Counting statistics in closed and multiple path geometries (2007-2008)
The amount of particles that are transported via a path of motion is
characterized by its expectation value and by its variance . In [1] we consider the full counting statistics which is associated with a two
level coherent transition in the context of a continuous quantum measurement
process. The conventional probabilistic point of view implies that if a particle has a
probability to make a transition from one site to another site, then the
average transport should be with a variance . In the
quantum mechanical context this observation becomes a non-trivial manifestation
of restricted quantum-classical correspondence. In particular we test the possibility of getting a valid result for
within the framework of the adiabatic picture, analyzing the simplest
non-trivial example of a Landau-Zener crossing.
In [2] we
analyze what happens if a particle has two optional paths available to get from
one site to another site, and in particular what is for the current
which is induced in a quantum stirring device (see below).
Both the coherent splitting of a wavepacket
and the quantum stirring effect are intimately related and cannot
be understood within a classical or stochastic framework.
Due to the multiple path geometry there is no longer a simple relation
between the "counting statistics" and the "occupation statistics".
In particular we demonstrate that interference shows up differently
in the second moment calculation.
[1] M. Chuchem and D. Cohen, Phys. Rev. A 77, 012109(2008). [arXiv]
[pdf]
[2] M. Chuchem and D. Cohen, J. Phys. A 41, 075302(2008). [arXiv]
[pdf]
[3] M. Chuchem and D. Cohen, Physica E, Proc. of FQMT(Prague, 2008). []
[pdf]