Transfer matrix for long-range potentials

• URL: http://arxiv.org/abs/2006.02989v1
• Date: Thu, 4 Jun 2020 16:21:13 GMT
• Title: Transfer matrix for long-range potentials
• Authors: Farhang Loran and Ali Mostafazadeh
• Abstract summary: We extend the notion of the transfer matrix of potential scattering to a large class of long-range potentials $v(x)$. For sufficiently large values of $|x|$, we express $v(x)$ as the sum of a short-range potential and an exactly solvable long-range potential.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We extend the notion of the transfer matrix of potential scattering to a large class of long-range potentials $v(x)$ and derive its basic properties. We outline a dynamical formulation of the time-independent scattering theory for this class of potentials where we identify their transfer matrix with the $S$-matrix of a certain effective non-unitary two-level quantum system. For sufficiently large values of $|x|$, we express $v(x)$ as the sum of a short-range potential and an exactly solvable long-range potential. Using this result and the composition property of the transfer matrix, we outline an approximation scheme for solving the scattering problem for $v(x)$. To demonstrate the effectiveness of this scheme, we construct an exactly solvable long-range potential and compare the exact values of its reflection and transmission coefficients with those we obtain using our approximation scheme.

Related papers

• Neutron-nucleus dynamics simulations for quantum computers [49.369935809497214]
  We develop a novel quantum algorithm for neutron-nucleus simulations with general potentials. It provides acceptable bound-state energies even in the presence of noise, through the noise-resilient training method. We introduce a new commutativity scheme called distance-grouped commutativity (DGC) and compare its performance with the well-known qubit-commutativity scheme.
  arXiv  Detail & Related papers  (2024-02-22T16:33:48Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Transfer-matrix summation of path integrals for transport through nanostructures [62.997667081978825]
  We develop a transfer-matrix method to describe the nonequilibrium properties of interacting quantum-dot systems. The method is referred to as "transfer-matrix summation of path integrals" (TraSPI)
  arXiv  Detail & Related papers  (2022-08-16T09:13:19Z)
• Existence of the transfer matrix for a class of nonlocal potentials in two dimensions [0.0]
  Evanescent waves are waves that decay or grow exponentially in regions of the space void of interaction. In potential scattering defined by the Schr"odinger equation, $(-nabla2+v)psi=k2psi$ for a local potential $v$, they arise in dimensions greater than one and are present regardless of the details of $v$.
  arXiv  Detail & Related papers  (2022-07-20T17:34:05Z)
• Direct solution of multiple excitations in a matrix product state with block Lanczos [62.997667081978825]
  We introduce the multi-targeted density matrix renormalization group method that acts on a bundled matrix product state, holding many excitations. A large number of excitations can be obtained at a small bond dimension with highly reliable local observables throughout the chain.
  arXiv  Detail & Related papers  (2021-09-16T18:36:36Z)
• Fundamental transfer matrix and dynamical formulation of stationary scattering in two and three dimensions [0.0]
  We offer a consistent dynamical formulation of stationary scattering in two and three dimensions. We show that a proper formulation of this approach requires the introduction of a pair of intertwined transfer matrices each related to the time-evolution operator. We discuss the utility of our approach in characterizing invisible (scattering-free) potentials and potentials.
  arXiv  Detail & Related papers  (2021-09-14T08:50:31Z)
• Dynamical formulation of low-energy scattering in one dimension [0.0]
  A transfer matrix $mathbfM$ of a short-range potential may be expressed in terms of the time-evolution operator for an effective two-level quantum system. We explore the utility of this formulation in the study of the low-energy behavior of the scattering data.
  arXiv  Detail & Related papers  (2021-02-11T15:55:34Z)
• Mapping the charge-dyon system into the position-dependent effective mass background via Pauli equation [77.34726150561087]
  This work aims to reproduce a quantum system composed of a charged spin - $1/2$ fermion interacting with a dyon with an opposite electrical charge.
  arXiv  Detail & Related papers  (2020-11-01T14:38:34Z)
• Transfer matrix in scattering theory: A survey of basic properties and recent developments [0.0]
  We start by surveying basic notions of potential scattering such as transfer matrix and its analyticity, multi-delta-function and locally periodic potentials. We then offer a simple derivation of the Lippmann-Schwinger equation and Born series, and discuss the Born approximation. Next, we outline a recently developed dynamical formulation of time-independent scattering theory in one dimension.
  arXiv  Detail & Related papers  (2020-09-22T12:53:56Z)
• Variational optimization of continuous matrix product states [0.0]
  We show how to optimize continuous matrix product states for systems with inhomogeneous external potentials. We show how both the energy and its backwards derivative can be calculated exactly and at a cost that scales as the cube of the bond dimension. We illustrate this by finding ground states of interacting bosons in external potentials, and by calculating boundary or Casimir energy corrections of continuous many-body systems.
  arXiv  Detail & Related papers  (2020-06-02T17:35:41Z)
• Eigendecomposition-Free Training of Deep Networks for Linear Least-Square Problems [107.3868459697569]
  We introduce an eigendecomposition-free approach to training a deep network. We show that our approach is much more robust than explicit differentiation of the eigendecomposition. Our method has better convergence properties and yields state-of-the-art results.
  arXiv  Detail & Related papers  (2020-04-15T04:29:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.