• Corpus ID: 119155815

Propagation Estimates for Two-cluster Scattering Channels of N-body Schrödinger Operators

  title={Propagation Estimates for Two-cluster Scattering Channels of N-body Schr{\"o}dinger Operators},
  author={Sohei Ashida},
  journal={arXiv: Mathematical Physics},
  • Sohei Ashida
  • Published 22 August 2018
  • Mathematics
  • arXiv: Mathematical Physics
In this paper we prove propagation estimates for two-cluster scattering channels of N-body Schr\"odinger operators. These estimates are based on the estimate similar to Mourre's commutator estimate and the method of Skibsted. We also obtain propagation estimates with better indices using projections onto almost invariant subspaces close to two-cluster scattering channels. As an application of these estimates we obtain the resolvent estimate for two-cluster scattering channels and microlocal… 



Resolvent estimates and scattering matrix for N-particle Hamiltonians

New estimates for the resolvent of theN-particle Schrödinger operator are established. The estimates obtained allow us to give stationary representations for the corresponding scattering matrix. In

On the three-body long-range scattering problems

In this Letter, we give results on precise microlocalized time-decay estimates in three-body long-range scattering problems. We prove the asymptotic completeness of wave operators in three-body

Propagation Estimates and Asymptotic Completeness in Three-Body Long Range Scattering

Abstract In this work, we establish precise microlocalized propagation estimates in three-body problems and give a proof for the asymptotic completeness of waves operators in three-body long range

Commutator Algebra and Resolvent Estimates

In studying the detailed properties of Schrodinger operators, the method of micro-localization seems to be indispensable. For the manybody problem, this point of view was introduced by Enss [3],

Propagation of states in dilation analytic potentials and asymptotic completeness

We estimate the space-time behavior of scattering states for two-body Schrödinger operators with smooth, dilation analytic potentials. We use our estimates to give a simple proof of asymptotic

Asymptotic Completeness for N-Body Quantum Systems with Long-Range Interactions in a Time-Periodic Electric Field

We show the asymptotic completeness for N-body quantum systems with long-range interactions in a time-periodic electric field whose mean in time is non-zero, where N ≥ 2. One of the main ingredients

Propagation estimates forN-body Schroedinger operators

We prove propagation estimates (of strong type) for long-rangeN-body Hamiltonians. Emphasis is on phase-space analysis in the free channel region.

Born–Oppenheimer Approximation for an Atom in Constant Magnetic Fields

We obtain a reduction scheme for the study of the quantum evolution of an atom in constant magnetic fields using the method developed by Martinez, Nenciu and Sordoni based on the construction of

Radiation conditions and scattering theory forN-particle Hamiltonians

The correct form of the angular part of radiation conditions is found in scattering problem forN-particle quantum systems. The estimates obtained allow us to give an elementary proof of asymptotic