Summary
In this paper we present some hydrodynamical consequences of a previously proposed stochastic model for superfluid4He. We discuss in particular the possibility of time-dependent evolutions which, starting from a rotational initial state, lead to asymptotic stationary solutions where the vorticity is concentrated in singular regions. An example of such asymptotic stationary solutions is the quantized vortex line solution. We also recall the concept of quantum critical slipping velocity and investigate some possible consequences on the spin-up problem and on the creation of systems of vortex lines.
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References
L. Onsager:Nuovo Cimento,6, Suppl. 2, 279 (1949), and discussion on pp. 249-250.
W. I. Glaberson andR. J. Donnelly: inProg. Low Temp. Phys. Vol. IX, edited byD. F. Brewer (North-Holland, Amsterdam, 1986).
J. T. Though: inProg. Low Temp. Phys. Vol. VIII, edited byD. F. Brewer (North-Holland, Amsterdam, 1982).
M. I. Loffredo andL. M. Morato:Phys. Rev. B,35, 1742 (1987); inProceedings of the International Conference on Solitons, Instabilities and Chaotic Processes in Fluid Dynamics, Cetraro (CS),Italy 1987.
V. L. Ginzburg andL. P. Pitaevskii:Sov. Phys. JEPT,7, 858 (1958).
E. P. Gross:Nuovo Cimento,20, 454 (1961); L. P. Pitaevskii:Sov. Phys. JETP,13, 451 (1961).
E. P. Gross:J. Math. Phys.,4, 195 (1963).
G. B. Hess andW. M. Fairbank:Phys. Rev. Lett,19, 216 (1967).
E. J. Yarmchuk, M. J. V. Gordon andR. E. Packard:Phys. Rev. Lett.,43, 214 (1979); E. J. Yarmchuk and R. E. Packard:J. Low Temp. Phys.,46, 479 (1982); R. E. Packard:Physica B,109–110, 1474 (1982).
J. D. Reppy andC. T. Lane:Phys. Rev. A,140, 106 (1965).
E. Nelson:Dynamical Theories of Brownian Motion (Princeton University Press, Princeton, N.J., 1967);Quantum Fluctuations (Princeton University Press, Princeton, N.J., 1984).
M. H. Kalos, D. Levesque andL. Verlet:Phys. Rev. A,9, 2178 (1974).
P. A. Whitlock, G. V. Chester andM. H. Kalos:Phys. Rev. B,38, 418 (1988).
L. M. Morato:Nuovo Cimento B,106, 763 (1991).
L. M. Morato:Phys. Rev. D,31, 1982 (1985).
M. I. Loffredo andL. M. Morato:J. Math. Phys.,30, 354 (1989).
H. E. Wilhelm:Phys. Rev. D,1, 2278 (1970); L. J. F. Broer:Physica,76, 364 (1974); C. Y. Wong:J. Math. Phys.,16, 1008 (1976); S. K. Ghosh and B. M. Deb:Phys. Rep.,92, 1 (1982).
M. I. Loffredo: Rapporto matematico n. 226, Preprint Università di Siena (1990).
E. Madelung:Z. Phys.,40, 322 (1926).
F. London:Superfluids, Vol.2 (Wiley, New York, N.Y., 1954).
S. de Toffol:Teorie idrodinamiche di 4Hesuperfluido a T = 0 e problema della formazione dei vortici, Tesi, Università di Padova (1990).
W. F. Vinen:Proc. R. Soc. London, Ser. A,260, 218 (1961).
E. R. Benton andA. Clark jr.:Ann. Rev. Fluid Mech.,6, 257 (1974); P. D. Weidman:J. Fluid Mech.,77, 685, 709 (1976).
Z. Peradzynski, S. Filipkowski andW. Fiszdon:Eur. J. Mech B,9, 259 (1990).
I. L. Bekarevich andI. M. Khalatnikov:Sov. Phys. JETP,13, 643 (1961); H. E. Hall and W. F. Vinen:Proc. R. Soc. London, Ser. A,238, 204, 215 (1956); I. M. Khalatnikov:An Introduction to the Theory of Superfluidity (Benjamin, New York, N.Y., 1965).
G. K. Batchelor:An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, UK, 1967).
S. Goldstein (Editor):Modern Developments in Fluid Dynamics (Dover Publications, New York, N.Y., 1965).
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Loffredo, M.I., Morato, L.M. On the creation of quantized vortex lines in rotating He II. Nuov Cim B 108, 205–215 (1993). https://doi.org/10.1007/BF02874411
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DOI: https://doi.org/10.1007/BF02874411