Wavelet analysis and Arnold web picture for detecting energy transfer in a Hamiltonian dynamical system

Our motivation is to understand how, in chemical reactions, the reaction coordinate effectively gains dynamical energy from the other degrees of freedom (i.e., bath coordinates) avoiding thermalization of the redistributed energy. In such a system, the phase space structure should be not homogeneous; i.e., the system is never ergodic. In this study, we introduce a way to capture the inhomogeneity of the phase space and to monitor energy transfers among their partial degrees of freedom in nonergodic systems using wavelet analysis and a picture of the Arnold web. First, we examine several simple energy transfer processes, i.e., a motion on a resonance line, between resonance lines, and around a resonance junction in a simple three-degree-of-freedom (DOF) system and show how the elemental processes of the intramolecular vibrational energy redistribution (IVR) are detected by our tools. We especially note that the structure of the higher order resonance of the system can be detected by wavelet analysis and motion in the action space. Next, we analyze a reaction process in a simple Hamiltonian system of 3 DOF with a double-well potential, i.e., a system with a transition state of the center-saddle-center type, and detect energy transfers in the reactive process. The aim of the study is to propose a way to characterize the inhomogeneity of the phase space, e.g., the reactive doorway, which leads to controllability of the chemical reaction by light, i.e., control of the reaction by selectively preparing an initial state in the reactive doorway by optical excitation.     

Numerical simulations of the dynamical behavior of the SK model

We study the dynamical behavior of the Sherrington Kirkpatrick model. Thanks to the APE supercomputer we are able to analyze large lattice volumes, and to investigate the low T region. We present a new and precise determination of the remnant magnetization and of its time decay exponent, of the energy time decay exponent, and we discuss aging phenomena in the model. We exclude validity of naive aging, and propose different options that fit the numerical data. Received: 14 August 1997 / Revised: 2 December 1997 / Accepted: 30 January 1998     

Analytical results on the magnetization of the Hamiltonian Mean-Field model

The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time evolution of selected macroscopic observables, e.g., the global magnetization. The high- and low-energy limits are investigated and the analytical predictions are compared with direct N-body simulations. The method we use enables us to re-interpret the out-of-equilibrium phase transition separating magnetized and (almost) unmagnetized regimes.     

利用Eckart势求玻尔哈密顿量的解析解(英文)

本文中讨论了用Eckart势求解玻尔哈密顿量的新方法.在γ不稳定和γ≈0的两种情况下,对于离心项l/β~2用近似表达的条件下,分别求解了玻尔哈密顿量的解析解,且通过N-U方法,利用Eckart势成功的获得了玻尔哈密顿量解析解的表达式.     

Fiber-optic sensors for the estimation of oxygen gradients within biofilms on metals

This paper presents an optical approach to measure the oxygen gradients in biofilms grown on stainless-steel 316L. The sensor is constructed by immobilizing an oxygen-quenchable fluorophore at the tip of an optical fiber. The response time and reversibility of fiber-optic sensor have been analyzed. By mounting the optical fiber using a computerized micromanipulator, the vertical profiles of oxygen are measured with 10 μm depth resolution across biofilms on metal coupons. Steep concentration gradients of oxygen have been observed within the biofilm, both perpendicular and parallel to the metal surface. Optical response of the biofilm grown metal surface is found to be a consistent measure of the oxygen profiles within biofilms.     

Weak violation of universality for polyelectrolyte chains: Variational theory and simulations

A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in d dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present, in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain length N. We find R≃N ^ν(log N)^γ, where ν = and λ is the exponent which characterizes the long-range interaction U∝ 1/r ^λ. The exponent γ is shown to be non-universal, depending on the strength of the Coulomb interaction. We check our findings by a direct numerical minimization of the variational energy for chains of increasing size 2⁴ < N < 2¹⁵. The electrostatic blob picture, expected for small enough values of the interaction strength, is quantitatively described by the variational approach. We perform a Monte Carlo simulation for chains of length 2⁴ < N < 2¹⁰. The non-universal behavior of the exponent γ previously derived within the variational method is also confirmed by the simulation results. Non-universal behavior is found for a polyelectrolyte chain in d = 3 dimension. Particular attention is devoted to the homopolymer chain problem, when short-range contact interactions are present. Received 8 August 2000 and Received in final form 19 December 2000     

On the kinks and dynamical phase transitions of α-helix protein chains

Summary Heuristic insights into a physical picture of Davydov's solitonic model of the one-dimensional protein chain are presented supporting the idea of a non-equilibrium competition between the Davydov phase and a complementary, dynamical-?ferroelectric? phase along the chain. The author of this paper has agreed to not receive the proofs for correction     

An estimate for the magnetization reversal time of antiferromagnetic chains within the Heisenberg model

Within the Heisenberg model in the presence of uniaxial magnetic anisotropy, formulas are obtained that allow one to estimate both the spontaneous magnetization reversal time of an antiferromagnetic chain and the magnetization reversal time due to interaction with the conducting tip of a scanning tunneling microscope (STM). Corrections due to a possible difference between the properties of the end and inner atoms of the chain are calculated. Numerical estimates are obtained for typical parameter values of the Heisenberg Hamiltonian.     

On the discontinuities in the energy spectrum of a model Hamiltonian

The occurrence of discontinuities in the energy spectrum of thes-wave Hamiltonian in three dimensionsH(μ, λ) =p ²/2 − 1/r + 2μr + 2λ ² r ² has been reported by us. In this communication we develop a unified understanding, based principally on the topography of the energy surfaces, of the different discontinuities we reported earlier. These discontinuities do not in general occur wherever the corresponding classical system would display catastrophic behaviour.     

Al196团簇结构及熔化行为的分子动力学模拟

运用分子动力学方法结合退火及淬火技术,采用半经验的Gupta原子间多体势,系统研究了Al₁₉₆团簇的熔化特性.模拟结果表明:从不同的初始结构出发得到的熔化行为明显不同.从较低能量稳定结构出发,会出现明显的比热呈现双峰的熔化行为;而从基态或接近于基态的低能稳定结构出发.则呈现出比热显示单峰的熔化现象.通过分析不同温度点上团簇淬火结构的势能分布图给出了Al₁₉₆团簇的不同（比热出现双峰或单峰）熔化行为的成因.     

Quantum states far from the energy eigenstates of any local Hamiltonian

What quantum states are possible energy eigenstates of a many-body Hamiltonian? Suppose the Hamiltonian is nontrivial, i.e., not a multiple of the identity, and L local, in the sense of containing interaction terms involving at most L bodies, for some fixed L. We construct quantum states psi which are "far away" from all the eigenstates E of any nontrivial L-local Hamiltonian, in the sense that ||psi-E|| is greater than some constant lower bound, independent of the form of the Hamiltonian.     

Determination of the spin Hamiltonian constants for electron spin resonance at energy level crossing points

The crossing point of the Cr⁺³ ion energy-levels in single-crystal K₃Co(CN)₆, with the applied magnetic field parallel to the y-axis, is determined experimentally. Precisely calculated values of the constants E and D of the EPR spin Hamiltonian are shown to agree closely with those obtained by other authors.In conclusion, I wish to thank Professor V. S. Grechishkin for supervising my work and discussing the results.