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Journal

2004 | 2 | 3 | 420-455

Article title

Quantum diffusion

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EN

Abstracts

EN
Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities etc.) and they turn into quasiparticles of a new type-defectons, which are characterized not by their position in the crystal lattice but by their quasimomentum and dispersion law. Defecton-defecton and defecton-phonon scattering are considered and an interpolation formula for the diffusion coefficient valid in all interesting temperature and concentration regions is presented. A comparison with the experimental data is made. Some alternative points of view are discussed in detail and the inconsistency of the Kisvarsanyi-Sullivan theory is shown.

Keywords

Publisher

Journal

Year

Volume

2

Issue

3

Pages

420-455

Physical description

Dates

published
1 - 9 - 2004
online
1 - 9 - 2004

Contributors

  • Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko Chaussee, 1784, Sofia, Bulgaria

References

  • [1] D.I. Pushkarov: “Microscopic Quantum Theory of Defects at Low Temperatures”, Zh. Eksp. Teor. Fiz., Vol. 59, (1970), pp. 1755–1764; Sov. Phys. JETP, Vol. 32, (1971), pp. 954–958.
  • [2] D.I. Pushkarov: Quasiparticle Theory of Defectons in Solids, World Scientific, Singapore-New Jersey-London-Hong Kong, 1990.
  • [3] D.I. Pushkarov: Defektony v kristallah; metod kvazichastic v kvantovoj teorii defektov, Nauka, Moscow, (1993), (in Russian).
  • [4] D.I. Pushkarov: “Defecton Kinetics in Quantum Crystals”, Fiz. Nizk. Temp., Vol.1, (1975), pp.586–589; Sov. J. Low. Temp. Phys., Vol. 1, (1975), pp. 283–285.
  • [5] A.E. Meierovich: “Internal friction in solid helium”, Zh. Eksp. Teor. Fiz., Vol. 67, No. 2(8), (1974), pp. 744–755.
  • [6] D.I. Pushkarov and Kh.I. Pushkarov: “Delocalization and Diffusion of Defects in Quantum Crystals at T=0”, Phys. Stat. Sol. (b), Vol. 67, (1975), pp. K23-K25. http://dx.doi.org/10.1002/pssb.2220670147[Crossref]
  • [7] B.N. Eselson, V.G. Ivantsov, V.A. Koval, E.Ya. Rudavskii and I.A. Serbin: Properties of Liquid and Solid Helium. Solutions 3He−4He, Naukova Dumka, Kiev, 1982 (in Russian).
  • [8] B.N. Eselson, V.N. Grigorjev, V.G. Ivantsov, V.A. Koval, E.Ya. Rudavskii and I.A. Serbin: Solutions of He3−He4 Quantum Liquids, Nauka, Moscow, 1973 (in Russian).
  • [9] I.F. Silvera: “The solid molecular hydrogens in the condensed phase: Fundamentals and static properties”, Rev. Mod. Phys., Vol.52, (1980), pp.393–452 http://dx.doi.org/10.1103/RevModPhys.52.393[Crossref]
  • [10] A. Abragam and M. Goldman: Nuclear Magnetism: Order and Disorder, Clarendon Press, Oxford, 1982.
  • [11] D.I. Pushkarov: “On the Defecton Statistics in Quantum Crystals”, Phys. Stat. Sol. (b), Vol.133, (1986), pp.525–531. http://dx.doi.org/10.1002/pssb.2221330212[Crossref]
