that terrace deformation along a fold's strike not only can constrain the lateral lengthening rate but can serve to quantify the magnitude and rate of lateral rotation: attributes that are commonly difficult to define when relying on other geomorphic criteria

High throughput accelerator interface framework for a linear time-multiplexed FPGA overlay

Coarse-grained FPGA overlays improve design productivity through software-like programmability and fast compilation. However, the effectiveness of overlays as accelerators is dependent on suitable interface and programming integration into a typically processor-based computing system, an aspect which has often been neglected in evaluations of overlays. We explore the integration of a time-multiplexed FPGA overlay over a server-class PCI Express interface. We show how this integration can be optimised to maximise performance, and evaluate the area overhead. We also propose a user-friendly programming model for such an overlay accelerator system

Breaking of PT-symmetry in bounded and unbounded scattering systems

PT-symmetric scattering systems with balanced gain and loss can undergo a symmetry-breaking transition in which the eigenvalues of the non-unitary scattering matrix change their phase shifts from real to complex values. We relate the PT-symmetry breaking points of such an unbounded scattering system to those of underlying bounded systems. In particular, we show how the PT-thresholds in the scattering matrix of the unbounded system translate into analogous transitions in the Robin boundary conditions of the corresponding bounded systems. Based on this relation, we argue and then confirm that the PT-transitions in the scattering matrix are, under very general conditions, entirely insensitive to a variable coupling strength between the bounded region and the unbounded asymptotic region, a result that can be tested experimentally and visualized using the concept of Smith charts.Comment: 9 pages, 6 figures (final version, including newly added connection to the concept of "Smith charts"

Driver Accelerator Design for the 10 kW Upgrade of the Jefferson Lab IR FEL

An upgrade of the Jefferson Lab IR FEL is now under construction. It will provide 10 kW output light power in a wavelength range of 2-10 microns. The FEL will be driven by a modest-sized 80-210 MeV, 10 mA energy-recovering superconducting RF (SRF) linac. Stringent phase space requirements at the wiggler, low beam energy, and high beam current subject the design to numerous constraints. These are imposed by the need for both transverse and longitudinal phase space management, the potential impact of collective phenomena (space charge, wakefields, beam break-up (BBU), and coherent synchrotron radiation (CSR)), and interactions between the FEL and the accelerator RF system. This report addresses these issues and presents an accelerator design solution meeting the requirements imposed by physical phenomena and operational necessities.Comment: submission THC03 for LINAC200

Virtual-Sparticle Threshold Effects on Large E_T Jet Cross Sections

We discuss the one-loop virtual-sparticle corrections to QCD jet cross sections at large $E_T$ and large dijet invariant masses, with reference to present Tevatron and future LHC collider experiments. We find characteristic peaks and dips in the sparticle threshold region, due to interferences with tree-level QCD diagrams. Their magnitudes may be several per cent of the total jet cross section, so they might provide a useful search tool that is complementary to the usual missing-energy signature for supersymmetry.Comment: 8 pages, uses epsf.sty, 5 figures; New version to be published in Phys. Letts. B: We have displayed the corrections to cross sections for various different scattering angles as opposed to different t. We have corrected certain erroneous statements concerning the high energy behaviour of the correction