Related papers: Weyl law for contractive maps
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
In the semiclassical limit of open ballistic quantum systems, we demonstrate the emergence of instantaneous decay modes guided by classical escape faster than the Ehrenfest time. The decay time of the associated quasi-bound states is…
For fractals on Riemannian manifolds, the theory of iterated function systems often does not apply well directly, as fractal sets are often defined by relations that are multivalued or non-contractive. To overcome this difficulty, we…
Via the Weyl correspondence approach, we construct multipartite entangled state which is the common eigenvector of their center-of-mass coordinate and mass-weighted relative momenta. This approach is concise and effective for setting up the…
In this paper we investigate commuting involution graphs in classical affine Weyl groups. Let $W$ be a classical Weyl group of rank $n$, with $\tilde W$ its corresponding affine Weyl group. Our main result is that if $X$ is a conjugacy…
We solve the Weyl electron scattered by a spherical step potential barrier. Tuning the incident energy and the potential radius, one can enter both quasiclassical and quantum regimes. Transport features related to far-field currents and…
There exist two consistent theories of self-interacting gravitons: general relativity and Weyl transverse gravity. The latter has the same classical solutions as general relativity, but different local symmetries. We argue that Weyl…
We establish the converse of Weyl's eigenvalue inequality for additive Hermitian perturbations of a Hermitian matrix.
Just after Weyl's paper (Weyl in Gravitation und Elektrizit\"at, Sitzungsber. Preuss. Akad., Berlin, 1918) Einstein claimed that a gravity model written in a spacetime geometry with non-metricity suffers from a phenomenon, the so-called…
We study the asymptotic behaviour of the eigenvalue counting function for self-adjoint elliptic linear operators defined through classical weighted symbols of order $(1,1)$, on an asymptotically Euclidean manifold. We first prove a two term…
Weyl fermions, which are fermions with definite chiralities, can give rise to anomalous breaking of the symmetry of the physical system which they are a part of. In their (3+1)-dimensional realizations in condensed matter systems, i.e., the…
Bipartite fluctuations can provide interesting information about entanglement properties and correlations in many-body quantum systems. We address such fluctuations in relation with the topology of Dirac and Weyl quantum systems, in…
It has been argued that the existence of time crystals requires a spontaneous breakdown of the continuous time translation symmetry so to account for the unexpected non-stationary behavior of quantum observables in the ground state. Our…
In this paper we revisit the motivation and construction of a unified theory of gravity and electromagnetism, following Weyl's insights regarding the appealing potential connection between the gauge invariance of electromagnetism and the…
We explore the connection between the holographic Weyl anomaly and the superconformal index in six-dimensional $(1,0)$ theories. Using earlier results from holographic computations of the $\mathcal O(1)$ contributions $\delta a$ and…
According to folklore in general relativity, the Weyl tensor can be decomposed into parts corresponding to Newton-like, incoming and outgoing wavelike field components. It is shown here that this one-to-one correspondence does not hold for…
An important problem from invariant theory is to describe the subspace of a tensor power of a representation invariant under the action of the group. According to Weyl's classic, the first main (later: 'fundamental') theorem of invariant…
Weyl-invariant extensions of three-dimensional New Massive Gravity, generic n-dimensional Quadratic Curvature Gravity theories and three-dimensional Born-Infeld gravity theory are analyzed in details. As required by Weyl-invariance, the…
Conformally invariant massless field systems involving only dimensionless parameters are known to describe particle physics at very high energy. In the presence of an external gravitational field, the conformal symmetry may generalize to…
In a previous paper we considered a sequence of maps on a complete metric space $(X,d)$ and derived an extension of the Banach fixed point theorem. We showed that backward trajectories of maps $X\to X$ converge under mild conditions and…