603 research outputs found
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 .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 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 over the ensemble of
relevant particle paths which mainly contribute to the total partition
function. In the low 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. 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
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 () 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 larger than , the helical repeat
grows linearly with the size and the twist number is constant. On the other
hand, by reducing the size below base pairs, the double helices sharply
unwind and the twist number drops to one for . 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
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
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 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.+
Polaron Crossover in Molecular Solids
An analytical variational method is applied to the molecular Holstein
Hamiltonian in which the dispersive features of the dimension dependent phonon
spectrum are taken into account by a force constant approach. The crossover
between a large and a small size polaron is monitored, in one, two and three
dimensions and for different values of the adiabatic parameter, through the
behavior of the effective mass as a function of the electron-phonon coupling.
By increasing the strength of the inter-molecular forces the crossover becomes
smoother and occurs at higher {\it e-ph} couplings. These effects are more
evident in three dimensions. We show that our Modified Lang-Firsov method
starts to capture the occurence of a polaron self-trapping transition when the
electron energies become of order of the phonon energies. The self-trapping
event persists in the fully adiabatic regime. At the crossover we estimate
polaron effective masses of order times the bare band mass
according to dimensionality and value of the adiabatic parameter. Modified
Lang-Firsov polaron masses are substantially reduced in two and three
dimensions. There is no self-trapping in the antiadiabatic regime.Comment: To be published in J.Phys.:Condensed Matte
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