Publications (67)215.41 Total impact
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ABSTRACT: It is shown theoretically that a onedimensional crystal with time reversal symmetry is characterized by a Z_{2} topological invariant that predicts the existence or otherwise of edge states. This is confirmed experimentally through the construction and simulation of a photonic crystal analogue in the microwave regime.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the application of a small inplane magnetic field to electrons on a helium surface in a perpendicular magnetic field. Certain states that were bound to the helium surface then dissolve into the continuum, turning into longlived resonances. As a result microwave absorption lines acquire an asymmetric Fano lineshape that is tunable by varying the microwave polarization or the inplane magnetic field. Electrons trapped in a formerly bound state will tunnel off the surface of helium; we show that under suitable circumstances this "radioactive decay" can show damped oscillations rather than a simple exponential decay. The mechanism for oscillatory exponential decay is not specific to electrons on helium and this effect may also be relevant elsewhere in physics.  [Show abstract] [Hide abstract]
ABSTRACT: The surprisingly large value of $r$, the ratio of power in tensor to scalar density perturbations in the CMB reported by the BICEP2 Collaboration provides strong evidence for Inflation at the GUT scale. In order to provide compelling evidence, other possible sources of the signal need to be ruled out. While the Inflationary signal remains the best motivated source, the current measurement unfortunately still allows for the possibility that a comparable gravitational wave background might result from a self ordering scalar field transition that takes place later at somewhat lower energy. However even marginally improved limits on the possible isocurvature contribution to CMB anistropies could rule out this possibility, and essentially all other sources of the observed signal other than Inflation.  [Show abstract] [Hide abstract]
ABSTRACT: In PTsymmetric quantum mechanics a fundamental principle of quantum mechanics, that the Hamiltonian must be Hermitian, is replaced by another set of requirements, including notably symmetry under PT, where P denotes parity and T denotes time reversal. Here we study the role of boundary conditions in PTsymmetric quantum mechanics by constructing a simple model that is the PTsymmetric analog of a particle in a box. The model has the usual particleinabox Hamiltonian but boundary conditions that respect PT symmetry rather than Hermiticity. We find that for a broad class of PTsymmetric boundary conditions the model respects the condition of unbroken PT symmetry, namely, that the Hamiltonian and the symmetry operator PT have simultaneous eigenfunctions, implying that the energy eigenvalues are real. We also find that the Hamiltonian is selfadjoint under the PTsymmetric inner product. Thus we obtain a simple soluble model that fulfills all the requirements of PTsymmetric quantum mechanics. In the second part of this paper we formulate a variational principle for PTsymmetric quantum mechanics that is the analog of the textbook RayleighRitz principle. Finally we consider electromagnetic analogs of the PTsymmetric particle in a box. We show that the isolated particle in a box may be realized as a FabryPerot cavity between an absorbing medium and its conjugate gain medium. Coupling the cavity to an external continuum of incoming and outgoing states turns the energy levels of the box into sharp resonances. Remarkably we find that the resonances have a BreitWigner line shape in transmission and a Fano line shape in reflection; by contrast, in the corresponding Hermitian case the line shapes always have a BreitWigner form in both transmission and reflection.  [Show abstract] [Hide abstract]
ABSTRACT: The qmodel is a random walk model used to describe the flow of stress in a stationary granular medium. Here we derive the exact horizontal and vertical correlation functions for the qmodel in two dimensions. We show that close to a critical point identified in earlier work these correlation functions have a universal scaling form reminiscent of thermodynamic critical phenomena. We determine the form of the universal scaling function and the associated critical exponents $\nu$ and $z$.  [Show abstract] [Hide abstract]
ABSTRACT: We show that the band structure of a onedimensional solid with particlehole symmetry may be characterized by a topological index that owes its existence to the nontrivial homotopy of the space of nondegenerate real symmetric matrices. Moreover we explicitly demonstrate a theorem linking the topological index to the existence of bound states on the surface of a semiinfinite one dimensional solid. Our analysis is a onedimensional analogue of the analysis of topological insulators in two and three dimensions by Balents and Moore; our results may be relevant to long molecules that are the one dimensional analogue of topological insulators. We propose the realization of this physics in a onedimensional photonic crystal. In this case the topology of the bandstructure reveals itself not as a bound surface state but as a Lorentzian feature in the time delay of light that is otherwise perfectly reflected by the photonic crystal.  [Show abstract] [Hide abstract]
ABSTRACT: We formulate quantum mechanics for nonHermitian Hamiltonians that are invariant under PT, where P is the parity and T denotes time reversal, for the case that timereversal symmetry is odd (T2=1), generalizing prior work for the even case (T2=1). We discover an analog of Kramer’s theorem for PT quantum mechanics, present a prototypical example of a PT quantum system with odd time reversal, and discuss potential applications of the formalism.  [Show abstract] [Hide abstract]
ABSTRACT: We present a new signature by which to one could potentially discriminate between a spectrum of gravitational radiation generated by a selfordering scalar field vs that of inflation, specifically a comparison of the magnitude of a flat spectrum at frequencies probed by future direct detection experiments to the magnitude of a possible polarization signal in the Cosmic Microwave Background (CMB) radiation. In the process we clarify several issues related to the proper calculation of such modes, focusing on the effect of posthorizoncrossing evolution. Comment: 4 pages, Phys. Rev D version (revised in response to referee's comments) 
Article: AharonovBohm Radiation of Fermions
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ABSTRACT: We analyze AharonovBohm radiation of charged fermions from oscillating solenoids and cosmic strings. We find that the angular pattern of the radiation has features that differ significantly from that for bosons. For example, fermionic radiation in the lowest harmonic is approximately isotropically distributed around an oscillating solenoid, whereas for bosons the radiation is dipolar. We also investigate the spin polarization of the emitted fermionantifermion pair. Fermionic radiation from kinks and cusps on cosmic strings is shown to depend linearly on the ultraviolet cutoff, suggesting strong emission at an energy scale comparable to the string energy scale. 
