On and Off-diagonal Sturmian operator: dynamic and spectral dimension

We study two versions of quasicrystal model, both subcases of Jacobi matrices. For Off-diagonal model, we show an upper bound of dynamical exponent and the norm of the transfer matrix. We apply this result to the Off-diagonal Fibonacci Hamiltonian and obtain a sub-ballistic bound for coupling large enough. In diagonal case, we improve previous lower bounds on the fractal box-counting dimension of the spectrum.Comment: arXiv admin note: text overlap with arXiv:math-ph/0502044 and arXiv:0807.3024 by other author

Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

We find a Hermite-type basis for which the eigenvalue problem associated to the operator $H_{A,B}:=B(-\partial_x^2)+Ax^2$ acting on $L^2({\bf R};{\bf C}^2)$ becomes a three-terms recurrence. Here $A$ and $B$ are two constant positive definite matrices with no other restriction. Our main result provides an explicit characterization of the eigenvectors of $H_{A,B}$ that lie in the span of the first four elements of this basis when $AB\not= BA$.Comment: 11 pages, 1 figure. Some typos where corrected in this new versio

Multiple classical limits in relativistic and nonrelativistic quantum mechanics

The existence of a classical limit describing interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to a previously established classical limit with a classical field behavior, showing that the limit $\hbar \to 0$ of the theory is not unique. An analogous result is valid for a free massive scalar field: two distinct classical limits are proved to exist, describing a system of particles or a classical field. The introduction of local operators in order to represent kinematical properties of interest is shown to break the permutation symmetry under some localizability conditions, allowing the study of individual particle properties.Comment: 13 page

Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?

For a weakly pseudo-Hermitian linear operator, we give a spectral condition that ensures its pseudo-Hermiticity. This condition is always satisfied whenever the operator acts in a finite-dimensional Hilbert space. Hence weak pseudo-Hermiticity and pseudo-Hermiticity are equivalent in finite-dimensions. This equivalence extends to a much larger class of operators. Quantum systems whose Hamiltonian is selected from among these operators correspond to pseudo-Hermitian quantum systems possessing certain symmetries.Comment: published version, 10 page

Dynamical Ambiguities in Singular Gravitational Field

We consider particle dynamics in singular gravitational field. In 2d spacetime the system splits into two independent gravitational systems without singularity. Dynamical integrals of each system define $sl(2,R)$ algebra, but the corresponding symmetry transformations are not defined globally. Quantization leads to ambiguity. By including singularity one can get the global $SO(2.1)$ symmetry. Quantization in this case leads to unique quantum theory.Comment: 7 pages, latex, no figures, submitted for publicatio

FINITE H-DIMENSION DOES NOT IMPLY EXPRESSIVE COMPLETENESS

Accepted versio

The effect of the dispersal kernel on isolation-by-distance in a continuous population

Under models of isolation-by-distance, population structure is determined by the probability of identity-by-descent between pairs of genes according to the geographic distance between them. Well established analytical results indicate that the relationship between geographical and genetic distance depends mostly on the neighborhood size of the population, $N_b = 4{\pi}{\sigma}^2 D_e$, which represents a standardized measure of dispersal. To test this prediction, we model local dispersal of haploid individuals on a two-dimensional torus using four dispersal kernels: Rayleigh, exponential, half-normal and triangular. When neighborhood size is held constant, the distributions produce similar patterns of isolation-by-distance, confirming predictions. Considering this, we propose that the triangular distribution is the appropriate null distribution for isolation-by-distance studies. Under the triangular distribution, dispersal is uniform within an area of $4{\pi}{\sigma}^2$ (i.e. the neighborhood area), which suggests that the common description of neighborhood size as a measure of a local panmictic population is valid for popular families of dispersal distributions. We further show how to draw from the triangular distribution efficiently and argue that it should be utilized in other studies in which computational efficiency is importantComment: 18 pages (main); 4 pages (supp

Asymptotics of Regulated Field Commutators for Einstein-Rosen Waves

We discuss the asymptotic behavior of regulated field commutators for linearly polarized, cylindrically symmetric gravitational waves and the mathematical techniques needed for this analysis. We concentrate our attention on the effects brought about by the introduction of a physical cut-off in the study of the microcausality of the model and describe how the different physically relevant regimes are affected by its presence. Specifically we discuss how genuine quantum gravity effects can be disentangled from those originating in the introduction of a regulator.Comment: 9 figures, 19 pages in DIN A4 format. Accepted for publication in Journal of Mathematical Physic

Magnetic transport in a straight parabolic channel

We study a charged two-dimensional particle confined to a straight parabolic-potential channel and exposed to a homogeneous magnetic field under influence of a potential perturbation $W$. If $W$ is bounded and periodic along the channel, a perturbative argument yields the absolute continuity of the bottom of the spectrum. We show it can have any finite number of open gaps provided the confining potential is sufficiently strong. However, if $W$ depends on the periodic variable only, we prove by Thomas argument that the whole spectrum is absolutely continuous, irrespectively of the size of the perturbation. On the other hand, if $W$ is small and satisfies a weak localization condition in the the longitudinal direction, we prove by Mourre method that a part of the absolutely continuous spectrum persists