Megascopic Quantum Phenomena
311
λ =
mc 2
4π ne 2
(9.8)
The London Eq. (9.5) differs from the Becker’s one (9.4) in one small detail:
an ansatz in the form of zero integration constant, corresponding to the simple but
important fact, that real superconductors, in contrast to ideal conductors, exhibits no
memory effects.
A similar distinction is observed for the case of rotating objects, i.e. both ideal
conductors and superconductors exhibit the same behavior, if they are accelerated
below the critical temperature. Becker et al. [63] derived the relation between the
angular velocity ω and a generated magnetic field in the interior of ideal conductor.
Substituting for v in Eq. (9.1) i.e.
v = ω × r
(9.9)
one obtains from the Becker’s Eq. (9.4) after integration the final relation
B = −
2mc
e
ω
(9.10)
If an ideal conductor is first accelerated and subsequently cooled, instead of (9.10)
after the integration, we get only the trivial solution with B equal to zero. Related
to the Meissner effect, London [66] predicted an analogous effect also for rotating superconductors, where the Becker’s relation (9.10) holds for superconductors
regardless of its history, i.e. including the case when acceleration occurred first,
followed by the cooling. London’s derivation of Eq. (9.10) is based on a direct
substitution in his Eq. (9.5), so that the generated magnetic field would always be
the same, independent of the order of the acceleration and the cooling events. The
generated magnetic moment is called the London moment. London’s prediction for
rotating superconductors was for the first time experimentally verified in 1964 by
Hildebrandt [67].
It is intriguing to ask whether London’s ansatz to Becker’s equations is necessary?
Alternatively, can we have an ansatz-free classical description of superconductors
with an ab initio derivation of the London equations based solely on the laws of
classical mechanics and classical electrodynamics? This question has in fact divided
the scientific community into two camps. For instance Eq. (9.5) was elegantly derived
by de Gennes [68] by minimizing the total energy. He wrote the expressions for the
kinetic energy and the energy of magnetic field:
E k =
1
2
nmv
2 dV =
1
2
m
ne 2 j
2 dV
(9.11)
E f =
1
8π
B
2 dV
(9.12)
Using Ampere’s law (9.6) the total energy reads
311
λ =
mc 2
4π ne 2
(9.8)
The London Eq. (9.5) differs from the Becker’s one (9.4) in one small detail:
an ansatz in the form of zero integration constant, corresponding to the simple but
important fact, that real superconductors, in contrast to ideal conductors, exhibits no
memory effects.
A similar distinction is observed for the case of rotating objects, i.e. both ideal
conductors and superconductors exhibit the same behavior, if they are accelerated
below the critical temperature. Becker et al. [63] derived the relation between the
angular velocity ω and a generated magnetic field in the interior of ideal conductor.
Substituting for v in Eq. (9.1) i.e.
v = ω × r
(9.9)
one obtains from the Becker’s Eq. (9.4) after integration the final relation
B = −
2mc
e
ω
(9.10)
If an ideal conductor is first accelerated and subsequently cooled, instead of (9.10)
after the integration, we get only the trivial solution with B equal to zero. Related
to the Meissner effect, London [66] predicted an analogous effect also for rotating superconductors, where the Becker’s relation (9.10) holds for superconductors
regardless of its history, i.e. including the case when acceleration occurred first,
followed by the cooling. London’s derivation of Eq. (9.10) is based on a direct
substitution in his Eq. (9.5), so that the generated magnetic field would always be
the same, independent of the order of the acceleration and the cooling events. The
generated magnetic moment is called the London moment. London’s prediction for
rotating superconductors was for the first time experimentally verified in 1964 by
Hildebrandt [67].
It is intriguing to ask whether London’s ansatz to Becker’s equations is necessary?
Alternatively, can we have an ansatz-free classical description of superconductors
with an ab initio derivation of the London equations based solely on the laws of
classical mechanics and classical electrodynamics? This question has in fact divided
the scientific community into two camps. For instance Eq. (9.5) was elegantly derived
by de Gennes [68] by minimizing the total energy. He wrote the expressions for the
kinetic energy and the energy of magnetic field:
E k =
1
2
nmv
2 dV =
1
2
m
ne 2 j
2 dV
(9.11)
E f =
1
8π
B
2 dV
(9.12)
Using Ampere’s law (9.6) the total energy reads