arXiv subjects

G. Costanza

Publications and source records attributed to G. Costanza.

3 recordsLinked to original sources

arXiv2019

A class of stochastic and distributions-free quantum mechanics evolution equations: The Schrödinger-like equations

A procedure allowing to construct rigorously discrete as well as continuum deterministic evolution equations from stochastic evolution equations is developed using a Dirac's bra and ket notation. This procedure is an extension of an approach previously used by the authors coined Discrete Stochastic Evolution Equations. Definitions and examples of discretes as well as continuum one-dimensional lattices are developed in detail in order to show the basic tools that allows to construct Schrödinger-like equations. Extension to d-dimensional lattices are studied in order to provide a wider exposition and the one-dimensional cases are derived as special cases, as expected. Some variants of the procedure allows to construct other evolution equations. Also, using a limiting procedure, it is possible to derive the Schrödinger equations from the Schrödinger like equations.

quant-ph↗

arXiv2008

Adsorption-Desorption Kinetics: A Review of a Classical Problem

In this work we have analyzed the adsorption-desorption kinetics in the framework of the lattice gas model. We have shown that the coefficients representing the transition probabilities must be carefully chosen even when they fulfill the principle of detailed balance, otherwise the observables arising from the kinetics present anomalous behavior. We have demonstrated that when the adsorption $A_i$ and desorption $D_i$ coefficients are linearly related through a parameter $γ$, there are values of lateral interaction, $V$, that lead to bad behavior in the kinetics. We have shown a phase diagram for the allowed values of $V$ and $γ$, concluding that detailed balance does not guarantee a correct physical behavior of the observables obtained from the rate equations like adsorption isotherms, sticking coefficients and thermal desorption spectra. Alternatively, we have introduced a description of the adsorption-desorption processes based in a simple but consistent energetic argument that leads to a correct behavior of the observables without physical inconsistencies.

cond-mat.stat-mech↗

arXiv1999

Theoretical Continuous Equation Derived from the Microscopic Dynamics for Growing Interfaces in Quenched Media

We present an analytical continuous equation for the Tang and Leschhorn model [Phys. Rev A {\bf 45}, R8309 (1992)] derived from his microscopic rules using a regularization procedure. As well in this approach the nonlinear term $(\nabla h)^2$ arises naturally from the microscopic dynamics even if the continuous equation is not the Kardar-Parisi-Zhang equation [Phys. Rev. Lett. {\bf 56}, 889 (1986)] with quenched noise (QKPZ). Our equation looks like a QKPZ but with multiplicative quenched and thermal noise. The numerical integration of our equation reproduce the scaling exponents of the roughness of this directed percolation depinning model.

cond-mat.stat-mech↗