Article: AharonovBohm Radiation
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ABSTRACT: A solenoid oscillating in vacuum will pair produce charged particles due to the AharonovBohm (AB) interaction. We calculate the radiation pattern and power emitted for charged scalar particles. We extend the solenoid analysis to cosmic strings, and find enhanced radiation from cusps and kinks on loops. We argue by analogy with the electromagnetic AB interaction that cosmic strings should emit photons due to the gravitational AB interaction of fields in the conical spacetime of a cosmic string. We calculate the emission from a kink and find that it is of similar order as emission from a cusp, but kinks are vastly more numerous than cusps and may provide a more interesting observational signature. Comment: Accepted for publication in Phys Rev D  [Show abstract] [Hide abstract]
ABSTRACT: We develop relativistic wave equations in the framework of the new nonhermitian PT quantum mechanics. The familiar hermitian Dirac equation emerges as an exact result; we also find new models with properties that have no counterpart in hermitian quantum mechanics. For example in an 8dimensional representation of the PTgeneralized Dirac equation, nonhermitian mass matrices allow for flavor oscillation of two generations of neutrinos, even with an effective mass of zero for the neutrino. This violates what has become in recent years the conventional wisdom, that neutrinos must have mass in order to account for the observation of flavor oscillations. The PTgeneralized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a noninteracting theory it violates P and T individually. The relativistic wave equations are reformulated as canonical fermionic field theories to facilitate the study of interactions, and shown to maintain many of the canonical structures from hermitian field theory, but with tantalizing new possibilities permitted by the nonhermiticity parameter m_2. Comment: submitted to PRL  [Show abstract] [Hide abstract]
ABSTRACT: Inflation produces superhorizon sized perturbations that ultimately return within the horizon and are thought to form the seeds of all observed large scale structure in the Universe. But inflationary predictions can only be compared with present day observations if, as conventional wisdom dictates, they remain unpolluted by subsequent subhorizon causal physical processes and therefore remain immune from the vicissitudes of unknown universal dynamics in the intervening period. Here we demonstrate that conventional wisdom need not be correct, and as a result cosmological signatures arising from intervening unknown noninflationary processes may confuse the interpretation of observational data today. Comment: changed title 
Conference Paper: Probing Inflation with CMB Polarization
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ABSTRACT: We summarize the utility of precise cosmic microwave background (CMB) polarization measurements as probes of the physics of inflation. We focus on the prospects for using CMB measurements to differentiate various inflationary mechanisms. In particular, a detection of primordial B‐mode polarization would demonstrate that inflation occurred at a very high energy scale, and that the inflaton traversed a super‐Planckian distance in field space. We explain how such a detection or constraint would illuminate aspects of physics at the Planck scale. Moreover, CMB measurements can constrain the scale‐dependence and non‐Gaussianity of the primordial fluctuations and limit the possibility of a significant isocurvature contribution. Each such limit provides crucial information on the underlying inflationary dynamics. Finally, we quantify these considerations by presenting forecasts for the sensitivities of a future satellite experiment to the inflationary parameters. 