  • [12] A.F. Andreev and I.M. Lifshitz: “Quantum theory of crystal defects”, Zh. Eksp. Teor. Fiz., Vol.56, (1969), pp.2057–2068.
  • [13] R.A. Guyer and L.I. Zane: “Mass-Fluctuation Waves”, Phys. Rev. Lett., Vol.24, (1970), pp.660–663. http://dx.doi.org/10.1103/PhysRevLett.24.660[Crossref]
  • [14] V.N. Grigoriev, B.N. Eselson and V.A. Mikheev: “Spin diffusion in solid He3−He4 solutions”, Zh. Eksp. Teor. Fiz., Vol.64, (1973), pp.608–611.
  • [15] V.N. Grigoriev, B.N. Eselson and V.A. Mikheev: “Diffusion of He3 in the body-centered cubic and hexagonal close packed phases of isotopic helium solutions”, Zh. Eksp. Teor. Fiz., Vol.66, (1974), pp.321–329; Sov. Phys.-JETP, Vol. 39, (1974), p. 153.
  • [16] C.P. Flynn and A.M. Stoneham: “Quantum Theory of Diffusion with Application to Light Interstitials in Metals”, Phys. Rev., Vol. 1, (1970), pp. 3966–3978. http://dx.doi.org/10.1103/PhysRevB.1.3966[Crossref]
  • [17] D.I. Pushkarov: Quantum Theory of Defects in Crystals at Low Temp., Thesis (PhD), Moscow Univ., 1972.
  • [18] D.I. Pushkarov: “Concerning Impuriton Diffusion in Solid4He”, Pis'ma v Zh. Eksp. Teor. Fiz., Vol.19, (1974), pp.751–754; Sov. Phys. JETP, Vol. 19, (1974), pp. 386–387.
  • [19] D.I. Pushkarov: “Defecton Diffusion in Quantum Crystals”, Zh. Eksp. Teor. Fiz., Vol.68, (1975), pp.1471–1476; Sov. Phys. JETP, Vol. 41, (1976), pp. 735–737.
  • [20] D.S. Miyoshi, R.M. Cotts, A.S. Greenberg and R.C. Richardson: “Nuclear Magnetic Resonance in Solid Helium-3-Helium-4 Mixtures between 0.3 and 2.0 K”, Phys. Rev. A, Vol. 2, (1970), pp. 870–882. http://dx.doi.org/10.1103/PhysRevA.2.870
  • [21] R.G. Richards, J. Pope and A. Widom: “Evidence for Isotopic Impuritons in Solid Helium”, Phys. Rev. Lett., Vol.29, (1972), pp.708–711. http://dx.doi.org/10.1103/PhysRevLett.29.708[Crossref]
  • [22] V.N. Grigoriev, B.N. Eselson, V.A. Mikheev and Yu.E. Shulman: “Quantum Diffusion of3He Impurities in Solid 4He”, Pis'ma v Zh. Eksp. Teor. Fiz., Vol.17, (1973), pp.25–27.
  • [23] V.N. Grigoriev, B.N. Eselson et al.: “3He impurity excitations in solid4He”, J. Low Temp. Phys., Vol.13, (1973), pp.65–79. http://dx.doi.org/10.1007/BF00654398[Crossref]
  • [24] A. Landesman and J.M. Winter: “Calculation of the Diffusion Rate of3He Impurities in Solid4He”, In: K.D. Timmerhaus, W.J. O'Sullivan and E.F. Hammel (Eds), Low Temperature Physics-LT 13, Vol. 2, Quantum Crystals and Magnetism, Plenum Press, New York-London, 1974, pp. 73–78.
  • [25] W. Huang, H.A. Goldberg and R.A. Guyer: “Quantum-crystal alloys I: Massfluctuation waves”, Phys. Rev. B, Vol. 11, (1975), pp. 3374–3392. http://dx.doi.org/10.1103/PhysRevB.11.3374[Crossref]
  • [26] A. Landesman: “Theory of magnetic relaxation for dilute 3He atoms tunneling in hep solid 4He”, Phys. Lett. A, Vol. 54, (1975), pp. 137–139 http://dx.doi.org/10.1016/0375-9601(75)90839-7[Crossref]
