Abstract
Embedded GOE generated by random two-body interactions in the presence of a one-body mean-field for spinless boson systems is introduced [it is called BEGOE(1+2) with ‘B’ for bosons] and a method for its construction is given. Using unitary decomposition and trace propagation, formulas for the lowest four moments of the eigenvalue density generated by a general one plus two-body interaction are obtained. These are used to show that in the dense limit, the eigenvalue density for BEGOE(1+2) will approach Gaussian form and for strong enough two-body interaction there is average fluctuation separation. In addition, using numerical calculations, it is shown that BEGOE(1+2) admits three transition (or chaos) markers just as EGOE(1+2) and EGOE(1+2)-s.
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References
T. Asaga, L. Benet, T. Rupp, H.A. Weidenmüller, Spectral properties of the k-body embedded Gaussian ensembles of random matrices for bosons. Ann. Phys. (N.Y.) 298, 229–247 (2002)
F. Iachello, A. Arima, The Interacting Boson Model (Cambridge University Press, Cambridge, 1987)
F. Iachello, R.D. Levine, Algebraic Theory of Molecules (Oxford University Press, New York, 1995)
A. Frank, P. Van Isacker, Algebraic Methods in Molecular and Nuclear Physics (Wiley, New York, 1994)
V.K.B. Kota, Group theoretical and statistical properties of interacting boson models of atomic nuclei: recent developments, in Focus on Boson Research, ed. by A.V. Ling (Nova Science Publishers Inc., New York, 2006), pp. 57–105
K. Patel, M.S. Desai, V. Potbhare, V.K.B. Kota, Average-fluctuations separation in energy levels in dense interacting boson systems. Phys. Lett. A 275, 329–337 (2000)
M. Vyas, Some studies on two-body random matrix ensembles, Ph.D. Thesis, M.S. University of Baroda, India (2012)
T. Asaga, L. Benet, T. Rupp, H.A. Weidenmüller, Non-ergodic behaviour of the k-body embedded Gaussian random ensembles for bosons. Europhys. Lett. 56, 340–346 (2001)
N.D. Chavda, V. Potbhare, V.K.B. Kota, Statistical properties of dense interacting Boson systems with one plus two-body random matrix ensembles. Phys. Lett. A 311, 331–339 (2003)
N.D. Chavda, V. Potbhare, V.K.B. Kota, Strength functions for interacting bosons in a mean-field with random two-body interactions. Phys. Lett. A 326, 47–54 (2004)
M. Vyas, N.D. Chavda, V.K.B. Kota, V. Potbhare, One plus two-body random matrix ensembles for boson systems with F-spin: analysis using spectral variances. J. Phys. A, Math. Theor. 45, 265203 (2012)
V.K.B. Kota, V. Potbhare, Shape of the eigenvalue distribution for bosons in scalar space. Phys. Rev. C 21, 2637–2642 (1980)
V.K.B. Kota, A symmetry for the widths of the eigenvalue spectra of boson and fermion systems. J. Phys. Lett. 40, L579–L582 (1979)
V.K.B. Kota, Studies on the goodness of IBA group symmetries: centroids, widths and partial widths for irreducible representations of IBA group symmetries. Ann. Phys. (N.Y.) 134, 221–258 (1981)
P. Cvitanovic, A.D. Kennedy, Spinors in negative dimensions. Phys. Scr. 26, 5–14 (1982)
R.J. Leclair, R.U. Haq, V.K.B. Kota, N.D. Chavda, Power spectrum analysis of the average-fluctuation density separation in interacting particle systems. Phys. Lett. A 372, 4373–4378 (2008)
B.J. Dalton, S.M. Grimes, J.P. Vary, S.A. Williams (eds.), Moment Methods in Many Fermion Systems (Plenum, New York, 1980)
S.S.M. Wong, Nuclear Statistical Spectroscopy (Oxford University Press, New York, 1986)
N.D. Chavda, Study of random matrix ensembles for bosonic systems, Ph.D. Thesis, M.S. University of Baroda, Vadodara, India (2004)
V.K.B. Kota, R. Sahu, Breit-Wigner to Gaussian transition in strength functions, arXiv:nucl-th/0006079
N.D. Chavda, V.K.B. Kota, V. Potbhare, Thermalization in one- plus two-body ensembles for dense interacting boson systems. Phys. Lett. A 376, 2972–2976 (2012)
F. Borgonovi, I. Guarneri, F.M. Izrailev, G. Casati, Chaos and thermalization in a dynamical model of two interacting particles. Phys. Lett. A 247, 140–144 (1998)
M. Rigol, V. Dunjko, M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems. Nature (London) 452, 854–858 (2008)
V.V. Flambaum, F.M. Izrailev, Statistical theory of finite Fermi systems based on the structure of chaotic eigenstates. Phys. Rev. E 56, 5144–5159 (1997)
V.V. Flambaum, G.F. Gribakin, F.M. Izrailev, Correlations within eigenvectors and transition amplitudes in the two-body random interaction model. Phys. Rev. E 53, 5729–5741 (1996)
V.K.B. Kota, A. Relaño, J. Retamosa, M. Vyas, Thermalization in the two-body random ensemble, J. Stat. Mech. P10028 (2011)
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Kota, V.K.B. (2014). Embedded GOE Ensembles for Interacting Boson Systems: BEGOE(1+2) for Spinless Bosons. In: Embedded Random Matrix Ensembles in Quantum Physics. Lecture Notes in Physics, vol 884. Springer, Cham. https://doi.org/10.1007/978-3-319-04567-2_9
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DOI: https://doi.org/10.1007/978-3-319-04567-2_9
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