Exactly solvable approximating models for Rabi Hamiltonian dynamics

The interaction between an atom and a one mode external driving field is an ubiquitous problem in many branches of physics and is often modeled using the Rabi Hamiltonian. In this paper we present a series of analytically solvable Hamiltonians that approximate the Rabi Hamiltonian and compare our results to the Jaynes-Cummings model which neglects the so-called counter-rotating term in the Rabi Hamiltonian. Through a unitary transformation that diagonlizes the Jaynes-Cummings model, we transform the counter-rotating term into separate terms representing several different physical processes. By keeping only certain terms, we can achieve an excellent approximation to the exact dynamics within specified parameter ranges

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic R\"ossler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.Comment: 12 pages, 13 figure

A global disorder of imprinting in the human female germ line

Imprinted genes are expressed differently depending on whether they are carried by a chromosome of maternal or paternal origin. Correct imprinting is established by germline-specific modifications; failure of this process underlies several inherited human syndromes. All these imprinting control defects are cis-acting, disrupting establishment or maintenance of allele-specific epigenetic modifications across one contiguous segment of the genome. In contrast, we report here an inherited global imprinting defect. This recessive maternal-effect mutation disrupts the specification of imprints at multiple, non-contiguous loci, with the result that genes normally carrying a maternal methylation imprint assume a paternal epigenetic pattern on the maternal allele. The resulting conception is phenotypically indistinguishable from an androgenetic complete hydatidiform mole, in which abnormal extra-embryonic tissue proliferates while development of the embryo is absent or nearly so. This disorder offers a genetic route to the identification of trans-acting oocyte factors that mediate maternal imprint establishment

Functional integral treatment of some quantum nondemolition systems

In the scheme of a quantum nondemolition (QND) measurement, an observable is measured without perturbing its evolution. In the context of studies of decoherence in quantum computing, we examine the `open' quantum system of a two-level atom, or equivalently, a spin-1/2 system, in interaction with quantum reservoirs of either oscillators or spins, under the QND condition of the Hamiltonian of the system commuting with the system-reservoir interaction. For completeness, we also examine the well-known non-QND spin-Bose problem. For all these many-body systems, we use the methods of functional integration to work out the propagators. The propagators for the QND Hamiltonians are shown to be analogous to the squeezing and rotation operators, respectively, for the two kinds of baths considered. Squeezing and rotation being both phase space area-preserving canonical transformations, this brings out an interesting connection between the energy-preserving QND Hamiltonians and the homogeneous linear canonical transformations.Comment: 16 pages, no figure

Photoinduced IR absorption in (La(1-x)Sr(x)Mn)(1-\delta)O3: changes of the anti-Jahn-Teller polaron binding energy with doping

Photoinduced IR absorption was measured in (La(1-x)Sr(x)Mn)(1-\delta)O3. A midinfrared peak centered at ~ 5000 cm$^{-1}$ was observed in the x=0 antiferromagnetic sample. The peak diminishes and softens as hole doping is increased. The origin of the photoinduced absorption peak is atributted to the photon assisted hopping of anti-Jahn-Teller polarons formed by photoexcited charge carriers, whose binding energy decreases with increasing hole doping. The shape of the peak indicates that the polarons are small.Comment: 5 pages, 3 figures, submitted to PR

Development of an approximate method for quantum optical models and their pseudo-Hermicity

An approximate method is suggested to obtain analytical expressions for the eigenvalues and eigenfunctions of the some quantum optical models. The method is based on the Lie-type transformation of the Hamiltonians. In a particular case it is demonstrated that $E\times \epsilon$ Jahn-Teller Hamiltonian can easily be solved within the framework of the suggested approximation. The method presented here is conceptually simple and can easily be extended to the other quantum optical models. We also show that for a purely imaginary coupling the $E\times \epsilon$ Hamiltonian becomes non-Hermitian but $P\sigma _{0}$-symmetric. Possible generalization of this approach is outlined.Comment: Paper prepared fo the "3rd International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics" June 2005 Istanbul. To be published in Czechoslovak Journal of Physic

