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Breaking of separability condition for dynamical collective subspace; Onset of quantum chaos in large-amplitude collective motion

Journal Article:

Abstract

It is the purpose of the present paper to study 'global structure' of the state space of an N-body interacting fermion system, which exhibits regular, transient and stochastic phases depending on strength of the interaction. An optimum representation called a dynamical representation plays an essential role in this investigation. The concept of the dynamical representation has been introduced in the quantum theory of dynamical subspace in our previous paper, in order to determine self-consistently an optimum collective subspace as well as an optimum collective Hamiltonian. In the theory, furthermore, dynamical conditions called separability and stability conditions have been provided in order to identify the optimum collective subspace as an approximate invariant subspace of the Hamiltonian. Physical meaning of these conditions are clarified from a viewpoint to relate breaking of them with bifurcation of the collectivity and an onset of quantum chaos from the regular collective motion, by illustrating the general idea with numerical results obtained for a simple soluble model. It turns out that the onset of the stochastic phase is associated with dissolution of the quantum numbers to specify the collective subspace and this dissolution is induced by the breaking of the separability condition in the dynamical representation. (author).
Authors:
Sakata, Fumihiko; [1]  Yamamoto, Yoshifumi; Marumori, Toshio; Iida, Shinji; Tsukuma, Hidehiko
  1. Tokyo Univ., Tanashi (Japan). Inst. for Nuclear Study
Publication Date:
Nov 01, 1989
Product Type:
Journal Article
Reference Number:
JPN-90-003105; EDB-90-073344
Resource Relation:
Journal Name: Progress of Theoretical Physics (Kyoto); (Japan); Journal Volume: 82:5
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; COLLECTIVE MODEL; NONLINEAR PROBLEMS; BOSON EXPANSION; FERMIONS; HAMILTONIANS; HARTREE-FOCK METHOD; MANY-BODY PROBLEM; PHASE TRANSFORMATIONS; TIME DEPENDENCE; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NUCLEAR MODELS; QUANTUM OPERATORS; 653001* - Nuclear Theory- Nuclear Structure, Moments, Spin, & Models
OSTI ID:
6989404
Country of Origin:
Japan
Language:
English
Other Identifying Numbers:
Journal ID: ISSN 0033-068X; CODEN: PTPKA
Submitting Site:
JPN
Size:
Pages: 965-987
Announcement Date:
May 15, 1990

Journal Article:

Citation Formats

Sakata, Fumihiko, Yamamoto, Yoshifumi, Marumori, Toshio, Iida, Shinji, and Tsukuma, Hidehiko. Breaking of separability condition for dynamical collective subspace; Onset of quantum chaos in large-amplitude collective motion. Japan: N. p., 1989. Web. doi:10.1143/PTP.82.965.
Sakata, Fumihiko, Yamamoto, Yoshifumi, Marumori, Toshio, Iida, Shinji, & Tsukuma, Hidehiko. Breaking of separability condition for dynamical collective subspace; Onset of quantum chaos in large-amplitude collective motion. Japan. doi:10.1143/PTP.82.965.
Sakata, Fumihiko, Yamamoto, Yoshifumi, Marumori, Toshio, Iida, Shinji, and Tsukuma, Hidehiko. 1989. "Breaking of separability condition for dynamical collective subspace; Onset of quantum chaos in large-amplitude collective motion." Japan. doi:10.1143/PTP.82.965. https://www.osti.gov/servlets/purl/10.1143/PTP.82.965.
@misc{etde_6989404,
title = {Breaking of separability condition for dynamical collective subspace; Onset of quantum chaos in large-amplitude collective motion}
author = {Sakata, Fumihiko, Yamamoto, Yoshifumi, Marumori, Toshio, Iida, Shinji, and Tsukuma, Hidehiko}
abstractNote = {It is the purpose of the present paper to study 'global structure' of the state space of an N-body interacting fermion system, which exhibits regular, transient and stochastic phases depending on strength of the interaction. An optimum representation called a dynamical representation plays an essential role in this investigation. The concept of the dynamical representation has been introduced in the quantum theory of dynamical subspace in our previous paper, in order to determine self-consistently an optimum collective subspace as well as an optimum collective Hamiltonian. In the theory, furthermore, dynamical conditions called separability and stability conditions have been provided in order to identify the optimum collective subspace as an approximate invariant subspace of the Hamiltonian. Physical meaning of these conditions are clarified from a viewpoint to relate breaking of them with bifurcation of the collectivity and an onset of quantum chaos from the regular collective motion, by illustrating the general idea with numerical results obtained for a simple soluble model. It turns out that the onset of the stochastic phase is associated with dissolution of the quantum numbers to specify the collective subspace and this dissolution is induced by the breaking of the separability condition in the dynamical representation. (author).}
doi = {10.1143/PTP.82.965}
journal = {Progress of Theoretical Physics (Kyoto); (Japan)}
volume = {82:5}
journal type = {AC}
place = {Japan}
year = {1989}
month = {Nov}
}