Fourth Order Algorithms for Solving the Multivariable Langevin Equation and the Kramers Equation

We develop a fourth order simulation algorithm for solving the stochastic Langevin equation. The method consists of identifying solvable operators in the Fokker-Planck equation, factorizing the evolution operator for small time steps to fourth order and implementing the factorization process numerically. A key contribution of this work is to show how certain double commutators in the factorization process can be simulated in practice. The method is general, applicable to the multivariable case, and systematic, with known procedures for doing fourth order factorizations. The fourth order convergence of the resulting algorithm allowed very large time steps to be used. In simulating the Brownian dynamics of 121 Yukawa particles in two dimensions, the converged result of a first order algorithm can be obtained by using time steps 50 times as large. To further demostrate the versatility of our method, we derive two new classes of fourth order algorithms for solving the simpler Kramers equation without requiring the derivative of the force. The convergence of many fourth order algorithms for solving this equation are compared.Comment: 19 pages, 2 figure

Terahertz magneto-spectroscopy of transient plasmas in semiconductors

Using synchronized near-infrared (NIR) and terahertz (THz) lasers, we have performed picosecond time-resolved THz spectroscopy of transient carriers in semiconductors. Specifically, we measured the temporal evolution of THz transmission and reflectivity after NIR excitation. We systematically investigated transient carrier relaxation in GaAs and InSb with varying NIR intensities and magnetic fields. Using this information, we were able to determine the evolution of the THz absorption to study the dynamics of photocreated carriers. We developed a theory based on a Drude conductivity with time-dependent density and density-dependent scattering lifetime, which successfully reproduced the observed plasma dynamics. Detailed comparison between experimental and theoretical results revealed a linear dependence of the scattering frequency on density, which suggests that electron-electron scattering is the dominant scattering mechanism for determining the scattering time. In InSb, plasma dynamics was dramatically modified by the application of a magnetic field, showing rich magneto-reflection spectra, while GaAs did not show any significant magnetic field dependence. We attribute this to the small effective masses of the carriers in InSb compared to GaAs, which made the plasma, cyclotron, and photon energies all comparable in the density, magnetic field, and wavelength ranges of the current study.Comment: 8 pages, 9 figures, submitted to Phys. Rev.

Coherence and Decoherence in Biological Systems: Principles of Noise Assisted Transport and the Origin of Long-lived Coherences

The quantum dynamics of transport networks in the presence of noisy environments have recently received renewed attention with the discovery of long-lived coherences in different photosynthetic complexes. This experimental evidence has raised two fundamental questions: Firstly, what are the mechanisms supporting long-lived coherences and secondly, how can we assess the possible functional role that the interplay of noise and quantum coherence might play in the seemingly optimal operation of biological systems under natural conditions? Here we review recent results, illuminate them at the hand of two paradigmatic systems, the Fenna-Matthew-Olson (FMO) complex and the light harvesting complex LHII, and present new progress on both questions. In particular we introduce the concept of the phonon antennae and discuss the possible microscopic origin or long-lived electronic coherences.Comment: Paper delivered at the Royal Society Discussion Meeting "Quantum-coherent energy transfer: implications for biology and new energy technologies", 27 - 28 April 2011 at The Kavli Royal Society International Centre, Buckinghamshire, UK. Accepted for publication in Philosophical Transactions of the Royal Society

The Asymmetric Avalanche Process

An asymmetric stochastic process describing the avalanche dynamics on a ring is proposed. A general kinetic equation which incorporates the exclusion and avalanche processes is considered. The Bethe ansatz method is used to calculate the generating function for the total distance covered by all particles. It gives the average velocity of particles which exhibits a phase transition from an intermittent to continuous flow. We calculated also higher cumulants and the large deviation function for the particle flow. The latter has the universal form obtained earlier for the asymmetric exclusion process and conjectured to be common for all models of the Kardar-Parisi-Zhang universality class .Comment: 33 pages, 3 figures, revised versio

Extrapolated High-Order Propagators for Path Integral Monte Carlo Simulations

We present a new class of high-order imaginary time propagators for path-integral Monte Carlo simulations by subtracting lower order propagators. By requiring all terms of the extrapolated propagator be sampled uniformly, the subtraction only affects the potential part of the path integral. The negligible violation of positivity of the resulting path integral at small time steps has no discernable affect on the accuracy of our method. Thus in principle arbitrarily high order algorithms can be devised for path-integral Monte Carlo simulations. We verify this claim is by showing that fourth, sixth, and eighth order convergence can indeed be achieved in solving for the ground state of strongly interacting quantum many-body systems such as bulk liquid $^4$He.Comment: 9 pages and 3 figures. Submitted to J. Chem. Phy

The detection of extragalactic 15^{15}N: Consequences for nitrogen nucleosynthesis and chemical evolution

Detections of extragalactic $^{15}$N are reported from observations of the rare hydrogen cyanide isotope HC$^{15}$N toward the Large Magellanic Cloud (LMC) and the core of the (post-) starburst galaxy NGC 4945. Accounting for optical depth effects, the LMC data from the massive star-forming region N113 infer a $^{14}N/^{15}$N ratio of 111 $\pm$ 17, about twice the $^{12}C/^{13}$C value. For the LMC star-forming region N159HW and for the central region of NGC 4945, $^{14}N/^{15}$N ratios are also $\approx$ 100. The $^{14}N/^{15}$N ratios are smaller than all interstellar nitrogen isotope ratios measured in the disk and center of the Milky Way, strongly supporting the idea that $^{15}$N is predominantly of `primary' nature, with massive stars being its dominant source. Although this appears to be in contradiction with standard stellar evolution and nucleosynthesis calculations, it supports recent findings of abundant $^{15}$N production due to rotationally induced mixing of protons into the helium-burning shells of massive stars.Comment: 15 pages including one postscript figure, accepted for publication by ApJ Letter, further comments: please contact Yi-nan Chi