Related papers: Quantum graphs with two-particle contact interacti…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
Quantum simulators enable studies of many-body phenomena which are intractable with classical hardware. Spins in devices based on semiconductor quantum dots promise precise electrical control and scalability advantages, but accessing…
The delta interaction at a vertex generalizes the Robin (generalized Neumann) boundary condition on an interval. Study of a single vertex with N infinite leads suffices to determine the localized effects of such a vertex on densities of…
We prove spectral localization for infinite metric graphs with a self-adjoint Laplace operator and a random potential. To do so we adapt the multiscale analysis (MSA) from the R^d-case to metric graphs. In the MSA a covering of the graph is…
Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U_q(su_n) corresponding to…
This article delves into an analysis of the intrinsic entanglement and separability feature in quantum states as depicted by graph Laplacian. We show that the presence or absence of edges in the graph plays a pivotal role in defining the…
The quantum circuit model allows gates between any pair of qubits yet physical instantiations allow only limited interactions. We address this problem by providing an interaction graph together with an efficient method for compiling quantum…
We study spectral and scattering properties of a spinless quantum particle confined to an infinite planar layer with hard walls containing a finite number of point perturbations. A solvable character of the model follows from the explicit…
We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several…
We study ratios of eigenvalues of the Laplacian on compact metric graphs. Our goals are threefold: First, we prove a sharp Ashbaugh--Benguria-type bound for the ratio of the first two eigenvalues on compact trees with Dirichlet conditions…
Using bi-spinor fields we write the pseudo-scalar and bi-spinor fields that are characterized by the field functions of coordinates of several particles, namely multi-particle fields. By applying the quantization procedure to these…
We report on some recent work of the authors showing the relations between singular (point) perturbation of the Laplacian and the dynamical system describing a charged point particle interacting with the self-generated radiation field (the…
Quantum graphity is a background independent model for emergent locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly…
The nonlinear interaction, due to quantum electrodynamical (QED) effects, between photons is investigated using a wave-kinetic description. Starting from a coherent wave description, we use the Wigner transform technique to obtain a set of…
We examine the relation between inter-particle interactions and real-time equilibration in one-dimensional lattice systems with hard-core constraints. Focusing on the roles of interactions, our results demonstrate that in the presence of…
We show that topological phases with fractional excitations can occur in two-dimensional ultracold dipolar gases on a particular class of optical lattices. Due to the dipolar interaction and lattice confinement, a quantum dimer model…
We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study…
Using Schwinger's quantum action principle, dispersion relations are obtained for neutral scalar mesons interacting with bi-local sources. These relations are used as the basis of a method for representing the effect of interactions in the…
Non-equilibrium properties of strongly interacting gauge theories are often intractable with classical simulation methods. Due to recent developments of quantum simulations, studies of their properties in two spatial dimensions are becoming…
We introduce a connection between a near-term quantum computing device, specifically a Gaussian boson sampler, and the graph isomorphism problem. We propose a scheme where graphs are encoded into quantum states of light, whose properties…