Improvement of the Envelope Theory for Systems with Different Particles

[en] The envelope theory is a method to compute approximate eigensolutions of quantum N-body Hamiltonians with a quite general structure in D dimensions. The advantages of the method are that it is easy to implement and that N is treated as any other parameters of the Hamiltonian, allowing the computation for systems of all sizes. If solutions are reliable, they are generally not very accurate. In the case of systems with identical particles for D≥2, it is possible to improve the precision of the eigenvalues by combining the envelope theory with a generalisation to N-body of the dominantly orbital state method. It is shown that a similar improvement can be achieved in the case of systems composed of identical particles plus a different one. The quality of the new procedure is tested with different systems.

Research center :

Algèbre, Géométrie et Interactions fondamentales

Disciplines :

Physics

Author, co-author :

Chevalier, Cyrille ; Université de Mons > Faculté des Sciences > Service de Physique nucléaire et subnucléaire

Willemyns, Cintia ; Université de Mons > Faculté des Sciences > Service de Physique nucléaire et subnucléaire

Cimino, Lorenzo ; Université de Mons > Faculté des Sciences > Service de Physique nucléaire et subnucléaire

Semay, Claude ; Université de Mons > Faculté des Sciences > Service de Physique nucléaire et subnucléaire

Language :

English

Title :

Improvement of the Envelope Theory for Systems with Different Particles

Publication date :

31 March 2022

Journal title :

Few-Body Systems

ISSN :

0177-7963

Publisher :

Springer, Germany

Volume :

Peer reviewed :

Peer Reviewed verified by ORBi

Research unit :

Physique nucléaire et subnucléaire

Research institute :

Institut de Recherche sur les Systèmes Complexes

Name of the research project :

Physique Nucléaire Théorique - Fédération Wallonie Bruxelles

Commentary :

https://rdcu.be/cKf7j

Available on ORBi UMONS :

