5,044 research outputs found
Realization of 2D (2,2)-periodic encoders by means of 2D periodic separable Roesser models
It is well-known that convolutional codes are linear systems when they are defined over a finite field. A fundamental issue in the implementation of convolutional codes is to obtain a minimal state representation of the code. In comparison to the literature on one-dimensional (1D) time-invariant convolutional codes, there exists only relatively few results on the realization problem for the time-varying 1D convolutional codes and even fewer if the convolutional codes are two-dimensional (2D). In this paper we consider 2D periodic convolutional codes and address the minimal state space realization problem for this class of codes. This is, in general, a highly nontrivial problem. Here, we focus on separable Roesser models and show that in this case it is possible to derive, under weak conditions, concrete formulas for obtaining a 2D Roesser state space representation. Moreover, we study minimility and present necessary conditions for these representations to be minimal. Our results immediately lead to constructive algorithms to build these representations.publishe
Bloch oscillations of cold atoms in optical lattices
This work is devoted to Bloch oscillations (BO) of cold neutral atoms in
optical lattices. After a general introduction to the phenomenon of BO and its
realization in optical lattices, we study different extentions of this problem,
which account for recent developments in this field. These are two-dimensional
BO, decoherence of BO, and BO in correlated systems. Although these problems
are discussed in relation to the system of cold atoms in optical lattices, many
of the results are of general validity and can be well applied to other systems
showing the phenomenon of BO.Comment: submitted to the review section of IJMPB, few misprints are correcte
Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability
We show that the phenomenon of modulational instability in arrays of
Bose-Einstein condensates confined to optical lattices gives rise to coherent
spatial structures of localized excitations. These excitations represent thin
disks in 1D, narrow tubes in 2D, and small hollows in 3D arrays, filled in with
condensed atoms of much greater density compared to surrounding array sites.
Aspects of the developed pattern depend on the initial distribution function of
the condensate over the optical lattice, corresponding to particular points of
the Brillouin zone. The long-time behavior of the spatial structures emerging
due to modulational instability is characterized by the periodic recurrence to
the initial low-density state in a finite optical lattice. We propose a simple
way to retain the localized spatial structures with high atomic concentration,
which may be of interest for applications. Theoretical model, based on the
multiple scale expansion, describes the basic features of the phenomenon.
Results of numerical simulations confirm the analytical predictions.Comment: 17 pages, 13 figure
Topological Band Theory for Non-Hermitian Hamiltonians
We develop the topological band theory for systems described by non-Hermitian
Hamiltonians, whose energy spectra are generally complex. After generalizing
the notion of gapped band structures to the non-Hermitian case, we classify
"gapped" bands in one and two dimensions by explicitly finding their
topological invariants. We find nontrivial generalizations of the Chern number
in two dimensions, and a new classification in one dimension, whose topology is
determined by the energy dispersion rather than the energy eigenstates. We then
study the bulk-edge correspondence and the topological phase transition in two
dimensions. Different from the Hermitian case, the transition generically
involves an extended intermediate phase with complex-energy band degeneracies
at isolated "exceptional points" in momentum space. We also systematically
classify all types of band degeneracies.Comment: 6 pages, 3 figures + 6 pages of supplemental materia
Intertwining Symmetry Algebras of Quantum Superintegrable Systems
We present an algebraic study of a kind of quantum systems belonging to a
family of superintegrable Hamiltonian systems in terms of shape-invariant
intertwinig operators, that span pairs of Lie algebras like or
. The eigenstates of the associated Hamiltonian
hierarchies belong to unitary representations of these algebras. It is shown
that these intertwining operators, related with separable coordinates for the
system, are very useful to determine eigenvalues and eigenfunctions of the
Hamiltonians in the hierarchy. An study of the corresponding superintegrable
classical systems is also included for the sake of completness
Landau-Stark states and cyclotron-Bloch oscillations of a quantum particle
Recent experimental progress in the creation of synthetic electric and
magnetic fields, acting on cold atoms in a two-dimensional lattice, has
attracted renewed interest to the problem of a quantum particle in the Hall
configuration. The present work contains a detailed analysis of the eigenstates
of this system, called Landau-Stark states, and of the associated dynamical
phenomenon of cyclotron-Bloch oscillations. It is shown that Landau-Stark
states and cyclotron-Bloch oscillations crucially depend on two factors. The
first is the orientation of the electric field relative to the primary axes of
the lattice. The second is ratio between the frequencies of Bloch and cyclotron
oscillations, that is also the ratio between the magnitudes of electric and
magnetic fields. The analysis is first carried out in the tight-binding
approximation, where the magnetic field is characterized by the Peierls phase
entering the hopping matrix elements. Agreement of this analysis with the full
quantum theory is also studied.Comment: 39 pages, 26 figure
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