Related papers: Green function approach for scattering quantum wal…
On the basis of the tight-binding formalism and Green function technique we obtain all the Green functions matrix elements for a biased chain with a linear variation of the electron on-site energy. Their dependence on the system parameters…
The multiple scattering theory (MST) is a Green's function method that has been widely used in electronic structure calculations for crystalline disordered systems. The key property of the MST method is the scattering path matrix (SPM) that…
The concept of open quantum walks (OQW), quantum walks exclusively driven by the interaction with the external environment, is reviewed. OQWs are formulated as discrete completely positive maps on graphs. The basic properties of OQWs are…
The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible…
We present a numerically efficient and accurate Multiple Scattering formalism, which is a generalization of the Multiple Scattering method with a truncated basis set [X. -G. Zhang and W. H. Butler, Phys. Rev. B 46,7433 (1992)]. Compared to…
In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the…
We propose an approach for calculating one-loop effective actions and vacuum energies in quantum field theory. Spectral functions are functions defined by the eigenvalues of an operator. One-loop effective actions and vacuum energies in…
The quantum theory can be formulated in the language of positive functionals on Weyl or Clifford algebra ($L$-functionals). It is shown that this language gives simple understanding of diagrams of Keldysh formalism (that coincide in our…
Exact Green's functions related to Dirac particle submitted to the combination of Aharonov-Bohm and Coulomb fields in (2+1) coordinate space are analytically calculated via path integral formalism in both global and local representations.…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
The discrete Green's function (without boundary) $\mathbb{G}$ is a pseudo-inverse of the combinatorial Laplace operator of a graph $G=(V,E)$. We reveal the intimate connection between Green's function and the theory of exact stopping rules…
We consider an asymptotically stable multidimensional random walk $S(n)=(S_1(n),\ldots, S_d(n) )$. Let $\tau_x:=\min\{n>0: x_{1}+S_1(n)\le 0\}$ be the first time the random walk $S(n)$ leaves the upper half-space. We obtain the asymptotics…
Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing many identical inclusions. Historically, this numerical…
This paper concerns the numerical simulation of time domain inverse acoustic scattering problems with a point-like scatterer, multiple point-like scatterers or normal size scatterers. Based on the Green's function and the application of the…
We develop a non-perturbative formulation based on the Green-function quantization method, that can describe spontaneous parametric down-conversion in the high-gain regime in nonlinear optical structures with arbitrary amount of loss and…
An analytical Green's function is developed to study the acoustic scattering by a flat plate with a serrated edge. The scattered pressure is solved using the Wiener-Hopf technique in conjunction with the adjoint technique. It is shown that…
Classical random walk formalism shows a significant role across a wide range of applications. As its quantum counterpart, the quantum walk is proposed as an important theoretical model for quantum computing. By exploiting the quantum…
Continuous-time quantum walk is one of the alternative approaches to quantum computation, where a universal set of quantum gates can be achieved by scattering a quantum walker on some specially-designed structures embedded in a sparse graph…
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…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…