Time evolution of the Rabi Hamiltonian from the unexcited vacuum

The Rabi Hamiltonian describes a single mode of electromagnetic radiation interacting with a two-level atom. Using the coupled cluster method, we investigate the time evolution of this system from an initially empty field mode and an unexcited atom. We give results for the atomic inversion and field occupation, and find that the virtual processes cause the field to be squeezed. No anti-bunching occurs.Comment: 25 pages, 8 figures, RevTe

Dnmt2-dependent methylomes lack defined DNA methylation patterns

Several organisms have retained methyltransferase 2 (Dnmt2) as their only candidate DNA methyltransferase gene. However, information about Dnmt2-dependent methylation patterns has been limited to a few isolated loci and the results have been discussed controversially. In addition, recent studies have shown that Dnmt2 functions as a tRNA methyltransferase, which raised the possibility that Dnmt2-only genomes might be unmethylated. We have now used whole-genome bisulfite sequencing to analyze the methylomes of Dnmt2-only organisms at single-base resolution. Our results show that the genomes of Schistosoma mansoni and Drosophila melanogaster lack detectable DNA methylation patterns. Residual unconverted cytosine residues shared many attributes with bisulfite deamination artifacts and were observed at comparable levels in Dnmt2-deficient flies. Furthermore, genetically modified Dnmt2-only mouse embryonic stem cells lost the DNA methylation patterns found in wild-type cells. Our results thus uncover fundamental differences among animal methylomes and suggest that DNA methylation is dispensable for a considerable number of eukaryotic organisms

Conductivity of CuO3_3-Chains: Disorder versus Electron-Phonon Coupling

The optical conductivity of the CuO$_3$-chains, a subsystem of the 1-2-3 materials, is dominated by a broad peak in the mid-infrared ($\omega \approx 0.2$eV), and a slowly falling high-frequency tail. The 1D $t$-$J$-model is proposed as the relevant low-energy Hamiltonian describing the intrinsic electronic structure of the CuO$_3$-chains. However, due to charge-spin decoupling, this model alone cannot reproduce the observed \sw. We consider two additional scattering mechanisms: (i) Disregarding the not so crucial spin degrees of freedom, the inclusion of strong potential disorder yields excellent agreement with experiment, but suffers from the unreasonable value of the disorder strength necessary for the fit. (ii) Moderately strong polaronic electron-phonon coupling to the mode involving Cu(1)-O(4) stretching, can be modeled within a 1D Holstein Hamiltonian of spinless fermions. Using a variational approximation for the phonon Hilbert space, we diagonalize the Hamiltonian exactly on finite lattices. As a result of the experimental hole density $\approx 1/2$, the chains can exhibit strong charge-density-wave (CDW) correlations, driven by phonon-mediated polaron-polaron interactions. In the vicinity of half filling, charge motion is identified as arising from moving domain walls, \ie defects in the CDW. Incorporating the effect of vacancy disorder by choosing open boundary conditions, good agreement with the experimental spectra is found. In particular, a high-frequency tail arises as a consequence of the polaron-polaron interactions.Comment: 42 pages, ETH-TH/93-31 (Postscript

Polaronic optical absorption in electron-doped and hole-doped cuprates

Polaronic features similar to those previously observed in the photoinduced spectra of cuprates have been detected in the reflectivity spectra of chemically doped parent compounds of high-critical-temperature superconductors, both $n$-type and $p$-type. In Nd$_2$CuO$_{4-y}$ these features, whose intensities depend both on doping and temperature, include local vibrational modes in the far infrared and a broad band centered at $\sim$ 1000 cm$^{-1}$. The latter band is produced by the overtones of two (or three) local modes and is well described in terms of a small-polaron model, with a binding energy of about 500 cm$^{-1}$. Most of the above infrared features are shown to survive in the metallic phase of Nd$_{2-x}$Ce$_x$Cu0$_{4-y}$, Bi$_2$Sr$_2$CuO$_6$, and YBa$_2$Cu$_3$O$_{7-y}$, where they appear as extra-Drude peaks. The occurrence of polarons is attributed to local modes strongly coupled to carriers, as shown by a comparison with tunneling results.Comment: File latex, 31 p., submitted to Physical Review B. Figures may be faxed upon reques