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| dc.contributor.author | Chang, B. Tsu‐shen | en_US |
| dc.date.accessioned | 2010-05-06T22:54:56Z | |
| dc.date.available | 2010-05-06T22:54:56Z | |
| dc.date.issued | 1971-06 | en_US |
| dc.identifier.citation | Chang, B. Tsu‐Shen (1971). "Density and Current Density as Coordinates for a System of Interacting Bosons at Absolute Zero." Journal of Mathematical Physics 12(6): 971-980. <http://hdl.handle.net/2027.42/70916> | en_US |
| dc.identifier.uri | https://hdl.handle.net/2027.42/70916 | |
| dc.description.abstract | The quantum field Hamiltonian expressed in terms of density and current density variables has been employed together with the equal‐time commutation relations among these variables to find the ground state energy and the density fluctuation excitation spectrum of a system of interacting bosons at T = 0°K. The approximation involved consists in assuming that the density fluctuation in space is small compared with the average density. The results easily obtained in the lowest‐order approximation agree with those of Bogoliubov. However, in our treatment no condensation of particles in zero‐momentum state is assumed or apparent. A connection between the present treatment and the quantum hydrodynamic approach to the irrotational flow of a Bose liquid has been made. | en_US |
| dc.format.extent | 3102 bytes | |
| dc.format.extent | 623468 bytes | |
| dc.format.mimetype | text/plain | |
| dc.format.mimetype | application/pdf | |
| dc.publisher | The American Institute of Physics | en_US |
| dc.rights | © The American Institute of Physics | en_US |
| dc.title | Density and Current Density as Coordinates for a System of Interacting Bosons at Absolute Zero | en_US |
| dc.type | Article | en_US |
| dc.subject.hlbsecondlevel | Physics | en_US |
| dc.subject.hlbtoplevel | Science | en_US |
| dc.description.peerreviewed | Peer Reviewed | en_US |
| dc.contributor.affiliationum | Department of Physics, University of Michigan, Ann Arbor, Michigan 48104 | en_US |
| dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/70916/2/JMAPAQ-12-6-971-1.pdf | |
| dc.identifier.doi | 10.1063/1.1665691 | en_US |
| dc.identifier.source | Journal of Mathematical Physics | en_US |
| dc.identifier.citedreference | L. D. Landau, J. Phys. (USSR) 5, 71 (1941); 11, 91 (1941). | en_US |
| dc.identifier.citedreference | R. P. Feynman, Phys. Rev. 91, 1291 (1953); 94, 262 (1954). Experimentally, see D. G. Henshaw and A. D. B. Woods, Phys. Rev. 121, 1266 (1961). | en_US |
| dc.identifier.citedreference | N. N. Bogoliubov, J. Phys. (USSR) 11, 23 (1947). | en_US |
| dc.identifier.citedreference | T. D. Lee, K. Huang, and C. N. Yang, Phys. Rev. 106, 1135 (1957). | en_US |
| dc.identifier.citedreference | K. A. Brueckner and K. Sawada, Phys. Rev. 106, 1117 (1957). | en_US |
| dc.identifier.citedreference | S. T. Beliaev, Zh. Eksp. Teor. Fiz. 34, 417 (1958) [Sov. Phys. JETP 7, 289 (1958)]. | en_US |
| dc.identifier.citedreference | N. M. Hugenholtz and D. Pines, Phys. Rev. 116, 489 (1959). | en_US |
| dc.identifier.citedreference | D. Bohm and B. Salt, Rev. Mod. Phys. 39, 894 (1967). | en_US |
| dc.identifier.citedreference | R. F. Dashen and D. H. Sharp, Phys. Rev. 165, 1857 (1968); see also D. H. Sharp, ibid. 1867 (1968). | en_US |
| dc.identifier.citedreference | R. Kronig and A. Thellung, Physica 18, 749 (1952). See also F. London, Superfluids (Dover, New York, 1964), Vol. II, pp. 114–18. | en_US |
| dc.identifier.citedreference | D. D. H. Yee, Phys. Rev. 184, 196 (1969). | en_US |
