Related papers: Dimensionless Units in the SI
We consider the classical algebra of observables that are diagonal in a given orthonormal basis, and define a complete decoherence process as a completely positive map that asymptotically converts any quantum observable into a diagonal one,…
Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly…
Notions of (pointwise) tangential dimension are considered, for measures of R^n. Under regularity conditions (volume doubling), the upper resp. lower dimension at a point x of a measure can be defined as the supremum, resp. infimum, of…
Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of…
We obtain a new characterization for irrational numbers of constant type -- defined as irrationals with bounded partial quotients in their continued fraction expansion. The result is essential in the formulation of stability criteria for…
Even if a ring A is coherent, the polynomial ring A[X] in one variable could fail to be coherent. In this note we show that A[X] is graded coherent with the standard grading deg X=1. More generally, we give a criterion of graded…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
We construct the systems of generalised coherent states for the discrete and continuous spectra of the hydrogen atom. These systems are expressed in elementary functions and are invariant under the $SO(3, 2)$ (discrete spectrum) and $SO(4,…
We analyse the quantum geometry of 3-dimensional deformed special relativity (DSR) and the notion of spacetime points in such a context, identified with coherent states that minimize the uncertainty relations among spacetime coordinates…
Identical quantum subsystems can possess a property which does not have any classical counterpart: indistinguishability. As a long-debated phenomenon, identical particles' indistinguishability has been shown to be at the heart of various…
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
Through defining irreducible loop integrals (ILIs), a set of consistency conditions for the regularized (quadratically and logarithmically) divergent ILIs are obtained to maintain the generalized Ward identities of gauge invariance in…
We investigate the influence of spontaneous symmetry breaking on the decoherence of a many-particle quantum system. This decoherence process is analyzed in an exactly solvable model system that is known to be representative of symmetry…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
This note comments on the special CODATA 2017 adjustment of the fundamental constants of July 2017 involved in the revision of the SI (based on: P.J. Mohr et al., Data and Analysis for the CODATA 2017 Special Fundamental Constants…
The "self-induced decoherence" (SID) approach suggests that (1) the expectation value of any observable becomes diagonal in the eigenstates of the total Hamiltonian for systems endowed with a continuous energy spectrum, and (2), that this…
We consider conformal deformations within a class of incomplete Riemannian metrics which generalize conic orbifold singularities by allowing both warping and any compact manifold (not just quotients of the sphere) to be the "link" of the…
A brief description of the main methods for determining the fine structure constant is given. It is shown that the exact value of the fine structure constant is important for the new International System of Units (SI) and for fundamental…
The canonical coherent states are expressed as infinite series in powers of a complex number $z$ in their infinite series version. In this article we present classes of coherent states by replacing this complex number $z$ by other choices,…
Unavoidable disturbance caused by a quantum measurement implies that the realizable subsequent measurements are getting limited after one performs some measurement. The obvious general limitation that one cannot circumvent by sequential or…