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 $S^{3}\to S^{2}$ 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 $\hbar /2$ 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 $m g\geq 0$ 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-