Tag: Lattices

Free Download Benjamin J. Fuentes, "Optical Lattices: Structures, Atoms and Solitons "
English | ISBN: 1613249373 | 2012 | 241 pages | PDF | 9 MB
An optical lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift. Atoms are cooled and congregate in the locations of potential minima. The resulting arrangement of trapped atoms resembles a crystal lattice. This book presents current research from across the globe in the study of optical lattices, including optical lattices prepared by laser treatment on polymers, peculiarities of magnetooptical properties in crystals with mixed valence centers; the interplay of optical lattices with localized nonlinearity and matter wave dark solitons in optical superlattices..

Free Download Semigroups and Their Subsemigroup Lattices By Lev N. Shevrin, Alexander J. Ovsyannikov (auth.)
1996 | 380 Pages | ISBN: 9048147492 | PDF | 12 MB
0.1. General remarks. For any algebraic system A, the set SubA of all subsystems of A partially ordered by inclusion forms a lattice. This is the subsystem lattice of A. (In certain cases, such as that of semigroups, in order to have the right always to say that SubA is a lattice, we have to treat the empty set as a subsystem.) The study of various inter-relationships between systems and their subsystem lattices is a rather large field of investigation developed over many years. This trend was formed first in group theory; basic relevant information up to the early seventies is contained in the book [Suz] and the surveys [K Pek St], [Sad 2], [Ar Sad], there is also a quite recent book [Schm 2]. As another inspiring source, one should point out a branch of mathematics to which the book aer was devoted. One of the key objects of examination in this branch is the subspace lattice of a vector space over a skew field. A more general approach deals with modules and their submodule lattices. Examining subsystem lattices for the case of modules as well as for rings and algebras (both associative and non-associative, in particular, Lie algebras) began more than thirty years ago; there are results on this subject also for lattices, Boolean algebras and some other types of algebraic systems, both concrete and general. A lot of works including several surveys have been published here.

Free Download Synergetic Phenomena in Active Lattices: Patterns, Waves, Solitons, Chaos by Vladimir I. Nekorkin , Manuel G. Velarde
English | PDF (True) | 2002 | 371 Pages | ISBN : 3540427155 | 8.7 MB
In recent years there has been growing interest in the study of the nonlinear spatio-temporal dynamics of problems appearing in various ?elds of science and engineering. In a wide class of such systems an important place is – cupied by active lattice dynamical systems. Active lattice systems are, e. g. , networks of identical or almost identical interacting units ordered in space. The activity of lattices is provided by the activity of units in them that possess energy or matter sources. In real (1D, 2D or 3D) space, processes develop by means of various types of connections, the simplest being di?usion. The uniqueness of lattice systems is that they represent spatially extended systems while having a ?nite-dimensional phase space. Therefore, active lattice s- tems are of interest for the study of multidimensional dynamical systems and the theory of nonlinear waves and dissipative structures of extended systems as well. The theory of nonlinear waves and dissipative structures of spatially distributed systems demands using theoretical methods and approaches of the qualitative theory of dynamical systems, bifurcation theory, and numerical methods or computer experiments. In other words, the investigation of spat- temporal dynamics in active lattice systems demands a multitool, synergetic approach, which we shall use in this book.

Free Download Quantum Spin Systems on Infinite Lattices: A Concise Introduction by Pieter Naaijkens
English | PDF | 2017 | 184 Pages | ISBN : 3319514563 | 3 MB
This course-based primer offers readers a concise introduction to the description of quantum mechanical systems with infinitely many degrees of freedom – and quantum spin systems in particular – using the operator algebraic approach. Here, the observables are modeled using elements of some operator algebra, usually a C*-algebra. This text introduces readers to the framework and the necessary mathematical tools without assuming much mathematical background, making it more accessible than advanced monographs.