Nose-Hoover sampling of quantum entangled distribution functions

While thermostated time evolutions stand on firm grounds and are widely used in classical molecular dynamics (MD) simulations, similar methods for quantum MD schemes are still lacking. In the special case of a quantum particle in a harmonic potential, it has been shown that the framework of coherent states permits to set up equations of motion for an isothermal quantum dynamics. In the present article, these results are generalized to indistinguishable quantum particles. We investigate the consequences of the (anti-)symmetry of the many-particle wavefunction which leads to quantum entangled distribution functions. The resulting isothermal equations of motion for bosons and fermions contain new terms which cause Bose-attraction and Pauli-blocking. Questions of ergodicity are discussed for different coupling schemes.Comment: 15 pages, 4 figures, submitted to PHYSICA A. More information at http://www.physik.uni-osnabrueck.de/makrosysteme

Nose-Hoover dynamics for coherent states

The popular method of Nose and Hoover to create canonically distributed positions and momenta in classical molecular dynamics simulations is generalized to a genuine quantum system of infinite dimensionality. We show that for the quantum harmonic oscillator, the equations of motion in terms of coherent states can easily be modified in an analogous manner to mimic the coupling of the system to a thermal bath and create a quantum canonical ensemble. Possible applications to more complex systems, especially interacting Fermion systems, are proposed.Comment: 13 pages, 3 figure

Spin dynamics of quantum and classical Heisenberg dimers

Analytical solutions for the time-dependent autocorrelation function of the classical and quantum mechanical spin dimer with arbitrary spin are presented and compared. For large spin quantum numbers or high temperature the classical and the quantum dimer become more and more similar, yet with the major difference that the quantum autocorrelation function is periodic in time whereas the classical is not.Comment: 10 pages, 4 postscript figures, uses 'epsfig.sty'. Submitted to Physica A. More information available at http://www.physik.uni-osnabrueck.de/makrosysteme

Time Correlation Functions of Three Classical Heisenberg Spins on an Isosceles Triangle and on a Chain: Strong Effects of Broken Symmetry

At arbitrary temperature $T$, we solve for the dynamics of single molecule magnets composed of three classical Heisenberg spins either on a chain with two equal exchange constants $J_1$, or on an isosceles triangle with a third, different exchange constant $J_2$. As T\rightrarrow\infty, the Fourier transforms and long-time asymptotic behaviors of the two-spin time correlation functions are evaluated exactly. The lack of translational symmetry on a chain or an isosceles triangle yields time correlation functions that differ strikingly from those on an equilateral trinagle with $J_1=J_2$. At low $T$, the Fourier transforms of the two autocorrelation functions with $J_1\ne J_2$ show one and four modes, respectively. For a semi-infinite $J_2/J_1$ range, one mode is a central peak. At the origin of this range, this mode has a novel scaling form.Comment: 9 pages, 14 figures, accepted for publication in Phys. Rev.

Heisenberg Dimer Single Molecule Magnets in a Strong Magnetic Field

We calculate the static and dynamic properties of single crystal, single molecule magnets consisting of equal spin $S=1/2$ or 5/2 dimers. The spins in each dimer interact with each other via the Heisenberg exchange interaction and with the magnetic induction ${\bf B}$ via the Zeeman interaction, and interdimer interactions are negligible. For antiferromagnetic couplings, the static magnetization and specific heat exhibit interesting low temperature $T$ and strong ${\bf B}$ quantum effects. We calculate the frequency spectrum of the Fourier transform of the real part of the time autocorrelation function ${\cal C}_{11}(t)$ for arbitrary $T, {\bf B}$, and compare our results with those obtained for classical spins. We also calculate the inelastic neutron magnetic dynamical structure factor $S({\bf q},\omega)$ at arbitrary $T, {\bf B}$.Comment: 11 pages, 14 figures, submitted to Phys. Rev.

Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory

\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962 - 968 (2003)] introduced in connection with the summation of the divergent perturbation expansion of the hydrogen atom in an external magnetic field a new sequence transformation which uses as input data not only the elements of a sequence $\{s_n \}_{n=0}^{\infty}$ of partial sums, but also explicit estimates $\{\omega_n \}_{n=0}^{\infty}$ for the truncation errors. The explicit incorporation of the information contained in the truncation error estimates makes this and related transformations potentially much more powerful than for instance Pad\'{e} approximants. Special cases of the new transformation are sequence transformations introduced by Levin [Int. J. Comput. Math. B \textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189 - 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A \textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations - explicit expressions, recurrence formulas, explicit expressions in the case of special remainder estimates, and asymptotic order estimates satisfied by rational approximants to power series - is formulated in terms of hitherto unknown mathematical properties of the new transformation introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of Mathematical Physic

Epithelial NAD+ depletion drives mitochondrial dysfunction and contributes to intestinal inflammation

IntroductionWe have previously demonstrated that a pathologic downregulation of peroxisome proliferator-activated receptor–gamma coactivator 1-alpha (PGC1α) within the intestinal epithelium contributes to the pathogenesis of inflammatory bowel disease (IBD). However, the mechanism underlying downregulation of PGC1α expression and activity during IBD is not yet clear.MethodsMice (male; C57Bl/6, Villincre/+;Pgc1afl/fl mice, and Pgc1afl/fl) were subjected to experimental colitis and treated with nicotinamide riboside. Western blot, high-resolution respirometry, nicotinamide adenine dinucleotide (NAD+) quantification, and immunoprecipitation were used to in this study.ResultsWe demonstrate a significant depletion in the NAD+ levels within the intestinal epithelium of mice undergoing experimental colitis, as well as humans with ulcerative colitis. While we found no decrease in the levels of NAD+-synthesizing enzymes within the intestinal epithelium of mice undergoing experimental colitis, we did find an increase in the mRNA level, as well as the enzymatic activity, of the NAD+-consuming enzyme poly(ADP-ribose) polymerase-1 (PARP1). Treatment of mice undergoing experimental colitis with an NAD+ precursor reduced the severity of colitis, restored mitochondrial function, and increased active PGC1α levels; however, NAD+ repletion did not benefit transgenic mice that lack PGC1α within the intestinal epithelium, suggesting that the therapeutic effects require an intact PGC1α axis.DiscussionOur results emphasize the importance of PGC1α expression to both mitochondrial health and homeostasis within the intestinal epithelium and suggest a novel therapeutic approach for disease management. These findings also provide a mechanistic basis for clinical trials of nicotinamide riboside in IBD patients

Decreased CD90 expression in human mesenchymal stem cells by applying mechanical stimulation

BACKGROUND: Mesenchymal stem cells (MSC) are multipotent cells which can differentiate along osteogenic, chondrogenic, and adipogenic lineages. The present study was designed to investigate the influence of mechanical force as a specific physiological stress on the differentiation of (MSC) to osteoblast-like cells. METHODS: Human MSC were cultured in osteoinductive medium with or without cyclic uniaxial mechanical stimulation (2000 μstrain, 200 cycles per day, 1 Hz). Cultured cells were analysed for expression of collagen type I, osteocalcin, osteonectin, and CD90. To evaluate the biomineral formation the content of bound calcium in the cultures was determined. RESULTS: After 14 days in culture immunfluorescence staining revealed enhancement of collagen type I and osteonectin expression in response to mechanical stimulation. In contrast, mechanically stimulated cultures stained negative for CD90. In stimulated and unstimulated cultures an increase in the calcium content over time was observed. After 21 days in culture the calcium content in mechanical stimulated cultures was significantly higher compared to unstimulated control cultures. CONCLUSION: These results demonstrate the influence of mechanical force on the differentiation of human MSC into osteoblast-like cells in vitro. While significant enhancement of the biomineral formation by mechanical stimulation is not detected before 21 days, effects on the extracellular matrix became already obvious after 14 days. The decrease of CD90 expression in mechanically stimulated cultures compared to unstimulated control cultures suggests that CD90 is only transiently expressed expression during the differentiation of MSC to osteoblast-like cells in culture