Related papers: Notes on coarse grainings and functions of observa…
We present a collection of different types of observation systems that work as differentiators. These observer-based differentiators can produce estimates for derivatives of a given signal, even though the given signal is prone to noise.
The Lueders postulate is reviewed and implications for the distinguishability of observables are discussed. As an example the distinguishability of two similar observables for spin-1/2 particles is described. Implementation issues are…
For any pair of bounded observables $A$ and $B$ with pure point spectra, we construct an associated "joint observable" which gives rise to a notion of a joint (projective) measurement of $A$ and $B$, and which conforms to the intuition that…
Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful…
Two very basic constructions involving experimental procedures are the formation of coarse-grained versions of experiments, and the formation of branching sequential experiments. The latter allow for the conditioning of states on the…
We study the motion of an overdamped particle connected to a thermal heat bath in the presence of an external periodic potential in one dimension. When we coarse-grain, i.e., bin the particle positions using bin sizes that are larger than…
To study materials phenomena simultaneously at various length scales, descriptions in which matter can be coarse grained to arbitrary levels, are necessary. Attempts to do this in the static regime (i.e. zero temperature) have already been…
Window functions describe, as a function of orbital period, the probability that an existing planetary transit is detectable in one's data for a given observing strategy. We show the dependence of this probability upon several strategy and…
A class of k-particle observables in a two-mode system of Bose particles is characterized by typicality: if the state of the system is sampled out of a suitable ensemble, an experimental measurement of that observable yields (almost) always…
We show how the mathematical structure of large-deviation principles matches well with the concept of coarse-graining. For those systems with a large-deviation principle, this may lead to a general approach to coarse-graining through the…
The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate…
A microscopic theory for coarse graining diblock copolymers into dumbbells of interacting soft colloidal particles has been developed, based on the solution of liquid-state integral equations. The Ornstein-Zernike equation is solved to…
A continuum dislocation model of formation of grains whose boundaries have a non-vanishing thickness is proposed. For a single crystal deforming in simple shear the lamellar structure of grains with thin layers containing dislocations as…
Introduction to the theory of decoherence. Contents: 1. The phenomenon of decoherence: superpositions, superselection rules, decoherence by "measurements". 2. Observables as a derivable concept. 3. The measurement problem. 4. Density…
The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…
In this article we explore under which conditions on the interior function the composition of functions is measurable. We also study the sharpness of the result by providing a counterexample for weaker hypotheses.
We discuss the observability of a one-dimensional Schr\"odinger equation on certain time dependent domain. In linear moving case, we give the exact boundary and pointwise internal observability for arbitrary time. For the general moving, we…
Coarse graining techniques offer a promising alternative to large-scale simulations of complex dynamical systems, as long as the coarse-grained system is truly representative of the initial one. Here, we investigate how the dynamical…
The representation of quark distribution and fragmentation functions in terms of non-local operators is combined with a simple spectator model. This allows us to estimate these functions for the nucleon and the pion ensuring correct…
Coarse-grained models are widely used to explain the effective behavior of partially observable physical systems with hidden degrees of freedom. Reduction procedures in state space typically disrupt Markovianity and a fluctuation relation…