Localization properties of electronic states in a polaron model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers

We numerically investigate localization properties of electronic states in a static model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers with realistic parameters obtained by quantum-chemical calculation. The randomness in the on-site energies caused by the electron-phonon coupling is completely correlated to the off-diagonal parts. In the single electron model, the effect of the hydrogen-bond stretchings, the twist angles between the base pairs and the finite system size effects on the energy dependence of the localization length and on the Lyapunov exponent are given. The localization length is reduced by the influence of the fluctuations in the hydrogen bond stretchings. It is also shown that the helical twist angle affects the localization length in the poly(dG)-poly(dC) DNA polymer more strongly than in the poly(dA)-poly(dT) one. Furthermore, we show resonance structures in the energy dependence of the localization length when the system size is relatively small.     

Quantum diffusion in polaron model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers

We numerically investigate quantum diffusion of an electron in a model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers with fluctuation of the parameters due to the impact of colored noise. The randomness is introduced by fluctuations of distance between two consecutive bases along the stacked base pairs. We demonstrate that in the model the decay time of the correlation can control the spread of the electronic wavepacket. Furthermore it is shown that in a motional narrowing regime the averaging over fluctuation causes ballistic propagation of the wavepacket, and in the adiabatic regime the electronic states are affected by localization.     

Next-nearest neighbor interaction and localized solutions of polymer chains

We study localization in polymer chains modeled by the nonlinear discrete Schr?dinger equation (DNLS) with next-nearest-neighbor (n-n-n) interaction extending beyond the usual nearest-neighbor exchange approximation. Modulational instability of plane carrier waves is discussed and it is shown that localization gets amplified under the influence of an enhanced interaction radius. Furthermore, we construct exact localized solitonlike solutions of the n-n-n interaction DNLS. To this end the stationary lattice system is cast into a nonlinear map. The homoclinic orbits of unstable equilibria of this map are attributed to standing solitonlike solutions of the lattice system. We note that in comparison with the standard next-neighbor interaction DNLS which bears only one type of static soliton-like states (either staggering or unstaggering) the one with n-n-n interaction radius can support unstaggering as well as staggering stationary localized states with frequencies lying above respectively below the linear band. Generally, the stronger the n-n-n interaction on the DNLS lattice the smaller are the maximal amplitudes of the standing solitonlike solutions and the less rapid are their exponential decays. Received 4 October 2000     

A study of Peierls instabilities for a two-dimensional t-t' model

In this paper we study Peierls instabilities for a half-filled two-dimensional tight-binding model with nearest-neighbour hopping t and next nearest-neighbour hopping t' at zero and finite temperatures. Two dimerization patterns corresponding to the same phonon vector (π,π) are considered to be realizations of Peierls states. The effect of imperfect nesting introduced by t' on the Peierls instability, the properties of the dimerized ground state, as well as the competition between two dimerized states for each t' and temperature T, are investigated. It is found: (i). The Peierls instability will be frustrated by t' for each of the dimerized states. The Peierls transition itself, as well as its suppression by t', may be of second- or first-order. (ii). When the two dimerized states are considered jointly, one of them will dominate the other depending on parameters t' and T. Two successive Peierls transitions, that is, the system passing from the uniform state to one dimerized state and then to the other may take place with decrease of temperature. Implications of our results to real materials are discussed. Received 31 July 2001     

Anharmonic excitations in the FPU and FK models

The properties of vibrational localized (breathers) and traveling (anharmonic phonons) waves are discussed in an infinite, one-dimensional, monoatomic crystal for the Fermi-Pasta-Ulam and Frenkel-Kontorova models. The shooting and finite difference schemes have been implemented to reckon the displacement fields of breathers and anharmonic phonons, respectively. These tools provide localized and traveling waves proving to be indefinitely stable in simulations carried out by solving the equations of motion. The emphasis is laid on the role of the cubic and quartic terms of the anharmonic potential which turn out to oppose and to shore up the restoring force, respectively. The case of vibrational modes arising in an anharmonic crystal subject to a soft phonon induced instability is also addressed. Received 7 November 2001 and Received in final form 5 February 2002 Published online 6 June 2002     

Imperfect nesting and Peierls instability for a two-dimensional tight-binding model

Based on a half-filled two-dimensional tight-binding model with nearest-neighbour and next nearest-neighbour hopping the effect of imperfect Fermi surface nesting on the Peierls instability is studied at zero temperature. Two dimerization patterns corresponding to a phonon vector (π,π) are considered. It is found that the Peierls instability will be suppressed with an increase of next nearest-neighbour hopping which characterizes the nesting deviation. First and second order transitions to a homogeneous state are possible. The competition between the two dimerized states is discussed. Received 22 December 2000     

Probing electron-phonon coupling in high-Tc superconductors by site-selective isotope substitution

