Related papers: Many-particle quantum graphs: A review
The integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) $\delta$-function interaction there is another…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
Recently normalized Laplacian matrices of graphs are studied as density matrices in quantum mechanics. Separability and entanglement of density matrices are important properties as they determine the nonclassical behavior in quantum…
The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum…
A multiply connected system in both its open and closed form variations but in equilibrium is studied using quantum waveguide theory. The system exhibits remarkable features, in its open form variation we see current enhancement, hitherto…
Gases of doubly-dipolar particles, with both magnetic and electric dipole moments, offer intriguing novel possibilities. We show that the interplay between doubly-dipolar interactions, quantum stabilization, and external confinement results…
This is a pre-publication version of a forthcoming book on quantum atom optics. It is written as a senior undergraduate to junior graduate level textbook, assuming knowledge of basic quantum mechanics, and covers the basic principles of…
The theory of strong interactions, quantum chromodynamics (QCD), is quite successful in the prediction and description of main features of multiparticle production processes at high energies. The general perturbative QCD approach to these…
We explore the tunneling behavior of a quantum particle on a finite graph, in the presence of an asymptotically large potential. Surprisingly the behavior is governed by the local symmetry of the graph around the wells.
This paper introduces a novel architecture for Quantum Graph Neural Networks, which is significantly different from previous approaches found in the literature. The proposed approach produces similar outcomes with respect to previous models…
We summarize the recent developments in the model design and computation for a few representative quantum many-body systems, encompassing quantum critical metals beyond the Hertz-Millis-Moriya framework with pseudogap and superconductivity,…
When interactions between particles are strong, at low temperature, these particles can form self-organized quantum crystals, and when the particles interact weakly, periodic structures can be imposed by external fields, e.g. by optical…
Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the…
This brief review discusses electronic properties of mesoscopic graphene-based structures. These allow controlling the confinement and transport of charge and spin; thus, they are of interest not only for fundamental research, but also for…
In this book chapter, we introduce different schemes to create quantum states of matter in engineered graphene nanoribbons. We will focus on the emergence of controllable magnetic interactions, topological quantum magnets, and the interplay…
The complex ac-response of a quasi-one dimensional electron system in the one-band approximation with an interaction potential of finite range is investigated. It is shown that linear response is exact for this model. The influence of the…
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…
Quantum nanosystems involve the coupled dynamics of fermions or bosons across multiple scales in space and time. Examples include quantum dots, superconducting or magnetic nanoparticles, molecular wires, and graphene nanoribbons. The number…
We review the theory of multi-particle entanglement. In this book chapter we aim at briefly ``setting the coordinates'' and guiding through the extensive literature in this field. Our coordinate system chosen for this chapter has the axes…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…