Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions

• URL: http://arxiv.org/abs/2207.00313v1
• Date: Fri, 1 Jul 2022 10:01:14 GMT
• Title: Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions
• Authors: Daniele Ferretti and Alessandro Teta
• Abstract summary: We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In particular, starting from a suitable quadratic form $Q$, the self-adjoint and bounded from below Hamiltonian $mathcal H$ can be constructed. We show that the threshold value $gamma_c$ is optimal, in the sense that the quadratic form $Q$ is unbounded from below if $gammagamma_c$.
• Score: 77.34726150561087
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In order to avoid the well known instability phenomenon, we consider the so-called Minlos-Faddeev regularization of such Hamiltonian, heuristically corresponding to the introduction of a three-body repulsion. We review the main concerning results recently obtained. In particular, starting from a suitable quadratic form $Q$, the self-adjoint and bounded from below Hamiltonian $\mathcal H$ can be constructed provided that the strength $\gamma$ of the three-body force is larger than a threshold parameter $\gamma_c$. Moreover, we give an alternative and much simpler proof of the above result whenever $\gamma > \gamma'_c$, with $\gamma'_c$ strictly larger than $\gamma_c$. Finally, we show that the threshold value $\gamma_c$ is optimal, in the sense that the quadratic form $Q$ is unbounded from below if $\gamma<\gamma_c$.

Related papers

• The SUSY partners of the QES sextic potential revisited [0.0]
  We study the SUSY partner Hamiltonians of the quasi- solvable (QES) sextic potential $Vrm qes(x) = nu, x6 + 2, nu, mu,x4 + left[mu2-(4N+3)nu right], x2$, $N in mathbbZ+$.
  arXiv  Detail & Related papers  (2023-11-10T18:38:02Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• 3-body harmonic molecule [0.0]
  It governs the near-equilibrium $S$-states eigenfunctions $psi(r_12,r_13,r_23)$ of three identical point particles interacting by means of any pairwise confining potential $V(r_12,r_13,r_23)$ that entirely depends on the relative distances $r_ij=|mathbf r_i-mathbf r_j|$ between particles. The whole spectra of excited states is degenerate, and to analyze it a detailed
  arXiv  Detail & Related papers  (2022-08-18T16:44:07Z)
• Generalized uncertainty principle and Asymptotic Safe gravity [0.0]
  We compute the Hawking temperature of a black hole in two different ways. The relation between $beta$ and $om$, $xi$ allow us to transfer upper bounds from one parameter to the others.
  arXiv  Detail & Related papers  (2022-04-15T10:45:33Z)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)
• Unitary unfoldings of Bose-Hubbard exceptional point with and without particle number conservation [0.0]
  Non-Hermitian but $cal PT-$symmetric quantum system of an $N-$plet of bosons described by Bose-Hubbard Hamiltonian $H(gamma,v,c)$ is picked up. Non-Hermitian but $cal PT-$symmetric quantum system of an $N-$plet of bosons described by the three-parametric Bose-Hubbard Hamiltonian $H(gamma,v,c)$ is picked up.
  arXiv  Detail & Related papers  (2020-08-28T21:06:17Z)
• Non-Hermitian extension of the Nambu--Jona-Lasinio model in 3+1 and 1+1 dimensions [68.8204255655161]
  We present a non-Hermitian PT-symmetric extension of the Nambu--Jona-Lasinio model of quantum chromodynamics in 3+1 and 1+1 dimensions. We find that in both cases, in 3+1 and in 1+1 dimensions, the inclusion of a non-Hermitian bilinear term can contribute to the generated mass.
  arXiv  Detail & Related papers  (2020-04-08T14:29:36Z)
• Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness [151.67113334248464]
  We show that extending the smoothing technique to defend against other attack models can be challenging. We present experimental results on CIFAR to validate our theory.
  arXiv  Detail & Related papers  (2020-02-08T22:02:14Z)

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.