48,810 research outputs found
Antisymmetric PT-photonic structures with balanced positive and negative index materials
We propose a new class of synthetic optical materials in which the refractive
index satisfies n(-\bx)=-n^*(\bx). We term such systems antisymmetric
parity-time (APT) structures. Unlike PT-symmetric systems which require
balanced gain and loss, i.e. n(-\bx)=n^*(\bx), APT systems consist of
balanced positive and negative index materials. Despite the seemingly
PT-symmetric optical potential V(\bx)\equiv n(\bx)^2\omega^2/c^2, APT systems
are not invariant under combined PT operations due to the discontinuity of the
spatial derivative of the wavefunction. We show that APT systems can display
intriguing properties such as spontaneous phase transition of the scattering
matrix, bidirectional invisibility, and a continuous lasing spectrum.Comment: 5 pages, 4 figure
The limits of Hamiltonian structures in three-dimensional elasticity, shells, and rods
This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure.
The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model.
We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material andderive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to the well-known Euler elastica if one adds an additional single constraint that the director lines up with the Frenet frame
Gain-tunable optomechanical cooling in a laser cavity
We study the optical cooling of the resonator mirror in a
cavity-optomechanical system that contains an optical gain medium. We find that
the optical damping rate is vanishingly small for an incoherently pumped laser
above threshold. In the presence of an external coherent drive however, the
optical damping rate can be enhanced substantially with respect to that of a
passive cavity. We show that the strength of the incoherent pump provides a
conduit to tune the damping rate and the minimum attainable phonon number with
the same radiation pressure force, and the latter can be lowered from that of a
passive cavity if the thermal contribution is nonnegligible. We also show that
the system can undergo a transition from the weak optomechanical coupling
regime to the strong optomechanical coupling regime as the incoherent pump
strength is varied.Comment: 7 pages, 5 figure
Statistical description of small quantum systems beyond weak-coupling limit
An explicit expression is derived for the statistical description of small
quantum systems, which are relatively-weakly and directly coupled to only small
parts of their environments. The derived expression has a canonical form, but
is given by a renormalized self-Hamiltonian of the studied system, which
appropriately takes into account the influence of the system-environment
interaction. In the case that the system has a narrow spectrum and the
environment is sufficiently large, the modification to the self-Hamiltonian
usually has a mean-field feature, given by an environmental average of the
interaction Hamiltonian. In other cases, the modification may be beyond the
mean-field approximation.Comment: 9 pages, published versio
Diastereoselective three-component synthesis of beta-amino carbonyl compounds using diazo compounds, boranes, and acyl imines under catalyst-free conditions
Diazo compounds, boranes, and acyl imines undergo a three-component Mannich condensation reaction under catalyst-free conditions to give the anti β-amino carbonyl compounds in high diastereoselectivity. The reaction tolerates a variety of functional groups, and an asymmetric variant was achieved using the (−)-phenylmenthol as chiral auxiliary in good yield and selectivity. These β-amino carbonyl compounds are valuable intermediates, which can be transformed to many potential bioactive molecules.We gratefully acknowledge Philip N. Moquist for editorial review of the manuscript. Preliminary experiments were performed by Y.L. at Boston University. Completion of the work was accomplished under the direction of G.W. at the University of Science and Technology Beijing, China. S.E.S. and Y.L. gratefully acknowledge the NIH for support (NIGMS R01 GM078240). Y.L., J.Y., and G.W. thank the Innovative Foundation from China National Petroleum Corporation (Grant No. 2012D-5006-0504) for financial support. Y.L. also thanks the Beijing Natural Science Foundation (Grant No. 2144052) and China Postdoctoral Science Foundation (2013M540859) for financial support. (NIGMS R01 GM078240 - NIH; 2012D-5006-0504 - Innovative Foundation from China National Petroleum Corporation; 2144052 - Beijing Natural Science Foundation; 2013M540859 - China Postdoctoral Science Foundation)Published versio
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