Base pair opening and bubble transport in a DNA double helix induced by a protein molecule in a viscous medium

We study the nonlinear dynamics of a protein-DNA molecular system by treating DNA as a set of two coupled linear chains and protein in the form of a single linear chain sliding along the DNA at the physiological temperature in a viscous medium. The nonlinear dynamics of the above molecular system in general is governed by a perturbed nonlinear Schr\"{o}dinger equation. In the non-viscous limit, the equation reduces to the completely integrable nonlinear Schr\"{o}dinger (NLS) equation which admits N-soliton solutions. The soliton excitations of the DNA bases make localized base pair opening and travel along the DNA chain in the form of a bubble. This may represent the bubble generated during the transcription process when an RNA-polymerase binds to a promoter site in the DNA double helical chain. The perturbed NLS equation is solved using a perturbation theory by treating the viscous effect due to surrounding as a weak perturbation and the results show that the viscosity of the solvent in the surrounding damps out the amplitude of the soliton.Comment: 4. Submitted to Phys. Rev.

Atomic States Entanglement in Carbon Nanotubes

The entanglement of two atoms (ions) doped into a carbon nanotube has been investigated theoretically. Based on the photon Green function formalism for quantizing electromagnetic field in the presence of carbon nanotubes, small-diameter metallic nanotubes are shown to result in a high degree of the two-qubit atomic entanglement for long times due to the strong atom-field coupling.Comment: 4 pages, 2 figure

The oxygen isotope effect on critical temperature in superconducting copper oxides

The isotope effect provided a crucial key to the development of the BCS (Bardeen-Cooper-Schrieffer) microscopic theory of superconductivity for conventional superconductors. In superconducting cooper oxides (cuprates) showing an unconventional type of superconductivity, the oxygen isotope effect is very peculiar: the exponential coefficient strongly depends on doping level. No consensus has been reached so far on the origin of the isotope effect in the cuprates. Here we show that the oxygen isotope effect in cuprates is in agreement with the bisoliton theory of superconductivity.Comment: 3 pages including 4 figures; version 2 is with minor correction

A Variational Approach to Nonlocal Exciton-Phonon Coupling

In this paper we apply variational energy band theory to a form of the Holstein Hamiltonian in which the influence of lattice vibrations (optical phonons) on both local site energies (local coupling) and transfers of electronic excitations between neighboring sites (nonlocal coupling) is taken into account. A flexible spanning set of orthonormal eigenfunctions of the joint exciton-phonon crystal momentum is used to arrive at a variational estimate (bound) of the ground state energy for every value of the joint crystal momentum, yielding a variational estimate of the lowest polaron energy band across the entire Brillouin zone, as well as the complete set of polaron Bloch functions associated with this band. The variation is implemented numerically, avoiding restrictive assumptions that have limited the scope of previous assaults on the same and similar problems. Polaron energy bands and the structure of the associated Bloch states are studied at general points in the three-dimensional parameter space of the model Hamiltonian (electronic tunneling, local coupling, nonlocal coupling), though our principal emphasis lay in under-studied area of nonlocal coupling and its interplay with electronic tunneling; a phase diagram summarizing the latter is presented. The common notion of a "self-trapping transition" is addressed and generalized.Comment: 33 pages, 11 figure

Anomalous tunneling of bound pairs in crystal lattices

A novel method of solving scattering problems for bound pairs on a lattice is developed. Two different break ups of the hamiltonian are employed to calculate the full Green operator and the wave function of the scattered pair. The calculation converges exponentially in the number of basis states used to represent the non-translation invariant part of the Green operator. The method is general and applicable to a variety of scattering and tunneling problems. As the first application, the problem of pair tunneling through a weak link on a one-dimensional lattice is solved. It is found that at momenta close to \pi the pair tunnels much easier than one particle, with the transmission coefficient approaching unity. This anomalously high transmission is a consequence of the existence of a two-body resonant state localized at the weak link.Comment: REVTeX, 5 pages, 4 eps figure

