相关论文: Localization on a quantum graph with a random pote…
We prove exponential spectral localization in a two-particle lattice Anderson model, with a short-range interaction and external random i.i.d. potential, at sufficiently low energies. The proof is based on the multi-particle multi-scale…
We demonstrate that a site-dependent driving of a periodic potential allows for the controlled manipulation of a quantum particle on length scales of the lattice spacing. Specifically we observe for distinct driving frequencies a near…
A detailed mathematical proof is given that the energy spectrum of a non-relativistic quantum particle in multi-dimensional Euclidean space under the influence of suitable random potentials has almost surely a pure-point component. The…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
We develop a scattering theory for time-periodic Hamiltonians on discrete graphs, including long-range potentials with zero average for the period, and show the existence and completeness of wave operators.
A major application of the mathematical concept of graph in quantum mechanics is to model networks of electrical wires or electromagnetic wave-guides. In this paper, we address the dynamics of a particle trapped on such a network in…
We prove the complete spectral and the strong dynamical Anderson localization in a two-particle random Schr\"odinger operators with the Poisson potential. The results apply with sufficiently weak interaction between the particle system.
We consider a sequence of finite quantum graphs with few loops, so that they converge, in the sense of Benjamini-Schramm, to a random infinite quantum tree. We assume these quantum trees are spectrally delocalized in some interval $I$, in…
Laplacian operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of $\delta$ and $\delta'$ types. An infinite series of trace formulae is obtained which link together two…
Using our previously published algorithm, we analyze the eigenvectors of the generalized Laplacian for two metric graphs occurring in practical applications. As expected, localization of an eigenvector is rare and the network should be…
We study the effect of random scattering in quantum walks on a finite graph and compare it with the effect of repeated measurements. To this end, a constructive approach is employed by introducing a localized and a delocalized basis for the…
The graph translation operator has been defined with good spectral properties in mind, and in particular with the end goal of being an isometric operator. Unfortunately, the resulting definitions do not provide good intuitions on a…
This paper presents a formalism describing the dynamics of a quantum particle in a one-dimensional, time-dependent, tilted lattice. The formalism uses the Wannier-Stark states, which are localized in each site of the lattice, and provides a…
We consider magnetic Schroedinger operators on quantum graphs with identical edges. The spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the underlying combinatorial graph and a certain Hill operator.…
We study the cross-stitch flat band lattice with a $\mathcal{PT}$-symmetric on-site potential and uncover mobility edges with exact solutions. Furthermore, we study the relationship between the $\mathcal{PT}$ symmetry broken point and the…
The development of new superconducting circuits and the improvement of existing ones rely on the accurate modeling of spectral properties which are key to achieving the needed advances in qubit performance. Systematic circuit analysis at…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…
Numerical studies of lattice quantum field theories are conducted in finite spatial volumes, typically with cubic symmetry in the spatial coordinates. Motivated by these studies, this work presents a general algorithm to construct…
We consider discrete Schr\"odinger operators with periodic potentials on periodic graphs. Their spectra consist of a finite number of bands. We perturb a periodic graph by adding edges in a periodic way (without changing the vertex set) and…
We study the Hamiltonicity of the following model of a random graph. Suppose that we partition [n] into V_1,V_2,...,V_k and add edge {x,y} to our graph with probability p if there exists i such that x,y\in V_i. Otherwise, we add the edge…