Related papers: Quantum graphs with two-particle contact interacti…
We investigate the quantum dynamics of particles on graphs ("quantum random walks"), with the aim of developing quantum algorithms for determining if two graphs are isomorphic (related to each other by a relabeling of vertices). We focus on…
Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family…
Diagrammatic techniques are well-known in the calculation of dispersion interactions between atoms or molecules. The multipolar coupling scheme combined with Feynman ordered diagrams significantly reduces the number of graphs compared to…
Gibbs states of an infinite system of interacting quantum particles are considered. Each particle moves on a compact Riemannian manifold and is attached to a vertex of a graph (one particle per vertex). Two kinds of graphs are studied: (a)…
We construct a two-class asymmetric interacting particle system with $U_q(so_6)$ or $U_q(so_8)$ symmetry, in which up to two particles may occupy a site if the two particles have different class. The particles exhibit a drift, but there is…
Interactions between particles in quantum many-body systems play a crucial role in determining the electric, magnetic, optical, and thermal properties of the system. The recent progress in the laser-pulse technique has enabled the…
We address the old and widely debated question of the statistical properties of integrable quantum systems, through the analysis of the paradigmatic Lieb-Liniger model. This quantum many-body model of 1-d interacting bosons allows for the…
In this article, the interaction of an arbitrary number of quantum dots, behaving as artificial molecules, with different energy levels and multi-mode electromagnetic field is studied. We make the assumption that each quantum dot can be…
Using a graph approach to quantum systems, we prove that descriptions of 3-dim Kochen-Specker (KS) setups as well as descriptions of 3-dim spin systems by means of Greechie lattices that we find in the literature are wrong. Correct lattices…
We study properties of spectral minimal partitions of metric graphs within the framework recently introduced in [Kennedy et al, Calc. Var. 60 (2021), 61]. We provide sharp lower and upper estimates for minimal partition energies in…
We write the spectral zeta function of the Laplace operator on an equilateral metric graph in terms of the spectral zeta function of the normalized Laplace operator on the corresponding discrete graph. To do this, we apply a relation…
We show that the quantum dynamics of interacting and noninteracting quantum particles are fundamentally different in the context of solving a particular computational problem. Specifically, we consider the graph isomorphism problem, in…
We study the behavior of a quantum particle confined to a hard--wall strip of a constant width in which there is a finite number $ N $ of point perturbations. Constructing the resolvent of the corresponding Hamiltonian by means of Krein's…
Techniques for coherent multidimensional optical spectroscopy have been developed and utilised to understand many different processes, including energy transfer in photosynthesis and many-body effects in semiconductor nanostructures.…
We consider a general interacting particle system with interactions on a random graph, and study the large population limit of this system. When the sequence of underlying graphs converges to a graphon, we show convergence of the…
Braunstein et. al. have started the study of entanglement properties of the quantum states through graph theoretical approach. Their idea was to start from a simple unweighted graph $G$ and then they have defined the quantum state from the…
We use photoluminescence spectroscopy to investigate the ground state of single self-assembled InGaAs lateral quantum dot molecules. We apply a voltage along the growth direction that allows us to control the total charge occupancy of the…
In this thesis we develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to…
We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and attractive cross-interaction. After providing a suitable…
We study the location of the spectrum of the Laplacian on compact metric graphs with complex Robin-type vertex conditions, also known as $\delta$ conditions, on some or all of the graph vertices. We classify the eigenvalue asymptotics as…