arXiv subjects
Publications and source records attributed to Harsh Mathur.
It is shown theoretically that a one-dimensional 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.
The surprisingly large value of $r$, the ratio of power in tensor to scalar density perturbations in the CMB reported by the BICEP2 Collaboration, if confirmed, provides strong evidence for Inflation at the GUT scale. While the Inflationary signal remains the best motivated source, a large value of $r$ alone would still allow for the possibility that a comparable gravitational wave background might result from a self ordering scalar field (SOSF) transition that takes place later at somewhat lower energy. We find that even without detailed considerations of the predicted BICEP signature of such a transition, simple existing limits on the isocurvature contribution to CMB anisotropies would definitively rule out a contribution of more than $5\%$ to $r \approx 0.2$,. We also present a general relation for the allowed fractional SOSF contribution to $r$ as a function of the ultimate measured value of $r$. These results point strongly not only to an inflationary origin of the BICEP2 signal, if confirmed, but also to the fact that if the GUT scale is of order $10^{16} GeV$ then either the GUT transition happens before Inflation or the Inflationary transition and the GUT transition must be one and the same.
We develop relativistic wave equations in the framework of the new non-hermitian ${\cal PT}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\cal PT}$-symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no counterpart in conventional quantum mechanics. For example it is well-known that a quartet of Weyl spinors coupled by a Hermitian mass matrix reduces to two independent Dirac fermions; here we show that the same quartet of Weyl spinors, when coupled by a non-Hermitian but $\cal{PT}$ symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is non-zero.The ${\cal PT}$-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a non-interacting theory it violates ${\cal P}$ and ${\cal T}$ individually. The relativistic wave equations are reformulated as canonical fermionic field theories to facilitate the study of interactions, and are shown to maintain many of the canonical structures from Hermitian field theory, but with new and interesting new possibilities permitted by the non-hermiticity parameter $m_2$.
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 $z$.
In a remarkable development Bender and coworkers have shown that it is possible to formulate quantum mechanics consistently even if the Hamiltonian and other observables are not Hermitian. Their formulation, dubbed PT quantum mechanics, replaces hermiticity by another set of requirements, notably that the Hamiltonian should be invariant under the discrete symmetry PT, where P denotes parity and T denotes time reversal. All prior work has focused on the case that time reversal is even (T^2 = 1). We generalize the formalism to the case of odd time reversal (T^2 = -1). We discover an analogue 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. Odd time reversal symmetry applies to fermionic systems including quarks and leptons and a plethora of models in nuclear, atomic and condensed matter physics. PT quantum mechanics makes it possible to enlarge the set of possible Hamiltonians that physicists could deploy to describe fundamental physics beyond the standard model or for the effective description of condensed matter phenomena.
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.
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.
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.
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.
We investigate the contentions that Jackson Pollock's drip paintings are fractals produced by the artist's Levy distributed motion and that fractal analysis may be used to authenticate works of uncertain provenance[1-5]. We find that the paintings exhibit fractal characteristics over too small a range to be usefully considered as fractal; their limited fractal characteristics are easily generated without Levy motion, both by freehand drawing and gaussian random motion. Several problems must therefore be addressed before fractal analysis can be used to authenticate paintings.
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.
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.
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.
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.
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.
It has been claimed [1-6] 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 also led to two new results in fractal analysis of more general scientific significance. First, the composite of two fractals is not generally scale invariant and exhibits complex multifractal scaling in the small distance asymptotic limit. Second the statistics of box-counting and related staircases provide a new way to characterize geometry and distinguish fractals from Euclidean objects.
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=\pm 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 \ge 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 behaves as -R^{-2/3} and hence decays more slowly than the classical -R^{-1} Coulomb potential for large R. However, this correction to the zero point energy does not agree with the linear growth expected if the monopoles are confined.
A classical analysis suggests that an external magnetic field can cause trajectories of charge carriers on a superconducting domain wall or cosmic string to bend, thus expelling charge carriers with energy above the mass threshold into the bulk. We study this process by solving the Dirac equation for a fermion of mass $m_f$ and charge $e$, in the background of a domain wall and a magnetic field of strength $B$. We find that the modes of the charge carriers get shifted into the bulk, in agreement with classical expectations. However the dispersion relation for the zero modes changes dramatically -- instead of the usual linear dispersion relation, $ω_k =k$, the new dispersion relation is well fit by $ω\approx m_f tanh(k/k_*)$ where $k_*=m_f$ for a thin wall in the weak field limit, and $k_*=eBw$ for a thick wall of width $w$. This result shows that the energy of the charge carriers on the domain wall remains below the threshold for expulsion even in the presence of an external magnetic field. If charge carriers are expelled due to an additional perturbation, they are most likely to be ejected at the threshold energy $\sim m_f$.