Long-time dynamics of spontaneous parametric down-conversion and quantum limitations of conversion efficiency

We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motions fails in this case, since it is based on an expansion around an unstable classical solution and neglects pump depletion. Introducing a mean-field approximation we find a periodic exchange of energy between the pump and subharmonic mode goverened by an anharmonic pendulum equation. From this equation the optimum interaction time or crystal length for maximum conversion can be determined. A numerical integration of the 2-mode Schr"odinger equation using a dynamically optimized basis of displaced and squeezed number states verifies the characteristic times predicted by the mean-field approximation. In contrast to semiclassical and mean-field predictions it is found that quantum fluctuations of the pump mode lead to a substantial limitation of the efficiency of parametric down-conversion.Comment: 5 pages, 4 figure

Effective action for the Kondo lattice model. New approach for S=1/2

In the partition function of the Kondo lattice, spin matrices are exactly replaced by bilinear combinations of Fermi operators with the purely imaginary chemical potential lambda=-i.pi.T/2 (Popov representation). This new representation of spin operators allows one to introduce new Green's functions with Matsubara frequencies 2.pi.T(n+1/4) for S=1/2. A simple temperature diagram technique is constructed with the path integral method. This technique is standard and does not contain the complicated combinatoric rules characteristic of most of the known variants of the diagram techniques for spin systems. The effective action for the almost antiferromagnetic Kondo lattice is derived.Comment: 7 pages, Proceedings of SCES98/Paris; one reference adde

Enantioselective PCCP Brønsted acid-catalyzed aza-Piancatelli rearrangement.

An enantioselective aza-Piancatelli rearrangement has been developed using a chiral Brønsted acid based on pentacarboxycyclopentadiene (PCCP). This reaction provides rapid access to valuable chiral 4-amino-2-cyclopentenone building blocks from readily available starting material and is operationally simple

Quantum critical point in the spin glass-antiferromagnetism competition for fermionic Ising Models

The competition between spin glass ($SG$) and antiferromagnetic order ($AF$) is analyzed in two sublattice fermionic Ising models in the presence of a transverse $\Gamma$ and a parallel $H$ magnetic fields. The exchange interaction follows a Gaussian probability distribution with mean $-4J_0/N$ and standard deviation $J\sqrt{32/N}$, but only spins in different sublattices can interact. The problem is formulated in a path integral formalism, where the spin operators have been expressed as bilinear combinations of Grassmann fields. The results of two fermionic models are compared. In the first one, the diagonal $S^z$ operator has four states, where two eigenvalues vanish (4S model), which are suppressed by a restriction in the two states 2S model. The replica symmetry ansatz and the static approximation have been used to obtain the free energy. The results are showing in phase diagrams $T/J$ ($T$ is the temperature) {\it versus} $J_{0}/J$, $\Gamma/J$, and $H/J$. When $\Gamma$ is increased, $T_{f}$ (transition temperature to a nonergodic phase) reduces and the Neel temperature decreases towards a quantum critical point. The field $H$ always destroys $AF$; however, within a certain range, it favors the frustration. Therefore, the presence of both fields, $\Gamma$ and $H$, produces effects that are in competition. The critical temperatures are lower for the 4S model and it is less sensitive to the magnetic couplings than the 2S model.Comment: 15 pages, 6 figures, accepted in Physica

Heteronuclear 3 d/DyIII coordination clusters as catalysts in a domino reaction

Three isoskeletal tetranuclear coordination clusters with general formula [MII2DyIII2L4(EtOH)6](ClO4)2·2 EtOH, (M=Co, 1; M=Ni, 2) and [NiII2DyIII2L4Cl2(CH3CN)2]·2 CH3CN (3), have been synthesized and characterized. These air-stable compounds, and in particular 3, display efficient homogeneous catalytic behavior in the room-temperature synthesis of trans-4,5-diaminocyclopent-2-enones from 2-furaldehyde and primary or secondary amines under a non-inert atmosphere

The Role of Social Cognitions on Children\u27s Emotion Regulation Decisions: Links to Internalizing and Externalizing Symptomatology

PsychologyMaster of Arts (M.A.

Schwinger-Keldysh semionic approach for quantum spin systems

We derive a path-integral Schwinger-Keldysh approach for quantum spin systems. This is achieved by means of a semionic representation of spins as fermions with imaginary chemical potential. The major simplifying feature in comparison with other representations (Holstein-Primakoff, Dyson-Maleev, slave bosons/fermions etc) is that the local constraint is taken into account exactly. As a result, the standard diagram technique with usual Feynman codex is constructed. We illustrate the application of this technique for the N\'eel and spin-liquid states of the AFM Heisenberg model.Comment: 4 pages, RevTeX, 2 EPS figures included, corrected some typos, minor corrections in the tex

Tetranuclear Zn/4f coordination clusters as highly efficient catalysts for Friedel-Crafts alkylation

A series of custom-designed, high yield, isoskeletal tetranuclear Zn/4f coordination clusters showing high efficiency as catalysts with low catalytic loadings in Friedel-Crafts alkylation are described for the first time. The possibility of altering the 4f centers in these catalysts without altering the core topology allows us to further confirm their stability via EPR and NMR, as well to gain insights into the plausible reaction mechanism, showcasing the usefulness of these bimetallic systems as catalysts

Harnessing the Power of Furfuryl Cations: The Aza-Piancatelli Rearrangement and Beyond

Harnessing the Power of Furfuryl Cations:The Aza-Piancatelli Rearrangement and BeyondbyGesine Kerstin VeitsThe ubiquity of amine functional groups in all of nature as well as a large majority of pharmaceutically active molecules makes methodologies capable of quickly constructing carbon-nitrogen bonds invaluable. Reactions capable of constructing these highly desirable bonds in addition to introducing molecular complexity are highly sought-after. Therefore we set out to develop a novel cascade rearrangement of furylcarbinols, a sustainable starting material, to 4-aminocyclopentenones, the aza-Piancatelli rearrangement. Inspired by Piancatelli's rearrangement of furylcarbinols with water to form 4-hydroxycyclopentenones for the synthesis of prostaglandins, we explored the rearrangement with amine nucleophiles to access valuable 4-aminocyclopentenones. The product-forming cascade is initiated by dysprosium trifluoromethanesulfonate, a relatively underdeveloped Lewis acid catalyst. Activation results in the formation of a furfuryl cation (oxocarbenium ion) that is intercepted by an amine nucleophile and terminates in a 4π conrotatory electrocyclization establishing the observed trans-stereochemistry. The chemistry was initially developed with aniline nucleophiles, and was later extended to substituted hydroxylamines. Mechanistic investigations of the aza-Piancatelli rearrangement have shown that an off-cycle binding of the dysprosium catalyst and the amine nucleophile controls the rate, as observed by a Hammett plot. However, the selectivity of the rearrangement is determined by the ability of a nucleophile to efficiently capture the oxocarbenium ion upon its formation. The value of the aza-Piancatelli rearrangement has been highlighted by the synthesis of an hNK1 inhibitor and by efforts toward the total synthesis of homoharringtonine, a pharmaceutical drug approved for the treatment of chronic myeloid leukemia. Additionally, a Piancatelli rearrangement of macrocyclic furylcarbinols, to be applied to the total synthesis of coralloidolide F, has been explored. Finally, chiral phosphoric acids such as (R)-TRIP have been found to be catalysts for the aza-Piancatelli rearrangement capable of inducing enantioselectivity. This is the first example of asymmetric cascade rearrangements of its kind