arXiv subjects
Publications and source records attributed to A. R. Bishop.
We investigate propagation of slow-light solitons in atomic media described by the nonlinear $Λ$-model. Under a physical assumption, appropriate to the slow light propagation, we reduce the $Λ$-scheme to a simplified nonlinear model, which is also relevant to 2D dilatonic gravity. Exact solutions describing various regimes of stopping slow-light solitons can then be readily derived.
A study of the micromechanical unzipping of DNA in the framework of the Peyrard-Bishop-Dauxois model is presented. We introduce a Monte Carlo technique that allows accurate determination of the dependence of the unzipping forces on unzipping speed and temperature. Our findings agree quantitatively with experimental results for homogeneous DNA, and for $λ$-phage DNA we reproduce the recently obtained experimental force-temperature phase diagram. Finally, we argue that there may be fundamental differences between {\em in vivo} and {\em in vitro} DNA unzipping.
We study the structure and stability of discrete breathers (both pinned and mobile) in two-dimensional nonlinear anisotropic Schrodinger lattices. Starting from a set of identical one-dimensional systems we develop the continuation of the localized pulses from the weakly coupled regime (strongly anisotropic) to the homogeneous one (isotropic). Mobile discrete breathers are seen to be a superposition of a localized mobile core and an extended background of two-dimensional nonlinear plane waves. This structure is in agreement with previous results on onedimensional breather mobility. The study of the stability of both pinned and mobile solutions is performed using standard Floquet analysis. Regimes of quasi-collapse are found for both types of solutions, while another kind of instability (responsible for the discrete breather fission) is found for mobile solutions. The development of such instabilities is studied, examining typical trajectories on the unstable nonlinear manifold.
Electron- and phonon spectral functions of the one-dimensional, spinless-fermion Holstein model at half filling are calculated in the four distinct regimes of the phase diagram, corresponding to an attractive or repulsive Luttinger liquid at weak electron-phonon coupling, and a band- or polaronic insulator at strong coupling. The results obtained by means of kernel polynomial and systematic cluster approaches reveal substantially different physics in these regimes and further indicate that the size of the phonon frequency significantly affects the nature of the quantum Peierls phase transition.
A beam splitter is an important component of an atomic/optical Mach-Zehnder interferometer. Here we study a Bose Einstein Condensate beam splitter, realized with a double well potential of tunable height. We analyze how the sensitivity of a Mach Zehnder interferometer is degraded by the non-linear particle-particle interaction during the splitting dynamics. We distinguish three regimes, Rabi, Josephson and Fock, and associate to them a different scaling of the phase sensitivity with the total number of particles.
We study a hole-doped two-leg ladder system including metal ions, oxygen, and electron-lattice interaction, as a model for Sr_{14-x}Ca_xCu_{24}O_{41-δ}. Single- and bi-polaronic states at 1/4-hole doping are modeled as functions of pressure by applying an unrestricted Hartree-Fock approximation to a multiband Peierls-Hubbard Hamiltonian. We find evidence for a pressure-induced phase transition between single-polaron and bi-polaron states. The electronic and phononic excitations in those states, including distinctive local lattice vibrational modes, are calculated by means of a direct-space Random Phase approximation. Finally, as a function of pressure, we identify a transition between site- and bond-centered bi-polarons, accompanied by a soft mode and a low-energy charge-sliding mode. We suggest comparisons with available experimented data.
We consider a lattice equation (Salerno model) combining onsite self-focusing and intersite self-defocusing cubic terms, which may describe a Bose-Einstein condensate of dipolar atoms trapped in a strong periodic potential. In the continuum approximation, the model gives rise to solitons in a finite band of frequencies, with sechlike solitons near one edge, and an exact peakon solution at the other. A similar family of solitons is found in the discrete system, including a peakon; beyond the peakon, the family continues in the form of cuspons. Stability of the lattice solitons is explored through computation of eigenvalues for small perturbations, and by direct simulations. A small part of the family is unstable (in that case, the discrete solitons transform into robust pulsonic excitations); both peakons and cuspons are stable. The Vakhitov-Kolokolov criterion precisely explains the stability of regular solitons and peakons, but does not apply to cuspons. In-phase and out-of-phase bound states of solitons are also constructed. They exchange their stability at a point where the bound solitons are peakons. Mobile solitons, composed of a moving core and background, exist up to a critical value of the strength of the self-defocusing intersite nonlinearity. Colliding solitons always merge into a single pulse.
We introduce an inhomogeneously-nonlinear Schr{ö}dinger lattice, featuring a defocusing segment, a focusing segment and a transitional interface between the two. We illustrate that such inhomogeneous settings present vastly different dynamical behavior than the one expected in their homogeneous counterparts in the vicinity of the interface. We analyze the relevant stationary states, as well as their stability by means of perturbation theory and linear stability analysis. We find good agreement with the numerical findings in the vicinity of the anti-continuum limit. For larger values of the coupling, we follow the relevant branches numerically and show that they terminate at values of the coupling strength which are larger for more extended solutions. The dynamical development of relevant instabilities is also monitored in the case of unstable solutions.
The dynamical properties of double-stranded DNA are studied in the framework of the Peyrard-Bishop-Dauxois model using Langevin dynamics. Our simulations are analyzed in terms of two probability functions describing coherently localized separations ("bubbles") of the double strand. We find that the resulting bubble distributions are more sharply peaked at the active sites than found in thermodynamically obtained distributions. Our analysis ascribes this to the fact that the bubble life-times significantly afects the distribution function. We find that certain base-pair sequences promote long-lived bubbles and we argue that this is due to a length scale competition between the nonlinearity and disorder present in the system.
