Temporary HW: Difference between revisions
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What is the spin polarization of these two currents? Comment on the physical meaning of the difference between the spin state transported by two currents. | What is the spin polarization of these two currents? Comment on the physical meaning of the difference between the spin state transported by two currents. | ||
HINT: Compute the x, y, and z components of the spin polarization vector using both of these density matrices following the ''quantum-mechanical definition'' of an average value <math> \langle | HINT: Compute the x, y, and z components of the spin polarization vector using both of these density matrices following the ''quantum-mechanical definition'' of an average value <math> P_{x,y,z} = \langle \sigma_{x,y,z}\rangle =\mathrm{Tr}\, [\hat{\rho} \hat{\sigma}_{x,y,z}] </math>. | ||
== Problem 2 == | == Problem 2 == | ||
== Problem 3 == | == Problem 3 == |
Revision as of 14:48, 8 February 2011
Problem 1
A researcher in spintronics is investigated two devices in order to generate spin-polarized currents. One of those devices has spins comprising the current described by the density matrix:
,
while the spins comprising the current in the other device are described by the density matrix
, where .
Here and are the eigenstates of the Pauli spin matrix :
.
What is the spin polarization of these two currents? Comment on the physical meaning of the difference between the spin state transported by two currents.
HINT: Compute the x, y, and z components of the spin polarization vector using both of these density matrices following the quantum-mechanical definition of an average value .