Zero-Threshold Resolvent Asymptotics of Three-Body Schrödinger Operators

Wang, Xue Ping

doi:10.1007/s00601-011-0232-y

Few-Body Syst

2011

DOI: 10.1007/s00601-011-0232-y

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Zero-Threshold Resolvent Asymptotics of Three-Body Schrödinger Operators

Xue Ping Wang

Abstract: Abstract. We analyze the spectral properties for three-body Schrödinger operators at the threshold zero and give some results on the asymptotics of resolvent under the condition that zero is a regular point for all two-body Subhamiltonians.

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2013

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Why there is no Efimov effect for four bosons and related results on the finiteness of the discrete spectrum

Gridnev¹

2013

Journal of Mathematical Physics

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We consider a system of N pairwise interacting particles described by the Hamiltonian H, where σ ess (H) = [0, ∞) and none of the particle pairs has a zero energy resonance. The pair potentials are allowed to take both signs and obey certain restrictions regarding the fall off. It is proved that if N ≥ 4 and none of the Hamiltonians corresponding to the subsystems containing N − 2 or less particles has an eigenvalue equal to zero then H has a finite number of negative energy bound states. This result provides a positive proof to a long-standing conjecture of Amado and Greenwood stating that four bosons with an empty negative continuous spectrum have at most a finite number of negative energy bound states. Additionally, we give a short proof to the theorem of Vugal'ter and Zhislin on the finiteness of the discrete spectrum and pose a conjecture regarding the existence of the "true" four-body Efimov effect.

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Why there is no Efimov effect for four bosons and related results on the finiteness of the discrete spectrum

Gridnev¹

2013

Journal of Mathematical Physics

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Zero-Threshold Resolvent Asymptotics of Three-Body Schrödinger Operators

Abstract: Abstract. We analyze the spectral properties for three-body Schrödinger operators at the threshold zero and give some results on the asymptotics of resolvent under the condition that zero is a regular point for all two-body Subhamiltonians.

Cited by 1 publication

References 24 publications

Why there is no Efimov effect for four bosons and related results on the finiteness of the discrete spectrum

Why there is no Efimov effect for four bosons and related results on the finiteness of the discrete spectrum

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