734 research outputs found
Experimentally testable geometric phase of sequences of Everett's relative quantum states
Everett's concept of relative state is used to introduce a geometric phase
that depends nontrivially on entanglement in a pure quantum state. We show that
this phase can be measured in multiparticle interferometry. A
correlation-dependent generalization of the relative state geometric phase to
mixed quantum states is outlined.Comment: Minor changes, journal reference adde
Geometry of an adiabatic passage at a level crossing
We discuss adiabatic quantum phenomena at a level crossing. Given a path in
the parameter space which passes through a degeneracy point, we find a
criterion which determines whether the adiabaticity condition can be satisfied.
For paths that can be traversed adiabatically we also derive a differential
equation which specifies the time dependence of the system parameters, for
which transitions between distinct energy levels can be neglected. We also
generalize the well-known geometric connections to the case of adiabatic paths
containing arbitrarily many level-crossing points and degenerate levels.Comment: 7 pages, 6 figures, RevTeX4, changes requested by Phys. Rev.
Transport study of Berry's phase, the resistivity rule, and quantum Hall effect in graphite
Transport measurements indicate strong oscillations in the Hall-,,
and the diagonal-, , resistances and exhibit Hall plateaus at the
lowest temperatures, in three-dimensional Highly Oriented Pyrolytic Graphite
(HOPG). At the same time, a comparative Shubnikov-de Haas-oscillations-based
Berry's phase analysis indicates that graphite is unlike the GaAs/AlGaAs 2D
electron system, the 3D n-GaAs epilayer, semiconducting ,
and some other systems. Finally, we observe the transport data to follow
. This feature is consistent with
the observed relative phases of the oscillatory and .Comment: 5 pages, 4 figure
Geometric phase for an accelerated two-level atom and the Unruh effect
We study, in the framework of open quantum systems, the geometric phase
acquired by a uniformly accelerated two-level atom undergoing nonunitary
evolution due to its coupling to a bath of fluctuating vacuum electromagnetic
fields in the multipolar scheme. We find that the phase variation due to the
acceleration can be in principle observed via atomic interferometry between the
accelerated atom and the inertial one, thus providing an evidence of the Unruh
effect.Comment: 12 pages, no figure
Fractional topological phase for entangled qudits
We investigate the topological structure of entangled qudits under unitary
local operations. Different sectors are identified in the evolution, and their
geometrical and topological aspects are analyzed. The geometric phase is
explicitly calculated in terms of the concurrence. As a main result, we predict
a fractional topological phase for cyclic evolutions in the multiply connected
space of maximally entangled states.Comment: REVTex, 4 page
On Geometric Phase from Pure Projections
The geometric phase is usually treated as a quantity modulo 2\pi, a
convention carried over from early work on the subject. The results of a series
of optical interference experiments involving polarization of light, done by
the present author (reviewed in R.Bhandari, Phys. Rep. 281 (1997) p.1) question
the usefulness of such a definition of the geometric phase in that it throws
away useful and measurable information about the system, for example strengths
of singularities giving rise to the geometric phase. Such singularities have
been directly demonstrated by phase-shift measurement in interference
experiments. In this paper, two recent polarization experiments (Hariharan
et.al., J.Mod.Opt. 44 (1997)p.707 and Berry and Klein, J.Mod.Opt. 43
(1996)p.165) are analysed and compared with previous experiments and
potentially detectible singularities in these experiments pointed out.Comment: Latex, 15 pages, 6 figures; ([email protected]
Geometric Phase, Bundle Classification, and Group Representation
The line bundles which arise in the holonomy interpretations of the geometric
phase display curious similarities to those encountered in the statement of the
Borel-Weil-Bott theorem of the representation theory. The remarkable relation
of the geometric phase to the classification of complex line bundles provides
the necessary tools for establishing the relevance of the Borel-Weil-Bott
theorem to Berry's adiabatic phase. This enables one to define a set of
topological charges for arbitrary compact connected semisimple dynamical Lie
groups. In this paper, the problem of the determination of the parameter space
of the Hamiltonian is also addressed. A simple topological argument is
presented to indicate the relation between the Riemannian structure on the
parameter space and Berry's connection. The results about the fibre bundles and
group theory are used to introduce a procedure to reduce the problem of the
non-adiabatic (geometric) phase to Berry's adiabatic phase for cranked
Hamiltonians. Finally, the possible relevance of the topological charges of the
geometric phase to those of the non-abelian monopoles is pointed out.Comment: 30 pages (LaTeX); UT-CR-12-9
Three Essays on the Relationship between Economic Development and Environmental Quality
This thesis is concerned with examining the relationship between indicators of
economic growth and environmental quality. During this process, the analysis explores and
attempts to interlink the following theoretical and empirical frameworks: Angelsen and
Kaimowitz’s theories for deforestation, the Environmental Kuznets Curve (EKC) hypothesis
and the forest transition theory. Macro-level data are used to examine the implications of
these frameworks. The implications of the first essay suggest that different crops have a
different impact on rate of change of agricultural land use. The second analysis suggests that
the results from a Directed Acyclical Graph Approach present a uni-directional causal
relationship between income and pollution emissions. The third and final essay suggests that
property rights structures and economic incentives appear to be the most probable
explanations for the forest transition in India. The macro-level nature of the data sets
employed provides information on the broad trends and patterns. For policy
recommendations, a more detailed and specific analysis needs to be carried out concentrating
on a certain region
Fidelity and coherence measures from interference
By utilizing single particle interferometry, the fidelity or coherence of a pair of quantum states is identified with their capacity for interference. We consider processes acting on the internal degree of freedom (e.g., spin or polarization) of the interfering particle, preparing it in states ρA or ρB in the respective path of the interferometer. The maximal visibility depends on the choice of interferometer, as well as the locality or nonlocality of the preparations, but otherwise depends only on the states ρA and ρB and not the individual preparation processes themselves. This allows us to define interferometric measures which probe locality and correlation properties of spatially or temporally separated processes, and can be used to differentiate between processes that cannot be distinguished by direct process tomography using only the internal state of the particle
Phase Dynamics of Two Entangled Qubits
We make a geometric study of the phases acquired by a general pure bipartite
two level system after a cyclic unitary evolution. The geometric representation
of the two particle Hilbert space makes use of Hopf fibrations. It allows for a
simple description of the dynamics of the entangled state's phase during the
whole evolution. The global phase after a cyclic evolution is always an entire
multiple of for all bipartite states, a result that does not depend on
the degree of entanglement. There are three different types of phases combining
themselves so as to result in the global phase. They can be identified
as dynamical, geometrical and topological. Each one of them can be easily
identified using the presented geometric description. The interplay between
them depends on the initial state and on its trajectory and the results
obtained are shown to be in connection to those on mixed states phases.Comment: 9 figures, slightly different version from the accepted on
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