Approximate solutions for N-body Hamiltonians with identical particles in D dimensions

Sicorello

2018

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Many-body forces are sometimes a relevant ingredient in various fields, such as atomic, nuclear or hadronic physics. Their precise structure is generally difficult to uncover. So, phenomenological effective forces are often used in practice. Nevertheless, they are always very heavy to treat numerically. The envelope theory, also known as the auxiliary field method, is a very efficient technique to obtain approximate, but reliable, solutions of many-body systems interacting via one-or two-body forces. It is adapted here to allow the treatment of a special form of many-body forces. In the most favourable cases, the approximate eigenvalues are analytical lower or upper bounds. Otherwise, numerical approximation can always be computed. Two examples of many-body forces are presented, and the critical coupling constants for generic attractive many-body potentials are computed. Finally, a semiclassical interpretation is given for the generic formula of the eigenvalues. *

Section: Critical Coupling Constantssupporting

confidence: 88%

Section: Envelope Theory Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Many-Body Forces with the Envelope Theory

Sicorello

2018

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“…Computations for D = 1 show that formulas obtained in [4,6] are still valid, but with the momentums and the positions of particles which are now scalar quantities, and the global quantum number Q with the centre of mass removed which is defined by ( = 1)…”

Section: Introductionmentioning

confidence: 98%

“…Then, the approximate energy E can be computed with (5). An upper bound is obtained if [2,4]. A lower bound is obtained if both "≥" are replaced by "≤".…”

Section: Introductionmentioning

confidence: 99%

Tests of the Envelope Theory in One Dimension

Cimino

2019

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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. *

Numerical Tests of the Envelope Theory for Few-Boson Systems

2015

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The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for N identical particles in D-dimension. The accuracy of this method is tested by computing the ground state of N identical bosons for various systems. A method is proposed to improve the quality of the approximations by modifying the characteristic global quantum number of the method.