4,482 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
Interplay of causticity and vorticality within the complex quantum Hamilton-Jacobi formalism
Interference dynamics is analyzed in the light of the complex quantum
Hamilton-Jacobi formalism, using as a working model the collision of two
Gaussian wave packets. Though simple, this model nicely shows that interference
in quantum scattering processes gives rise to rich dynamics and trajectory
topologies in the complex plane, both ruled by two types of singularities:
caustics and vortices, where the former are associated with the regime of free
wave-packet propagation, and the latter with the collision (interference)
process. Furthermore, an unambiguous picture connecting the complex and real
frameworks is also provided and discussed.Comment: 12 pages, 3 figure
Bohmian Trajectories of Airy Packets
The discovery of Berry and Balazs in 1979 that the free-particle
Schr\"odinger equation allows a non-dispersive and accelerating Airy-packet
solution has taken the folklore of quantum mechanics by surprise. Over the
years, this intriguing class of wave packets has sparked enormous theoretical
and experimental activities in related areas of optics and atom physics. Within
the Bohmian mechanics framework, we present new features of Airy wave packet
solutions to Schr\"odinger equation with time-dependent quadratic potentials.
In particular, we provide some insights to the problem by calculating the
corresponding Bohmian trajectories. It is shown that by using general
space-time transformations, these trajectories can display a unique variety of
cases depending upon the initial position of the individual particle in the
Airy wave packet. Further, we report here a myriad of nontrivial Bohmian
trajectories associated to the Airy wave packet. These new features are worth
introducing to the subject's theoretical folklore in light of the fact that the
evolution of a quantum mechanical Airy wave packet governed by the
Schr\"odinger equation is analogous to the propagation of a finite energy Airy
beam satisfying the paraxial equation. Numerous experimental configurations of
optics and atom physics have shown that the dynamics of Airy beams depends
significantly on initial parameters and configurations of the experimental
set-up.Comment: 8 page
Quantum phase analysis with quantum trajectories: A step towards the creation of a Bohmian thinking
We introduce a pedagogical discussion on Bohmian mechanics and its physical
implications in connection with the important role played by the quantum phase
in the dynamics of quantum processes. In particular, we focus on phenomena such
as quantum coherence, diffraction, and interference, due to their historical
relevance in the development of the quantum theory and their key role in a
myriad of fundamental and applied problems of current interest.Comment: 10 pages, 5 figure
A trajectory-based understanding of quantum interference
Interference is one of the most fundamental features which characterizes
quantum systems. Here we provide an exhaustive analysis of the interfere
dynamics associated with wave-packet superpositions from both the standard
quantum-mechanical perspective and the Bohmian one.
From this analysis, clear and insightful pictures of the physics involved in
this kind of processes are obtained, which are of general validity (i.e.,
regardless of the type of wave packets considered) in the understanding of more
complex cases where interference is crucial (e.g., scattering problems, slit
diffraction, quantum control scenarios or, even, multipartite interactions). In
particular, we show how problems involving wave-packet interference can be
mapped onto problems of wave packets scattered off potential barriers.Comment: 27 pages, 12 figures (shortened version
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