  • [27] Y. Yamashita: “Diffusion of He3 Impurities in Solid He4”, J. Phys. Soc. Japan, Vol.37, (1974), pp.1210–1214. http://dx.doi.org/10.1143/JPSJ.37.1210
  • [28] A.R. Allen, M.G. Richards and J. Schratter: “Anomalous Temperature Dependence of D andT 2 for Dilute Solutions of3He in4He”, J. Low Temp Phys., Vol.47, (1982), pp.289–320. http://dx.doi.org/10.1007/BF00683732[Crossref]
  • [29] V.A. Slusarev et al.: “Quantum Diffusion of He3 in Solid He4. I. The Role of Impurity interaction Anisotropy”, Fiz. Nizkih Temp., Vol.3, (1977), pp.1229–1239.
  • [30] D.I. Pushkarov and Kh.I. Pushkarov: “Defecton Diffusion in the Very Quantum Region”, Phys. Stat. Sol. (b), Vol. 74, (1976), pp. K97-K100. http://dx.doi.org/10.1002/pssb.2220740244[Crossref]
  • [31] J.E. Sacco and A. Widom: “Effects of Dimensionality and Crystal Structure on Bound States of Point Defects in Quantum Solids”, J. Low. Temp. Phys., Vol.24, (1976), pp.241–251. http://dx.doi.org/10.1007/BF00659209[Crossref]
  • [32] R. Feynman: The Feynman Lectures on Physics, Addison-Wesley publ. comp., Massachusetts, 1963, (Chpt. 43 “Diffusion”).
  • [33] A.F. Andreev: “Diffusion in quantum crystals”, Usp. Fiz. Nauk, Vol.118, (1976), pp.251–272. [Crossref]
  • [34] I.M. Lifshitz: “Scattering of short elastic waves in a crystal lattice”, Zh. Eksp. Teor. Fiz., Vol.18, (1948), pp.293–300.
  • [35] I.M. Lifshitz and M.I. Kaganov: “Some problems of the electron theory of metals”, Usp. Fiz. Nauk, Vol.69, (1959), pp.419–458. [Crossref]
  • [36] I.M. Lifshitz, M.Ya. Azbel and M.I. Kaganov: Electron Theory of Metals, Nauka, Moscow, 1971 (in Russian).
  • [37] A.A. Maradudin, E.W. Montroll and G.H. Weiss: Theory of Lattice Dynamics in the Harmonic Approximation, Acad. Press, New York and London, 1963.
  • [38] V.A. Slusarev et al.: “Quantum Diffusion of He3 in Solid He4. II. Tunneling-Jumping Approximation”, Fiz. Nizkih Temp., Vol.4, (1978), pp.698–705.
  • [39] Yu. Kagan and M.I. Klinger: “Theory of quantum diffusion of atoms in crystals”, J. Phys. C: Solid-State Phys., Vol.7, (1974), pp.2791–2807. http://dx.doi.org/10.1088/0022-3719/7/16/012[Crossref]
  • [40] J. Schratter and A.R. Allen: “Concentration Dependence of D, T 1, andT 2 for Dilute Solutions of3He in Solid4He”, J. Low Temp. Phys., Vol.57, (1984), pp.179–187. http://dx.doi.org/10.1007/BF00681522[Crossref]
  • [41] B.N. Esel'son, V.A. Mikheev, V.N. Grigorev and N.P. Mikhin: “Impuriton diffusion in solid solutions of helium isotops”, In: Proc. 20-th Soviet Conf. at Low Temp. Phys., NT-20, Vol. 2, Moscow, 1979, pp. 236–238.
  • [42] B.N. Esel'son, V.A. Mikheev, V.N. Grigorev and N.P. Mikhin: “Quantum diffusion of He3 impurity quasiparticles in Solid He4”, Zh. Eksp. Teor. Fiz., Vol.74, (1978), pp.2311–2319
  • [43] A.R. Allen, M.G. Richards and J. Schratter: “Diffusion coefficient of3He in solid4He”, J. de Phys., Vol. 39, (Coll. C6), (1978), pp.
