Harsh Mathur

Case Western Reserve University, Cleveland, Ohio, United States

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Publications (57)161.39 Total impact

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    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.
    Physics Letters B. 03/2014; 736.
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    ABSTRACT: In PT-symmetric 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 PT-symmetric quantum mechanics by constructing a simple model that is the PT-symmetric analog of a particle in a box. The model has the usual particle-in-a-box Hamiltonian but boundary conditions that respect PT symmetry rather than Hermiticity. We find that for a broad class of PT-symmetric 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 self-adjoint under the PT-symmetric inner product. Thus we obtain a simple soluble model that fulfills all the requirements of PT-symmetric quantum mechanics. In the second part of this paper we formulate a variational principle for PT-symmetric quantum mechanics that is the analog of the textbook Rayleigh-Ritz principle. Finally we consider electromagnetic analogs of the PT-symmetric particle in a box. We show that the isolated particle in a box may be realized as a Fabry-Perot 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 Breit-Wigner line shape in transmission and a Fano line shape in reflection; by contrast, in the corresponding Hermitian case the line shapes always have a Breit-Wigner form in both transmission and reflection.
    Physical Review A. 06/2013; 87(6).
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    Alexander St John, Harsh Mathur
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    ABSTRACT: The q model 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 q model 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 ν and z.
    Physical Review E 11/2011; 84(5 Pt 1):051303. · 2.31 Impact Factor
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    Katherine Jones-Smith, Harsh Mathur
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    ABSTRACT: We formulate quantum mechanics for non-Hermitian Hamiltonians that are invariant under PT, where P is the parity and T denotes time reversal, for the case that time-reversal 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.
    Physical Review A 10/2010; 82(4). · 3.04 Impact Factor
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    ABSTRACT: We present a new signature by which to one could potentially discriminate between a spectrum of gravitational radiation generated by a self-ordering 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 post-horizon-crossing evolution. Comment: 4 pages, Phys. Rev D version (revised in response to referee's comments)
    Physical review D: Particles and fields 03/2010;
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    Yi-Zen Chu, Harsh Mathur, Tanmay Vachaspati
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    ABSTRACT: We analyze Aharonov-Bohm 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 fermion-antifermion pair. Fermionic radiation from kinks and cusps on cosmic strings is shown to depend linearly on the ultraviolet cut-off, suggesting strong emission at an energy scale comparable to the string energy scale. Comment: 14 pages, 6 figures. Version 2: Expanded discussion on boundary conditions obeyed by Dirac equation mode functions (in Section V B). Acknowledgements and references added. Version 3: Minor changes made in response to referee's comments
    Physical review D: Particles and fields 03/2010;
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    ABSTRACT: A solenoid oscillating in vacuum will pair produce charged particles due to the Aharonov-Bohm (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
    Physical review D: Particles and fields 11/2009;
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    Katherine Jones-Smith, Harsh Mathur
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    ABSTRACT: We develop relativistic wave equations in the framework of the new non-hermitian 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 8-dimensional representation of the PT-generalized Dirac equation, non-hermitian 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 PT-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a non-interacting 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 non-hermiticity parameter m_2. Comment: submitted to PRL
    08/2009;
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    ABSTRACT: Inflation produces super-horizon 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 sub-horizon 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 non-inflationary processes may confuse the interpretation of observational data today. Comment: changed title
    07/2009;
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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 box-counting 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.
    Physical Review E 05/2009; 79(4 Pt 2):046111. · 2.31 Impact Factor
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    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 mm-wave kilo-pixel arrays. Additional instruments are in the planning stages.
    04/2009;
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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. Comment: 107 pages, 14 figures, 17 tables; Inflation Working Group contribution to the CMBPol Mission Concept Study; v2: typos fixed and references added
