相关论文: Localization on a quantum graph with a random pote…

Because of the mass gap, lattice QCD simulations exhibit stochastic locality: distant regions of the lattice fluctuate independently. There is a long history of exploiting this to increase statistics by obtaining multiple…

We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…

We consider Schroedinger operators with a random potential of alloy type on infinite metric graphs which obey certain uniformity conditions. For single site potentials of fixed sign we prove that the random Schroedinger operator restricted…

We investigate spectral properties of periodic quantum graphs in the form of a kagome or a triangular lattice in the situation when the condition matching the wave functions at the lattice vertices is chosen of a particular form violating…

A quantum walk model which reflects the $2$-cell embedding on the orientable closed surface of a graph in the dynamics is introduced. We show that the scattering matrix is obtained by finding the faces on the underlying surface which have…

We analyze the scattering dynamics and spectrum of a quantum particle on a tight-binding lattice subject to a non-Hermitian (purely imaginary) local potential. The reflection, transmission and absorption coefficients are studied as a…

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…

We study the dynamical localization of discrete time evolution of topological split-step quantum random walk (QRW) on a single-site defect starting from a uniform distribution. Using analytical and numerical calculations, we determine the…

A finite discrete graph is turned into a quantum (metric) graph once a finite length is assigned to each edge and the one-dimensional Laplacian is taken to be the operator. We study the dependence of the spectral gap (the first positive…

We study the spectrum of some periodic differential operators, in particular the periodic Schr\"{o}dinger operator acting on infinite $n$-cubic graphs. Using Floquet-Bloch theory, we derive and analyze on the dispersion relations of the…

Local sets, a graph structure invariant under local complementation, have been originally introduced in the context of quantum computing for the study of quantum entanglement within the so-called graph state formalism. A local set in a…

We consider exact and asymptotic solutions of the stationary cubic nonlinear Schr\"odinger equation (NLSE) on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation…

Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…

We discuss the possibility of exponential quantum localization in systems of ultracold bosonic atoms with repulsive interactions in open optical lattices without disorder. We show that exponential localization occurs in the maximally…

The study of the properties of quantum particles in a periodic potential subject to a magnetic field is an active area of research both in physics and mathematics; it has been and it is still deeply investigated. In this review we discuss…

Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable…

We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and…

We consider a random Schro\"dinger operator in an external magnetic field. The random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the spectrum in the…

Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…

We present an analog to classic potential theory on weighted graphs. With nodes partitioned into exterior, boundary and interior nodes and an appropriate decomposition of the Laplacian, we define discrete analogues to the trace operators,…