Polynomially large ground-state energy gaps are rare in many-body quantum systems, but useful in quantum information and an interesting feature of the one-dimensional quantum Ising model. We show analytically that the...
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Polynomially large ground-state energy gaps are rare in many-body quantum systems, but useful in quantum information and an interesting feature of the one-dimensional quantum Ising model. We show analytically that the gap is generically polynomially large not just for the quantum Ising model, but for one-, two-, and three-dimensional interaction lattices and Hamiltonians with certain random interactions. We extend the analysis to Hamiltonian evolutions and we use the Jordan-Wigner transformation and a related transformation for spin-3/2 particles to show that our results can be restated using spin operators in a surprisingly simple manner. These results also yield a new perspective on the one-dimensional cluster state.
We introduce the problem of communication with partial information, where there is an asymmetry between the transmitter and the receiver codebooks. Practical applications of the proposed setup include the robust signa...
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We introduce the problem of communication with partial information, where there is an asymmetry between the transmitter and the receiver codebooks. Practical applications of the proposed setup include the robust signal hashing problem within the context of multimedia security and asymmetric communications with resource-lacking receivers. We study this setup in a binary detection theoretic context for the additive colored Gaussian noise channel. In our proposed setup, the partial information available at the detector consists of dimensionality-reduced versions of the transmitter codewords, where the dimensionality reduction is achieved via a linear transform. We first derive the corresponding MAP-optimal detection rule and the corresponding conditional probability of error (conditioned on the partial information the detector possesses). Then, we constructively quantify an optimal class of linear transforms, where the cost function is the expected Chernoff bound on the conditional probability of error of the MAP-optimal detector.
We show that classical many-particle systems interacting with certain soft pair interactions in two dimensions exhibit novel low-temperature behaviors. Ground states span from disordered to crystalline. At some densit...
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We show that classical many-particle systems interacting with certain soft pair interactions in two dimensions exhibit novel low-temperature behaviors. Ground states span from disordered to crystalline. At some densities, a large fraction of normal-mode frequencies vanish. Lattice ground-state configurations have more vanishing frequencies than disordered ground states at the same density and exhibit vanishing shear moduli. For the melting transition from a crystal, the thermal expansion coefficient is negative. These unusual results are attributed to the topography of the energy landscape.
Charge transport in DNA molecules has raised considerable interest because of its importance in biological processes and potential applications in nanoscale devices. A DNA molecule can be viewed as a quasi-one-dimensi...
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Charge transport in DNA molecules has raised considerable interest because of its importance in biological processes and potential applications in nanoscale devices. A DNA molecule can be viewed as a quasi-one-dimensional system composed of stacked base pairs (AT, CG) together with backbones of sugar phosphates. Motivated by recent experimental observations on the importance of the backbone integrity, we investigate the interplay between charge transport through the ordered backbone and disordered base stacks with random sequences. By analytical and numerical calculations, we find that the coupling between the backbone and base-pair channels plays an important role in charge transport. The backbone can generate effective hopping constants well beyond the adjacent base pairs, enhancing charge transport through the base-pair channel. The corresponding enhancement of the localization length is nearly independent of the length of the DNA and increases with increasing coupling between backbone and base pair. Our model can explain qualitatively several experimental observations.
Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in thr...
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Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have considered spherical shapes, and it is only more recently that nonspherical shapes (e.g., ellipsoids) have been investigated. Superballs (whose shapes are defined by |x1|2p+|x2|2p+|x3|2p≤1) provide a versatile family of convex particles (p≥0.5) with both cubic-like and octahedral-like shapes as well as concave particles (0
The chiral susceptibility is given by the scalar vacuum polarization at zero total momentum. This follows directly from the expression for the vacuum quark condensate so long as a nonperturbative symmetry preserving t...
The chiral susceptibility is given by the scalar vacuum polarization at zero total momentum. This follows directly from the expression for the vacuum quark condensate so long as a nonperturbative symmetry preserving truncation scheme is employed. For QCD in-vacuum the susceptibility can rigorously be defined via a Pauli-Villars regularization procedure. Owing to the scalar Ward identity, irrespective of the form or Ansatz for the kernel of the gap equation, the consistent scalar vertex at zero total momentum can automatically be obtained and hence the consistent susceptibility. This enables calculation of the chiral susceptibility for markedly different vertex Ansätze. For the two cases considered, the results were consistent and the minor quantitative differences easily understood. The susceptibility can be used to demarcate the domain of coupling strength within a theory upon which chiral symmetry is dynamically broken. Degenerate massless scalar and pseudoscalar bound-states appear at the critical coupling for dynamical chiral symmetry breaking.
Asymmetric profiles have been observed in the recombination cross section of Be-like Bi obtained by measuring the electron energy dependence of the ion abundance ratio in an electron-beam ion trap. In contrast to the ...
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Asymmetric profiles have been observed in the recombination cross section of Be-like Bi obtained by measuring the electron energy dependence of the ion abundance ratio in an electron-beam ion trap. In contrast to the previous x-ray measurements, the present measurement gives the integrated recombination cross section with higher statistical quality, which provides a benchmark to test the relativistic theory involving the interference between the resonant and continuum states. The comparison with our theoretical study shows that the Breit interaction plays an important role in this case.
We propose a time-domain “interferometer” based on double-well ultracold atoms through a so-called adiabatic Rosen-Zener process, that is, the barrier between two wells is ramped down slowly, held for a while, and t...
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We propose a time-domain “interferometer” based on double-well ultracold atoms through a so-called adiabatic Rosen-Zener process, that is, the barrier between two wells is ramped down slowly, held for a while, and then ramped back. After the adiabatic Rosen-Zener process, we count the particle population in each well. We find that the final occupation probability shows nice interference fringes. The fringe pattern is sensitive to the initial state as well as the intrinsic parameters of the system such as interatomic interaction or energy bias between two wells. The underlying mechanism is revealed and possible applications are discussed.
After a brief review of the processes taking place in electron beam ions traps (EBITs), the means by which EBITs are used to make measurements of electron impact ionization cross‐sections and dielectronic recombinati...
After a brief review of the processes taking place in electron beam ions traps (EBITs), the means by which EBITs are used to make measurements of electron impact ionization cross‐sections and dielectronic recombination resonance strengths are discussed. In particular, results from a study involving holmium ions extracted from an electron beam ion trap are used to illustrate a technique for studying dielectronic recombination in open‐shell target ions.
We present a method to calculate upper bounds on the photonic band gaps of two-component photonic crystals. The method involves calculating both upper and lower bounds on the frequency bands for a given structure, and...
We present a method to calculate upper bounds on the photonic band gaps of two-component photonic crystals. The method involves calculating both upper and lower bounds on the frequency bands for a given structure, and then maximizing over all possible two-component structures. We apply this method to a number of examples, including a one-dimensional photonic crystal (or “Bragg grating”) and two-dimensional photonic crystals (in both the TM and TE polarizations) with both four and sixfold rotational symmetries. We compare the bounds to band gaps of numerically optimized structures and find that the bounds are extremely tight. We prove that the bounds are “sharp” in the limit of low dielectric contrast ratio between the two components. This method and the bounds derived here have important implications in the search for optimal photonic band-gap structures.
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