Title | Quasimomentum of an elementary excitation for a system of point bosons under zero boundary conditions |
Publication Type | Journal Article |
Year of Publication | 2019 |
Authors | Tomchenko, MD |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2019.12.049 |
Issue | 12 |
Section | Physics |
Pagination | 49-56 |
Date Published | 12/2019 |
Language | English |
Abstract | As is known, an elementary excitation of a many-particle system with boundaries is not characterized by a definite momentum. We obtain the formula for the quasimomentum of an elementary excitation for a one-dimensional system of N spinless point bosons under zero boundary conditions (BCs). In this case, we use Gaudin's solutions obtained with the help of the Bethe ansatz. We have also found the dispersion laws of the particle-like and hole-like excita tions under zero BCs. They coincide with the known dispersion laws obtained under periodic BCs. |
Keywords | elementary excitation, point bosons, quasimomentum, zero boundary conditions |
1. Girardeau, M. (1960). Relationship between systems of impenetrable bosons and fermions in one dimension. J. Math. Phys. (N.Y.), 1, Iss. 6, pp. 516-523. Doi: https://doi.org/10.1063/1.1703687
2. Lieb, E. H. & Liniger, W. (1963). Exact analysis of an interacting Bose gas. I. The general solution and the ground state. Phys. Rev., 130, Iss. 4, pp. 1605-1616. Doi: https://doi.org/10.1103/PhysRev.130.1605
3. Lieb, E. H. (1963). Exact analysis of an interacting Bose gas. II. The excitation spectrum. Phys. Rev., 130, Iss. 4, pp. 1616-1624. Doi: https://doi.org/10.1103/PhysRev.130.1616
4. Yang, C. N. & Yang, C. P. (1969). Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. J. Math. Phys. (N.Y.), 10, Iss. 7, pp. 1115-1122. Doi: https://doi.org/10.1063/1.1664947
5. Gaudin, M. (1971). Boundary energy of a Bose gas in one dimension. Phys. Rev. A, 4, Iss. 1, pp. 386-394. Doi: https://doi.org/10.1103/PhysRevA.4.386
6. Takahashi, M. (1999). Thermodynamics of One-Dimensional Solvable Models. Cambridge: Cambridge Univ. Press. Doi: https://doi.org/10.1017/CBO9780511524332
7. Tomchenko, M. (2015). Point bosons in a one-dimensional box: the ground state, excitations and thermodynamics. J. Phys. A: Math. Theor., 48, No. 36, 365003. Doi: https://doi.org/10.1088/1751-8113/48/36/365003
8. Batchelor, M. T., Bortz, M., Guan X. W. & Oelkers, N. (2006). Collective dispersion relations for the one-dimensional interacting two-component Bose and Fermi gases. J. Stat. Mech., No. 3, P03016. Doi: https://doi.org/10.1088/1742-5468/2006/03/P03016
9. Lang, G., Hekking, F. & Minguzzi, A. (2017). Ground-state energy and excitation spectrum of the Lieb—Liniger model: accurate analytical results and conjectures about the exact solution. Sci. Post. Phys., 3, Iss. 1, 003. Doi: https://doi.org/10.21468/SciPostPhys.3.1.003
10. Gu, S.J., Li, Y.Q. & Ying, Z.J. (2001). Trapped interacting two-component bosons in one dimension. J. Phys. A: Math. Gen., 34, No. 42, pp. 8995-9008. Doi: https://doi.org/10.1088/0305-4470/34/42/317
11. Tomchenko, M. (2017). Uniqueness of the solution of the Gaudin’s equations, which describe a one-dimensional system of point bosons with zero boundary conditions. J. Phys. A: Math. Theor., 50, No. 5, 055203. Doi: https://doi.org/10.1088/1751-8121/aa5197
12. Tomchenko, M. (2019). Nature of Lieb’s “hole” excitations and two-phonon states of a Bose gas. arXiv: 1905.03712 [cond-mat.quant-gas].
13. Bogoliubov, N. N. (1947). On the theory of superfluidity. J. Phys. USSR, 11, No. 1, pp. 23-32.
14. Cazalilla, M. A. (2004). Bosonizing one-dimensional cold atomic gases. J. Phys. B: At. Mol. Opt. Phys., 37, No. 7, pp. S1-S48. Doi: https://doi.org/10.1088/0953-4075/37/7/051
15. Tomchenko, M. D. (2019). Low-lying energy levels of a one-dimensional weakly interacting Bose gas under zero boundary conditions. Ukr. J. Phys., 64, No. 3, pp. 250-265. Doi: https://doi.org/10.15407/ujpe64.3.250