We consider changes in the electron-phonon coupling in high-T _c cuprates caused by site-selective oxygen isotope substitution. Contrary to the total substitution, the site-selective replacement influences the coupling constant for each phonon mode due to the induced changes in the phonon eigenvectors. The relative changes for some modes can be larger than 100%. The measured properties sensitive to these changes are discussed. Received 9 August 2001 and Received in final form 11 January 2002     

Localized modes in a one-dimensional sphalerite-structure lattice with anharmonicity

The nonlinear localized vibrational modes of a one-dimensional atomic chain with two periodically alternating masses and force constants are analytically investigated using a discrete multiple-scale expansion method. This model simulates a row of atoms in the <1 1 1>-direction of sphalerite, or zinc blende, crystals. Owing to the structural asymmetry, the vibrational amplitude is governed by a perturbed nonlinear Schr?dinger equation instead of the standard one found in one-dimensional lattices with two alternating masses but uniform force constant. Although the stationary localized modes with carrier wavevector at the Brillouin-zone boundary are similar to those of ionic lattices, the moving localized modes with wavevectors within the zone are different owing to the perturbation. The calculation shows that the height of the moving localized modes in this lattice dampens with time. Received 14 May 2001 and Received in final form 12 July 2001     

Crowdion dynamics in a nonuniformly deformed three-dimensional crystal

The problem of crowdion motion is formulated and analyzed as a dynamical problem of a three-dimensional crystal lattice formed by atoms of several kinds, which interact with each other by means of short-range pair potentials. It is explained that in order for the the crowdion excitations of the close-packed atomic rows to be distinguishable against the background of small dynamic deformations of the crystal as a whole, the microscopic parameters of the crystal structure must meet certain stated requirements. The equation of motion of a crowdion in an arbitrary elastic strain field of the crystal is derived in the Lagrangian formalism. Expressions are obtained which relate the effective mass and the rest energy of a crowdion with the geometric and force parameters of the crystal lattice. Received 4 October 2001 / Received in final form 27 February 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: nazarenko@ksame.kharkov.ua     

Slow nucleic acid unzipping kinetics from sequence-defined barriers

Recent experiments on unzipping of RNA helix-loop structures by force have shown that ≈40-base molecules can undergo kinetic transitions between two well-defined “open” and “closed” states, on a timescale ≈1 sec [Liphardt et al., Science 297, 733-737 (2001)]. Using a simple dynamical model, we show that these phenomena result from the slow kinetics of crossing large free energy barriers which separate the open and closed conformations. The dependence of barriers on sequence along the helix, and on the size of the loop(s) is analyzed. Some DNA and RNA sequences that could show dynamics on different time scales, or three(or more)-state unzipping, are proposed. Our dynamical model is also applied to the unzipping of long (kilo-basepair) DNA molecules at constant force. Received 29 July 2002 / Received in final form 5 February 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: cocco@ldfc.u-strasbg.fr RID="b" ID="b"e-mail: jmarko@uic.edu RID="c" ID="c"e-mail: monasson@lpt.ens.fr     

Soliton dynamics in chiral molecular chains with first- and third-neighbour interactions

We investigate the propagation and interaction of solitons associated with circularly polarized vibrations in gyrotropic media. The chirality of the structure yields different dispersion laws and hence different phase and group velocities for the left- and right-handed modes. The helical arrangement of the monomers is modelled through first- and third-neighbour interactions. The dynamics of the excitations is governed by a system of coupled discrete nonlinear Schr?dinger equations which is studied both analytically and numerically. Depending on the initial conditions and the interaction constants, different evolutionary patterns are obtained corresponding to unbound or bound one- and two-soliton solutions. The results can be applied to the process of energy transfer in helical polymers. Received 1st October 2001 / Received in final form 30 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: krad@issp.bas.bg     

Magnetic transition and polaron crossover in a two-site single polaron model including double exchange interaction

A two-site double exchange model with a single polaron is studied using a perturbation expansion based on the modified Lang-Firsov transformation. The antiferromagnetic to ferromagnetic transition and the crossover from small to large polaron are investigated for different values of the antiferromagnetic interaction (J) between the core spins and the hopping (t) of the itinerant electron. Effect of the external magnetic field on the small to large polaron crossover and on the polaronic kinetic energy are studied. When the magnetic transition and the small to large polaron crossover coincide for some suitable range of J/t, the magnetic field has very pronounced effect on the dynamics of polarons. Received 1 June 2000     

Sphere packing, helices and the polytope {3, 3, 5}

The packing of tetrahedra in face contact is well-known to be relevant to atomic clustering in many complex alloys. We briefly review some of the structures that can arise in this way, and introduce methods of dealing with the geometry of the polytope {3, 3, 5}, which is highly relevant to an understanding of these structures. Finally, we present a method of projection from S₃ to E₃ that enables coordinates for the key vertices of the collagen model of Sadoc and Rivier to be calculated. Received 27 March 2001     

