%0 Journal Article %1 berry1984quantal %A Berry, M. V. %D 1984 %J Proc. R. Soc. Lond. A %K adiabatic berry quantum topology %N 1802 %P 45--57 %T Quantal Phase Factors Accompanying Adiabatic Changes %U http://rspa.royalsocietypublishing.org/content/392/1802/45 %V 392 %X A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters $R$ in its Hamiltonian $H(R)$, will acquire a geometrical phase factor $i\gamma(C)$ in addition to the familiar dynamical phase factor. An explicit general formula for $\gamma$(C) is derived in terms of the spectrum and eigenstates of $H(R)$ over a surface spanning C. If C lies near a degeneracy of $H, \gamma$(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 $\gamma$(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.

@article{berry1984quantal, abstract = {A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters $\mathbf{R}$ in its Hamiltonian $\hat{H}(\mathrm{R})$, will acquire a geometrical phase factor $\exp {i\gamma(\mathrm{C})}$ in addition to the familiar dynamical phase factor. An explicit general formula for $\gamma$(C) is derived in terms of the spectrum and eigenstates of $\hat{H}(\mathbf{R})$ over a surface spanning C. If C lies near a degeneracy of $\hat{H}, \gamma$(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 $\gamma$(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.}, added-at = {2013-02-06T00:45:42.000+0100}, author = {Berry, M. V.}, biburl = {https://www.bibsonomy.org/bibtex/2e84db4753bc7280037191812ebafe0b2/ttuegel}, day = 8, interhash = {8d7c26c19d24576b17a706b751a5f037}, intrahash = {e84db4753bc7280037191812ebafe0b2}, journal = {Proc. R. Soc. Lond. A}, keywords = {adiabatic berry quantum topology}, month = {March}, number = 1802, pages = {45--57}, timestamp = {2013-02-06T00:46:12.000+0100}, title = {Quantal Phase Factors Accompanying Adiabatic Changes}, url = {http://rspa.royalsocietypublishing.org/content/392/1802/45}, volume = 392, year = 1984 }