Related papers: Unitary equivalence between the Green's function a…
A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schroedinger equation. Specially a new expression of the perturbed energy is…
We propose a simple method for resolution of co-spectrality of Schr\"odinger operators on metric graphs. Our approach consists of attaching a lead to them and comparing the $S$-functions of the corresponding scattering problems on these…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
We develop an equivariant theory of graphs with respect to quantum symmetries and present a detailed exposition of various examples. We portray unitary tensor categories as a unifying framework encompassing all finite classical simple…
A local-orbital based ab initio approach to obtain the Green function for large heterogeneous systems is developed. First a Green function formalism is introduced based on exact diagonalization. Then the self energy is constructed from an…
This paper presents a full-spectrum Green function methodology (which is valid, in particular, at and around Wood-anomaly frequencies) for evaluation of scattering by periodic arrays of cylinders of arbitrary cross section-with application…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
Since the initial development of one-dimensional electron gases (1DEG) two decades ago, there has been intense interest in both the fundamental physics and the potential applications, including quantum computation, of these quantum…
Using a path integral approach and bosonization, we calculate the low energy asymptotics of the one particle Green's function for a ``magnetically incoherent'' one dimensional strongly interacting electron gas at temperatures much greater…
A new method for non-perturbative calculation of Green functions in quantum mechanics and quantum field theory is proposed. The method is based on an approximation of Schwinger-Dyson equation for the generating functional by exactly soluble…
We present a proof of an exact equivalence of the two approaches that are most used in computing conductance in quantum electron and phonon transport: the wave function matching and Green's functions methods. We can obtain all the…
An ensemble Green's function formalism, based on the von Neumann density matrix approach, to calculate one-electron excitation spectra of a many-electron system with degenerate ground states is proposed. A set of iterative equations for the…
Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However,…
We derive a method to efficiently compute the Green function of on arbitrary Hamiltonians defined on semi-infinite and periodic quasi-one-dimensional lattices. Computing the Green function is the backbone of quantum transport, electronic…
We present a possible candidate of construction of a scalable, uniform and universal quantum network, which is built from quantum gates to elements of quantum circuit, again to quantum subnetworks and finally to an entire quantum network.…
We generalize the known solution of the Schr\"odinger equation, describing a particle confined to a triangular area, for a triangular graphene quantum dot with armchair-type boundaries. The quantization conditions, wave functions, and the…
The 2D space-fractional Schrodinger equation in the time-independent and time-dependent cases for the scattering problem in the fractional quantum mechanics is studied. We define and give the mathematical expression of the Green's functions…
Starting from the original Einstein action, sometimes called the Gamma squared action, we propose a new setup to formulate modified theories of gravity. This can yield a theory with second order field equations similar to those found in…
We investigate the properties of the zeros of the eigenfunctions on quantum graphs (metric graphs with a Schr\"odinger-type differential operator). Using tools such as scattering approach and eigenvalue interlacing inequalities we derive…
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…