Nonlinear Optical Dynamics and High Reflectance of a Monolayer of Three-Level Quantum Emitters with a Doublet in the Excited State

Abstract: We study theoretically the nonlinear optical response of a monolayer of regularly arranged three-level identical quantum emitters with a doublet in the excited state to the action of a monochromatic electromagnetic field quasi-resonant to optical transitions in the emitter. The total retarded dipole–dipole interaction of the emitters is accounted for in the mean-field approximation. This interaction plays the role of a positive feedback, which (in combination with the immanent nonlinearity of emitters themselves) leads to multistability of the monolayer response. The stability of different response branches is analyzed using the Lyapunov exponents method. It is found that the instability type depends on the doublet splitting and changes from self-oscillations to chaos upon increasing the splitting. Another important property of the monolayer is its high (almost 100%) reflectance in a certain frequency range; i.e., within this range, the monolayer operates as a perfect nanometer mirror; moreover, reflection can be switched to transmission changing slightly the incident field amplitude (bistability). The possibility of application of the above mentioned monolayer optical properties in nanophotonics is discussed

‘Pole Test’ Measurements in Critical Leg Ischaemia

AbstractBackgroundFor the quantification of critical limb ischaemia (CLI) most vascular surgery units use sphygmo-manometric and transcutaneous oxygen pressure (TcPO2) measurements. However, measurements obtained by cuff-manometry can be overestimated especially in diabetic patients because of medial calcification that makes leg arteries less compressible. TcPO2 measurements present a considerable overlap in the values obtained for patients with different degrees of ischaemia and its reproducibility has been questioned. Arterial wall stiffness has less influence on the pole test, based on hydrostatic pressure derived by leg elevation, and this test seems to provide a reliable index of CLI.ObjectiveThe objective of this study was to evaluate the pole pressure test for detection of critical lower limb ischaemia, correlating results with cuff-manometry and transcutaneous oxygen pressure.DesignUniversity hospital-prospective study.Materials and methodsSeventy-four patients (83 legs) with rest pain or gangrene were evaluated by four methods: pole test, cuff-manometry, TcPO2 and arteriography. CLI was present if the following criteria were met: (a) important arteriographic lesions+rest pain with an ankle systolic pressure (ASP) ≤40mmHg and/or a TcPO2 ≤30mmHg, or (b) important arteriographic lesions+tissue loss with an ASP ≤60mmHg and/or a TcPO2 ≤40mmHg. Fifty-seven lower limbs met the criteria for CLI.ResultsMeasurements obtained by cuff-manometry were significantly higher to those obtained by pole test (mean pressure difference: 40mmHg, p<0.001). The difference between the two methods remained statistically significant for both diabetics (50.73, p<0.001) and non-diabetics (31.46, p<0.001). Mean TcPO2 value was 15.51mmHg and there was no important difference between patients with and without diabetes. Overall, there was a correlation between sphygmomanometry and pole test (r=0.481). The correlation persisted for patients without diabetes (r=0.581), but was not evident in patients with diabetes. Correlation between pole test and TcPO2 was observed only for patients with diabetes (r=0.444). There was no correlation between cuff-manometry and TcPO2. The pole test offered an accuracy of 88% for the detection of CLI. The sensitivity of this test was 95% and the specificity 73%

Two-Dimensional Twisted Sigma Models, the Mirror Chiral de Rham Complex, and Twisted Generalised Mirror Symmetry

In this paper, we study the perturbative aspects of a "B-twisted" two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle $\mathcal E$ over a complex, hermitian manifold $X$. We show that the model can be naturally described in terms of the mathematical theory of ``Chiral Differential Operators". In particular, the physical anomalies of the sigma model can be reinterpreted as an obstruction to a global definition of the associated sheaf of vertex superalgebras derived from the free conformal field theory describing the model locally on $X$. In addition, one can also obtain a novel understanding of the sigma model one-loop beta function solely in terms of holomorphic data. At the $(2,2)$ locus, one can describe the resulting half-twisted variant of the topological B-model in terms of a $\it{mirror}$ "Chiral de Rham complex" (or CDR) defined by Malikov et al. in \cite{GMS1}. Via mirror symmetry, one can also derive various conjectural expressions relating the sheaf cohomology of the mirror CDR to that of the original CDR on pairs of Calabi-Yau mirror manifolds. An analysis of the half-twisted model on a non-K\"ahler group manifold with torsion also allows one to draw conclusions about the corresponding sheaves of CDR (and its mirror) that are consistent with mathematically established results by Ben-Bassat in \cite{ben} on the mirror symmetry of generalised complex manifolds. These conclusions therefore suggest an interesting relevance of the sheaf of CDR in the recent study of generalised mirror symmetry.Comment: 97 pages. Companion paper to hep-th/0604179. Published versio

