Related papers: Dimensionality as a Perturbation Parameter in the …
In this note, we consider the implications of the Heisenberg uncertainty principle (HUP) when computing uncertainties that affect the main dynamical quantities, from the perspective of special relativity. Using the well-known formula for…
The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…
This note was motivated by natural questions related to oriented percolation on a layered environment that introduces long range dependence. As a convenient tool, we are led to deal with questions on the strict decrease of the percolation…
Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the…
We derive the uncertainty principle for a Dirac fermion in a torsion field obeying the Hehl-Datta (HD) equation. We first discuss that there should be a correction factor to the Heisenberg uncertainty principle (HUP) when torsional effects…
The concept of a hyperuniformity disorder length $h$ was recently introduced for analyzing volume fraction fluctuations for a set of measuring windows. This length permits a direct connection to the nature of disorder in the spatial…
The generalized parton distributions are non-perturbative objects, which encode information on long distance dynamics in a number of exclusive processes. They are hybrids of conventional parton densities, distribution amplitudes and hadron…
This note presents two ideas. The first one is that quantum theory has a fundamentally perturbative basis but leads to nonperturbative states which it would seem natural to take into account in the foundation of a theory of quantum…
We compute, via a variational mixed-base method, the energy spectrum of a two dimensional relativistic atom in the presence of a constant magnetic field of arbitrary strength. The results are compared to those obtained in the…
We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians…
Major observational efforts in the coming decade are designed to probe the equation of state of dark energy. Measuring a deviation of the equation-of-state parameter w from -1 would indicate a dark energy that cannot be represented solely…
A generalized uncertainty principle is obtained from a conformally transformed action containing a scalar field and a unique constraint. The constraint's Lagrange multiplier is found to obey a relativistic diffusion equation transforming…
The omnipresent disorder in physical systems makes it imperative to investigate its effect on the spatial range of interactions for which system remains thermodynamically extensive. Previously known bounds on the statistical free energy for…
Various theories of Quantum Gravity argue that near the Planck scale, the Heisenberg Uncertainty Principle should be replaced by the so called Generalized Uncertainty Principle (GUP). We show that the GUP gives rise to two additional terms…
We show that limit cycle systems in Langevin bath exhibit uncertainty in observables that define the limit-cycle plane, and maintain a positive lower bound. The uncertainty-bound depends on the parameters that determine the shape and…
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…
A discussion is presented of the manner in which uncertainties in parton distributions and related quantities are determined. One of the central problems is the criteria used to judge what variation of the parameters describing a set of…
Deviation from standard dispersion relations for electrons and photons in the form of an extra term proportional to an arbitrarily high power of momentum is studied. It is shown that observational constraints lead to a region in the…
The entropic uncertainty measures of the multidimensional hydrogenic states quantify the multiple facets of the spatial delocalization of the electronic probability density of the system. The Shannon entropy is the most adequate uncertainty…
The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more dimensions than other regions. Imagine a situation where two…