  • [44] V.N. Grigoriev et al.: “Observation and investrigation of quantum diffusion in solid mixtures of helium isotopes”, Fizika Nizkih Temp., Vol.1, (1975), pp.5–26.
  • [45] A. Widom and M.G. Richards: “Quantum Theory of Diffusion with Application to Solid Helium”, Phys. Rev. A, Vol.6, (1972), pp.1196–1199. http://dx.doi.org/10.1103/PhysRevA.6.1196[Crossref]
  • [46] D.O. Edwards and R.C. Pandorf: “Heat Capacity and Other Properties of Hexagonal Close-Packed Helium-4”, Phys. Rev., Vol. 140, (1965), pp. A 816–825. http://dx.doi.org/10.1103/PhysRev.140.A816[Crossref]
  • [47] E.G. Kisvarsanyi, K. Runge and N.S. Sullivan: “The quantum diffusion of isotopic impurities in solid hydrogen”, Phys. Lett. A, Vol.155, (1991), pp.337–341. http://dx.doi.org/10.1016/0375-9601(91)90495-T[Crossref]
  • [48] M. Rall, D. Zhou, E.G. Kisvarsanyi and N.S. Sullivan: “Nuclear Spin-Spin Relaxation of Isotopic Impurities in Solid Hydrogen”, Phys. Rev. B, Vol.45, (1992), pp.2800–2808. http://dx.doi.org/10.1103/PhysRevB.45.2800[Crossref]
  • [49] E.G. Kisvarsanyi and N.S. Sullivan: “Quantum diffusion of3He impurities in solid4He”, Phys. Rev. B, Vol.48, (1993), pp.16577–16581. http://dx.doi.org/10.1103/PhysRevB.48.16577[Crossref]
  • [50] E.G. Kisvarsanyi and N.S. Sullivan: “Reply to “Comment on ‘Quantum diffusion of3He impurities in solid4He’”, Phys. Rev. B, Vol.55, (1997), pp.3989–3989. http://dx.doi.org/10.1103/PhysRevB.55.3989[Crossref]
  • [51] E.G. Kisvarsanyi and N.S. Sullivan: “Reply to “Comment on ‘Quantum diffusion of3He impurities in solid4He’”, Phys. Rev. B, Vol.61, (2000), pp.15476–15476. http://dx.doi.org/10.1103/PhysRevB.61.15476[Crossref]
  • [52] D.P. Locke: “Impuriton Vacancy ‘Molecules’ in Solid4He”, J. Low. Temp. Phys, Vol.32, (1978), pp.159–172. http://dx.doi.org/10.1007/BF00116911[Crossref]
  • [53] V.N. Grigorev: “Comment on ‘Quantum diffusion of3He impurities in solid4He’”, Phys. Rev. B, Vol.55, (1997), pp.3987–3988. http://dx.doi.org/10.1103/PhysRevB.55.3987[Crossref]
  • [54] D.I. Pushkarov: “Comment on ‘Quantum diffusion of3He impurities in solid4He’”, Phys. Rev. B, Vol.61, (2000), pp.15474–15475. http://dx.doi.org/10.1103/PhysRevB.61.15474[Crossref]
  • [55] H. Goldstein: Classical Mechanics, Addison-Wesley, Reading, MA, 1980 (Chapt. 3 Eq. 397).
  • [56] Yu. Kagan andL.A. Maksimov: “Quantum diffusion in irregular crystals’, Zh. Eksp. Teor. Fiz., Vol.84, (1983), pp.792–810.
  • [57] V.A. Mikheev, N.P. Mikhin and V.A. Maidanov: “Quantum diffusion in solid solutions of helium isotopes with high localization of3He atoms”, Fizika Nizkih Temp., Vol.9, (1983), pp.901–912.

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Publication order reference

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bwmeta1.element.-psjd-doi-10_2478_BF02476424
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