Abstract:
Two-level systems are routinely represented in terms of pseudo-spin-1/2
degrees of freedom, and such pseudo-spins are usually considered to be
entirely analogous to the real spin angular momentum. Here we consider time
reversal (TR) of pseudo-spins from a completely general perspective and find
that there exist two different types. One type behaves like ordinary spin,
for which all of its three Cartesian components are odd under TR. In
addition, a second type of pseudo-spin exists, behaving counter-intuitively
in that only one Cartesian component is odd and the other two are even under
TR. The second type is not merely of academic interest, as it is realised,
eg, by the pseudo-spin representation of the 2D isotropic harmonic
oscillator (Schwinger model of spin-1/2). We show that the
sublattice-related pseudospin of quasi-relativistic charge carriers in
graphene also belongs to the second type and discuss observable implications
of this fact.
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