Prog. Theor. Phys. Vol. 66 No. 3 (1981) pp. 831-851

[ Full Text PDF : FREE ACCESS (712K) ]

One-Dimensional Many Boson System. IV

— Condensation and Excitation Energy —

Shosuke Sasaki and Takeji Kebukawa

Department of Physics, College of General Education, Osaka University, Toyonaka 560

(Received April 21, 1981)

Abstract:

The analysis for a one-dimensional many boson system with a repulsive delta-function potential is continued. It is shown that the expectation value of the number a₀^*a₀ of bare bosons with zero momentum for the exact ground state ∣Ψ_0,0,\dots,0> is negligibly small compared with the total number n in the limit of an infinitely large coupling constant g; i.e., <Ψ_0,\dots,0∣a₀^*a₀∣Ψ_0,\dots,0>/n→0(for n→∞, g→∞). This result shows a striking contrast to the result <Ψ_0,\dots,0∣A₀^*A₀∣Ψ_0,\dots,0>/n=1 for an arbitrary g, where A₀^*A₀ indicates the number operator of exactly dressed bosons with zero momentum. It is clarified that the energy of a dressed boson strongly depends upon the number distribution {n_q} of the other dressed bosons in the system. The excitation energy of a dressed boson has phonon character when n₀/n ≠0, where n₀ denotes the number of dressed bosons with zero momentum. When n₀/n tends to zero, the phonon character disappears in a drastic way. Some characteristic phenomena in liquid helium II are discussed on the basis of the results of our previous papers and the present paper.

URL : http://ptp.ipap.jp/link?PTP/66/831/
DOI : 10.1143/PTP.66.831

References:

S. Sasaki and T. Kebukawa, Prog. Theor. Phys. 65 (1981), 1198[PTP].
S. Sasaki and T. Kebukawa, Prog. Theor. Phys. 65 (1981), 1217[PTP].
S. Sasaki and T. Kebukawa, Prog. Theor. Phys. 65 (1981), 1798[PTP].
A. Lenard, J. Math. Phys. 5 (1964), 930[CrossRef].
T. D. Shultz, J. Math. Phys. 4 (1963), 666[CrossRef].
M. Girardeau, J. Math. Phys. 1 (1960), 516[CrossRef].
V. Grenander and G. Szego, Toeplitz Forms and Their Applications (University of California Press, Berkley, California, 1958) (see page 75-80).
H. London, Proc. R. Soc. A 171 (1939), 484.
L. Landau, J. of Phys. 5 (1941), 71; ibid. 11 (1947), 91.
S. Sasaki and K. Matsuda, Prog. Theor. Phys. 56 (1976), 375[PTP].
R. A. Cowley and A. D. B. Woods, Can. J. Phys. 49 (1971), 177.
H. A. Mook, R. Scherm and M. K. Wilkinson, Phys. Rev. A 6 (1962), 2278[APS].
L. J. Rodriguez, H. A. Gersch and H. A. Mook, Phys. Rev. A 9 (1974), 2085[APS].
O. K. Harling, Phys. Rev. A 3 (1971), 1073[APS].
A. G. Gibbs and O. K. Harling, Phys. Rev. A 3 (1971), 1713[APS].

Citing Article(s) :

Journal of the Physical Society of Japan 59 (1990) pp. 1593-1599 :
Thermodynamic Functions of One-Dimensional Many-Boson System

Shosuke Sasaki and Tosaku Kunimasa
Progress of Theoretical Physics Vol. 73 No. 5 (1985) pp. 1098-1121 :
One-Dimensional Many-Fermion System. I

Takeji Kebukawa
Progress of Theoretical Physics Vol. 81 No. 6 (1989) pp. 1158-1173 :
Energy Spectrum of One-Dimensional Many Boson System

Shosuke Sasaki