Numerical Tests of the Envelope Theory for Few-Boson Systems

Semay, Claude

doi:10.1007/s00601-015-0960-5

Cited by 26 publications

(53 citation statements)

References 21 publications

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“…Let us first remark that irrelevant values for the energies (complex or positive real numbers) are computed with the ET when the number of particles is too small. Such a behaviour was already observed for D = 3 [7]. The quality of the bound strongly depends on the value of a.…”

Section: Gaussian Potentialsupporting

confidence: 61%

“…The ET has already been tested in the D = 3 space for various Hamiltonians up to 10 bosons [7,8]. It was shown that reliable results can be obtained for energies and some observables.…”

Section: Discussionmentioning

confidence: 99%

“…2 K, and V g = V 0 /( √ π a) with V 0 = 10 a.u K and a = {0, 0.05, 0.1, 0.2, 0.5, 1} a.u. The ground state upper bound E ET , computed with (5-7) and Q = Q B 0 , is given by [7]…”

Section: Gaussian Potentialmentioning

confidence: 99%

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Tests of the Envelope Theory in One Dimension

Semay

Cimino

2019

Few-Body Syst

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The envelope theory is a simple technique to obtain approximate, but reliable, solutions of manybody systems with identical particles. The accuracy of this method is tested here for two systems in one dimension with pairwise forces. The first one is the fermionic ground state of the analytical Calogero model with linear forces supplemented by inverse-cube forces. The second one is the ground state of up to 100 bosons interacting via a Gaussian potential. Good bounds can be obtained depending on values of the model parameters. *

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Section: Gaussian Potentialsupporting

confidence: 61%

“…The ET has already been tested in the D = 3 space for various Hamiltonians up to 10 bosons [7,8]. It was shown that reliable results can be obtained for energies and some observables.…”

Section: Discussionmentioning

confidence: 99%

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Tests of the Envelope Theory in One Dimension

Semay

Cimino

2019

Few-Body Syst

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“…The envelope theory is an efficient and convenient tool to obtain approximate solutions for quantum systems made of N identical particles [7][8][9]. With this method, the quantum energy of N self-gravitating particles with a mass m in D-dimensional space is given by [10]…”

mentioning

confidence: 99%

Quantum support to BoHua Sun’s conjecture

Semay

2019

Results in Physics

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A generalization of the Kepler's third law has been proposed by BoHua Sun for N -body periodic orbits in a Newtonian gravitation field. In this paper, it is shown that this formula can apply for a quantum system of N self-gravitating identical particles, for a good choice of the period for the quantum motion.The Kepler's third law is certainly a milestone in the development of mechanics. But this peculiar relation between the period and the size of the orbit (or the period and the energy of the orbit) seemed only relevant for two-body systems. Nevertheless, the computation of a great number of Newtonian periodic planar collisionless three-body orbits suggests the existence of a quasi Kepler's third law [1]. A definition of an average period

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“…where the quantum period T q and quantum energy E q of N self-gravitating particles with a mass m in Ddimensional space [1,8,9]. For further discussion, we call Eq.…”

Section: Fig 2: N-body Systemmentioning

confidence: 99%

Classical and Quantum Kepler's Third Law of N-Body System

Sun

2019

Preprint

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Inspired by amazing result obtained by Semay [1], this study revisits generalised Kepler's third law of an n-body system from the perspective of dimension analysis. To be compatible with Semay's quantum n-body result, this letter reports a conjecture which had not be included in author's early publication [2] but formulated in the author's research memo. The new conjecture for quantum N-body system is proposed as follows: Tq|Eq| 3/2 = π √ 2 G

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Numerical Tests of the Envelope Theory for Few-Boson Systems

Cited by 26 publications

References 21 publications

Tests of the Envelope Theory in One Dimension

Tests of the Envelope Theory in One Dimension

Quantum support to BoHua Sun’s conjecture

Classical and Quantum Kepler's Third Law of N-Body System

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