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• W2039278766 abstract "The Hamiltonian of a system of three quantum mechanical particles moving on the three-dimensional lattice $Z^3$ and interacting via zero-range attractive potentials is considered. For the two-particle energy operator $h(k),$ with $kin T^3=(-pi,pi]^3$ the two-particle quasi-momentum, the existence of a unique positive eigenvalue below the bottom of the continuous spectrum of $h(k)$ for $kneq0$ is proven, provided that $h(0)$ has a zero energy resonance. The location of the essential and discrete spectra of the three-particle discrete Schr{o}dinger operator $H(K), Kin T^3$ being the three-particle quasi-momentum, is studied. The existence of infinitely many eigenvalues of H(0) is proven. It is found that for the number $N(0,z)$ of eigenvalues of H(0) lying below $z<0$ the following limit exists $$ lim_{zto 0-} frac {N(0,z)}{mid logmid zmidmid}=cU_0 $$ with $cU_0>0$. Moreover, for all sufficiently small nonzero values of the three-particle quasi-momentum $K$ the finiteness of the number $ N(K,tau_{ess}(K))$ of eigenvalues of $H(K)$ below the essential spectrum is established and the asymptotics for the number $N(K,0)$ of eigenvalues lying below zero is given." @default.
• W2039278766 created "2016-06-24" @default.
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• W2039278766 date "2004-08-01" @default.
• W2039278766 modified "2023-10-05" @default.
• W2039278766 title "Schrödinger Operators on Lattices. The Efimov Effect and Discrete Spectrum Asymptotics" @default.
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• W2039278766 doi "https://doi.org/10.1007/s00023-004-0181-9" @default.
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