TY - JOUR

T1 - New methods in spectral theory of N -body Schrödinger operators

AU - Adachi, T.

AU - Itakura, K.

AU - Ito, K.

AU - Skibsted, E.

N1 - Publisher Copyright:
© 2021 World Scientific Publishing Company.

PY - 2021/6

Y1 - 2021/6

N2 - We develop a new scheme of proofs for spectral theory of the N-body Schrödinger operators, reproducing and extending a series of sharp results under minimum conditions. Our main results include Rellich's theorem, limiting absorption principle bounds, microlocal resolvent bounds, Hölder continuity of the resolvent and a microlocal Sommerfeld uniqueness result. We present a new proof of Rellich's theorem which is unified with exponential decay estimates studied previously only for L2-eigenfunctions. Each pair-potential is a sum of a long-range term with first-order derivatives, a short-range term without derivatives and a singular term of operator- or form-bounded type, and the setup includes hard-core interaction. Our proofs consist of a systematic use of commutators with 'zeroth order' operators. In particular, they do not rely on Mourre's differential inequality technique.

AB - We develop a new scheme of proofs for spectral theory of the N-body Schrödinger operators, reproducing and extending a series of sharp results under minimum conditions. Our main results include Rellich's theorem, limiting absorption principle bounds, microlocal resolvent bounds, Hölder continuity of the resolvent and a microlocal Sommerfeld uniqueness result. We present a new proof of Rellich's theorem which is unified with exponential decay estimates studied previously only for L2-eigenfunctions. Each pair-potential is a sum of a long-range term with first-order derivatives, a short-range term without derivatives and a singular term of operator- or form-bounded type, and the setup includes hard-core interaction. Our proofs consist of a systematic use of commutators with 'zeroth order' operators. In particular, they do not rely on Mourre's differential inequality technique.

KW - minimal non-threshold generalized eigenfunctions

KW - N -body Schrödinger operators

UR - http://www.scopus.com/inward/record.url?scp=85100492756&partnerID=8YFLogxK

U2 - 10.1142/S0129055X2150015X

DO - 10.1142/S0129055X2150015X

M3 - Journal article

AN - SCOPUS:85100492756

SN - 0129-055X

VL - 33

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

IS - 5

M1 - 2150015

ER -