The Hannay geometric phase is the classical analog of the well-known Berry phase. Its most familiar example is the effect of the latitude λ on the motion of a Foucault pendulum. We describe an electronic network whose behavior is exactly equivalent to that of the pendulum. The circuit can be constructed from off-the-shelf components using two matched transconductance amplifiers that comprise a gyrator to introduce the non-reciprocal behavior needed to mimic the pendulum. One may precisely measure the dependence of the Hannay phase on λ by circuit simulation and by laboratory measurements on a constructed circuit.
REFERENCES
1.
M. V.
Berry
, “
Quantal phase factors accompanying adiabatic changes
,” Proc. R. Soc. London, Ser. A
392
(1802
), 45
–57
(1984
).2.
S.
Pancharatnam
, “Generalized theory of interference and its applications. Part I. Coherent pencils,” Proc. Ind. Acad. Sci. A
44
, 247
(1956
). [reprinted in S. Pancharatnam, Collected Works (Oxford University Press, 1975)].3.
J. H.
Hannay
, “
Angle variable holonomy in adiabatic excursion of an integrable Hamiltonian
,” J. Phys. A
18
, 221
(1985
).4.
For a very recent visit to the pendulum see for example:
J. A.
Giacometti
, “
Foucault pendulum revisited, the determination of precession angular velocity using Cartesian coordinates
,” Rev. Bras. Ensino Fis.
43
, e20190140
(2021
).5.
A.
Khein
and
D. F.
Nelson
, “
Hannay angle study of the Foucault pendulum in action-angle variables
”, Am. J. Phys.
61
, 170
(1993
).6.
D.
Xu
, “
Hannay angle in an LCR circuit with time-dependent inductance, capacity and resistance
,” J. Phys. A
35
, L455
(2002
).7.
J. H.
Hannay
, “
Comment on Hannay angle in an LCR circuit with time-dependent inductance, capacity and resistance
,” J. Phys. A
35
, 9699
(2002
).8.
Sharba
Bhattacharjee
et al, “
Study of geometric phase using classical coupled oscillators
,” Eur. J. Phys.
39
, 035404
(2018
).9.
A. D. A. M.
Spallicci
, “
Satellite measurement of the Hannay angle
,” Nuovo Cimento B
119
, 1215
(2004
).10.
J. B.
Marion
, Classical Dynamics of Particles and Systems
(
Elsevier
,
New York
, 2014
).11.
W. B.
Somerville
, “
The description of Foucault's pendulum
,” Q. J. R. Astron. Soc.
13
, 40
–62
(1972
).12.
J.
von Bergmann
, “
Foucault pendulum through basic geometry
,” Am. J. Phys.
75
, 888
–892
(2007
).13.
M.
Caruso
,
H.
Fanchiotti
,
C. A.
Garcia Canal
,
M.
Mayosky
, and
A.
Veiga
, “
The quantum CP-violating kaon system reproduced in the electronic laboratory
,” Proc. R. Soc. London, Ser. A
472
(2195
), 20160615
(2016
).14.
See supplementary material at https://www.scitation.org/doi/suppl/10.1119/5.0081149 for a description of the elements of the experimental circuit, their calibration procedure, the proposed initial conditions for a better visualization and the measurement procedure.
15.
I.
Tatai
and
I.
Zaharie
, “
The energy transfer between the ports of an implemented gyrator using LM13700 operational transconductance amplifier
,” Rev. Sci. Instrum.
83
(11
), 114702
(2012
).© 2022 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2022
Author(s)
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.