3,573 research outputs found
Darboux and binary Darboux transformations for discrete integrable systems 1. Discrete potential KdV equation
The Hirota-Miwa equation can be written in `nonlinear' form in two ways: the
discrete KP equation and, by using a compatible continuous variable, the
discrete potential KP equation. For both systems, we consider the Darboux and
binary Darboux transformations, expressed in terms of the continuous variable,
and obtain exact solutions in Wronskian and Grammian form. We discuss
reductions of both systems to the discrete KdV and discrete potential KdV
equations, respectively, and exploit this connection to find the Darboux and
binary Darboux transformations and exact solutions of these equations
Nanoscale capacitance: a classical charge-dipole approximation
Modeling nanoscale capacitance presents particular challenge because of
dynamic contribution from electrodes, which can usually be neglected in
modeling macroscopic capacitance and nanoscale conductance. We present a model
to calculate capacitances of nano-gap configurations and define effective
capacitances of nanoscale structures. The model is implemented by using a
classical atomic charge-dipole approximation and applied to calculate
capacitance of a carbon nanotube nano-gap and effective capacitance of a
buckyball inside the nano-gap. Our results show that capacitance of the carbon
nanotube nano-gap increases with length of electrodes which demonstrates the
important roles played by the electrodes in dynamic properties of nanoscale
circuits.Comment: 11 pages, 6 figure
Theory and simulation of two-dimensional nematic and tetratic phases
Recent experiments and simulations have shown that two-dimensional systems
can form tetratic phases with four-fold rotational symmetry, even if they are
composed of particles with only two-fold symmetry. To understand this effect,
we propose a model for the statistical mechanics of particles with almost
four-fold symmetry, which is weakly broken down to two-fold. We introduce a
coefficient to characterize the symmetry breaking, and find that the
tetratic phase can still exist even up to a substantial value of .
Through a Landau expansion of the free energy, we calculate the mean-field
phase diagram, which is similar to the result of a previous hard-particle
excluded-volume model. To verify our mean-field calculation, we develop a Monte
Carlo simulation of spins on a triangular lattice. The results of the
simulation agree very well with the Landau theory.Comment: 7 pages, including 12 postscript figures, uses REVTeX
Resolution and sensitivity of a Fabry-Perot interferometer with a photon-number-resolving detector
With photon-number resolving detectors, we show compression of interference
fringes with increasing photon numbers for a Fabry-Perot interferometer. This
feature provides a higher precision in determining the position of the
interference maxima compared to a classical detection strategy. We also
theoretically show supersensitivity if N-photon states are sent into the
interferometer and a photon-number resolving measurement is performed.Comment: 8 pages, 12 figures, 1 table, minor extensions, title changed, new
figures added, reference correcte
Chiral Quantum Walks
Given its importance to many other areas of physics, from condensed matter
physics to thermodynamics, time-reversal symmetry has had relatively little
influence on quantum information science. Here we develop a network-based
picture of time-reversal theory, classifying Hamiltonians and quantum circuits
as time-symmetric or not in terms of the elements and geometries of their
underlying networks. Many of the typical circuits of quantum information
science are found to exhibit time-asymmetry. Moreover, we show that
time-asymmetry in circuits can be controlled using local gates only, and can
simulate time-asymmetry in Hamiltonian evolution. We experimentally implement a
fundamental example in which controlled time-reversal asymmetry in a
palindromic quantum circuit leads to near-perfect transport. Our results pave
the way for using time-symmetry breaking to control coherent transport, and
imply that time-asymmetry represents an omnipresent yet poorly understood
effect in quantum information science.Comment: 9 pages, 4 figures, REVTeX 4.1 - published versio
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