On Markov operators preserving polynomials

The paper is concerned with a special class of positive linear operators acting on the space C(K) of all continuous functions defined on a convex compact subset K of R^d, d \geq 1, having non-empty interior. Actually, this class consists of all positive linear operators T on C(K) which leave invariant the polynomials of degree at most 1 and which, in addition, map polynomials into polynomials of the same degree. Among other things, we discuss the existence of such operators in the special case where K is strictly convex by also characterizing them within the class of positive projections. In particular we show that such operators exist if and only if ∂K is an ellipsoid. Furthermore, a characterization of balls of R^d in terms of a special class of them is furnished. Additional results and illustrative examples are presented as well

Odd and Even Lidstone-type polynomial sequences. Part 1: basic topics

Abstract Two new general classes of polynomial sequences called respectively odd and even Lidstone-type polynomials are considered. These classes include classic Lidstone polynomials of first and second kind. Some characterizations of the two classes are given, including matrix form, conjugate sequences, generating function, recurrence relations, and determinant forms. Some examples are presented and some applications are sketched

Measurement crosstalk between two phase qubits coupled by a coplanar waveguide

We analyze the measurement crosstalk between two flux-biased phase qubits coupled by a resonant coplanar waveguide cavity. After the first qubit is measured, the superconducting phase can undergo damped oscillations resulting in an a.c. voltage that produces a frequency chirped noise signal whose frequency crosses that of the cavity. We show experimentally that the coplanar waveguide cavity acts as a bandpass filter that can significantly reduce the crosstalk signal seen by the second qubit when its frequency is far from the cavity's resonant frequency. We present a simple classical description of the qubit behavior that agrees well with the experimental data. These results suggest that measurement crosstalk between superconducting phase qubits can be reduced by use of linear or possibly nonlinear resonant cavities as coupling elements.Comment: 4 pages, 3 figure

Circuit QED scheme for realization of the Lipkin-Meshkov-Glick model

We propose a scheme in which the Lipkin-Meshkov-Glick model is realized within a circuit QED system. An array of N superconducting qubits interacts with a driven cavity mode. In the dispersive regime, the cavity mode is adiabatically eliminated generating an effective model for the qubits alone. The characteristic long-range order of the Lipkin-Meshkov-Glick model is here mediated by the cavity field. For a closed qubit system, the inherent second order phase transition of the qubits is reflected in the intensity of the output cavity field. In the broken symmetry phase, the many-body ground state is highly entangled. Relaxation of the qubits is analyzed within a mean-field treatment. The second order phase transition is lost, while new bistable regimes occur.Comment: 5 pages, 2 figure

Synthesis and Biological Evaluation of Dantrolene-Like Hydrazide and Hydrazone Analogues as Multitarget Agents for Neurodegenerative Diseases

Dantrolene, a drug used for the management of malignant hyperthermia, had been recently evaluated for prospective repurposing as multitarget agent for neurodegenerative syndromes, including Alzheimer's disease (AD). Herein, twenty-one dantrolene-like hydrazide and hydrazone analogues were synthesized with the aim of exploring structure-activity relationships (SARs) for the inhibition of human monoamine oxidases (MAOs) and acetylcholinesterase (AChE), two well-established target enzymes for anti-AD drugs. With few exceptions, the newly synthesized compounds exhibited selectivity toward MAO B over either MAO A or AChE, with the secondary aldimine 9 and phenylhydrazone 20 attaining IC50 values of 0.68 and 0.81 μM, respectively. While no general SAR trend was observed with lipophilicity descriptors, a molecular simplification strategy allowed the main pharmacophore features to be identified, which are responsible for the inhibitory activity toward MAO B. Finally, further in vitro investigations revealed cell protection from oxidative insult and activation of carnitine/acylcarnitine carrier as concomitant biological activities responsible for neuroprotection by hits 9 and 20 and other promising compounds in the examined series

Decoherence, Autler-Townes effect, and dark states in two-tone driving of a three-level superconducting system

We present a detailed theoretical analysis of a multi-level quantum system coupled to two radiation fields and subject to decoherence. We concentrate on an effect known from quantum optics as the Autler-Townes splitting, which has been recently demonstrated experimentally [M. A. Sillanpaa et al., Phys. Rev. Lett. 103, 193601 (2009)] in a superconducting phase qubit. In the three-level approximation, we derive analytical solutions and describe how they can be used to extract the decoherence rates and to account for the measurement data. Better agreement with the experiment can be obtained by extending this model to five levels. Finally, we investigate the stationary states created in the experiment and show that their structure is close to that of dark states.Comment: 16 pages, 8 figure

Parametric coupling between macroscopic quantum resonators

Time-dependent linear coupling between macroscopic quantum resonator modes generates both a parametric amplification also known as a {}"squeezing operation" and a beam splitter operation, analogous to quantum optical systems. These operations, when applied properly, can robustly generate entanglement and squeezing for the quantum resonator modes. Here, we present such coupling schemes between a nanomechanical resonator and a superconducting electrical resonator using applied microwave voltages as well as between two superconducting lumped-element electrical resonators using a r.f. SQUID-mediated tunable coupler. By calculating the logarithmic negativity of the partially transposed density matrix, we quantitatively study the entanglement generated at finite temperatures. We also show that characterization of the nanomechanical resonator state after the quantum operations can be achieved by detecting the electrical resonator only. Thus, one of the electrical resonator modes can act as a probe to measure the entanglement of the coupled systems and the degree of squeezing for the other resonator mode.Comment: 15 pages, 4 figures, submitte

trans-rac-[1-Oxo-2-phenethyl-3-(2-thien­yl)-1,2,3,4-tetra­hydro­isoquinolin-4-yl]methyl 4-methyl­benzene­sulfonate

The title compound, C29H27NO4S2, was synthesized by reaction of trans-rac-4-(hydroxy­meth­yl)-2-phenethyl-3-(thio­phen-2-yl)-3,4-dihydro­isoquinolin-1(2H)-one and 4-methyl­benzene-1-sulfonyl chloride in the presence of Et3N in CH2Cl2. The relative orientations of the benzene ring (A) of the 3,4-dihydro­isoquinolinone ring system, the thio­phene ring (B), the benzene ring (C) of the methyl­benzene group and the phenyl ring (D) result in the following dihedral angles: A/B = 80.91 (16), A/C = 22.79 (18), A/D = 9.9 (2), B/C = 80.73 (19), B/D = 88.9 (2) and C/D = 29.9 (2)°. The crystal structure is stabilized by weak inter­molecular C—H⋯O hydrogen bonds and C—H⋯π inter­actions