Resistivity peculiarities in systems with lattice distortions

We study a molecular lattice Hamiltonian in which polaronic charge carriers interact with non linear potentials provided by local atomic fluctuations between two equilibrium sites. The path integral formalism is applied to select the class of atomic oscillations which mainly contributes to the partition function and the electrical resistivity is computed in a number of representative cases. Non metallic resistivity behaviors are found at temperatures above $\simeq 100K$.Comment: 3 pages, 2 figure

Twist-stretch profiles of DNA chains

Helical molecules change their twist number under the effect of a mechanical load. We study the twist-stretch relation for a set of short DNA molecules modeled by a mesoscopic Hamiltonian. Finite temperature path integral techniques are applied to generate a large ensemble of possible configurations for the base pairs of the sequence. The model also accounts for the bending and twisting fluctuations between adjacent base pairs along the molecules stack. Simulating a broad range of twisting conformation, we compute the helix structural parameters by averaging over the ensemble of base pairs configurations. The method selects, for any applied force, the average twist angle which minimizes the molecule's free energy. It is found that the chains generally over-twist under an applied stretching and the over-twisting is physically associated to the contraction of the average helix diameter, i.e. to the damping of the base pair fluctuations. Instead, assuming that the maximum amplitude of the bending fluctuations may decrease against the external load, the DNA molecule first over-twists for weak applied forces and then untwists above a characteristic force value. Our results are discussed in relation to available experimental information albeit for kilo-base long molecules

Helical Disruptions in Small Loops of DNA

The thermodynamical stability of DNA minicircles is investigated by means of path integral techniques. Hydrogen bonds between base pairs on complementary strands can be broken by thermal fluctuations and temporary fluctuational openings along the double helix are essential to biological functions such as transcription and replication of the genetic information. Helix unwinding and bubble formation patterns are computed in circular sequences with variable radius in order to analyze the interplay between molecule size and appearance of helical disruptions. The latter are found in minicircles with $< 100$ base pairs and appear as a strategy to soften the stress due to the bending and torsion of the helix.Comment: International Conference on Mathematical Modeling in Physical Sciences, August 28-31, 2014, Madrid, Spai

Path Integral Methods in the Su-Schrieffer-Heeger Polaron Problem

I propose a path integral description of the Su-Schrieffer-Heeger Hamiltonian, both in one and two dimensions, after mapping the real space model onto the time scale. While the lattice degrees of freedom are classical functions of time and are integrated out exactly, the electron particle paths are treated quantum mechanically. The method accounts for the variable range of the electronic hopping processes. The free energy of the system and its temperature derivatives are computed by summing at any $T$ over the ensemble of relevant particle paths which mainly contribute to the total partition function. In the low $T$ regime, the {\it heat capacity over T} ratio shows un upturn peculiar to a glass-like behavior. This feature is more sizeable in the square lattice than in the linear chain as the overall hopping potential contribution to the total action is larger in higher dimensionality. The effects of the electron-phonon anharmonic interactions on the phonon subsystem are studied by the path integral cumulant expansion method.Comment: to appear in "Polarons in Advanced Materials" ed. A.S. Alexandrov (Canopus Books, 2007

Twist versus Nonlinear Stacking in Short DNA Molecules

The denaturation of the double helix is a template for fundamental biological functions such as replication and transcription involving the formation of local fluctuational openings. The denaturation transition is studied for heterogeneous short sequences of DNA, i.e. $\sim 100$ base pairs, in the framework of a mesoscopic Hamiltonian model which accounts for the helicoidal geometry of the molecule. The theoretical background for the application of the path integral formalism to predictive analysis of the molecule thermodynamical properties is discussed. The base pair displacements with respect to the ground state are treated as paths whose temperature dependent amplitudes are governed by the thermal wavelength. The ensemble of base pairs paths is selected, at any temperature, consistently with both the model potential and the second law of thermodynamics. The partition function incorporates the effects of the base pair thermal fluctuations which become stronger close to the denaturation. The transition appears as a gradual phenomenon starting from the molecule segments rich in adenine-thymine base pairs. Computing the equilibrium thermodynamics, we focus on the interplay between twisting of the complementary strands around the molecule axis and nonlinear stacking potential: it is shown that the latter affects the melting profiles only if the rotational degrees of freedom are included in the Hamiltonian. The use of ladder Hamiltonian models for the DNA complementary strands in the pre-melting regime is questioned.Comment: Journal of Theoretical Biology (2014