Microscopic derivation of Frenkel excitons in second quantization

Starting from the microscopic hamiltonian describing free electrons in a periodic lattice, we derive the hamiltonian appropriate to Frenkel excitons. This is done through a grouping of terms different from the one leading to Wannier excitons. This grouping makes appearing the atomic states as a relevant basis to describe Frenkel excitons in the second quantization. Using them, we derive the Frenkel exciton creation operators as well as the commutators which rule these operators and which make the Frenkel excitons differing from elementary bosons. The main goal of the present paper is to provide the necessary grounds for future works on Frenkel exciton many-body effects, with the composite nature of these particles treated exactly through a procedure similar to the one we have recently developed for Wannier excitons.Comment: 16 pages, 4 figure

Control of scroll wave turbulence using resonant perturbations

Turbulence of scroll waves is a sort of spatio-temporal chaos that exists in three-dimensional excitable media. Cardiac tissue and the Belousov-Zhabotinsky reaction are examples of such media. In cardiac tissue, chaotic behaviour is believed to underlie fibrillation which, without intervention, precedes cardiac death. In this study we investigate suppression of the turbulence using stimulation of two different types, "modulation of excitability" and "extra transmembrane current". With cardiac defibrillation in mind, we used a single pulse as well as repetitive extra current with both constant and feedback controlled frequency. We show that turbulence can be terminated using either a resonant modulation of excitability or a resonant extra current. The turbulence is terminated with much higher probability using a resonant frequency perturbation than a non-resonant one. Suppression of the turbulence using a resonant frequency is up to fifty times faster than using a non-resonant frequency, in both the modulation of excitability and the extra current modes. We also demonstrate that resonant perturbation requires strength one order of magnitude lower than that of a single pulse, which is currently used in clinical practice to terminate cardiac fibrillation. Our results provide a robust method of controlling complex chaotic spatio-temporal processes. Resonant drift of spiral waves has been studied extensively in two dimensions, however, these results show for the first time that it also works in three dimensions, despite the complex nature of the scroll wave turbulence.Comment: 13 pages, 12 figures, submitted to Phys Rev E 2008/06/13. Last version: 2008/09/18, after revie

Second quantization method in the presence of bound states of particles

We develop an approximate second quantization method for describing the many-particle systems in the presence of bound states of particles at low energies (the kinetic energy of particles is small in comparison to the binding energy of compound particles). In this approximation the compound and elementary particles are considered on an equal basis. This means that creation and annihilation operators of compound particles can be introduced. The Hamiltonians, which specify the interactions between compound and elementary particles and between compound particles themselves are found in terms of the interaction amplitudes for elementary particles. The nonrelativistic quantum electrodynamics is developed for systems containing both elementary and compound particles. Some applications of this theory are considered.Comment: 35 page

Cylindrically symmetric solitons in Einstein-Yang-Mills theory

Recently new Einstein-Yang-Mills (EYM) soliton solutions were presented which describe superconducting strings with Kasner asymptotic (hep-th/0610183). Here we study the static cylindrically symmetric SU(2) EYM system in more detail. The ansatz for the gauge field corresponds to superposition of the azimuthal $B_\phi$ and the longitudinal $B_z$ components of the color magnetic field. We derive sum rules relating data on the symmetry axis to asymptotic data and show that generic asymptotic structure of regular solutions is Kasner. Solutions starting with vacuum data on the axis generically are divergent. Regular solutions correspond to some bifurcation manifold in the space of parameters which has the low-energy limiting point corresponding to string solutions in flat space (with the divergent total energy) and the high-curvature point where gravity is crucial. Some analytical results are presented for the low energy limit, and numerical bifurcation curves are constructed in the gravitating case. Depending on the parameters, the solution looks like a straight string or a pair of straight and circular strings. The existence of such non-linear superposition of two strings becomes possible due to self-interaction terms in the Yang-Mills action which suppress contribution of the circular string near the polar axis.Comment: 21 pages, 11 figure