Data di Pubblicazione:
2013
Citazione:
q-Deformed Loewner Evolution / M. Gherardi, A. Nigro. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 152:3(2013), pp. 452-472. [10.1007/s10955-013-0771-3]
Abstract:
The Loewner equation, in its stochastic incarnation introduced by Schramm, is an insightful method for the description of critical random curves and interfaces in two-dimensional statistical mechanics. Two features are crucial, namely conformal invariance and a conformal version of the Markov property. Extensions of the equation have been explored in various directions, in order to expand the reach of such a powerful method. We propose a new generalization based on q-calculus, a concept rooted in quantum geometry and non-extensive thermodynamics; the main motivation is the explicit breaking of the Markov property, while retaining scale invariance in the stochastic version. We focus on the deterministic equation and give some exact solutions; the formalism naturally gives rise to multiple mutually-intersecting curves. A general method of simulation is constructed-which can be easily extended to other q-deformed equations-and is applied to both the deterministic and the stochastic realms. The way the q≠1 picture converges to the classical one is explored as well.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
CUDA; Loewner equation; q-calculus; q-deformation; Schramm-Loewner evolution; Statistical and Nonlinear Physics; Mathematical Physics
Elenco autori:
M. Gherardi, A. Nigro
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