2,719 research outputs found
On Nonlocality, Lattices and Internal Symmetries
We study functional analytic aspects of two types of correction terms to the
Heisenberg algebra. One type is known to induce a finite lower bound to the resolution of distances, a short distance cutoff which is motivated
from string theory and quantum gravity. It implies the existence of families of
self-adjoint extensions of the position operators with lattices of eigenvalues.
These lattices, which form representations of certain unitary groups cannot be
resolved on the given geometry. This leads us to conjecture that, within this
framework, degrees of freedom that correspond to structure smaller than the
resolvable (Planck) scale turn into internal degrees of freedom with these
unitary groups as symmetries. The second type of correction terms is related to
the previous essentially by "Wick rotation", and its basics are here considered
for the first time. In particular, we investigate unitarily inequivalent
representations.Comment: 6 pages, LaTe
Method for atomic-layer-resolved measurement of polarization fields by nuclear magnetic resonance
A nuclear magnetic resonance (NMR) method of probing the dielectric response to an alternating electric field is described, which is applicable to noncentrosymmetric sites with nuclear spin I>1/2. A radio-frequency electric field induces a linear quadrupole Stark effect at a multiple of the nuclear Larmor frequency. This perturbation is applied in the windows of an NMR multiple-pulse line-narrowing sequence in such a way that the resulting nonsecular spin interactions are observed as first-order quadrupole satellites, free of line broadening by the usual dominant static interactions. A simulation of the 69Ga spectrum for the nuclei within the two-dimensional electron gas of a 10 nm quantum well predicts resolution of individual atomic layers in single devices due to the spatial dependence of the polarization response of the quantum-confined carriers to the applied field. This method is part of a more general strategy, perturbations observed with enhanced resolution NMR. Experimentally realized examples in GaAs include spectrally resolving electron probability densities surrounding optically relevant point defects and probing the changes in radial electric field associated with the light-on and light-off states of these shallow traps. Adequate sensitivity for such experiments in individual epitaxial structures is achieved by optical nuclear polarization followed by time-domain NMR observed via nuclear Larmor-beat detection of luminescence
Endogenizing leadership in tax competition: a timing game perspective
In this paper we extend the standard approach of horizontal tax competition by endogenizing the timing of decisions made by the competing jurisdictions. Following the literature on the endogenous timing in duopoly games, we consider a pre-play stage, where jurisdictions commit themselves to more early or late, i.e. to fix their tax rate at a first or second stage. We highlight that at least one jurisdiction experiments a second-mover advantage. We show that the Subgame Perfect Equilibria (SPEs) correspond to the two Stackelberg situations yielding to a coordination problem. In order to solve this issue, we consider a quadratic specification of the production function, and we use two criteria of selection: Pareto-dominance and risk-dominance. We emphasize that at the safer equilibrium the less productive or smaller jurisdiction leads and hence loses the second-mover advantage. If asymmetry among jurisdictions is sufficient, Pareto-dominance reinforces risk-domination in selecting the same SPE. Three results may be deduced from our analysis: (i) the downward pressure on tax rates is less severe than predicted; (ii) the smaller jurisdiction leads; (iii) the 'big-country-higher-tax-rate' rule does not always hold. Classification-JEL: H30, H87, C72.Endogenous timing; tax competition; first/second-mover advantage; strategic complements; stackelberg ; risk dominance.
Nonpointlike Particles in Harmonic Oscillators
Quantum mechanics ordinarily describes particles as being pointlike, in the
sense that the uncertainty can, in principle, be made arbitrarily
small. It has been shown that suitable correction terms to the canonical
commutation relations induce a finite lower bound to spatial localisation.
Here, we perturbatively calculate the corrections to the energy levels of an in
this sense nonpointlike particle in isotropic harmonic oscillators. Apart from
a special case the degeneracy of the energy levels is removed.Comment: LaTeX, 9 pages, 1 figure included via epsf optio
Comment on "Quantum mechanics of smeared particles"
In a recent article, Sastry has proposed a quantum mechanics of smeared
particles. We show that the effects induced by the modification of the
Heisenberg algebra, proposed to take into account the delocalization of a
particle defined via its Compton wavelength, are important enough to be
excluded experimentally.Comment: 2 page
Unsharp Degrees of Freedom and the Generating of Symmetries
In quantum theory, real degrees of freedom are usually described by operators
which are self-adjoint. There are, however, exceptions to the rule. This is
because, in infinite dimensional Hilbert spaces, an operator is not necessarily
self-adjoint even if its expectation values are real. Instead, the operator may
be merely symmetric. Such operators are not diagonalizable - and as a
consequence they describe real degrees of freedom which display a form of
"unsharpness" or "fuzzyness". For example, there are indications that this type
of operators could arise with the description of space-time at the string or at
the Planck scale, where some form of unsharpness or fuzzyness has long been
conjectured.
A priori, however, a potential problem with merely symmetric operators is the
fact that, unlike self-adjoint operators, they do not generate unitaries - at
least not straightforwardly. Here, we show for a large class of these operators
that they do generate unitaries in a well defined way, and that these operators
even generate the entire unitary group of the Hilbert space. This shows that
merely symmetric operators, in addition to describing unsharp physical
entities, may indeed also play a r{\^o}le in the generation of symmetries, e.g.
within a fundamental theory of quantum gravity.Comment: 23 pages, LaTe
On Fields with Finite Information Density
The existence of a natural ultraviolet cutoff at the Planck scale is widely
expected. In a previous Letter, it has been proposed to model this cutoff as an
information density bound by utilizing suitably generalized methods from the
mathematical theory of communication. Here, we prove the mathematical
conjectures that were made in this Letter.Comment: 31 pages, to appear in Phys.Rev.
- …