Related papers: Dimensionless Units in the SI
We analyze the light scattered by a single InAs quantum dot interacting with a resonant continuous-wave laser. High resolution spectra reveal clear distinctions between coherent and incoherent scattering, with the laser intensity spanning…
We give a sufficient condition for the Fourier dimension of a countable union of sets to equal the supremum of the Fourier dimensions of the sets in the union, and show by example that the Fourier dimension is not countably stable in…
Advantages and disadvantages of fixation of fundamental physical constants' values for definition of SI units are considered. The case with a new definition of the mass unit on the base of a fixed value of the Avogadro constant is studied…
The 'rigid unit mode' (RUM) model requires unit blocks, in our case tetrahedra of SiO_4 groups, to be rigid within first order of the displacements of the O-ions. The wave-vectors of the lattice vibrations, which obey this rigidity, are…
The inclusion ideal graph of a commutative unitary ring $R$ is the (undirected) graph $In(R)$ whose vertices all non-trivial ideals of $R$ and two distinct vertices are adjacent if and only if one of them is a proper subset of the other…
The possibility of consistency between the basic quantum principles of quantum mechanics and wave function collapse is reexamined. A specific interpretation of environment is proposed for this aim and applied to decoherence. When the…
Coherent fraction is a concept widely used in the synchrotron radiation community. Here I discuss the meaning of coherent fraction, an accurate way to define it, and the different formulations found in literature to calculate it. After…
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…
The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement…
On the example of a quantum oscillator the connection of the dynamical coherent state with the phase symmetry breaking and the existence of the nondissipative motion is considered. In multiparticle systems of interacting particles similar…
Symmetric informationally complete measurements (SICs) are elegant, celebrated and broadly useful discrete structures in Hilbert space. We introduce a more sophisticated discrete structure compounded by several SICs. A SIC-compound is…
A complete apparatus is defined as reacting to every state of the measured system. Standard quantum mechanics of indistinguishable particles is shown to imply that apparatuses must be incomplete or else they would be drowned out by noise.…
We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality…
Measurement incompatibility underpins randomness generation in nonlocal phenomena. However, at its root, a more fundamental quantum feature is noncommuting (or coherent) measurements. This raises a central question: How can we operationally…
A global effort to redefine our International System of Units (SI) is underway and the change to the new system is expected to occur in 2018. Within the newly redefined SI, the present base units will still exist but be derived from fixed…
It is shown that having degenerate ground states over the domain of the wavefunction of a system is a sufficient condition for a quantum system to act as a measuring apparatus for the system. Measurements are then instances of spontaneous…
The resonance arrangement $\mathcal{A}_n$ is the arrangement of hyperplanes which has all non-zero $0/1$-vectors in $\mathbb{R}^n$ as normal vectors. It is the adjoint of the Braid arrangement and is also called the all-subsets arrangement.…
We introduce the notion of angular values for deterministic linear difference equations and random linear cocycles. We measure the principal angles between subspaces of fixed dimension as they evolve under nonautonomous or random linear…
The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or…
Let $D,Q$ be natural numbers, $(D,Q)=1$, such that $D/Q>1$ and $D/Q$ is not a square. Let $q$ be the smallest divisor of $Q$ such that $Q|\, q^2$. We show that the units $>1$ of the ring $\mathbb Z[\sqrt{Dq^2/Q}]$ are connected with certain…