    11/2008;
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    Solomon Duki, Harsh Mathur
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    ABSTRACT: We consider the application of a small in-plane 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 long-lived resonances. As a result microwave absorption lines acquire an asymmetric Fano lineshape that is tunable by varying the microwave polarisation or the in-plane 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.
    05/2008;
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    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 box-counting algorithm and of the interpretation of multi-layered 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.
    04/2008;
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    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.
    Physical Review Letters 04/2008; 100(13):131302. · 7.73 Impact Factor
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    ABSTRACT: We obtain analytic formulae for the spacing between conductance peaks in the Coulomb blockade regime, based on the universal Hamiltonian model of quantum dots. New random matrix theory results are developed in order to treat correlations between two and three consecutive spacings in the energy level spectrum. These are generalizations of the Wigner surmise for the probability distribution of single level spacing. The analytic formulae are shown to be in good agreement with numerical evaluation.
    Physical review. B, Condensed matter 08/2007; · 3.77 Impact Factor
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    ABSTRACT: Dependence of the polarizability of a QD on the number of excitons in it was investigated. A simple model of weakly interacting charge carriers in an infinite spherical potential well agrees well with the experiment.
    Quantum Electronics and Laser Science Conference, 2007. QELS '07; 06/2007
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    ABSTRACT: We have used random matrix theory to obtain an exact result for the probability distribution of the nematic order parameter in a randomly oriented array of rod-shaped molecules. The result for the average order parameter is that S(N) = √81/40πN + (N−1). This disproves a conjecture that S(N) should tend to √2/3N.
    EPL (Europhysics Letters) 01/2007; 59(3):398. · 2.26 Impact Factor
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    Irit Maor, Harsh Mathur, Tanmay Vachaspati
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    ABSTRACT: A possible electric-magnetic duality suggests that the confinement of non-Abelian electric charges manifests itself as a perturbative quantum effect for the dual magnetic charges. Motivated by this possibility, we study vacuum fluctuations around a non-Abelian monopole-antimonopole pair treated as point objects with charges g={+-}n/2 (n=1,2,...), and placed on the antipodes of a three sphere of radius R. We explicitly find all the fluctuation modes by linearizing and solving the Yang-Mills equations about this background field on a three sphere. We recover, generalize, and extend earlier results, including those on the stability analysis of non-Abelian magnetic monopoles. We find that for g{>=}1 monopoles there is an unstable mode that tends to squeeze magnetic flux in the angular directions. We sum the vacuum energy contributions of the fluctuation modes for the g=1/2 case and find oscillatory dependence on the cutoff scale. Subject to certain assumptions, we find that the contribution of the fluctuation modes to the quantum zero-point energy grows as -R²³ and hence decays more slowly than the classical -R¹ Coulomb potential for large R. However, the growth of the zero-point energy does not agree with the linear growth expected if the monopoles are confined.
    Physical review D: Particles and fields 01/2007; 76(10):105013-105013.
  • Solomon Duki, Harsh Mathur
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    ABSTRACT: SU(4) symmetry in quantum dots has become a growing interest in both semiconductor quantum dots and carbon nanotube quantum dots[1]. We investigate theoretically the properties of an SU(4) Kondo model out of equilibrium by solving the problem exactly at a special point in the parameter space. The solution reveals that, in contrast to the SU(2) model, there are two more excitations in the system other than the charge and spin excitations. We investigate the differential conductance for arbitrary voltage bias. [1] P. Jarillo-Herrero, J. Kong, H.S.J. van der Zant, C. Dekker, L.P. Kouwenhoven and S. De Franceschi, http://www.nature.com/openurl?urlver=Z39.88-2004&rftvalfmt=info:ofi/fmt:kev:mtx:journal&rft.genre=journal&rft. volume=434&rft.spage=484 &rft.date=2005 (Nature) 434, 484, (2005).
    01/2007;

Publication Stats

511 Citations
161.39 Total Impact Points

Institutions

  • 1996–2014
    • Case Western Reserve University
      • Department of Physics
      Cleveland, Ohio, United States
  • 2011
    • University of Wisconsin - Parkside
      Somers, Wisconsin, United States
  • 2002
    • University of Kentucky
      • Department of Physics & Astronomy
      Lexington, KY, United States
  • 1991–1992
    • Yale University
      • Department of Applied Physics
      New Haven, Connecticut, United States