A DFT study of electron or hole localization in a peptide containing asparagin

The mechanisms of protein degradation induced by ionisation are of great interest for radiobiology, improvement of mass spectroscopy and industrial processes such as radio sterilisation. Sequences containing asparagin are very sensitive especially if surrounded by glycine. Very few techniques allow a satisfying understanding of the processes induced by creation of an anionic or cationic site in a peptide. We used the methods of quantum chemistry (DFT/B3LYP with 6-31G^* basis set) to characterise the geometry modifications induced in the cations or in the anions derived from peptide Gly Asn Gly. The cationic sites are localised mostly close to the first peptidic bond and induce a lengthening of the Ca-C(O) bond. Conversely the anionic sites are localised on a carbonyl function. Implications are discussed considering the radiolytic products and the proposed mechanisms. Received 21 January 2002 Published online 13 September 2002     

Surface and interface optical phonon modes and electron-phonon interaction in a multi-shell spherical system

Within the framework of the dielectric continuum model, interface optical(IO) and surface optical(SO) phonon modes and the Fr?hlich electron-IO (SO) phonon interaction Hamiltonian in a multi-shell spherical system were derived and studied. Numerical calculation on CdS/HgS/H₂O and CdS/HgS/CdS/H₂O spherical systems have been performed. Results reveal that there are two IO modes and one SO mode for the CdS/HgS/H₂O system, one SO mode and four IO modes whose frequencies approach the IO phonon frequencies of the single CdS/HgS heterostructure with the increasing of the quantum number l for CdS/HgS/CdS/H₂O. It also showed that smaller l and SO phonon compared with IO phonon, have more significant contribution to the electron-IO (SO) phonon interaction. Received 16 October 2001 and Received in final form 23 January 2002 Published online 25 June 2002     

Polaronic effects on the energy levels of a double donor impurity in quantum wells in the presence of a magnetic field

In the presence of a magnetic field the Hamiltonian of the single or double polaron bound to a helium-type donor impurity in semiconductor quantum wells (QWs) are given in the case of positively charged donor center and neutral donor center. The couplings of an electron and the impurity with various phonon modes are considered. The binding energy of the single and double bound polaron in Al_xlGa _1-xlAs/GaAs/Al_xrGa _1-xrAs QWs are calculated. The results show that for a thin well the cumulative effects of the electron-phonon coupling and the impurity-phonon coupling can contribute appreciably to the binding energy in the case of ionized donor. In the case of neutral donor the contribution of polaronic effects are not very important, however the magnetic field significantly modifies the binding energy of the double donor. The comparison between the binding energies in the case of the impurity placed at the quantum well center and at the quantum well edge is also given. Received 16 February 1999     

Jahn-Teller, charge and magnetic ordering in half-doped manganese oxides

The phase diagram of half-doped manganite systems of formula A _0.5 A ^′ _0.5MnO₃ is investigated within a single-orbital model incorporating magnetic double-exchange and superexchange, together with intersite Coulomb and electron-lattice interactions. Strong Jahn-Teller and breathing mode deformations compete together and result in shear lattice deformations. The latter stabilize the charge-ordered CE-type phase, which undergo first-order transitions with temperature or magnetic field to either Ferromagnetic metallic or Paramagnetic insulating phases. An essential feature is the self-consistent screening of Coulomb and electron-phonon interactions in the ferromagnetic phase. Received 28 November 2000     

Ground state description of bound polarons in parabolic quantum wires

The Feynman-Haken variational path integral theory is, for the first time, generalized to calculate the ground-state energy of an electron coupled simultaneously to a Coulomb potential and to a longitudinal-optical (LO) phonon field in parabolic quantum wires. It is shown that the polaronic correction to the ground-state energy is more sensitive to the electron-phonon coupling constant than the Coulomb binding parameter and monotonically stronger as the effective wire radius decreases. We apply our calculations to several semiconductor quantum wires and find that the polaronic correction can be considerably large. Received 16 November 1998     

Deformation in cooperative molecular motors

We implement a model to represent the effect of the deformation of the backbone of a system of motor proteins while sliding on a track filament. This model incorporates a nearest neighbor interaction term among the motors for the deformation energy. Correlations induced by this term result in increased motor force for inter-particle distances small compared to the ratchet period. Received 20 February 2001 and Received in final form 31 May 2001     

One-dimensional moving polarons with extended coherent states

The general properties of one-dimensional large Fr?hlich polarons in motion are investigated with the previous extended coherent states where two-phonon correlations are considered. As a result, the polaron energy, velocity, effective mass, and average number of virtual phonons as a function the polaron total momentum are evaluated in a wide range of the coupling constant. In addition, rich information about virtual phonons emitted by the electron in motion is obtained. More importantly, some intrinsic features of 1D moving polarons are presented for the first time, which may also be suited to moving polarons in more than one dimensions. Received: 23 October 1997 / Revised and Accepted: 27 January 1998