High-Order Adiabatic Approximation for Non-Hermitian Quantum System and Complexization of Berry's Phase

In this paper the evolution of a quantum system drived by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation(HOAA) method with Berry's phase ,which is valid for either the Hermitian or the non-Hermitian cases. This method can be regarded as a non-trivial generalization of the HOAA method for closed quantum system presented by this author before. In a general situation, the probabilities of adiabatic decay and non-adiabatic transitions are explicitly obtained for the evolution of the non-Hermitian quantum system. It is also shown that the non-Hermitian analog of the Berry's phase factor for the non-Hermitian case just enjoys the holonomy structure of the dual linear bundle over the parameter manifold. The non-Hermitian evolution of the generalized forced harmonic oscillator is discussed as an illustrative examples.Comment: ITP.SB-93-22,17 page

Uniform attractors for non-autonomous wave equations with nonlinear damping

We consider dynamical behavior of non-autonomous wave-type evolutionary equations with nonlinear damping, critical nonlinearity, and time-dependent external forcing which is translation bounded but not translation compact (i.e., external forcing is not necessarily time-periodic, quasi-periodic or almost periodic). A sufficient and necessary condition for the existence of uniform attractors is established using the concept of uniform asymptotic compactness. The required compactness for the existence of uniform attractors is then fulfilled by some new a priori estimates for concrete wave type equations arising from applications. The structure of uniform attractors is obtained by constructing a skew product flow on the extended phase space for the norm-to-weak continuous process.Comment: 33 pages, no figur

Bayesian methods to overcome the winner's curse in genetic studies

Parameter estimates for associated genetic variants, report ed in the initial discovery samples, are often grossly inflated compared to the values observed in the follow-up replication samples. This type of bias is a consequence of the sequential procedure in which the estimated effect of an associated genetic marker must first pass a stringent significance threshold. We propose a hierarchical Bayes method in which a spike-and-slab prior is used to account for the possibility that the significant test result may be due to chance. We examine the robustness of the method using different priors corresponding to different degrees of confidence in the testing results and propose a Bayesian model averaging procedure to combine estimates produced by different models. The Bayesian estimators yield smaller variance compared to the conditional likelihood estimator and outperform the latter in studies with low power. We investigate the performance of the method with simulations and applications to four real data examples.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS373 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

X-ray Structure Analysis and the Intervalent Electron Transfer in Organic Mixed-Valence Crystals with Bridged Aromatic Cation Radicals

X-ray crystallography identifies the aromatic donor group D = 2,5-dimethoxy-4-methylphenyl to be a suitable redox center for the construction of organic mixed-valence crystals owing to its large structural change attendant upon 1e oxidation to the cation−radical (D•+). The combination of cyclic voltammetry, dynamic ESR line broadening, and electronic (NIR) spectroscopy allows the intervalence electron transfer between the redox centers in the mixed-valence system D-br-D•+ [where br can be an aliphatic trimethylene or an aromatic (poly)phenylene bridge] to be probed quantitatively. Independent measures of the electronic coupling matrix element (H) for D/D•+ electron exchange via Mulliken−Hush theory accord with the X-ray crystallographic databoth sufficient to consistently identify the various D-br-D•+ according to the Robin−Day classification. Thus, the directly coupled biaryl D−D•+ is a completely delocalized cation in class III with the charge distributed equally over both redox centers. The trimethylene- and biphenylene-bridged cations D(CH2)3D•+ and D(ph)2D•+ with highly localized charge distributions are prototypical class II systems involving moderately coupled redox centers with H ≈ 400 cm-1. The borderline region between class II/III is occupied by the phenylene-bridged cation D(ph)D•+; and the X-ray, CV, and NIR analyses yield ambivalent H values (which we believe to be) largely a result of an unusually asymmetric (20/80) charge distribution that is polarized between the D/D•+ redox centers

Intervalence (Charge-Resonance) Transitions in Organic Mixed-Valence Systems. Through-Space versus Through-Bond Electron Transfer between Bridged Aromatic (Redox) Centers

Intervalence absorption bands appearing in the diagnostic near-IR region are consistently observed in the electronic spectra of mixed-valence systems containing a pair of aromatic redox centers (Ar•+/Ar) that are connected by two basically different types of molecular bridges. The through-space pathway for intramolecular electron transfer is dictated by an o-xylylene bridge in the mixed-valence cation radical 3•+ with Ar = 2,5-dimethoxy-p-tolyl (T), in which conformational mobility allows the proximal syn disposition of planar T•+/T redox centers. Four independent experimental probes indicate the large through-space electronic interaction between such cofacial Ar•+/Ar redox centers from the measurements of (a) sizable potential splitting in the cyclic voltammogram, (b) quinonoidal distortion of T•+/T centers by X-ray crystallography, (c) “doubling” of the ESR hyperfine splittings, and (d) a pronounced intervalence charge-resonance band. The through (br)-bond pathway for intramolecular electron transfer is enforced in the mixed-valence cation radical 2a•+ by the p-phenylene bridge which provides the structurally inflexible and linear connection between Ar•+/Ar redox centers. The direct comparison of intramolecular rates of electron transfer (kET) between identical T•+/T centers in 3•+ and 2a•+indicates that through-space and through-bond mechanisms are equally effective, despite widely different separations between their redox centers. The same picture obtains for 3•+ and 2a•+from theoretical computations of the first-order rate constants for intramolecular electron transfer from Marcus−Hush theory using the electronic coupling elements evaluated from the diagnostic intervalence (charge-transfer) transitions. Such a strong coherence between theory and experiment also applies to the mixed-valence cation radical 7•+, in which the aromatic redox S center is sterically encumbered by annulation

Self-consistency in the Projected Shell Model

The Projected Shell Model is a shell model theory built up over a deformed BCS mean field. Ground state and excited bands in even-even nuclei are obtained through diagonalization of a pairing plus quadrupole Hamiltonian in an angular momentum projected 0-, 2-, and 4-quasiparticle basis. The residual quadrupole-quadrupole interaction strength is fixed self-consistently with the deformed mean field and the pairing constants are the same used in constructing the quasiparticle basis. Taking $^{160}Dy$ as an example, we calculate low-lying states and compare them with experimental data. We exhibit the effect of changing the residual interaction strengths on the spectra. It is clearly seen that there are many $J^\pi = 0^+, 1^+, 4^+$ bandheads whose energies can only be reproduced using the self-consistent strengths. It is thus concluded that the Projected Shell Model is a model essentially with no free parameters.Comment: 13 pages, 10 figures, submitted to Nuclear Physics