An algebraic method for solving the inverse problem of quantum scattering theory

• URL: http://arxiv.org/abs/2102.01464v1
• Date: Tue, 2 Feb 2021 12:33:43 GMT
• Title: An algebraic method for solving the inverse problem of quantum scattering theory
• Authors: N.A. Khokhlov
• Abstract summary: We present a new method for solving the inverse problem of quantum scattering theory based on the Marchenko theory. For the zero orbital angular momentum, a linear expression of the kernel expansion coefficients is obtained in terms of the Fourier series coefficients of a function.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a new algebraic method for solving the inverse problem of quantum scattering theory based on the Marchenko theory. We applied a triangular wave set for the Marchenko equation kernel expansion in a separable form. The separable form allows a reduction of the Marchenko equation to a system of linear equations. For the zero orbital angular momentum, a linear expression of the kernel expansion coefficients is obtained in terms of the Fourier series coefficients of a function depending on the momentum q and determined by the scattering data on the finite range of q.

Related papers

• Dynamical formulation of low-frequency scattering in two and three dimensions [0.0]
  Theory of scattering in one dimension can be expressed in terms of the time-evolution operator for an effective non-unitary quantum system. In two and three dimensions, there is a similar formulation of stationary scattering where the scattering properties of the scatterer are extracted from the evolution operator. We obtain explicit formulas for low-frequency scattering amplitude, examine their effectiveness in the study of a class of exactly solvable scattering problems, and outline their application in devising a low-frequency cloaking scheme.
  arXiv  Detail & Related papers  (2024-10-22T11:26:58Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Dispersion chain of quantum mechanics equations [0.0]
  The paper considers the construction of a new chain of equations of quantum mechanics of high kinematical values. The proposed approach can be applied to consideration of classical and quantum systems with radiation.
  arXiv  Detail & Related papers  (2022-09-28T12:58:19Z)
• Field-theoretical approach to open quantum systems and the Lindblad equation [0.0]
  We develop a field-theoretical approach to open quantum systems based on condensed-matter many-body methods. Applying a condensed-matter pole or, equivalently, a quasi-type approximation, equivalent to the usual assumption of a timescale separation, we derive a master equation of the Markov type.
  arXiv  Detail & Related papers  (2022-02-10T18:04:19Z)
• An algebraic form of the Marchenko inversion. Partial waves with orbital momentum $l\ge 0$ [0.0]
  We expand the Marchenko equation kernel in a separable form using a triangular wave set. The linear expression is valid for any orbital angular momentum $l$. The kernel allows one to find the potential function of the radial Schr"odinger equation with $h$-step accuracy.
  arXiv  Detail & Related papers  (2021-12-29T00:48:13Z)
• Energy-independent optical $^{1}S_{0}NN$ potential from Marchenko equation [0.0]
  We present a new method for solving the inverse problem of quantum scattering theory based on the Marchenko theory. A numerical algorithm is developed for the reconstruction of the optical potential from scattering data.
  arXiv  Detail & Related papers  (2021-04-08T17:33:00Z)
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach [51.819912248960804]
  We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system.
  arXiv  Detail & Related papers  (2021-03-12T13:16:18Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Dissipative flow equations [62.997667081978825]
  We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode.
  arXiv  Detail & Related papers  (2020-07-23T14:47:17Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

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.