Nonlinear optical dynamics of a 2D semiconductor quantum dot super-crystal: emerging multistability, self-oscillations and chaos

We conduct a theoretical study of the nonlinear optical dynamics of a 2D super-crystal comprising regularly spaced identical semiconductor quantum dots (SQDs), subjected to a resonant continuous wave excitation. A single SQD is considered as three-level ladder-like systems involving the ground, one-exciton and bi-exction states. We show that the super-crystal reveals a rich nonlinear dynamics, exhibiting multistability, self-oscillations and chaos. The behaviour is driven by the retarded SQD-SQD interactions and bi-exciton binding energy

A heterotic sigma model with novel target geometry

We construct a (1,2) heterotic sigma model whose target space geometry consists of a transitive Lie algebroid with complex structure on a Kaehler manifold. We show that, under certain geometrical and topological conditions, there are two distinguished topological half--twists of the heterotic sigma model leading to A and B type half--topological models. Each of these models is characterized by the usual topological BRST operator, stemming from the heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with the former, originating from the (1,0) supersymmetry. These BRST operators combined in a certain way provide each half--topological model with two inequivalent BRST structures and, correspondingly, two distinct perturbative chiral algebras and chiral rings. The latter are studied in detail and characterized geometrically in terms of Lie algebroid cohomology in the quasiclassical limit.Comment: 83 pages, no figures, 2 references adde

Chiral de Rham complex on Riemannian manifolds and special holonomy

Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model, we suggest a setup for the study of CDR on manifolds with special holonomy. We show how to systematically construct global sections of CDR from differential forms, and investigate the algebra of the sections corresponding to the covariantly constant forms associated with the special holonomy. As a concrete example, we construct two commuting copies of the Odake algebra (an extension of the N=2 superconformal algebra) on the space of global sections of CDR of a Calabi-Yau threefold and conjecture similar results for G_2 manifolds. We also discuss quasi-classical limits of these algebras.Comment: 49 pages, title changed, major rewrite with no changes in the main theorems, published versio

Gepner-like models and Landau-Ginzburg/sigma-model correspondence

The Gepner-like models of $k^{K}$-type is considered. When $k+2$ is multiple of $K$ the elliptic genus and the Euler characteristic is calculated. Using free-field representation we relate these models with $\sigma$-models on hypersurfaces in the total space of anticanonical bundle over the projective space $\mathbb{P}^{K-1}$

Unitarity of rational N=2 superconformal theories

We demonstrate that all rational models of the N=2 super Virasoro algebra are unitary. Our arguments are based on three different methods: we determine Zhu's algebra (for which we give a physically motivated derivation) explicitly for certain theories, we analyse the modular properties of some of the vacuum characters, and we use the coset realisation of the algebra in terms of su_2 and two free fermions. Some of our arguments generalise to the Kazama-Suzuki models indicating that all rational N=2 supersymmetric models might be unitary.Comment: LaTeX (+amssym.def), 28 pages; minor changes in content, some references added, final versio

Gaudin Model, Bethe Ansatz and Critical Level

We propose a new method of diagonalization of hamiltonians of the Gaudin model associated to an arbitrary simple Lie algebra, which is based on Wakimoto modules over affine algebras at the critical level. We construct eigenvectors of these hamiltonians by restricting certain invariant functionals on tensor products of Wakimoto modules. In conformal field theory language, the eigenvectors are given by certain bosonic correlation functions. Analogues of Bethe ansatz equations naturally appear as Kac-Kazhdan type equations on the existence of certain singular vectors in Wakimoto modules. We use this construction to expalain a connection between Gaudin's model and correlation functions of WZNW models.Comment: 40 pages, postscript-file (references added and corrected

On the six-dimensional origin of the AGT correspondence

We argue that the six-dimensional (2,0) superconformal theory defined on M \times C, with M being a four-manifold and C a Riemann surface, can be twisted in a way that makes it topological on M and holomorphic on C. Assuming the existence of such a twisted theory, we show that its chiral algebra contains a W-algebra when M = R^4, possibly in the presence of a codimension-two defect operator supported on R^2 \times C \subset M \times C. We expect this structure to survive the \Omega-deformation.Comment: References added. 14 page