Related papers: Scarring for Quantum Maps with Simple Spectrum

We prove the conjectural relation between the Stokes matrix for the quantum cohomology and an exceptional collection generating the derived category of coherent sheaves in the case of smooth cubic surfaces. The proof is based on a toric…

Quantum geometric maps, which relate SU(2) spin networks and Lorentz covariant projected spin networks, are an important ingredient of spin foam models (and tensorial group field theories) for 4-dimensional quantum gravity. We give a…

Let C be a complex smooth projective algebraic curve endowed with an action of a finite group G such that the quotient curve has genus at least 3. We prove that if the G-curve C is very general for these properties, then the natural map…

The energy levels of a quantum graph with time reversal symmetry and unidirectional classical dynamics are doubly degenerate and obey the spectral statistics of the Gaussian Unitary Ensemble. These degeneracies, however, are lifted when the…

If a map has k transitivity classes of vertices that are subject to the action of the automorphism group, it is said to be k-uniform. The classification of 1-uniform maps on the torus is known. In this article, we classify 2-uniform maps on…

Let $N$ be a compact hyperbolic manifold, $M\subset N$ an embedded totally geodesic submanifold, and let $-\hbar^2\Delta_{N}$ be the semiclassical Laplace--Beltrami operator. For any $\varepsilon>0$, we explicitly construct families of…

We construct a class of quantum many-body systems hosting an $\mathfrak{su}(3)$-invariant scar subspace, extending the conventional paradigm of quantum many-body scars beyond equally spaced spectra and single-directional tower structures.…

Using the torus action method, we construct one variable polynomial representation of quantum cohomology ring for degree $k$ hypersurface in $CP^{N-1}$ . The results interpolate the well-known result of $CP^{N-2}$ model and the one of…

Very few examples of obstructed equsingular families of curves on surfaces other than the projective plane are known. Combining results from Westenberger and Hirano with an idea from math.AG/9802009 we give in the present paper series of…

In this note we summarize some of the quantum properties found since the early 80's until nowdays that characterize at quantum level the spectrum of the supermembrane. In particular we will focus on a topological sector of the 11D…

We investigate the emergence of quantum scars in a general ensemble of random Hamiltonians (of which the PXP is a particular realization), that we refer to as quantum local random networks. We find a class of scars, that we call…

A knot in a solid torus defines a map on the set of (smooth or topological) concordance classes of knots in $S^3$. This set admits a group structure, but a conjecture of Hedden suggests that satellite maps never induce interesting…

The aim of this note is to describe a geometric relation between simple plane curve singularities classified by simply laced Cartan matrices and cluster varieties of finite type also classified by the simply laced Cartan matrices. We…

We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are…

Topology has emerged as a fundamental property of many systems, manifesting in cosmology, condensed matter, high-energy physics and waves. Despite the rich textures, the topology has largely been limited to low dimensional systems that can…

A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…

We compactify and regularize the space of initial values of a planar map with a quartic invariant and use this construction to prove its integrability in the sense of algebraic entropy. The system turns out to have certain unusual…

Lagrange spectra have been defined for closed submanifolds of the moduli space of translation surfaces which are invariant under the action of SL(2,R). We consider the closed orbit generated by a specific covering of degree 7 of the…

Those elements of the second de Rham cohomology group of a connected, oriented Riemannian manifold which map its second homotopy group to zero or to a discrete subgroup of the reals induce deformations of the path algebra of the manifold.…

Getting signatures of quantum gravity is one of the topical lines of research in modern theoretical physics and cosmology. This short review faces this challenge under a novel perspective. Instead of separating quantum-gravity effects of a…