| dc.identifier.citedreference | Only after reading with much appreciation the referee’s comments about the present work, did the author realize that such a functional representation has been independently obtained by J. Grodnik and D. H. Sharp, and already appeared in their paper, Phys. Rev. D 1, 1531 (1970). While it provides a somewhat different and more formal treatment, that paper supports and amplifies our results in this section except our original functional representation for jα,l,jα,l, which did not contain the term ½lαρ1.12lαρ1. As was expected by the referee and will be seen in later sections, inclusion of this term does not affect appreciably our original calculations obtained without it in the lowest approximation; nor does it affect the formal connection of our method with the quantum hydrodynamic approach to the irrotational flow of the Bose liquid. | en_US |
| dc.identifier.citedreference | So the approximation (18) does not affect the validity of (24); it just enables us to ignore the other cases of the general relation (12). | en_US |
| dc.identifier.citedreference | See the Heisenberg equation of motion for ρk(t),ρk(t), as put in the form (43), Sec. 3. | en_US |
| dc.identifier.citedreference | The minimization of E0E0 with respect to λkλk involves calculating the average of ρkρ−kρkρ−k over the trial wavefunctional (28). This average ⟨rgr;kρ−k⟩⟨rgr;kρ−k⟩ can be easily calculated, as done by D. Bohm and D. Pines, Phys. Rev. 85, 338 (1952), through introducing a pair of real variables rkrk and θkθk to replace the pair of complex variables ρkρk and ρ−kρ−k with the relations ρk = rkeiθk,ρk=rkeiθk, ρ−k = rke−θk.ρ−k=rke−θk. Thus, noting r−k2 = rk2,r−k2=rk2, we have ⟨ρkρ−k⟩=∫∫rk2exp(−4λkrk2)∣J∣drkdθkint;∫exp(−4λkrk2)∣J∣drkdθk. ∣J∣∣J∣ here denotes the absolute value of the Jacobian for the transformation from the pair ρkρk and ρ−kρ−k to the new variables, and is 2rk.2rk. In this way, one finds ⟨ρkρ−k⟩ = .⟨ρkρ−k⟩=14λk. Similar kinds of calculations ⟨ρknρ−kn⟩(n = any positive integer)⟨ρknρ−kn⟩(n=anypositiveinteger) will be of frequent use. | en_US |
| dc.identifier.citedreference | The relation (40) can also be directly obtained from (39) by aid of the two commutation relations [ρk,ρl] = 0[ρk,ρl]=0 and [ρk,jα,l ≠ 0] = kαρavδ−k⋅l.[ρk,jα,l≠0]=kαρavδ−k⋅l. The latter relation is only approximately valid as pointed out previously in Sec. 3. It is connected with using the approximate functional representation for jα,−k ≠ 0,(25).jα,−k≠0,(25). | en_US |
| dc.identifier.citedreference | Although, in the hydrodynamic case, the two‐body interaction potential has to be interpreted as the average potential among particles, as mentioned by E. P. Gross. See J. Math. Phys. 4, 195 (1963), where the author used the conventional quantum field Hamiltonian in terms of ψ and ψ+ψ+ to discuss the hydrodynamics of a Bose liquid. | en_US |
| dc.identifier.citedreference | A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice‐Hall, New York, 1963), p. 229. | en_US |
| dc.identifier.citedreference | T. T. Wu, Phys. Rev. 115, 1390 (1959). | en_US |
| dc.identifier.citedreference | T. D. Lee and C. N. Yang, Phys. Rev. 105, 1119 (1957). | en_US |
| dc.identifier.citedreference | Although the range of validity of our approximation was considered before only for the ground state, it holds also for the low‐lying excited states when N is large. | en_US |
| dc.identifier.citedreference | J. Grodnik and D. H. Sharp, Phys. Rev. D 1, 1546 (1970). | en_US |
| dc.owningcollname | Physics, Department of |
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