123 research outputs found
Dissipative and stochastic geometric phase of a qubit within a canonical Langevin framework
Dissipative and stochastic effects in the geometric phase of a qubit are
taken into account using a geometrical description of the corresponding
open--system dynamics within a canonical Langevin framework based on a
Caldeira--Leggett like Hamiltonian. By extending the Hopf fibration to include such effects, the exact geometric phase for a dissipative
qubit is obtained, whereas numerical calculations are used to include finite
temperature effects on it.Comment: 5 pages, 2 figure
Time averaging of weak values - consequences for time-energy and coordinate-momentum uncertainty
Using the quantum transition path time probability distribution we show that
time averaging of weak values leads to unexpected results. We prove a weak
value time energy uncertainty principle and time energy commutation relation.
We also find that time averaging allows one to predict in advance the momentum
of a particle at a post selected point in space with accuracy greater than the
limit of as dictated by the uncertainty principle. This comes at a
cost - it is not possible at the same time to predict when the particle will
arrive at the post selected point. A specific example is provided for one
dimensional scattering from a square barrier.Comment: 14 pages, 2 figure
Dissipative quantum backflow
Dissipative backflow is studied in the context of open quantum systems. This
theoretical analysis is carried out within two frameworks, the effective
time-dependent Hamiltonian due to Caldirola-Kanai (CK) and the Caldeira-Leggett
(CL) one where a master equation is used to describe the reduced density matrix
in presence of dissipation and temperature of the environment. Two examples are
considered, the free evolution of one and two Gaussian wave packets as well as
the time evolution under a constant field. Backflow is shown to be reduced with
dissipation and temperature but never suppressed. Interestingly enough, quantum
backflow is observed when considering both one and two Gaussian wave packets
within the CL context. Surprisingly, in both cases, the backflow effect seems
to be persistent at long times. Furthermore, the constant force
behaves against backflow. However, the classical limit of this quantum effect
within the context of the classical Schr\"odinger equation is shown to be
present. Backflow is also analyzed as an eigenvalue problem in the
Caldirola-Kanai framework. In the free propagation case, eigenvalues are
independent on mass, Planck constant, friction and its duration but, in the
constant force case, eigenvalues depend on a factor which itself is a
combination of all of them as well as the force constant.Comment: The interpretation of quantum backflow is not correct in the
Caldeira-Leggett framework. See the erratum:
https://doi.org/10.1140/epjp/s13360-020-00655-
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