1,543 research outputs found

### 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

### Non Local Electron-Phonon Correlations in a Dispersive Holstein Model

Due to the dispersion of optical phonons, long range electron-phonon
correlations renormalize downwards the coupling strength in the Holstein model.
We evaluate the size of this effect both in a linear chain and in a square
lattice for a time averaged {\it e-ph} potential, where the time variable is
introduced according to the Matsubara formalism. Mapping the Holstein
Hamiltonian onto the time scale we derive the perturbing source current which
appears to be non time retarded. This property permits to disentangle phonon
and electron coordinates in the general path integral for an electron coupled
to dispersive phonons. While the phonon paths can be integrated out
analytically, the electron path integrations have to be done numerically. The
equilibrium thermodynamic properties of the model are thus obtained as a
function of the electron hopping value and of the phonon spectrum parameters.
We derive the {\it e-ph} corrections to the phonon free energy and show that
its temperature derivatives do not depend on the {\it e-ph} effective coupling
hence, the Holstein phonon heat capacity is strictly harmonic. A significant
upturn in the low temperature total heat capacity over $T$ ratio is attributed
to the electron hopping which largely contributes to the action.Comment: Phys.Rev.B (2005

### Mass enhancement in narrow band systems

A perturbative study of the Holstein Molecular Crystal Model which accounts
for lattice structure and dimensionality effects is presented. Antiadiabatic
conditions peculiar of narrow band materials and an intermediate to strong
electron-phonon coupling are assumed. The polaron effective mass depends
crucially in all dimensions on the intermolecular coupling strengths which also
affect the size of the lattice deformation associated with the small polaron
formation.Comment: Istituto Nazionale di Fisica della Materia - Dipartimento di
Matematica e Fisica, Istituto Nazionale di Fisica della Materia Universita'
di Camerino, 62032 Camerino, Ital

### Path Integral Method for DNA Denaturation

The statistical physics of homogeneous DNA is investigated by the imaginary
time path integral formalism. The base pair stretchings are described by an
ensemble of paths selected through a macroscopic constraint, the fulfillement
of the second law of thermodynamics. The number of paths contributing to the
partition function strongly increases around and above a specific temperature
$T^*_c$ whereas the fraction of unbound base pairs grows continuosly around and
above $T^*_c$. The latter is identified with the denaturation temperature.
Thus, the separation of the two complementary strands appears as a highly
cooperative phenomenon displaying a smooth crossover versus $T$. The
thermodynamical properties have been computed in a large temperature range by
varying the size of the path ensemble at the lower bound of the range. No
significant physical dependence on the system size has been envisaged. The
entropy grows continuosly versus $T$ while the specific heat displays a
remarkable peak at $T^*_c$. The location of the peak versus $T$ varies with the
stiffness of the anharmonic stacking interaction along the strand. The
presented results suggest that denaturation in homogeneous DNA has the features
of a second order phase transition. The method accounts for the cooperative
behavior of a very large number of degrees of freedom while the computation
time is kept within a reasonable limit.Comment: Physical Review E 2009 in pres

### Path Integral Description of a Semiclassical Su-Schrieffer-Heeger Model

The electron motion along a chain is described by a continuum version of the
Su-Schrieffer-Heeger Hamiltonian in which phonon fields and electronic
coordinates are mapped onto the time scale. The path integral formalism allows
us to derive the non local source action for the particle interacting with the
oscillators bath. The method can be applied for any value of the {\it e-ph}
coupling. The path integral dependence on the model parameters has been
analysed by computing the partition function and some thermodynamical
properties from $T= 1K$ up to room temperature. A peculiar upturn in the low
temperature {\it heat capacity over temperature} ratio (pointing to a glassy
like behavior) has been ascribed to the time dependent electronic hopping along
the chain