since 30 November 2021

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Bibliography

R.L. Hall, Energy trajectories for the N -boson problem by the method of potential envelopes. Phys. Rev. D 22, 2062 (1980)
R.L. Hall, A geometrical theory of energy trajectories in quantum mechanics. J. Math. Phys. 24, 324 (1983)
R.L. Hall, W. Lucha, F.F. Schöberl, Relativistic N -boson systems bound by pair potentials V(rij)=g(rij2). J. Math. Phys. 45, 3086 (2004)
B. Silvestre-Brac, C. Semay, F. Buisseret, F. Brau, The quantum N -body problem and the auxiliary field method. J. Math. Phys. 51, 032104 (2010)
B. Silvestre-Brac, C. Semay, F. Buisseret, The auxiliary field method in quantum mechanics. J. Phys. Math. 4, P120601 (2012)
C. Semay, C. Roland, Approximate solutions for N -body Hamiltonians with identical particles in D dimensions. Results Phys. 3, 231 (2013)
C. Semay, L. Cimino, C. Willemyns, Envelope theory for systems with different particles. Few-Body Syst. 61, 19 (2020)
C. Semay, F. Buisseret, Bound cyclic systems with the envelope theory. Few-Body Syst. 58, 151 (2017)
C. Semay, G. Sicorello, Many-Body Forces with the Envelope Theory. Few-Body Syst. 59, 119 (2018)
C. Semay, L. Cimino, Tests of the envelope theory in one dimension. Few-Body Syst. 60, 64 (2019)
R.L. Hall, B. Schwesinger, The complete exact solution to the translation-invariant N -body harmonic oscillator problem. J. Math. Phys. 20, 2481 (1979)
C.T. Willemyns, C. Semay, Some specific solutions to the translation-invariant N -body harmonic oscillator Hamiltonian. J. Phys. Commun. 5, 115002 (2021)
A.A. Lobashev, N.N. Trunov, A universal effective quantum number for centrally symmetric problems. J. Phys. A 42, 345202 (2009)
C. Semay, Numerical tests of the envelope theory for few-boson systems. Few-Body Syst. 56, 149 (2015)
J. Horne, J.A. Salas, K. Varga, Energy and structure of few-boson systems. Few-Body Syst. 55, 1245 (2014)
M.G. Olsson, Universal behavior in excited heavy-light and light-light mesons. Phys. Rev. D 55, 5479 (1997)
C. Semay, F. Buisseret, Two- and three-body calculations within the dominantly orbital state method. Phy. Lett. A 377, 1826 (2013)
C. Semay, Improvement of the envelope theory with the dominantly orbital state method. Eur. Phys. J. Plus 130, 156 (2015)
E. Witten, Baryons in the 1 / N expansion. Nucl. Phys. B 160, 57 (1979)
C. Willemyns, C. Schat, Operator analysis of effective spin-flavor interactions for L= 1 excited baryons. Phys. Rev. D 93, 034007 (2016)
F. Buisseret, C. Semay, Light baryon masses in different large- Nc limits. Phys. Rev. D 82, 056008 (2010)
F. Buisseret, N. Matagne, C. Semay, Spin contribution to light baryons in different large- N limits. Phys. Rev. D 85, 036010 (2012)
M. Gattobigio, A. Kievsky, M. Viviani, Spectra of helium clusters with up to six atoms using soft-core potentials. Phys. Rev. A 84, 052503 (2011)
M. Gattobigio, A. Kievsky, M. Viviani, Six-bodies calculations using the hyperspherical harmonics method. Few-Body Syst. 54, 657 (2013)
A. Kievsky, A. Polls, B. Juliá-Díaz, N.K. Timofeyuk, M. Gattobigio, Few bosons to many bosons inside the unitary window: A transition between universal and nonuniversal behavior. Phys. Rev. A 102, 063320 (2020)
C. Semay, C.T. Willemyns, Quasi Kepler’s third law for quantum many-body systems. Eur. Phys. J. Plus 136, 342 (2021)
C. Semay, Three theorems of quantum mechanics and their classical counterparts. Eur. J. Phys. 39, 055401 (2018)
Fl. Stancu, Group Theory in Subnuclear Physics. Oxford: Oxford University Press (1996)
J.L. Basdevant, A. Martin, J.M. Richard, Improved bounds on many-body Hamiltonians (II). Baryons from mesons in the quark model. Nucl. Phys. B 343, 69 (1990)
J.M. Richard, From mesons to baryons. Phys. Lett. B 100, 515 (1981)
L. Cimino, C. Semay, Compact equations for the envelope theory. Braz. J. Phys. 52, 45 (2022)
N.K. Timofeyuk, Convergence of the hyperspherical-harmonics expansion with increasing number of particles for bosonic systems. Phys. Rev. A 86, 032507 (2012)
N.K. Timofeyuk, D. Baye, Hyperspherical harmonics expansion on lagrange meshes for bosonic systems in one dimension. Few-Body Syst. 58, 157 (2017)
I. Salom, V. Dmitrašinović, Relativistic Three-Body Harmonic Oscillator. In: V. Dobrev (ed) Lie Theory and Its Applications in Physics 473, Springer Proceedings in Mathematics & Statistics 335, Springer Singapore (2020)
A. Kramida, Y. Ralchenko, J. Reader, NIST ASD Team, NIST Atomic Spectra Database (ver. 5.7.1). (National Institute of Standards and Technology, Gaithersburg, MD, 2019), https://physics.nist.gov/asd. Accessed 1 Nov 2021
Y. Chargui, A. Dhahbi, A. Trabelsi, Exact analytical treatment of the asymmetrical spinless Salpeter equation with a Coulomb-type potential. Phys. Scr. 90, 015201 (2015)
M. Ya Azbel, P.M. Platzman, Many-body aspects of the tunneling of electrons from a helium surface. Phys. Rev. Lett. 65, 1376 (1990)
F. Nissen, J. Keeling, Wentzel-Kramers-Brillouin approach and quantum corrections to classical dynamics in the Josephson problem. Phys. Rev. A 81, 063628 (2010)
M. Ferraris, M.M. Giannini, M. Pizzo, E. Santopinto, L. Tiator, A three-body force model for the baryon spectrum. Phys. Lett. B 364, 231 (1995)
V. Dmitrašinović, Cubic Casimir operator of SU C (3) and confinement in the nonrelativistic quark model. Phys. Lett. B 499, 135 (2001)
S. Pepin, Fl. Stancu, Three-body confinement force in hadron spectroscopy. Phys. Rev. D 65, 054032 (2002)
P. Naidon, S. Endo, Efimov physics: a review. Rep. Prog. Phys. 80, 056001 (2017)
P. Nunberg, D. Prosperi, E. Pace, An application of a new harmonic-oscillator basis to the calculation of trinucleon ground-state observables. Nucl. Phys. A 285, 58 (1977)
B. Silvestre-Brac, Spectrum and static properties of heavy baryons. Few-Body Syst. 20, 1 (1996)
B. Silvestre-Brac, R. Bonnaz, C. Semay, F. Brau, Quantum three-body problems using harmonic oscillator bases with different sizes. Internal Report ISN-00-66 (2000) [arXiv:2003.11028]
D.N. Makarov, Coupled harmonic oscillators and their quantum entanglement. Phys. Rev. E 97, 042203 (2018)
J.M. Lévy-Leblond, Generalized uncertainty relations for many-fermion system. Phys. Lett. A 26, 540 (1968)
R.J. Yáñez, W. Van Assche, J.S. Dehesa, Position and momentum information entropies of the D -dimensional harmonic oscillator and hydrogen atom. Phys. Rev. A 50, 3065 (1994)