Related papers: Green function approach for scattering quantum wal…
Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…
In this work we present a three step procedure for generating a closed form expression of the Green's function on both closed and open finite quantum graphs with general self-adjoint matching conditions. We first generalize and simplify the…
Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual…
In a previous work [Andrade \textit{et al.}, Phys. Rep. \textbf{647}, 1 (2016)], it was shown that the exact Green's function (GF) for an arbitrarily large (although finite) quantum graph is given as a sum over scattering paths, where local…
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 aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created at each bounce, which serves as a…
Quantum walks constitute important tools in different applications, especially in quantum algorithms. To a great extent their usefulness is due to unusual diffusive features, allowing much faster spreading than their classical counterparts.…
This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed…
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…
Quantum walks are roughly analogous to classical random walks, and like classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs it is useful to find the…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…
The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and…
In this paper, we consider the scattering theory for a one-dimensional quantum walk with impurities which make reflections and transmissions. We focus on an explicit expression of the scattering operator. Our construction of the formula is…
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
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 introduce the Green's functions technique as an alternative theory to the quantum regression theorem formalism for calculating the two-time correlation functions in open quantum systems. In particular, we investigate the potential of…
Sub-wavelength arrays of quantum emitters offer an efficient free-space approach to coherent light-matter interfacing, using ultracold atoms or two-dimensional solid-state quantum materials. The combination of collectively suppressed…
The single-particle Green's function (GF) of mesoscopic structures plays a central role in mesoscopic quantum transport. The recursive GF technique is a standard tool to compute this quantity numerically, but it lacks physical transparency…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of…