相关论文: Leaky Quantum Graphs: A Review

Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a…

This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…

Let $X=G/H$ be a reductive homogeneous space with $H$ noncompact, endowed with a $G$-invariant pseudo-Riemannian structure. Let $L$ be a reductive subgroup of $G$ acting properly on $X$ and $\Gamma$ a torsion-free discrete subgroup of $L$.…

An anomaly is said to occur when a symmetry that is valid classically becomes broken as a result of quantization. Although most manifestations of this phenomenon are in the context of quantum field theory, there are at least two cases in…

We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a…

We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…

We study quantum chains whose Hamiltonians are perturbations by interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above…

Non-hermitian quantum graphs possessing real (i.e., in principle, observable) spectra are studied via their discretization. The discretized Hamiltonians are assigned, constructively, an elementary pseudometric and/or a more complicated…

In the recent work [Dailey et al., Nature Astronomy 5, 150 (2021)], it was claimed that networks of quantum sensors can be used as sensitive multi-messenger probes of astrophysical phenomena that produce intense bursts of relativistic…

We consider a long-range scattering theory for discrete Schr\"odinger operators on the hexagonal lattice, which describe tight-binding Hamiltonians on the graphene sheet. We construct Isozaki-Kitada modifiers for a pair of the difference…

In this paper, we give a new and efficient algebraic criterion for the pure as well as non-pure shellability of simplicial complex $\Delta$ over [n]. We also give an algebraic characterization of a leaf in a simplicial complex (defined in…

We study the interaction of a two-level atom and two fields, one of them classical. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to…

We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…

The idealized theory of quantum vacuum energy density is a beautiful application of the spectral theory of differential operators with boundary conditions, but its conclusions are physically unacceptable. A more plausible model of a…

We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models…

Recently, much of the existing work in manifold learning has been done under the assumption that the data is sampled from a manifold without boundaries and singularities or that the functions of interest are evaluated away from such points.…

Recent advancements in the discipline of quantum algorithms have displayed the importance of the geometry of quantum operators. Given this thrust, this paper develops a rigorous geometric framework to analyze how the Riemannian structure of…

We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the…

In this article we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with $n$ open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the…

We prove that the asymptotic distribution of resonances has a multilevel internal structure for the following classes of Hamiltonians H: Schr\"odinger operators with point interactions in $\mathbb{R}^3$, quantum graphs, and 1-D photonic…