### Exact solutions of classical scalar field equations

We give a class of exact solutions of quartic scalar field theories. These
solutions prove to be interesting as are characterized by the production of
mass contributions arising from the nonlinear terms while maintaining a
wave-like behavior. So, a quartic massless equation has a nonlinear wave
solution with a dispersion relation of a massive wave and a quartic scalar
theory gets its mass term renormalized in the dispersion relation through a
term depending on the coupling and an integration constant. When spontaneous
breaking of symmetry is considered, such wave-like solutions show how a mass
term with the wrong sign and the nonlinearity give rise to a proper dispersion
relation. These latter solutions do not change the sign maintaining the
property of the selected value of the equilibrium state. Then, we use these
solutions to obtain a quantum field theory for the case of a quartic massless
field. We get the propagator from a first order correction showing that is
consistent in the limit of a very large coupling. The spectrum of a massless
quartic scalar field theory is then provided. From this we can conclude that,
for an infinite countable number of exact classical solutions, there exist an
infinite number of equivalent quantum field theories that are trivial in the
limit of the coupling going to infinity.Comment: 7 pages, no figures. Added proof of existence of a zero mode and two
more references. Accepted for publication in Journal of Nonlinear
Mathematical Physic

### Mass Renormalization in the Su-Schrieffer-Heeger Model

This study of the one dimensional Su-Schrieffer-Heeger model in a weak
coupling perturbative regime points out the effective mass behavior as a
function of the adiabatic parameter $\omega_{\pi}/J$, $\omega_{\pi}$ is the
zone boundary phonon energy and $J$ is the electron band hopping integral.
Computation of low order diagrams shows that two phonons scattering processes
become appreciable in the intermediate regime in which zone boundary phonons
energetically compete with band electrons. Consistently, in the intermediate
(and also moderately antiadiabatic) range the relevant mass renormalization
signals the onset of a polaronic crossover whereas the electrons are
essentially undressed in the fully adiabatic and antiadiabatic systems. The
effective mass is roughly twice as much the bare band value in the intermediate
regime while an abrupt increase (mainly related to the peculiar 1D dispersion
relations) is obtained at $\omega_{\pi}\sim \sqrt{2}J$.Comment: To be published in Phys.Rev.B - 3 figure

### Thermodynamics of Twisted DNA with Solvent Interaction

The imaginary time path integral formalism is applied to a nonlinear
Hamiltonian for a short fragment of heterogeneous DNA with a stabilizing
solvent interaction term. Torsional effects are modeled by a twist angle
between neighboring base pairs stacked along the molecule backbone. The base
pair displacements are described by an ensemble of temperature dependent paths
thus incorporating those fluctuational effects which shape the multisteps
thermal denaturation. By summing over $\sim 10^7 - 10^8$ base pair paths, a
large number of double helix configurations is taken into account consistently
with the physical requirements of the model potential. The partition function
is computed as a function of the twist. It is found that the equilibrium twist
angle, peculiar of B-DNA at room temperature, yields the stablest helicoidal
geometry against thermal disruption of the base pair hydrogen bonds. This
result is corroborated by the computation of thermodynamical properties such as
fractions of open base pairs and specific heat.Comment: The Journal of Chemical Physics (2011) in pres

### Thermodynamic properties of Holstein polarons and the effects of disorder

The ground state and finite temperature properties of polarons are studied
considering a two-site and a four-site Holstein model by exact diagonalization
of the Hamiltonian. The kinetic energy, Drude weight, correlation functions
involving charge and lattice deformations, and the specific heat have been
evaluated as a function of electron-phonon (e-ph) coupling strength and
temperature. The effects of site diagonal disorder on the above properties have
been investigated. The disorder is found to suppress the kinetic energy and the
Drude weight, reduces the spatial extension of the polaron, and makes the
large-to-small polaron crossover smoother. Increasing temperature also plays
similar role. For strong coupling the kinetic energy arises mainly from the
incoherent hopping processes owing to the motion of electrons within the
polaron and is almost independent of the disorder strength. From the coherent
and incoherent contributions to the kinetic energy, the temperature above which
the incoherent part dominates is determined as a function of e-ph coupling
strength.Comment: 17 pages. 17 figure

### Polaron self-trapping in a honeycomb net

Small polaron behavior in a two dimensional honeycomb net is studied by
applying the strong coupling perturbative method to the Holstein molecular
crystal model. We find that small optical polarons can be mobile also if the
electrons are strongly coupled to the lattice. Before the polarons localize and
become very heavy, there is infact a window of {\it e-ph} couplings in which
the polarons are small and have masses of order $\simeq 5 - 50$ times the bare
band mass according to the value of the adiabaticity parameter. The 2D
honeycomb net favors the mobility of small optical polarons in comparison with
the square lattice.Comment: 6 pages, 3 figures, to appear in J.Phys.:Condensed Matter {PACS:
63.10.+a, 63.20.Dj, 71.38.+i

- â€¦