A two-boson lattice Hamiltonian with interactions up to next-neighboring sites
- URL: http://arxiv.org/abs/2410.07070v1
- Date: Wed, 9 Oct 2024 17:15:21 GMT
- Title: A two-boson lattice Hamiltonian with interactions up to next-neighboring sites
- Authors: S. N. Lakaev, A. K. Motovilov, M. O. Akhmadova,
- Abstract summary: A partition of the $(gamma,lambda,mu)$-space into connected components is established.
For each connected component, a sharp lower bound is established on the number of isolated eigenvalues for the two-boson Schr"odinger operator.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: A system of two identical spinless bosons on the two-dimensional lattice is considered under the assumption that on-site and first and second nearest-neighboring site interactions between the bosons are only nontrivial and that these interactions are of magnitudes $\gamma$, $\lambda$, and $\mu$, respectively. A partition of the $(\gamma,\lambda,\mu)$-space into connected components is established such that, in each connected component, the two-boson Schroedinger operator corresponding to the zero quasi-momentum of the center of mass has a definite (fixed) number of eigenvalues, which are situated below the bottom of the essential (continuous) spectrum and above its top. Moreover, for each connected component, a sharp lower bound is established on the number of isolated eigenvalues for the two-boson Schr\"odinger operator corresponding to any admissible nonzero value of the center-of-mass quasimomentum.
Related papers
- Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions.
We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
arXiv Detail & Related papers (2024-07-09T14:04:11Z) - Borromean states in a one-dimensional three-body system [0.0]
We show the existence of Borromean bound states in a one-dimensional quantum three-body system composed of two identical bosons and a distinguishable particle.
It is assumed that there is no interaction between the two bosons, while the mass-imbalanced two-body subsystems can be tuned to be either bound or unbound.
arXiv Detail & Related papers (2024-05-23T17:59:43Z) - Hamiltonian for a Bose gas with Contact Interactions [49.1574468325115]
We study the Hamiltonian for a Bose gas in three dimensions of $N geq 3$ spinless particles interacting via zero-range or contact interactions.
arXiv Detail & Related papers (2024-03-19T10:00:12Z) - Photon-induced droplet-like bound states in one-dimensional qubit array [0.0]
We study the bandgap regime where the energy of two excited qubits is off-resonant with the two-photon bound state band.
A two-step adiabatic elimination of the photonic degrees of freedom gives rise to a one-dimensional spin Hamiltonian with effective interactions.
arXiv Detail & Related papers (2023-07-12T01:46:55Z) - Duality between open systems and closed bilayer systems, and thermofield double states as quantum many-body scars [49.1574468325115]
We find a duality between open many-body systems governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation.
Under this duality, the identity operator on the open system side maps to the thermofield double state.
We identify broad classes of many-body open systems with nontrivial explicit eigen operators $Q$ of the Lindbladian superoperator.
arXiv Detail & Related papers (2023-04-06T15:38:53Z) - Two-fermion lattice Hamiltonian with first and second
nearest-neighboring-site interactions [68.8204255655161]
We study the Schroedinger operators H_lambdamu(K), with K in T, the fixed quasi-momentum of the particles pair.
We establish a sharp lower bound for the number of isolated eigenvalues of H_lambdamu(K) in each connected component.
arXiv Detail & Related papers (2023-03-18T20:08:56Z) - 1-matrix functional for long-range interaction energy of two hydrogen
atoms [0.0]
Minimization of the resulting explicit functional yields the large-$R$s for the occupation numbers of the weakly occupied NOs.
The radial components of the $p$-type "half-space" orbitals and the corresponding occupation numbers (that decay like $R-6$) are available for the first time thanks to the development of the present formalism.
arXiv Detail & Related papers (2023-03-11T12:30:01Z) - Understanding the propagation of excitations in quantum spin chains with
different kind of interactions [68.8204255655161]
It is shown that the inhomogeneous chains are able to transfer excitations with near perfect fidelity.
It is shown that both designed chains have in common a partially ordered spectrum and well localized eigenvectors.
arXiv Detail & Related papers (2021-12-31T15:09:48Z) - Interacting holes in Si and Ge double quantum dots: from a multiband
approach to an effective-spin picture [0.0]
We investigate two-hole states in prototypical coupled Si and Ge quantum dots via different theoretical approaches.
We find that, in the weak interdot regime, the ground state and first excited multiplet of the two-hole system display -- unlike their electronic counterparts -- a high degree of $J$-mixing.
The light-hole component additionally induces $M$-mixing and a weak coupling between spinors characterized by different permutational symmetries.
arXiv Detail & Related papers (2021-04-15T19:18:50Z) - Radiative topological biphoton states in modulated qubit arrays [105.54048699217668]
We study topological properties of bound pairs of photons in spatially-modulated qubit arrays coupled to a waveguide.
For open boundary condition, we find exotic topological bound-pair edge states with radiative losses.
By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.
arXiv Detail & Related papers (2020-02-24T04:44:12Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.