Non-local divergence-free currents for the account of symmetries in two-dimensional wave scattering

• URL: http://arxiv.org/abs/2008.05542v1
• Date: Wed, 12 Aug 2020 19:29:51 GMT
• Title: Non-local divergence-free currents for the account of symmetries in two-dimensional wave scattering
• Authors: Marios Metaxas, Peter Schmelcher, Fotis Diakonos
• Abstract summary: We show that symmetry induced, non-local, divergence-free currents can be a useful tool for the description of the consequences of symmetries on wave scattering. We argue that the usual representation of the scattering wave function does not account for insufficient account for a proper description of the underlying potential symmetries.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We explore wave-mechanical scattering in two spatial dimensions assuming that the corresponding potential is invariant under linear symmetry transforms such as rotations, reflections and coordinate exchange. Usually the asymptotic scattering conditions do not respect the symmetries of the potential and there is no systematic way to predetermine their imprint on the scattered wave field. Here we show that symmetry induced, non-local, divergence-free currents can be a useful tool for the description of the consequences of symmetries on higher dimensional wave scattering, focusing on the two-dimensional case. The condition of a vanishing divergence of these non-local currents, being in one-to-one correspondence with the presence of a symmetry in the scattering potential, provides a systematic pathway to to take account if the symmetries in the scattering solution. It leads to a description of the scattering process which is valid in the entire space including the near field regime. Furthermore, we argue that the usual asymptotic representation of the scattering wave function does not account for insufficient account for a proper description of the underlying potential symmetries. Within our approach we derive symmetry induced conditions for the coefficients in the wave field expansion with respect to the angular momentum basis in two dimensions, which determine the transition probabilities between different angular momentum states.

Related papers

• Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
  entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
  arXiv  Detail & Related papers  (2024-04-04T14:45:28Z)
• Latent Space Symmetry Discovery [31.28537696897416]
  We propose a novel generative model, Latent LieGAN, which can discover symmetries of nonlinear group actions. We show that our method can express any nonlinear symmetry under some conditions about the group action. LaLiGAN also results in a well-structured latent space that is useful for downstream tasks including equation discovery and long-term forecasting.
  arXiv  Detail & Related papers  (2023-09-29T19:33:01Z)
• Dispersive Non-reciprocity between a Qubit and a Cavity [24.911532779175175]
  We present an experimental study of a non-reciprocal dispersive-type interaction between a transmon qubit and a superconducting cavity. We show that the qubit-cavity dynamics is well-described in a wide parameter regime by a simple non-reciprocal master-equation model.
  arXiv  Detail & Related papers  (2023-07-07T17:19:18Z)
• Spontaneous symmetry emergence in a Hermitian system without symmetry [0.0]
  We show that the system state can acquire symmetry, which is not inherent to the system Hamiltonian. The emergence of symmetry manifests itself in a change of the system dynamics, which can be interpreted as a phase transition in a Hermitian system without symmetry.
  arXiv  Detail & Related papers  (2022-09-26T08:11:10Z)
• Phase control of localization in the nonlinear two-mode system from harmonic mixing driving: Perturbative analysis and symmetry consideration [6.7407868933337145]
  We present a rigorous analysis of symmetry and underlying physics of the nonlinear two-mode system driven by a harmonic mixing field. The results are of relevance for the phase control of the atomic localization in Bose-Einstein condensates or switch of the optical signals in nonlinear mediums.
  arXiv  Detail & Related papers  (2022-07-11T10:35:55Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Machine Learning S-Wave Scattering Phase Shifts Bypassing the Radial Schr\"odinger Equation [77.34726150561087]
  We present a proof of concept machine learning model resting on a convolutional neural network capable to yield accurate scattering s-wave phase shifts. We discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor.
  arXiv  Detail & Related papers  (2021-06-25T17:25:38Z)
• Symmetry-Protected Scattering in Non-Hermitian Linear Systems [0.0]
  The symmetry-protected scattering in non-Hermitian linear systems is investigated by employing the discrete symmetries that classify the random matrices. The odd-parity symmetries including the particle-hole symmetry, chiral symmetry, and sublattice symmetry cannot ensure the scattering to be symmetric. Our findings provide fundamental insights into symmetry and scattering ranging from condensed matter physics to quantum physics and optics.
  arXiv  Detail & Related papers  (2021-01-04T10:30:00Z)
• Rectification induced by geometry in two-dimensional quantum spin lattices [58.720142291102135]
  We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains. We show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the XX model.
  arXiv  Detail & Related papers  (2020-12-02T18:10:02Z)
• Latent symmetry induced degeneracies [0.0]
  We develop an approach to explain degeneracies by tracing them back to symmetries of an isospectral effective Hamiltonian. As an application, we relate the degeneracies induced by the rotation symmetry of a real Hamiltonian to a non-abelian latent symmetry group.
  arXiv  Detail & Related papers  (2020-11-26T17:37:30Z)
• Quantum-optical implementation of non-Hermitian potentials for asymmetric scattering [0.0]
  We present a feasible quantum-optical implementation of non-Hermitian, non-local, non-PT potentials to implement different scattering asymmetries.
  arXiv  Detail & Related papers  (2020-08-04T17:06:00Z)

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.