Uranium is the only known element that features a charge-density wave (CDW) and superconductivity. We report a comparison of the specific heat of single-crystal and polycrystalline $α$-uranium. \red{Away from the the phase transition the specific heat of the polycrystal is larger than that of the single crystal, and the aim of this paper is to explain this difference.} In the single crystal we find excess contributions to the heat capacity at 41 K, 38 K, and 23 K, with a Debye temperature, $Θ_D$ = 256 K. In the polycrystalline sample the heat capacity curve is thermally broadened ($Θ_D$ = 184 K), but no excess heat capacity was observed. The excess heat capacity, $C_ϕ$ (taken as the difference between the single crystal and polycrystal heat capacities) is well described in terms of collective-mode excitations above their respective pinning frequencies. This attribution is represented by a modified Debye spectrum with two cutoff frequencies, a pinning frequency, $ν_o$, for the pinned CDW (due to grain boundaries in the polycrystal), and a normal Debye acoustic frequency occurring in the single crystal. We explain the 50-year-old difference in Debye temperatures between heat capacity and ultrasonic measurements.
We have recently suggested that the probability for the formation of thermally activated DNA bubbles is, to a very good approximation, proportional to the number of soft AT pairs over a length L(n) that depend on the size $n$ of the bubble and on the temperature of the DNA. Here we clarify the physical interpretation of this length by relating it to the (healing) length that is required for the effect of a base-pair defect to become neligible. This provides a simple criteria to calculate L(n) for bubbles of arbitrary size and for any temperature of the DNA. We verify our findings by exact calculations of the equilibrium statistical properties of the Peyrard-Bishop-Dauxois model. Our method permits calculations of equilibrium thermal openings with several order of magnitude less numerical expense as compared with direct evaluations.
We consider polarons in models of coupled electronic and vibrational degrees of freedom, in the presence of a soft nonlinear inter-particle potential (Morse potential). In particular, we focus on a a bound state of a polaron with a breather, a so-called ``polarobreather''. We analyze the existence of this branch based on frequency resonance conditions and illustrate its stability using Floquet spectrum techniques. Multi-site solutions of this type are also obtained both in the stationary case (two-site polarons) and in the breathing case (two-site polarobreathers). We also obtain a different branch of solutions, namely a polaronic nanopteron.
Comment on T.S. van Erp, S. Cuesta-Lopez, J.-G. Hagmann, and M. Peyrard, Phys. Rev. Lett. 95, 218104 (2005) [arXiv: physics/0508094].
We examine the one-dimensional spinless Falicov-Kimball model extended by a hybridization potential between the localized and itinerant electron states. Below half-filling we find a crossover from a mixed-valence metal to an integer-valence phase separated state with increasing on-site Coulomb repulsion. This crossover regime is characterized by local competition between the strong- and weak-coupling behaviour, manifested by the formation of an electronic polaron liquid. We identify this intermediate-coupling regime as a charge-analogy of the Griffiths phase; a phase diagram is presented and discussed in detail.
It appears that thermally activated DNA bubbles of different sizes play central roles in important genetic processes. Here we show that the probability for the formation of such bubbles is regulated by the number of soft AT pairs in specific regions with lengths which at physiological temperatures are of the order of (but not equal to) the size of the bubble. The analysis is based on the Peyrard- Bishop-Dauxois model, whose equilibrium statistical properties have been accurately calculated here with a transfer integral approach.
We present the first numerical study of the Falicov-Kimball model extended by an on-site hybridization away from the particle-hole symmetry point. Stable polaronic distortions of the charge-density wave (CDW) phase are observed when doping with a single hole. For moderate hole-doping, we find phase separation between a hole-rich homogeneous state and the usual CDW state. Excitonic order is enhanced around the hole-rich region, locally manifesting the global competition between this and the CDW phase. Associated with the hole-doping is a fractionalization of the electron density between the itinerant and localized electrons. The calculated local density of states at the polaron centre reveals this fractionalization to be the result of charge fluctuations induced by the hybridization. We propose a scanning tunneling microscope experiment to test our results.
We present a Hartree-Fock study of the Falicov-Kimball model extended by both on-site and non-local hybridization. We examine the interplay between excitonic effects and the charge-density wave (CDW) instability known to exist at zero hybridization. It is found that the CDW state remains stable in the presence of finite hybridization; for on-site hybridization the Coulomb interaction nevertheless strongly enhances the excitonic average above its value in the noninteracting system. In contrast, for non-local hybridization, we observe no such enhancement of the excitonic average or a spontaneous on-site hybridization potential. Instead, we find only a significant suppression of the excitonic correlations in the CDW state. A phenomenological Ginzburg-Landau analysis is also provided to understand the interplay.
We consider a dynamical generalization of the Eshelby problem: the strain profile due to an inclusion or "defect" in an isotropic elastic medium. We show that the higher the oscillation frequency of the defect, the more localized is the strain field around the defect. We then demonstrate that the qualitative nature of the interaction between two defects is strongly dependent on separation, frequency and direction, changing from "ferromagnetic" to "antiferromagnetic" like behavior. We generalize to a finite density of defects and show that the interactions in assemblies of defects can be mapped to XY spin-like models, and describe implications for frustration and frequency-driven pattern transitions.