Article: Drip Paintings and Fractal Analysis
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ABSTRACT: It has been claimed that fractal analysis can be applied to unambiguously characterize works of art such as the drip paintings of Jackson Pollock. This academic issue has become of more general interest following the recent discovery of a cache of disputed Pollock paintings. We definitively demonstrate here, by analyzing paintings by Pollock and others, that fractal criteria provide no information about artistic authenticity. This work has led us to a result in fractal analysis of more general scientific significance: we show that the statistics of the "covering staircase" (closely related to the boxcounting staircase) provide a way to characterize geometry and distinguish fractals from Euclidean objects. Finally we present a discussion of the composite of two fractals, a problem that was first investigated by Muzy. We show that the composite is not generally scale invariant and that it exhibits complex multifractal scaling in the small distance asymptotic limit.  [Show abstract] [Hide abstract]
ABSTRACT: How did the universe evolve? The fine angular scale (l>1000) temperature and polarization anisotropies in the CMB are a Rosetta stone for understanding the evolution of the universe. Through detailed measurements one may address everything from the physics of the birth of the universe to the history of star formation and the process by which galaxies formed. One may in addition track the evolution of the dark energy and discover the net neutrino mass. We are at the dawn of a new era in which hundreds of square degrees of sky can be mapped with arcminute resolution and sensitivities measured in microKelvin. Acquiring these data requires the use of special purpose telescopes such as the Atacama Cosmology Telescope (ACT), located in Chile, and the South Pole Telescope (SPT). These new telescopes are outfitted with a new generation of custom mmwave kilopixel arrays. Additional instruments are in the planning stages. 
Article: The Origin of the Universe as Revealed Through the Polarization of the Cosmic Microwave Background
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ABSTRACT: Modern cosmology has sharpened questions posed for millennia about the origin of our cosmic habitat. The ageold questions have been transformed into two pressing issues primed for attack in the coming decade: How did the Universe begin? and What physical laws govern the Universe at the highest energies? The clearest window onto these questions is the pattern of polarization in the Cosmic Microwave Background (CMB), which is uniquely sensitive to primordial gravity waves. A detection of the special pattern produced by gravity waves would be not only an unprecedented discovery, but also a direct probe of physics at the earliest observable instants of our Universe. Experiments which map CMB polarization over the coming decade will lead us on our first steps towards answering these ageold questions.  [Show abstract] [Hide abstract]
ABSTRACT: We summarize the utility of precise cosmic microwave background (CMB) polarization measurements as probes of the physics of inflation. We focus on the prospects for using CMB measurements to differentiate various inflationary mechanisms. In particular, a detection of primordial Bmode polarization would demonstrate that inflation occurred at a very high energy scale, and that the inflaton traversed a superPlanckian distance in field space. We explain how such a detection or constraint would illuminate aspects of physics at the Planck scale. Moreover, CMB measurements can constrain the scaledependence and nonGaussianity of the primordial fluctuations and limit the possibility of a significant isocurvature contribution. Each such limit provides crucial information on the underlying inflationary dynamics. Finally, we quantify these considerations by presenting forecasts for the sensitivities of a future satellite experiment to the inflationary parameters. Comment: 107 pages, 14 figures, 17 tables; Inflation Working Group contribution to the CMBPol Mission Concept Study; v2: typos fixed and references added  [Show abstract] [Hide abstract]
ABSTRACT: We consider the application of a small inplane magnetic field to electrons on a helium surface in a perpendicular magnetic field. Certain states that were bound to the helium surface then dissolve into the continuum turning into longlived resonances. As a result microwave absorption lines acquire an asymmetric Fano lineshape that is tunable by varying the microwave polarisation or the inplane magnetic field. Electrons trapped in a formerly bound state will tunnel off the surface of helium; we show that under suitable circumstances this ``radioactive decay'' can show damped oscillations rather than a simple exponential decay. The mechanism for oscillatory exponential decay is not specific to electrons on Helium and this effect may also be relevant elsewhere in physics.  [Show abstract] [Hide abstract]
ABSTRACT: We reply to the comment of Micolich et al and demonstrate that their criticisms are unfounded. In particular we provide a detailed discussion of our boxcounting algorithm and of the interpretation of multilayered paintings. We point out that in their entire body of work, Taylor et al have not provided the scientific community with sufficient empirical support of their claims, nor have they adequately addressed any of the problems we have identified with the application of fractal analysis to drip paintings.  [Show abstract] [Hide abstract]
ABSTRACT: Using a large N sigma model approximation we explicitly calculate the power spectrum of gravitational waves arising from a global phase transition in the early Universe and we confirm that it is scale invariant, implying an observation of such a spectrum may not be a unique feature of inflation. Moreover, the predicted amplitude can be over 3 orders of magnitude larger than the naive dimensional estimate, implying that even a transition that occurs after inflation may dominate in cosmic microwave background polarization or other gravity wave signals.
Publication Stats
922  Citations  
215.41  Total Impact Points  
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Institutions

19962014

Case Western Reserve University
 Department of Physics
Cleveland, Ohio, United States


19911992

Yale University
 Department of Applied Physics
New Haven, Connecticut, United States
