From nodal points to non-equidistribution at the Planck scale
نویسندگان
چکیده
In this note, we make an observation that Laplacian eigenfunctions fail equidistribution at the Planck scale. Furthermore, same scale also fails around points where have large values.
منابع مشابه
Computability at the Planck Scale
We consider the issue of computability at the most fundamental level of physical reality: the Planck scale. To this aim, we consider the theoretical model of a quantum computer on a non commutative space background, which is a computational model for quantum gravity. In this domain, all computable functions are the laws of physics in their most primordial form, and non computable mathematics fi...
متن کاملSupersymmetry : From the Fermi Scale to the Planck Scale 1
The physics of supersymmetry is reviewed from the perspective of physics at ever increasing energies. Starting from the minimal supersymmetric extension of the Standard Model at the electroweak scale, we proceed to higher energies seeking to understand the origin of the many model parameters. Supersymmetric grand unification, supergravity, and superstrings are introduced sequentially, and their...
متن کاملNonlinear Quantum Mechanics at the Planck Scale
Linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear effects can be of comparable magnitude to the linear ones and still be highly suppressed at low energies. This can offer alternative approaches to quantum gravity and to the...
متن کاملEquidistribution of Points via Energy
We study the asymptotic equidistribution of points with discrete energy close to Robin’s constant of a compact set in the plane. Our main tools are the energy estimates from potential theory. We also consider the quantitative aspects of this equidistribution. Applications include estimates of growth for the Fekete and Leja polynomials associated with large classes of compact sets, convergence r...
متن کاملQuantum Mechanics at the Planck Scale *
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2022
ISSN: ['1631-073X', '1778-3569']
DOI: https://doi.org/10.5802/crmath.311