Related papers: Noninteger flux - why it does not work
Let $L_0$ be a closed densely defined symmetric semi-bounded operator with nonzero defect indexes in a separable Hilbert space ${\cal H}$. With $L_0$ we associate a metric space $\Omega_{L_0}$ that is named a {\it wave spectrum} and…
We study the stationary problem of a charged Dirac particle in (2+1) dimensions in the presence of a uniform magnetic field B and a singular magnetic tube of flux Phi = 2 pi kappa/e. The rotational invariance of this configuration implies…
In a finite-dimensional Euclidian space we consider a connected metric graph with the following property: each two cycles can have at most one common point. Such graphs are called A-graphs. On noncompact A-graph we consider a scattering…
We study the action of conformal transformations of the ambient space on the Dirac operator coming into the Weierstrass (or spinor) representation of a torus in the Euclidean four-space. It is showed that such an action generates a flow…
We investigate the subject of speed of mixing for operators on infinite dimensional Hilbert spaces which are strongly mixing with respect to a nondegenerate Gaussian measure. We prove that there is no way to find a uniform speed of mixing…
We consider a 2D quantum spin model with ring-exchange interaction that has subsystem symmetries associated to conserved magnetization along rows and columns of a square lattice, which implies the conservation of the global dipole moment.…
In this article, we provide the spectral analysis of a Dirac-type operator on $\mathbb{Z}^2$ by describing the behavior of the spectral shift function associated with a sign-definite trace-class perturbation by a multiplication operator. We…
The machinery of noncommutative geometry is applied to a space of connections. A noncommutative function algebra of loops closely related to holonomy loops is investigated. The space of connections is identified as a projective limit of…
The eigenvalue problem of the Hamiltonian of an electron confined to a plane and subjected to a perpendicular time-independent magnetic field which is the sum of a homogeneous field and an additional field contributed by a singular flux…
In this article, we consider the Dirac operator with constant magnetic field in $\mathbb R^2$. Its spectrum consists of eigenvalues of infinite multiplicities, known as the Landau-Dirac levels. Under compactly supported perturbations, we…
Let $\mathcal{H}$ be a complex, separable Hilbert space, and set $\mathfrak{c}($NIL$_2)=\{ MN - NM : N, M \in \mathcal{B}(\mathcal{H}), M^2 = 0 = N^2 \}$. When $\dim\, \mathcal{H}$ is finite, we characterise the set $\mathfrak{c}($NIL$_2)$…
It is shown that the local axial anomaly in $2-$dimensions emerges naturally if one postulates an underlying noncommutative fuzzy structure of spacetime . In particular the Dirac-Ginsparg-Wilson relation on ${\bf S}^2_F$ is shown to contain…
Non-Hermitian phenomena offer a novel approach to analyze and interpret spectra in the presence of interactions. Using the density-matrix renormalization group (DMRG), we demonstrate the existence of exceptional points for the one-particle…
We study the algebra of differential operators on non-compact simply connected harmonic manifolds and provide sufficient conditions for them to have a radial fundamental solution and be surjective on the space of smooth function.…
If $T$ is a (densely defined) self-adjoint operator acting on a complex Hilbert space $\mathcal{H}$ and $I$ stands for the identity operator, we introduce the delta function operator $\lambda \mapsto \delta \left(\lambda I-T\right) $ at…
We show that an inverse scattering problem for a semilinear wave equation can be solved on a manifold having an asymptotically Minkowskian infinity, that is, scattering functionals determine the topology, differentiable structure, and the…
An odd Fredholm module for a given invertible operator on a Hilbert space is specified by an unbounded so-called Dirac operator with compact resolvent and bounded commutator with the given invertible. Associated to this is an index pairing…
Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double…
Spin 1 particle is investigated in 3-dimensional curved space of constant positive curvature. An extended helicity operator is defined and the variables are separated in a tetrad-based 10-dimensional Duffin-Kemmer equation in quasi…
Let $U$ be a unitary operator defined on some infinite-dimensional complex Hilbert space ${\cal H}$. Under some suitable regularity assumptions, it is known that a local positive commutation relation between $U$ and an auxiliary…