Quantal phase factors accompanying adiabatic changes

The Royal Society - Tập 392 Số 1802 - Trang 45-57 - 1984
Michael Berry1
1H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, U.K.

Tóm tắt

A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar dynamical phase factor. An explicit general formula for γ(C) is derived in terms of the spectrum and eigenstates of Ĥ(R) over a surface spanning C. If C lies near a degeneracy of Ĥ, γ(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration γ(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.

Từ khóa


Tài liệu tham khảo

10.1103/PhysRev.115.485

10.1103/PhysRev.158.1237

Arnold V. I. 1978 Mathematical methods of classical dynamics. New York: Springer.

Berry M. V., 1980, Eur, J. Phys., 1, 240

Berry M. V. 1981 Singularities in waves and rays. In Les Houches Lecture Notes for session XXXV (ed. R. Balian M. Kleman & J-P. Poirier) pp. 453-543. Amsterdam: North-Holland.

10.1098/rspa.1984.0022

Chambers R. G. i 960 Phys. Rev. Lett 5 3-5.

Ehrenburg W., 1949, Proc. phys, Soc. B, 62, 8

10.1039/df9633500077

Hwang J.-T., 1977, J . chem, Phys., 67, 4640

10.1098/rspa.1975.0095

Mead C. A., 1979, J. chem, Phys., 70, 2276

10.1016/0301-0104(80)85035-X

Mead C. A., 1980, 6 Chem, Phys., 49, 33

Mead C. A., 1979, J .chem, Phys., 70, 2284

Messiah A. 1962 Quantum mechanics vol. 2. Amsterdam: North-Holland.

Morandi G. & Menossi E. 1984 Nuovo Cim. B (Submitted.)

10.1098/rspa.1981.0149

10.1098/rspa.1974.0012

Rauch H., 1978, Z, Phys. B, 29, 281

Rauch H. Zeilinger A. Badurek G. Wilting A. Bauspiess W. & Bonse U. 1975 Physics Lett. A 54 425-427.

Schulman L. S. 1981 Techniques and Applications of Path Integration. New York: John Wiley.

Silverman M. P., 1980, Eur, J. Phys., 1, 116

Simon B., 1983, Phys. Rev. Lett. (In the press.)

10.1098/rspa.1976.0134

Von Neumann J. & Wigner E. P. 1929 Phys. Z. 30 467-470.

10.1103/PhysRevLett.35.1053

10.1103/PhysRevD.12.3845

Thông tin
Thông tin xuất bản

The Royal Society

Tập 392 Số 1802

45-57

Thông tin tác giả