Related papers: On quantum graph filters with flat passbands
The aim of this paper is twofold. First, we study eigenvalues and eigenvectors of the adjacency matrix of a bond percolation graph when the base graph is finite and well approximated locally by an infinite regular graph. We relate…
We generalize the scattering approach to quantum graphs to quantum graphs with with piecewise constant potentials and multiple excitation modes. The free single-mode case is well-known and leads to the trace formulas of Roth, Kottos and…
Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that…
Steady technological advances are paving the way for the implementation of the quantum internet, a network of locations interconnected by quantum channels. Here we propose a model to simulate a quantum internet based on optical fibers and…
Finding hidden layers in complex networks is an important and a non-trivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multi-layer system exist and if so then what is…
Electron transmission through semiconductor superlattices is studied with transfer matrix method and resonance theory. The formation of electron band-pass transmission is ascribed to the coupling of different modes in those semiconductor…
We present an alternative approach to unveil a different kind of entanglement in bipartite quantum states whose diagonal zero patterns in suitable matrix representations admit a nice description in terms of triangle-free graphs. Upon…
The quantum Hall effect is a remarkable manifestation of quantized transport in a two-dimensional electron gas. Given its technological relevance, it is important to understand its development in realistic nanoscale devices. In this work we…
The flux-across-surfaces theorem (FAST) describes the outgoing asymptotics of the quantum flux density of a scattering state. The FAST has been proven for potential scattering under conditions on the outgoing asymptote $\psi_{\text{out}}$…
Many fundamental and applied experiments in quantum optics require transferring nonclassical states of light through large distances. In this context the free-space channels are a very promising alternative to optical fibers as they are…
We investigate the performance of several continuous-variable quantum key distribution protocols in the presence of fading channels. These are lossy channels whose transmissivity changes according to a probability distribution. This is…
We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles,…
We consider branched quantum wires, whose connection rules provide PT-symmetry for the Schrodinger equation on graph. For such PT-symmetric quantum graph we derive general boundary conditions which keep the Hamiltonian as PT-symmetric with…
Quantum communication is a growing area of research, with quantum internet being one of the most promising applications. Studying the statistical properties of this network is essential to understanding its connectivity and the efficiency…
In a unified approach we consider transport properties of 1D and quasi-1D waveguides with rough surfaces. Main attention is paid to the possibility of perfect transmission of waves due to specific long-range correlations in the surface…
We explore the quantum transmission through open oval shaped quantum dots. The transmission spectra show periodic resonances and, depending on the geometry parameter, a strong suppression of the transmission for low energies. Applying a…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We conceptualise and numerically simulate a resonant metamaterial interface incorporating non-local, or beyond nearest neighbour, coupling that acts as a discrete angular filter. It can be designed to yield perfect transmission at…
In a continuous-time quantum walk on a network of qubits, pretty good state transfer is the phenomenon of state transfer between two vertices with fidelity arbitrarily close to 1. We construct families of graphs to demonstrate that there is…
The paper contains a simplified and improved version of the results obtained by the authors earlier. Wave propagation is discussed in a network of branched thin wave guides when the thickness vanishes and the wave guides shrink to a one…