Related papers: Spectral constants for the quantum annulus
Given a spectral triple $(\mathcal{A},\mathcal{H},D)\,$ Connes associated a canonical differential graded algebra $\,\Omega_D^\bullet(\mathcal{A})$. However, so far this has been computed for very few special cases. We identify suitable…
An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerged in this context are…
We study the spectrum of low-lying eigenmodes of the kinetic operator for scalar particles, in the color adjoint representation of Yang-Mills theory. The kinetic operator is the covariant Laplacian, plus a constant which serves to…
We show that the spectrum of orbital angular momentum in quantum mechanics consists of two parts when the underlying space has periodic boundaries. While the first part consists of the usual textbook integer quantized values, the second is…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…
It is by now well known that the wave functions of rational solutions to the KP hierarchy which can be achieved as limits of the pure $n$-soliton solutions satisfy an eigenvalue equation for ordinary differential operators in the spectral…
A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold Cesium atoms when driven…
We introduce the new concepts of pseu\-do numerical range for operator functions and families of sesquilinear forms as well as the pseu\-do block numerical range for $n \times n$ operator matrix functions. While these notions are new even…
It was recently shown that the point spectrum of the separated Coulomb-Dirac operator H_0(k) is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment H_a(k) as the anomaly parameter tends to 0; this spectral…
We study essentially bounded quantum random variables and show that the Gelfand spectrum of such a quantum random variable coincides with the hypoconvex hull of its essential range. Moreover, a notion of operator-valued variance is…
Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…
Quantum annealing (QA) is a way to solve combinational optimization problems. Kerr nonlinear parametric oscillators (KPOs) are promising devices for implementing QA. When we solve the combinational optimization problems using KPOs, it is…
We prove that if two closed disks X_1 and X_2 of the Riemann sphere are spectral sets for a bounded linear operator A on a Hilbert space, then the intersection X_1\cap X_2 is a complete (2+2/\sqrt{3})-spectral set for A. When the…
Complex scalar fields charged under a global U(1) symmetry can admit non-topological soliton configurations called Q-balls which are stable against decay into individual particles or smaller Q-balls. These Q-balls are interesting objects…
We consider discrete Schr\"odinger operators $H_{\mu Q}=\Delta+\mu Q$ with real periodic potentials $Q$ on periodic graphs, where $\Delta$ is the adjacency operator and $\mu\in\mathbb R$ is a coupling constant. The spectra of the operators…
We extend the notion of a spectral triple to that of a higher-order relative spectral triple, which accommodates several types of hypoelliptic differential operators on manifolds with boundary. The bounded transform of a higher-order…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
We look at invariance of a.e. boundary condition spectral behavior under perturbations, $W$, of half-line, continuum or discrete Schr\"odinger operators. We extend the results of del Rio, Simon, Stolz from compactly supported $W$'s to…
It is shown that in one spatial dimension the quantum oscillator is dual to the charged particle situated in the field described by the superposition of Coulomb and Calogero-Sutherland potentials.