19,005 research outputs found
Optimized pulse sequences for suppressing unwanted transitions in quantum systems
We investigate the nature of the pulse sequence so that unwanted transitions
in quantum systems can be inhibited optimally. For this purpose we show that
the sequence of pulses proposed by Uhrig [Phys. Rev. Lett. \textbf{98}, 100504
(2007)] in the context of inhibition of environmental dephasing effects is
optimal. We derive exact results for inhibiting the transitions and confirm the
results numerically. We posit a very significant improvement by usage of the
Uhrig sequence over an equidistant sequence in decoupling a quantum system from
unwanted transitions. The physics of inhibition is the destructive interference
between transition amplitudes before and after each pulse.Comment: 5 figure
Aspects of Integrability in N =4 SYM
Various recently developed connections between supersymmetric Yang-Mills
theories in four dimensions and two dimensional integrable systems serve as
crucial ingredients in improving our understanding of the AdS/CFT
correspondence. In this review, we highlight some connections between
superconformal four dimensional Yang-Mills theory and various integrable
systems. In particular, we focus on the role of Yangian symmetries in studying
the gauge theory dual of closed string excitations. We also briefly review how
the gauge theory connects to Calogero models and open quantum spin chains
through the study of the gauge theory duals of D3 branes and open strings
ending on them. This invited review, written for Modern Physics Letters-A, is
based on a seminar given at the Institute of Advanced Study, Princeton.Comment: Invited brief review for Mod. Phys. Lett. A based on a talk at I.A.S,
Princeto
Generating Preview Tables for Entity Graphs
Users are tapping into massive, heterogeneous entity graphs for many
applications. It is challenging to select entity graphs for a particular need,
given abundant datasets from many sources and the oftentimes scarce information
for them. We propose methods to produce preview tables for compact presentation
of important entity types and relationships in entity graphs. The preview
tables assist users in attaining a quick and rough preview of the data. They
can be shown in a limited display space for a user to browse and explore,
before she decides to spend time and resources to fetch and investigate the
complete dataset. We formulate several optimization problems that look for
previews with the highest scores according to intuitive goodness measures,
under various constraints on preview size and distance between preview tables.
The optimization problem under distance constraint is NP-hard. We design a
dynamic-programming algorithm and an Apriori-style algorithm for finding
optimal previews. Results from experiments, comparison with related work and
user studies demonstrated the scoring measures' accuracy and the discovery
algorithms' efficiency.Comment: This is the camera-ready version of a SIGMOD16 paper. There might be
tiny differences in layout, spacing and linebreaking, compared with the
version in the SIGMOD16 proceedings, since we must submit TeX files and use
arXiv to compile the file
On the expected diameter, width, and complexity of a stochastic convex-hull
We investigate several computational problems related to the stochastic
convex hull (SCH). Given a stochastic dataset consisting of points in
each of which has an existence probability, a SCH refers to the
convex hull of a realization of the dataset, i.e., a random sample including
each point with its existence probability. We are interested in computing
certain expected statistics of a SCH, including diameter, width, and
combinatorial complexity. For diameter, we establish the first deterministic
1.633-approximation algorithm with a time complexity polynomial in both and
. For width, two approximation algorithms are provided: a deterministic
-approximation running in time, and a fully
polynomial-time randomized approximation scheme (FPRAS). For combinatorial
complexity, we propose an exact -time algorithm. Our solutions exploit
many geometric insights in Euclidean space, some of which might be of
independent interest
Mass-Gaps and Spin Chains for (Super) Membranes
We present a method for computing the non-perturbative mass-gap in the theory
of Bosonic membranes in flat background spacetimes with or without background
fluxes. The computation of mass-gaps is carried out using a matrix
regularization of the membrane Hamiltonians. The mass gap is shown to be
naturally organized as an expansion in a 'hidden' parameter, which turns out to
be : d being the related to the dimensionality of the background
space. We then proceed to develop a large perturbation theory for the
membrane/matrix-model Hamiltonians around the quantum/mass corrected effective
potential. The same parameter that controls the perturbation theory for the
mass gap is also shown to control the Hamiltonian perturbation theory around
the effective potential. The large perturbation theory is then translated
into the language of quantum spin chains and the one loop spectra of various
Bosonic matrix models are computed by applying the Bethe ansatz to the one-loop
effective Hamiltonians for membranes in flat space times. Apart from membranes
in flat spacetimes, the recently proposed matrix models (hep-th/0607005) for
non-critical membranes in plane wave type spacetimes are also analyzed within
the paradigm of quantum spin chains and the Bosonic sectors of all the models
proposed in (hep-th/0607005) are diagonalized at the one-loop level.Comment: 36 Page
Off Resonant Pumping for Transition from Continuous to Discrete Spectrum and Quantum Revivals in Systems in Coherent States
We show that in parametrically driven systems and, more generally, in systems
in coherent states, off-resonant pumping can cause a transition from a
continuum energy spectrum of the system to a discrete one, and result in
quantum revivals of the initial state. The mechanism responsible for quantum
revivals in the present case is different from that in the non-linear
wavepacket dynamics of systems such as Rydberg atoms. We interpret the reported
phenomena as an optical analog of Bloch oscillations realized in Fock space and
propose a feasible scheme for inducing Bloch oscillations in trapped ions.Comment: 5 pages, 4 figures, submitted to Jnl. of Optics
Collective coherent population trapping in a thermal field
We analyzed the efficiency of coherent population trapping (CPT) in a
superposition of the ground states of three-level atoms under the influence of
the decoherence process induced by a broadband thermal field. We showed that in
a single atom there is no perfect CPT when the atomic transitions are affected
by the thermal field. The perfect CPT may occur when only one of the two atomic
transitions is affected by the thermal field. In the case when both atomic
transitions are affected by the thermal field, we demonstrated that regardless
of the intensity of the thermal field the destructive effect on the CPT can be
circumvented by the collective behavior of the atoms. An analytic expression
was obtained for the populations of the upper atomic levels which can be
considered as a measure of the level of thermal decoherence. The results show
that the collective interaction between the atoms can significantly enhance the
population trapping in that the population of the upper state decreases with
increased number of atoms. The physical origin of this feature was explained by
the semiclassical dressed atom model of the system. We introduced the concept
of multiatom collective coherent population trapping by demonstrating the
existence of collective (entangled) states whose storage capacity is larger
than that of the equivalent states of independent atoms.Comment: Accepted for publication in Phys. Rev.
Normal mode splitting in a coupled system of nanomechanical oscillator and parametric amplifier cavity
We study how an optical parametric amplifier inside the cavity can affect the
normal mode splitting behavior of the coupled movable mirror and the cavity
field. We work in the resolved sideband regime. The spectra exhibit a
double-peak structure as the parametric gain is increased. Moreover, for a
fixed parametric gain, the double-peak structure of the spectrum is more
pronounced with increasing the input laser power. We give results for mode
splitting. The widths of the split lines are sensitive to parametric gain.Comment: 7 pages,9 figure
Simple Wriggling is Hard unless You Are a Fat Hippo
We prove that it is NP-hard to decide whether two points in a polygonal
domain with holes can be connected by a wire. This implies that finding any
approximation to the shortest path for a long snake amidst polygonal obstacles
is NP-hard. On the positive side, we show that snake's problem is
"length-tractable": if the snake is "fat", i.e., its length/width ratio is
small, the shortest path can be computed in polynomial time.Comment: A shorter version is to be presented at FUN 201
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