In quantum mechanics, the Byers–Yang theorem states that all physical properties of a doubly connected system (an annulus) enclosing a magnetic flux
(the magnetic flux quantum).
The theorem was first stated and proven by Nina Byers and Chen-Ning Yang (1961),[1] and further developed by Felix Bloch (1970).
corresponds to a vector potential
inside the annulus with a line integral
One can try to eliminate this vector potential by the gauge transformation of the wave function
The gauge-transformed wave function satisfies the same Schrödinger equation as the original wave function, but with a different magnetic vector potential
It is assumed that the electrons experience zero magnetic field
inside the annulus, the field being nonzero only within the opening (where there are no electrons).
inside the annulus, so one would conclude that the system with enclosed flux
is equivalent to a system with zero enclosed flux.
the gauge transformed wave function is no longer single-valued: The phase of
is moved along the ring to its starting point.
The requirement of a single-valued wave function therefore restricts the gauge transformation to fluxes
Systems that enclose a flux differing by a multiple of
An overview of physical effects governed by the Byers–Yang theorem is given by Yoseph Imry.
[3] These include the Aharonov–Bohm effect, persistent current in normal metals, and flux quantization in superconductors.