Short DNA persistence length in a mesoscopic helical model

The flexibility of short DNA chains is investigated via computation of the average correlation function between dimers which defines the persistence length. Path integration techniques have been applied to confine the phase space available to base pair fluctuations and derive the partition function. The apparent persistence lengths of a set of short chains have been computed as a function of the twist conformation both in the over-twisted and the untwisted regimes, whereby the equilibrium twist is selected by free energy minimization. The obtained values are significantly lower than those generally attributed to kilo-base long DNA. This points to an intrinsic helix flexibility at short length scales, arising from large fluctuational effects and local bending, in line with recent experimental indications. The interplay between helical untwisting and persistence length has been discussed for a heterogeneous fragment by weighing the effects of the sequence specificities through the non-linear stacking potential

Unwinding of circular helicoidal molecules versus size

The thermodynamical stability of a set of circular double helical molecules is analyzed by path integral techniques. The minicircles differ only in \textit{i)} the radius and \textit{ii)} the number of base pairs ($N$) arranged along the molecule axis. Instead, the rise distance is kept constant. For any molecule size, the computational method simulates a broad ensemble of possible helicoidal configurations while the partition function is a sum over the path trajectories describing the base pair fluctuational states. The stablest helical repeat of every minicircle is determined by free energy minimization. We find that, for molecules with $N$ larger than $100$, the helical repeat grows linearly with the size and the twist number is constant. On the other hand, by reducing the size below $100$ base pairs, the double helices sharply unwind and the twist number drops to one for $N=\,20$. This is predicted as the minimum size for the existence of helicoidal molecules in the closed form. The helix unwinding appears as a strategy to release the bending stress associated to the circularization of the molecules.Comment: Europhysics Letters (2015

Polaron Mass and Electron-Phonon Correlations in the Holstein Model

The Holstein Molecular Crystal Model is investigated by a strong coupling perturbative method which, unlike the standard Lang-Firsov approach, accounts for retardation effects due to the spreading of the polaron size. The effective mass is calculated to the second perturbative order in any lattice dimensionality for a broad range of (anti)adiabatic regimes and electron-phonon couplings. The crossover from a large to a small polaron state is found in all dimensionalities for adiabatic and intermediate adiabatic regimes. The phonon dispersion largely smooths such crossover which is signalled by polaron mass enhancement and on site localization of the correlation function. The notion of self-trapping together with the conditions for the existence of light polarons, mainly in two- and three-dimensions, are discussed. By the imaginary time path integral formalism I show how non local electron-phonon correlations, due to dispersive phonons, renormalize downwards the {\it e-ph} coupling justifying the possibility for light and essentially small 2D Holstein polarons.Comment: Advances in Condensed Matter Physics (2009). Special Issue on "Phonons and Electron Correlations in High-Temperature and Other Novel Superconductors

Non Metallic Transport in Molecular Solids versus Dimensionality

Path integral techniques and Green functions formalism are applied to study the (time) temperature dependent scattering of a polaronic quasiparticle by a local anharmonic potential in a bath of diatomic molecules. The electrical resistivity has been computed in any molecular lattice dimensionality for different values of electron-phonon coupling and intermolecular forces. A broad resistivity peak with non metallic behavior at temperatures larger than $\simeq 100K$ is predicted by the model for sufficiently strong polaron-local potential coupling strengths. This peculiar behavior, ascribed to purely structural effects, is favoured in low dimensionality.Comment: Keywords: Path Integrals, Polarons, Anharmonicity PACS: 31.15.Kb, 63.20.Ry, 66.35.+