Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

Spectrum of a three-particle model Hamiltonian on a one-dimensional lattice with non-local potentials

Tulkin Husenovich Rasulov, Elyor B. Dilmurodov, Хайитова Хилола Гафуровна

Published Jan 1, 2023• 3 citations
Publisher
DOI
10.1063/5.0144164

Related papers

The spectrum of the Hamiltonian of a system of three quantum particles on a lattice

Saidakhmat Norzhigitovich Lakaev, M. Kh. Shermatov

Russian Mathematical Surveys•Dec 31, 1999•3 citations

On the essential spectrum of a four-particle Schrödinger operator on a lattice

Mukhiddin Ishkobilovich Muminov, U. R. Shodiev

The Hamiltonian of a system of four arbitrary quantum particles with three-particle short-range interaction potentials on a three-dimensional lattice is examined. The location of the essential spectrum of this Hamiltonian is described by Faddeev’s equations.

Siberian Advances in Mathematics•Oct 1, 2011•7 citations

Discrete Spectrum of the Three-Particle Hamiltonian Operator

Dimitri R. Yafaev

Soviet physics. Doklady•Mar 1, 1973•0 citations

Three Identical One-Dimensional Quantum Particles with Point Interaction as a Solvable Model: I. Discrete Spectrum

M. A. Lyalinov

The paper deals with a Hamiltonian, namely, with a semi-bounded self-adjoint operator that is attributed to the problem of scattering of three one-dimensional particles with point interaction in pairs, in other words, with $$ \delta $$ -functional singular potential of interaction. The support of the potential in the Hamiltonian coincides with a symmetric star-graph having six leads on the two-dimensional plane. Due to the symmetry, we find that such a model is exactly solvable, which means that the eigenfunctions of the discrete spectrum and the generalized eigenfunctions of the essential (absolutely continuous) spectrum are determined explicitly, i.e., by quadrature. In this (first part) of our work we describe the discrete spectrum and the eigenfunctions. DOI 10.1134/S1061920825600850

Russian Journal of Mathematical Physics•Sep 1, 2025•2 citations

Wave packets from the spectrum

ChunJun Cao, Oliver Friedrich, Marin Girard +2 more

The freedom to change Fock basis seems to ensure a minimum amount of locality in lattice theories in the following sense: If $\lbrace (\hat a_i^\dagger\,,\,\hat a_i)\rbrace$ for $i=1,\dots,n$ is a lattice of creation and annihilation operators and if a given Hamiltonian $\hat H$ induces highly non-local dynamics on that lattice, then it will usually be possible to change to a new set of operators $\lbrace (\hat b_i^\dagger\,,\,\hat b_i)\rbrace$ in terms of which the dynamics appear less non-local. We demonstrate this by turning a highly non-local random matrix model into a local, 1D lattice theory where particles can propagate in localized wave packets. More generally, we show that any Hamiltonian can be made to look like such a theory, with the lattice dispersion relation and the non-integrability of the theory depending on the spectrum of $\hat H$. We argue that our results are a step towards quantum mereology for fields.

quant-pharXiv:2606.10004•Jun 10, 2026•0 citations

The point spectrum of the three-particle Schrödinger operator for a system comprising two identical bosons and one fermion on Z

Zahriddin Ishkobilovich Muminov, Актамова Васила Уктамовна

We consider the Hamiltonian of a system of three quantum particles (two identical bosons and a fermion) on the one-dimensional lattice interacting by means of zero-range attractive or repulsive potentials. We investigate the point spectrum of the three-particle discrete Schrödinger operator H(K), K ∈ T which possesses infinitely many eigenvalues depending on repulsive or attractive interactions, under the assumption that the bosons in the system have infinite mass

Nanosystems Physics Chemistry Mathematics•Aug 30, 2024•3 citations
The paper deals with a Hamiltonian, namely, with a semi-bounded self-adjoint operator that is attributed to the problem of scattering of three one-dimensional particles with point interaction in pairs, in other words, with δ \delta δ -functional singular potential of interaction. The support of the potential in the Hamiltonian coincides with a symmetric star-graph having six leads on the two-dimensional plane. Due to the symmetry, we find that such a model is exactly solvable, which means that the eigenfunctions of the discrete spectrum and the generalized eigenfunctions of the essential (absolutely continuous) spectrum are determined explicitly, i.e., by quadrature. In this (first part) of our work we describe the discrete spectrum and the eigenfunctions. DOI 10.1134/S1061920825600850
The freedom to change Fock basis seems to ensure a minimum amount of locality in lattice theories in the following sense: If {(a^i† , a^i)}\lbrace (\hat a_i^\dagger\,,\,\hat a_i)\rbrace{(a^i†​,a^i​)} for i=1,…,ni=1,\dots,ni=1,…,n is a lattice of creation and annihilation operators and if a given Hamiltonian H^\hat HH^ induces highly non-local dynamics on that lattice, then it will usually be possible to change to a new set of operators {(b^i† , b^i)}\lbrace (\hat b_i^\dagger\,,\,\hat b_i)\rbrace{(b^i†​,b^i​)} in terms of which the dynamics appear less non-local. We demonstrate this by turning a highly non-local random matrix model into a local, 1D lattice theory where particles can propagate in localized wave packets. More generally, we show that any Hamiltonian can be made to look like such a theory, with the lattice dispersion relation and the non-integrability of the theory depending on the spectrum of H^\hat HH^. We argue that our results are a step towards quantum mereology for fields.