536 research outputs found
An Elementary Derivation of the Harmonic Oscillator Propagator
The harmonic oscillator propagator is found straightforwardly from the free
particle propagator, within the imaginary-time Feynman path integral formalism.
The derivation presented here is extremely simple, requiring only elementary
mathematical manipulations and no clever use of Hermite polynomials,
annihilation & creation operators, cumbersome determinant evaluations or any
kind of involved algebra.Comment: 1 page, RevTex
Conformal Invariance in (2+1)-Dimensional Stochastic Systems
Stochastic partial differential equations can be used to model second order
thermodynamical phase transitions, as well as a number of critical
out-of-equilibrium phenomena. In (2+1) dimensions, many of these systems are
conjectured (and some are indeed proved) to be described by conformal field
theories. We advance, in the framework of the Martin-Siggia-Rose field
theoretical formalism of stochastic dynamics, a general solution of the
translation Ward identities, which yields a putative conformal energy-momentum
tensor. Even though the computation of energy-momentum correlators is
obstructed, in principle, by dimensional reduction issues, these are bypassed
by the addition of replicated fields to the original (2+1)-dimensional model.
The method is illustrated with an application to the Kardar-Parisi-Zhang (KPZ)
model of surface growth. The consistency of the approach is checked by means of
a straightforward perturbative analysis of the KPZ ultraviolet region, leading,
as expected, to its conformal fixed point.Comment: Title, abstract and part of the text have been rewritten. To be
published in Physical Review E
Markovian Description of Unbiased Polymer Translocation
We perform, with the help of cloud computing resources, extensive Langevin
simulations which provide compelling evidence in favor of a general markovian
framework for unbiased polymer translocation. Our statistical analysis consists
of careful evaluations of (i) two-point correlation functions of the
translocation coordinate and (ii) the empirical probabilities of complete
polymer translocation (taken as a function of the initial number of monomers on
a given side of the membrane). We find good agreement with predictions derived
from the Markov chain approach recently addressed in the literature by the
present authors.Comment: 11 pages, 4 figure
Graphene Conductivity near the Charge Neutral Point
Disordered Fermi-Dirac distributions are used to model, within a
straightforward and essentially phenomenological Boltzmann equation approach,
the electron/hole transport across graphene puddles. We establish, with
striking experimental support, a functional relationship between the graphene
minimum conductivity, the mobility in the Boltzmann regime, and the steepness
of the conductivity parabolic profile usually observed through gate-voltage
scanning around the charge neutral point.Comment: 5 pages, 2 figures - Accepted for publication in Physical Review
Option Pricing from Wavelet-Filtered Financial Series
We perform wavelet decomposition of high frequency financial time series into
large and small time scale components. Taking the FTSE100 index as a case
study, and working with the Haar basis, it turns out that the small scale
component defined by most ( 99.6%) of the wavelet coefficients can be
neglected for the purpose of option premium evaluation. The relevance of the
hugely compressed information provided by low-pass wavelet-filtering is related
to the fact that the non-gaussian statistical structure of the original
financial time series is essentially preserved for expiration times which are
larger than just one trading day.Comment: 4 pages, 1 figur
3-D perturbations in conformal turbulence
The effects of three-dimensional perturbations in two-dimensional turbulence are investigated, through a conformal field theory approach. We compute scaling exponents for the energy spectra of enstrophy and energy cascades, in a strong coupling limit, and compare them to the values found in recent experiments. The extension of unperturbed conformal turbulence to the present situation is performed by means of simple physical picture in which the existence of small scale random forces is closely related to deviations of the exact two-dimensional fluid motion
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