79 research outputs found
Space-time Phase Transitions in Driven Kinetically Constrained Lattice Models
Kinetically constrained models (KCMs) have been used to study and understand
the origin of glassy dynamics. Despite having trivial thermodynamic properties,
their dynamics slows down dramatically at low temperatures while displaying
dynamical heterogeneity as seen in glass forming supercooled liquids. This
dynamics has its origin in an ergodic-nonergodic first-order phase transition
between phases of distinct dynamical "activity". This is a "space-time"
transition as it corresponds to a singular change in ensembles of trajectories
of the dynamics rather than ensembles of configurations. Here we extend these
ideas to driven glassy systems by considering KCMs driven into non-equilibrium
steady states through non-conservative forces. By classifying trajectories
through their entropy production we prove that driven KCMs also display an
analogous first-order space-time transition between dynamical phases of finite
and vanishing entropy production. We also discuss how trajectories with rare
values of entropy production can be realized as typical trajectories of a
mapped system with modified forces
Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model
Path integral techniques for the pricing of financial options are mostly
based on models that can be recast in terms of a Fokker-Planck differential
equation and that, consequently, neglect jumps and only describe drift and
diffusion. We present a method to adapt formulas for both the path-integral
propagators and the option prices themselves, so that jump processes are taken
into account in conjunction with the usual drift and diffusion terms. In
particular, we focus on stochastic volatility models, such as the exponential
Vasicek model, and extend the pricing formulas and propagator of this model to
incorporate jump diffusion with a given jump size distribution. This model is
of importance to include non-Gaussian fluctuations beyond the Black-Scholes
model, and moreover yields a lognormal distribution of the volatilities, in
agreement with results from superstatistical analysis. The results obtained in
the present formalism are checked with Monte Carlo simulations.Comment: 9 pages, 2 figures, 1 tabl
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