A bridge between hyperspherical and integro-differential approaches to the many-body bound states

Ripelle, M. Fabre de la

doi:10.1007/bf01076710

Cited by 55 publications

(17 citation statements)

References 7 publications

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“…In absence of any confinig potential the center of mass behaves as a free particle in laboratory frame and we set its energy as zero. Hence, after elimination of the center of mass motion and using standard Jacobi coordinates, defined as [37][38][39] …”

Section: Methodology:many-body Calculation With Potential Harmonimentioning

confidence: 99%

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Level-spacing statistics and spectral correlations in diffuse van der Waals clusters

Haldar¹,

Chakrabarti²,

Chavda

et al. 2014

Phys. Rev. A

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We present a statistical analysis of eigenenergies and discuss several measures of spectral fluctuations and spectral correlations for the van der Waals clusters of different sizes. We show that the clusters become more and more complex with increase in cluster size. We study nearest-neighbour level spacing distribution P (s), the level number variance Σ 2 (L), and the Dyson-Mehta ∆3−statistics for various cluster sizes. For large clusters we find that although the Bohigas-Giannoni-Schmit (BGS) conjecture seems to be valid, it does not exhibit true signatures of quantum chaos. However contrasting conjecture of Berry and Tabor is observed with smaller cluster size. For small number of bosons, we observe the existence of large number of quasi-degenerate states in low-lying excitation which exhibits the Shnirelman peak in P (s) distribution. We also find a narrow region of intermediate spectrum which can be described by semi-Poisson statistics whereas the higher levels are regular and exhibit Poisson statistics. These observations are further supported by the analysis of the distribution of the ratio of consecutive level spacings P (r) which is independent of unfolding procedure and thereby provides a tool for more transparent comparison with experimental findings than P (s). Thus our detail numerical study clearly shows that the van der Waals clusters become more correlated with the increase in cluster size.

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Section: Methodology:many-body Calculation With Potential Harmonimentioning

confidence: 99%

“…f Kl is a constant and represents the overlap of the PH for interacting partition with the sum of PHs corresponding to all partitions [39]. The potential matrix element V KK ′ (r) is given by…”

Section: Methodology:many-body Calculation With Potential Harmonimentioning

confidence: 99%

Level-spacing statistics and spectral correlations in diffuse van der Waals clusters

Haldar¹,

Chakrabarti²,

Chavda

et al. 2014

Phys. Rev. A

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“…After eliminating the center of mass motion by using the standard Jacobi vectors [32][33][34], defined by…”

Section: A Many-body Calculation With Potential Harmonic Basismentioning

confidence: 99%

“…, and β = l + 1/2; f Kl is a constant and represents the overlap of the PH for the interacting partition with the sum of PHs corresponding to all partitions [34]. The potential matrix element V KK (r) is given by…”

Section: A Many-body Calculation With Potential Harmonic Basismentioning

confidence: 99%

Spectral fluctuation and1/fαnoise in the energy level statistics of interacting trapped bosons

Roy¹,

Chakrabarti

Biswas

et al. 2012

Phys. Rev. E

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It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by 1/f α noise with 1 α 2. The system of interacting trapped bosons is inhomogeneous and complex. The presence of an external harmonic trap makes it more interesting as, in the atomic trap, the bosons occupy partly degenerate single-particle states. Earlier theoretical and experimental results show that at zero temperature the low-lying levels are of a collective nature and high-lying excitations are of a single-particle nature. We observe that for few bosons, the P (s) distribution shows the Shnirelman peak, which exhibits a large number of quasidegenerate states. For a large number of bosons the low-lying levels are strongly affected by the interatomic interaction, and the corresponding level fluctuation shows a transition to a Wigner distribution with an increase in particle number. It does not follow Gaussian orthogonal ensemble random matrix predictions. For high-lying levels we observe the uncorrelated Poisson distribution. Thus it may be a very realistic system to prove that 1/f α noise is ubiquitous in nature.

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“…We assume a spin-independent potential and for fermions the wave function must be antisymmetric under exchange of two nucleons. At low energies the threenucleon system is described by a spin-isospin fully antisymmetric state multiplied by a fully symmetric function of the coordinates, which can be written as a sum of three Faddeev amplitudes [19]. The problem is solved by applying the adiabatic- It behaves asymptotically as u[0] r~ sin(kr + 6o -3rc/2), (6.15) where the phase shift 6 0 vanishes when the interaction fades out.…”

Section: Scattering By Non-hypercentral Potentialsmentioning

confidence: 99%

Green function and scattering amplitudes in many-dimensional space

Fabre de la Ripelle

1993

Few-Body Systems

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Abstract. Methods for solving scattering are studied in many-dimensional space. Green function and scattering amplitudes are given in terms of the required asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many-dimensional space. Phase-shift analyses are performed for hypercentral potentials and for non-hypercentral potentials by use of the hyperspherical adiabatic approximation.

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A bridge between hyperspherical and integro-differential approaches to the many-body bound states

Cited by 55 publications

References 7 publications

Level-spacing statistics and spectral correlations in diffuse van der Waals clusters

Level-spacing statistics and spectral correlations in diffuse van der Waals clusters

Spectral fluctuation and1/fαnoise in the energy level statistics of interacting trapped bosons

Green function and scattering amplitudes in many-dimensional space

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