6,606 research outputs found

### Comment on "Neutron Interferometric Observation of Noncyclic Phase"

A critique of a recent experiment [Wagh et.al., Phys.Rev.Lett.81, 1992 (7 Sep
1998)] to measure the noncyclic phase associated with a precessing neutron spin
in a neutron interferometer, as given by the Pancharatnam criterion, is
presented. It is pointed out that since the experiment measures, not the
noncyclic phase itself, but a quantity derived from it, it misses the most
interesting feature of such a phase, namely the different sign associated with
states lying in the upper and the lower hemispheres, a feature originating in
the existence of a phase singularity. Such effects have earlier been predicted
and seen in optical interference experiments using polarization of light as the
spinor [Bhandari, Phys.Rep.281, 1 (Mar 1997)].Comment: 5 pages, 0 figures, submitted to Phys.Rev.Let

### 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]

### Observable Dirac-type singularities in Berry's phase and the monopole

The physical reality and observability of 2n\pi Berry phases, as opposed to
the usually considered modulo 2\pi topological phases is demonstrated with the
help of computer simulation of a model adiabatic evolution whose parameters are
varied along a closed loop in the parameter space. Using the analogy of Berry's
phase with the Dirac monopole, it is concluded that an interferometer loop
taken around a magnetic monopole of strength n/2 yields an observable 2n\pi
phase shift, where n is an integer. An experiment to observe the effect is
proposed.Comment: 12 pages Latex, 3 postscript figures; submitted to Physical Review
Letters 15 September 2000; revised 19 November 200

### On singularities of the mixed state phase

A recent proposal of Sjoqvist et.al. to extend Pancharatnam's criterion for
phase difference between two different pure states to the case of mixed states
in quantum mechanics is analyzed and the existence of phase singularities in
the parameter space of an interference experiment with particles in mixed
states pointed out. In the vicinity of such singular points the phase changes
sharply and precisely at these points it becomes undefined. A closed circuit in
the parameter space around such points results in a measurable phase shift
equal to 2n\pi, where n is an integer. Such effects have earlier been observed
in interference experiments with pure polarization states of light, a system
isomorphic to the spin-1/2 system in quantum mechanics. Implications of phase
singularities for the interpretation of experiments with partially polarized
and unpolarized neutrons are discussed. New kinds of topological phases
involving variables representing decoherence (depolarization) of pure states
are predicted and experiments to verify them suggested.Comment: 4 pages Latex, 1 postscript figure; submitted to Physical Review
Letters 12 Dec 2000; Revised on 13 August 200

### Exploring the Potentialities of Special Economic Zones in Nepal

Special Economic Zones (SEZs) have been established in many countries around the world as a way to promote economic growth and attract foreign investment. In Nepal, the potential of SEZs has been recognized as a way to boost the economy, but there is a lack of comprehensive research on the potentialities and challenges of establishing SEZs in the country. This study aims to explore the potentialities of SEZs in Nepal by examining the concept of SEZs, the current state of SEZs in Nepal, and the experiences of other countries with SEZs. The study will be conducted using a combination of literature review, data analysis, stakeholder interviews, case studies, and scenario planning. The study will use a combination of literature review, data analysis, stakeholder interviews, case studies, and scenario planning to explore the potentialities of SEZs in Nepal.
The findings of the study will provide valuable insights for policymakers and stakeholders in Nepal to support the growth and development of SEZs in the country. The study will also contribute to the larger body of knowledge on SEZs and their role in economic development. In conclusion, the study will provide a comprehensive analysis of the potentialities of SEZs in Nepal and offer recommendations for effective implementation and development. The study will contribute to the understanding of SEZs as a tool for promoting economic growth and attracting foreign investment in Nepal.How to cite this article: Bhandari, R., (2023). Exploring the Potentialities of Special Economic Zones in Nepal. GS Spark: Journal of Applied Academic Discourse. 1(1), 35-44. https://doi.org/10.5281/zenodo.837205

### Lattice polarization effects on the screened Coulomb interaction $W$ of the GW approximation

In polar insulators where longitudinal and transverse optical phonon modes
differ substantially, the electron-phonon coupling affects the energy-band
structure primarily through the long-range Fr\"ohlich contribution to the Fan
term. This diagram has the same structure as the $GW$ self-energy where $W$
originates from the electron part of the screened coulomb interaction. The two
can be conveniently combined by combining electron and lattice contributions to
the polarizability. Both contributions are nonanalytic at the origin, and
diverge as $1/q^2$ so that the predominant contribution comes from a small
region around $q{=}0$. Here we adopt a simple estimate for the Fr\"ohlich
contribution by assuming that the entire phonon part can be attributed to a
small volume of $q$ near $q{=}0$. We estimate the magnitude for
$\mathbf{q}{\rightarrow}0$ from a generalized Lyddane-Sachs-Teller relation,
and the radius from the inverse of the polaron length scale. The gap correction
is shown to agree with Fr\"ohlich's simple estimate $-\alpha_P\omega_L/2$ of
the polaron effect

### Relation between geometric phases of entangled bi-partite systems and their subsystems

This paper focuses on the geometric phase of entangled states of bi-partite
systems under bi-local unitary evolution. We investigate the relation between
the geometric phase of the system and those of the subsystems. It is shown that
(1) the geometric phase of cyclic entangled states with non-degenerate
eigenvalues can always be decomposed into a sum of weighted non-modular pure
state phases pertaining to the separable components of the Schmidt
decomposition, though the same cannot be said in the non-cyclic case, and (2)
the geometric phase of the mixed state of one subsystem is generally different
from that of the entangled state even by keeping the other subsystem fixed, but
the two phases are the same when the evolution operator satisfies conditions
where each component in the Schmidt decomposition is parallel transported

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