0 50 10 54 v 1 2 1 Ja n 20 05 Dynamical Delocalization for the 1 D Bernoulli Discrete Dirac Operator

Dynamical Delocalization for the 1D Bernoulli Discrete Dirac Operator

An 1D tight-binding version of the Dirac equation is considered; after checking that it recovers the usual discrete Schrödinger equation in the nonrelativistic limit, it is found that for two-valued Bernoulli potentials the zero mass case presents absence of dynamical localization for specific values of the energy, albeit it has no continuous spectrum. For the other energy values (again excludi...

Spectral and Localization Properties for the One-dimensional Bernoulli Discrete Dirac Operator

A 1D Dirac tight-binding model is considered and it is shown that its nonrelativistic limit is the 1D discrete Schrödinger model. For random Bernoulli potentials taking two values (without correlations), for typical realizations and for all values of the mass, it is shown that its spectrum is pure point, whereas the zero mass case presents dynamical delocalization for specific values of the ene...

Dynamical Lower Bounds for 1d Dirac Operators

with Dirichlet boundary conditions, acting on l2(N,C2), resp. L2([0,∞),C2), where c > 0 represents the speed of light, m ≥ 0 the mass of a particle, I2 is the 2× 2 identity matrix and V is a bounded real potential. In the discrete case D is the finite difference operator defined by (Dφ)(n) = φ(n+1)−φ(n), with adjoint (Dφ)(n) = φ(n − 1) − φ(n), and in the continuous case D = D = −i d dx . Model ...

ar X iv : m at h / 05 01 14 5 v 1 [ m at h . D S ] 1 0 Ja n 20 05 WAVELET CONSTRUCTIONS IN NON - LINEAR DYNAMICS

We construct certain Hilbert spaces associated with a class of non-linear dynamical systems X. These are systems which arise from a generalized self-similarity, and an iterated substitution. We show that when a weight function W on X is given, then we may construct associated Hilbert spaces H(W) of L 2-martingales which have wavelet bases.

ar X iv : m at h - ph / 0 50 10 33 v 1 1 2 Ja n 20 05 Indefinite metric