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 $\kappa$ to characterize the symmetry breaking, and find that the tetratic phase can still exist even up to a substantial value of $\kappa$. 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