arXiv subjects

Javier Rodriguez-Laguna

Publications and source records attributed to Javier Rodriguez-Laguna.

25 records · Page 2Linked to original sources

arXiv2005

Vertically extended Frenkel-Kontorova model: a real space renormalization group study

A modification of the Frenkel-Kontorova model is presented in which particles are allowed to move in the vertical direction. This model is used to study the formation of islands for a monolayer of 1D interfaces and the corresponding roughness transition. Both analytical and numerical approaches are employed, and the numerical algorithm is based upon real space renormalization group techniques.

cond-mat.mtrl-sci↗

arXiv2002

Real Space Renormalization Group Techniques and Applications

Real Space Renormalization Group (RSRG) techniques and their applications, mainly to quantum mechanics and to partial differential equations, are discussed. Special emphasis is given to the theoretical insight and the reasons for the success of some techniques, specially DMRG. Applications to the spectrum of dendrimers and excitons on random media are considered. This work is the Ph.D. of the author. Almost all the results have already been published. The main interest of this text is paedagogical and as a review.

cond-mat.stat-mech↗

arXiv2001

Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.

cond-mat.stat-mech↗

arXiv2001

A Real Space Renormalization Group Approach to Field Evolution Equations

A new operator formalism for the reduction of degrees of freedom in the evolution of discrete partial differential equations (PDE) via real space Renormalization Group is introduced, in which cell-overlapping is the key concept. Applications to 1+1-dimensional PDEs are presented for linear and quadratic equations which are first order in time.

cond-mat.stat-mech↗

arXiv1998

A Real-Space Discrete Inverse Renormalization Group Method

A numerical real-space version of the Inverse Renormalization Group proposed by Gawedzky et al is developed. It has been tested to obtain the scaling behaviour of the random-forced heat equation in the short scales limit. Prospectives are described, and the most important target for the procedure is fully developed turbulence.

cond-mat.stat-mech↗

arXiv1998

Chaos in the Classical Analogue of the Hofstadter Problem

The behaviour of an electron in a potential that resembles that of a bidimensional solid with a perpendicular magnetic field applied is studied from a classical point of view. This problem presents the standard features of chaos and some interesting new patterns. A new chaos indicator, called random walk indicator, is presented to describe som of these new patterns

chao-dyn↗

arXiv1995

The Correlated Block Renormalization Group

We formulate the standard real-space renormalization group method in a way which takes into account the correlation between blocks. This is achieved in a dynamical way by means of operators which reflect the influence on a given block of its neighbours. We illustrate our method in the example of the tight-binding model in 1D and 2D for various types of boundary conditions.

cond-mat↗