Related papers: Resonant tunneling effect for quantum walks on dir…
We study the resonant scattering for discrete time quantum walks on graphs with some tails. In our arguments, we reduce the study of resonances to the perturbation of eigenvalues of a finite rank matrix associated with the internal graph.…
Quantum transport on structured networks is strongly influenced by interference effects, which can dramatically modify how information propagates through a system. We develop a quantum-information-theoretic framework for scattering on…
A waveguide coincides with a strip having two narrows of diameter $\epsilon$. Electron motion is described by the Helmholtz equation with Dirichlet boundary condition. The part of waveguide between the narrows plays the role of resonator…
We present a microscopical theory and experimental results concerning resistance resonance in two tunneling coupled quantum wells with different mobilities. The shape of the resonance appears to be sensitive to the small angle scattering…
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.
The influence of quantum fluctuations on electron transport through small metallic islands with Coulomb blockade effects is studied beyond the perturbative regime. In tunnel junctions with low resistance higher order coherent processes and…
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
We consider the time-independent scattering theory for time evolution operators of one-dimensional two-state quantum walks. The scattering matrix associated with the position-dependent quantum walk naturally appears in the asymptotic…
We theoretically investigate resonant tunneling through a linear array of quantum dots with subsequent tunnel coupling. We consider two limiting cases: (i) strong Coulomb blockade, where only one extra electron can be present in the array…
One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed in momentum space. In this work we introduce an alternative approach to topology which is based on the…
We consider wave propagation across an infinite waveguide of an arbitrary bounded cross-section, whose interior is blocked by two identical thick barriers with holes. When the holes are small, the waves over a broad range of frequencies are…
A non-unitary version of quantum scattering is studied via an exactly solvable toy model. The model is merely asymptotically local since the smooth path of the coordinate is admitted complex in the non-asymptotic domain. At any real…
In this article we investigate the effects of shifting position decoherence, arisen from the tunneling effect in the experimental realization of the quantum walk, on the one-dimensional discreet time quantum walk. We show that in the regime…
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…
We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
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 study a class of Unitary Quantum Walks on arbitrary graphs, parameterized by a family of scattering matrices. These Scattering Quantum Walks model the discrete dynamics of a system on the edges of the graph, with a scattering process at…
In this paper, we consider a sequence of open quantum graphs, with uniformly bounded data, and we are interested in the asymptotic distribution of their scattering resonances. Supposing that the number of leads in our quantum graphs is…