546 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
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