Path Integral Computation of Phonon Anharmonicity

The partition function of an oscillator disturbed by a set of electron particle paths has been computed by a path integral method which permits to evaluate at any temperature the relevant cumulant terms in the series expansion. The time dependent source current peculiar of the semiclassical Su-Schrieffer-Heeger model induces large electron-phonon anharmonicities on the phonon subsystem. As a main signature of anharmonicity the phonon heat capacity shows a peak whose temperature location strongly varies with the strength of the {\it e-ph} coupling. High energy oscillators are less sensitive to anharmonic perturbations

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

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

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

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

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

Variable population welfare and poverty orderings satisfying replication properties

We discuss and compare the variable population axioms of Critical Level (CL) and Population Replication Invariance (PRI) introduced in the economic and philosophical literature for evaluating distributions with different population size. We provide a common framework for analyzing these competing views considering a strengthening of the Population Replication Principle (PRP) based on Dalton's (1920) "principle of proportionate additions to persons" that requires an ordering defined over populations of the same size to be invariant w.r.t. replication of the distributions. The strong version of PRP extends the invariance condition to hold also when distributions of different population size are compared. We suggest ethically meaningful general specifications of the invariance requirement underlying the Strong PRP and characterize the associated classes of parameterized evaluation functions that include CL principles and PRI properties. Moreover, we identify a general class of evaluation functions satisfying the Strong PRP: the social evaluation ordering will be represented by the simple formula considering the product of the population size times a strictly monotonic function of the Equally Distributed Equivalent Income (EDEI). Interesting ethical properties are shown to be associated with the shape of the function transforming the EDEI. Implications for poverty measurement are investigated.Variable Population Social Choice, Population Replication, Welfare Measurement, Poverty Measurement.

Spectral Properties of the Su-Schrieffer-Heeger Model

We present a study of the one dimensional Su-Schrieffer-Heeger model Hamiltonian by a diagrammatic perturbative method in the weak electron-phonon coupling regime. Exact computation of both the charge carrier effective mass and the electron spectral function shows that electrons are good quasiparticles in the adiabatic and antiadiabatic limits but novel features emerge in the intermediate regime, where the phonons and the electrons compare on the energy scale. Together with a sizeable mass enhancement we observe, in the latter regime, a spread of the spectral weight (among several transition peaks) associated with an increased relevance of multiphonons contributions at larger {\it e-ph} couplings. Accordingly electrons cease to be the good quasiparticles and an onset of polaron formation is favoured.Comment: To appear in Solid State Communications - 5 figure

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.+

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