Related papers: Application of the variational $R$-matrix method t…
We propose a new approach for computing tunneling rates in quantum or thermal field theory with multiple scalar fields. It is based on exact analytical solutions of piecewise linear potentials with many segments that describes any given…
We bring together the semiclassical approximation, matrix integrals and the theory of symmetric polynomials in order to solve a long standing problem in the field of quantum chaos: to compute transport moments when tunnel barriers are…
An innovative method based on the traversal of rays, originating from detected particles, through a three-dimensional grid of voxels is presented. The methodology has as main advantage that the outcome of the method is independent of the…
We develop the concept of scattering matrix and we use it to perform stable numerical calculations of resonant tunneling of electrons through a multiple potential barrier in a semiconductor heterostructure. Electrons move in two external…
One of the principal obstacles on the way to quantum computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set of basic operations (universal gates). A natural choice,…
One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask: Can this be achieved…
We study quantum mechanical tunneling using complex solutions of the classical field equations. Simple visualization techniques allow us to unify and generalize previous treatments, and straightforwardly show the connection to the standard…
Within the B\"{u}ttiker dephasing model, the backscattering in the dephasing process is eliminated by setting a proper boundary condition. Explicit expression is carried out for the effective total tunneling probability in the presence of…
The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual…
The J-matrix method was developed to handle regular short-range scattering potentials. Its accuracy, stability, and convergence properties compare favorably with other successful scattering methods. Recently, we extended the method to the…
We elaborate and validate a generalization of the renowned transition-path-sampling algorithm for a paradigmatic model of active particles, namely the Run-and-Tumble particles. Notwithstanding the non-equilibrium character of these…
We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…
We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a…
In this paper we show an approach to electron transport in double barrier structures which unifies the well known sequential and resonant tunneling models in the widest range of transport regimes, from completely coherent to completely…
We consider tunneling processes in QFT induced by collisions of elementary particles. We propose a semiclassical method for estimating the probability of these processes in the limit of very high collision energy. As an illustration, we…
Variational quantum algorithms have emerged as a powerful tool for harnessing the potential of near-term quantum devices to address complex challenges across quantum science and technology. Yet, the robust and scalable quantification of…
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
In this paper we revisit the one-dimensional tunneling problem. We consider Kemble's approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical…
Using the phenomenological quantum friction models introduced by Caldirola-Kanai, Kostin, and Albrecht, we study quantum tunneling of a one-dimensional potential in the presence of energy dissipation. To this end, we calculate the tunneling…
We employ the method used by Barbashov and collaborators in Quantum Field Theory to derive a path-integral representation of the $T$-matrix in nonrelativistic potential scattering which is free of functional integration over fictitious…