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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…
This work deals with the scattering entropy of quantum graphs in many different circumstances. We first consider the case of the Shannon entropy and then the R\'enyi and Tsallis entropies, which are more adequate to study distinct…
We have developed a scattering matrix approach to coherent transport through an adiabatically driven conductor based on photon-assisted processes. To describe the energy exchange with the pumping fields we expand the Floquet scattering…
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…
We suggest a new approach for the automatic and fully numerical evaluation of one-loop scattering amplitudes in perturbative quantum field theory. We use suitably formulated dispersion relations to perform the calculation as a convolution…
Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix $U$. Observing that if $U$ has at most two eigenvalues, then the scattering matrix $\mathcal{S}(k)$ of the vertex is a linear combination of the…
We provide a complete and exact quantum description of coherent light scattering in a one-dimensional multi-mode transmission line coupled to a two-level emitter. Using recently developed scattering approach we discuss transmission…
A transport methodology to study the electron transport between quantum dots arrays based in Transfer Hamiltonian approach is presented. The interactions between the quantum dots and between the quantum dots and the electrodes are…
Perturbation theory is applied to one-dimensional scattering systems consisting of a general class of inhomogeneous and isotropic slabs having size $L$ described by the relative permittivity $\varepsilon(z) = 1 + \alpha \chi(z)$, where…
The electronic states of an electrostatically confined cylindrical graphene quantum dot and the electric transport through this device are studied theoretically within the continuum Dirac-equation approximation and compared with numerical…
Coherent electron transport through a quantum channel in the presence of a general extended scattering potential is investigated using a T-matrix Lippmann-Schwinger approach. The formalism is applied to a quantum wire with Gaussian type…
The investigation of the electronic properties of semiconductors is inherently challenging due to the ensemble averaging of fundamentals to transport measurements (i.e., resistivity, Hall, and Seebeck coefficient measurements). Here, we…
We study a set of scattering matrices of quantum graphs containing minimal number of passbands, i.e., maximal number of zero elements. The cases of even and odd vertex degree are considered. Using a solution of inverse scattering problem,…
Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…
We present a direct and simple method for the computation of the total scattering matrix of an arbitrary finite noncompact connected quantum graph given its metric structure and local scattering data at each vertex. The method is inspired…
Two drift-diffusion models for the quantum transport of electrons in graphene, which account for the spin degree of freedom, are derived from a spinorial Wigner equation with relaxation-time or mass- and spin-conserving matrix collision…
We discuss the scattering of photons from a three-level emitter in a one-dimensional waveguide, where the transport is governed by the interference of spontaneously emitted and directly transmitted waves. The scattering problem is solved in…
The scattering amplitude in simple quantum graphs is a well-known process which may be highly complex. In this work, motivated by the Shannon entropy, we propose a methodology that associates to a graph a scattering entropy, which we call…
We introduce a formalism to solve the problem of photon scattering from a system of multi-level quantum emitters. Our approach provides a direct solution of the scattering dynamics. As such the formalism gives the scattered fields…
Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and…