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We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and…
We study families of time-frequency localization operators and derive a new characterization of modulation spaces. This characterization relates the size of the localization operators to the global time-frequency distribution. As a…
In the framework of geometric quantization we extend the Bohr-Sommerfeld rules to a full quantization theory which resembles Heisenberg's matrix theory. This extension is possible because Bohr-Sommerfeld rules not only provide an orthogonal…
By leveraging the fundamental doctrine of The Quantum Theory of Atoms in Molecules---the partitioning of the electron charge density ($\rho$) into regions bounded by surfaces of zero flux---we map the gradient field of $\rho$ onto a 2D…
The classical criterion for compactness in Banach spaces of functions can be reformulated into a simple tightness condition in the time-frequency domain. This description preserves more explicitly the symmetry between time and frequency…
Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular…
We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results.…
Coorbit spaces provide a rigorous framework for the assessment of the approximation theoretic properties of generalized wavelet systems. It is therefore useful to understand when two different wavelet systems give rise to the same scales of…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
The Euclidean operator radius of two bounded linear operators in the Hilbert $C^*$-module over $\A$ is given some precise bounds. Their relationship to recent findings in the literature that offer precise upper and lower bounds on the…
The most fundamental model of a molecule is a cloud of unordered atoms, even without chemical bonds that can depend on thresholds for distances and angles. The strongest equivalence between clouds of atoms is rigid motion, which is a…
The use of plane wave approximation in molecular orbital tomography via high-order harmonic generation has been questioned since it was proposed, owing to the fact that it ignores the essential property of the continuum wave function. To…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…
This paper is devoted to giving definitions of Besov spaces on an arbitrary open set of $\mathbb R^n$ via the spectral theorem for the Schr\"odinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test…
Problems associated with the Boltzmann collisional operator are unveiled and discussed. By careful investigation it is shown that collective effects of molecular collisions in the six-dimensional position and velocity space are more…
Starting with an integrable unitary representation of a locally compact group and its associated voice transform, coorbit theory describes the construction and investigation of the so-called coorbit spaces. A coorbit space consists of…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…
Several laser techniques have been suggested and demonstrated recently for preparing polarizable molecules in rapidly spinning states with a disc-like angular distribution. We consider motion of these spinning discs in inhomogeneous fields,…
In this paper we discuss some physical applications of topological *-algebras of unbounded operators. Our first example is a simple system of free bosons. Then we analyze different models which are related to this one. We also discuss the…