Homepage of Doron Cohen

Counting statistics in closed and multiple path geometries (2007-2008)

The amount $\blue Q$ of particles that are transported via a path of motion is characterized by its expectation value $\blue \langle Q \rangle$ and by its variance $\blue \text{Var}(Q)$ . 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 $\blue p$ to make a transition from one site to another site, then the average transport should be $\blue \langle Q \rangle=p$ with a variance $\blue \text{Var}(Q)=(1-p)p$ . 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 $\blue \text{Var}(Q)$ 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 $\blue \text{Var}(Q)$ 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]