18,040 research outputs found

### 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

### SU(2|2) for Theories with Sixteen Supercharges at Weak and Strong Coupling

We consider the dimensional reductions of N=4 Supersymmetric Yang-Mills
theory on R x S^3 to the three-dimensional theory on R x S^2, the orbifolded
theory on R x S^3/Z_k, and the plane-wave matrix model. With explicit emphasis
on the three-dimensional theory, we demonstrate the realization of the SU(2|3)
algebra in a radial Hamiltonian framework. Using this structure we constrain
the form of the spin chains, their S-matrices, and the corresponding one- and
two-loop Hamiltonian of the three dimensional theory and find putative signs of
integrability up to the two-loop order. The string duals of these theories
admit the IIA plane-wave geometry as their Penrose limit. Using known results
for strings quantized on this background, we explicitly construct the
strong-coupling dual extended SU(2|2) algebra and discuss its implications for
the gauge theories.Comment: 37 pages, 1 figure. v2 some minor improvements to the text, version
to appear in Phys.Rev.

### Localization and transport in a strongly driven Anderson insulator

We study localization and charge dynamics in a monochromatically driven
one-dimensional Anderson insulator focussing on the low-frequency,
strong-driving regime. We study this problem using a mapping of the Floquet
Hamiltonian to a hopping problem with correlated disorder in one higher
harmonic-space dimension. We show that (i) resonances in this model correspond
to \emph{adiabatic} Landau-Zener (LZ) transitions that occur due to level
crossings between lattice sites over the course of dynamics; (ii) the
proliferation of these resonances leads to dynamics that \emph{appear}
diffusive over a single drive cycle, but the system always remains localized;
(iii) actual charge transport occurs over many drive cycles due to slow
dephasing between these LZ orbits and is logarithmic-in-time, with a crucial
role being played by far-off Mott-like resonances; and (iv) applying a
spatially-varying random phase to the drive tends to decrease localization,
suggestive of weak-localization physics. We derive the conditions for the
strong driving regime, determining the parametric dependencies of the size of
Floquet eigenstates, and time-scales associated with the dynamics, and
corroborate the findings using both numerical scaling collapses and analytical
arguments.Comment: 7 pages + references, 6 figure

### Nutritional Status of Households of Rural Field Practice Area of a Tertiary Care Hospital in India

Introduction: In the world as a whole there appears to be a shift from under-nourishment towards over-nourishment making more and more children, adolescents, adults and even elderly to be overweight and obese. Objectives: Study aimed to find out the age and sex wise commonness of over-weight & obesity amongst the families of an overtly different socio-economic environment and its trend in the members of one type of families. Materials & Methods: The undergraduate medical students are supposed to maintain record of individual health (including height & weight) of their own family as well as that of the allotted family. The data collected (record maintained ) by students was utilized to calculate Body Mass Index (BMI). Results: Out of total 291 subjects (males 168; females 123) in students own family 28.9% (28.0%; 30.1%) were overweight and 5.9% (6.0%; 5.7%) were obese. The similar figures for 262 subjects (males 143 & females 119) in the allotted families were 20.2% (18.5%; 20.2%) and 6.5% (4.2%; 8.4%) respectively. The respective percentages of under nourished individuals were 18.6 (17.9; 19.5) and 35.5 (37.8; 32.8). Thus over-nutrition was more common amongst the members of students own families (34.8% vs. 26.7%) and under-nutrition was more common amongst the members of allotted families (35.5% vs. 18.6%) For the years 2000-2003, BMI amongst individuals of students own families the under-nutrition in the age group of 15-24 years amongst males increased from 15.9% to 32.9% and over-nutrition from 13.6% to 20.5%. There was no case of overweight and obesity up to the age of 34 years in the previous analysis which was 2.6% in the present analysis Previous results demonstrated overweight to be more common in males (32.4% Vs. 24.4% in females) and obesity being more common females ( 6.3% Vs. 2.6% in females). Conclusion: Males are increasingly becoming prey of malnutrition (adolescents for under-nutrition and adults & elderly for over-nutrition. More studies covering larger samples are required to be conducted on a more frequent basis

### Fast global convergence of gradient methods for high-dimensional statistical recovery

Many statistical $M$-estimators are based on convex optimization problems
formed by the combination of a data-dependent loss function with a norm-based
regularizer. We analyze the convergence rates of projected gradient and
composite gradient methods for solving such problems, working within a
high-dimensional framework that allows the data dimension \pdim to grow with
(and possibly exceed) the sample size \numobs. This high-dimensional
structure precludes the usual global assumptions---namely, strong convexity and
smoothness conditions---that underlie much of classical optimization analysis.
We define appropriately restricted versions of these conditions, and show that
they are satisfied with high probability for various statistical models. Under
these conditions, our theory guarantees that projected gradient descent has a
globally geometric rate of convergence up to the \emph{statistical precision}
of the model, meaning the typical distance between the true unknown parameter
$\theta^*$ and an optimal solution $\hat{\theta}$. This result is substantially
sharper than previous convergence results, which yielded sublinear convergence,
or linear convergence only up to the noise level. Our analysis applies to a
wide range of $M$-estimators and statistical models, including sparse linear
regression using Lasso ($\ell_1$-regularized regression); group Lasso for block
sparsity; log-linear models with regularization; low-rank matrix recovery using
nuclear norm regularization; and matrix decomposition. Overall, our analysis
reveals interesting connections between statistical precision and computational
efficiency in high-dimensional estimation

### Fast preparation of critical ground states using superluminal fronts

We propose a spatio-temporal quench protocol that allows for the fast
preparation of ground states of gapless models with Lorentz invariance.
Assuming the system initially resides in the ground state of a corresponding
massive model, we show that a superluminally-moving `front' that
$\textit{locally}$ quenches the mass, leaves behind it (in space) a state
$\textit{arbitrarily close}$ to the ground state of the gapless model.
Importantly, our protocol takes time $\mathcal{O} \left( L \right)$ to produce
the ground state of a system of size $\sim L^d$ ($d$ spatial dimensions), while
a fully adiabatic protocol requires time $\sim \mathcal{O} \left( L^2 \right)$
to produce a state with exponential accuracy in $L$. The physics of the
dynamical problem can be understood in terms of relativistic rarefaction of
excitations generated by the mass front. We provide proof-of-concept by solving
the proposed quench exactly for a system of free bosons in arbitrary
dimensions, and for free fermions in $d = 1$. We discuss the role of
interactions and UV effects on the free-theory idealization, before numerically
illustrating the usefulness of the approach via simulations on the quantum
Heisenberg spin-chain.Comment: 4.25 + 10 pages, 3 + 2 figure

### 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.

### Exactly solvable $\mathcal{PT}$-symmetric models in two dimensions

Non-hermitian, $\mathcal{PT}$-symmetric Hamiltonians, experimentally realized
in optical systems, accurately model the properties of open, bosonic systems
with balanced, spatially separated gain and loss. We present a family of
exactly solvable, two-dimensional, $\mathcal{PT}$ potentials for a
non-relativistic particle confined in a circular geometry. We show that the
$\mathcal{PT}$ symmetry threshold can be tuned by introducing a second
gain-loss potential or its hermitian counterpart. Our results explicitly
demonstrate that $\mathcal{PT}$ breaking in two dimensions has a rich phase
diagram, with multiple re-entrant $\mathcal{PT}$ symmetric phases.Comment: 6 pages, 6 figure

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