The partition function zeroes of quantum critical points

The Lee–Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity e^hΔτ, and the Euclidean-time lattice spacing Δτ can be divergent in the infrared (IR). We recently presented analytic arguments describing how a new space-Euclidean time zeroes expansion can be defined, which reproduces Lee and Yang's scaling but avoids the unresolved branch points associated with the breaking of nonlocal symmetries such as Parity. We now present a first numerical analysis for this new zeroes approach for a quantum spin chain system. We use our scheme to quantify the renormalization group flow of the physical lattice couplings to the IR fixed point of this system. We argue that the generic Finite-Size Scaling (FSS) function of our scheme is identically the entanglement entropy of the lattice partition function and, therefore, that we are able to directly extract the central charge, c, of the quantum spin chain system using conformal predictions for the scaling of the entanglement entropy.     

Microcanonical equations obtained from the Tsallis entropy

Microcanonical equations for some of the most usual thermodynamic properties of a system, suitable for molecular dynamics simulations, are derived from the Tsallis entropy functional using both the usual definition of temperature as a derivative of entropy and a modified physical one introduced by Abe. The practical consequences of each choice are then discussed.     

Progress and bottlenecks in simulating lattice gauge theory with fermions

We present a progress report in lattice gauge theory computer simulations which includes the effects of light, dynamical fermions. Microcanonical and hybrid microcanonical-Langevin alogrithms are presented and discussed. A method for “accelerating” stochastic differential equations and defeating critical slowing down is reviewed. Physics applications such as the thermodynamics of quantum chromodynamics, hierarchal energy scales in unified gauge theories, and the phase diagram of theories with many fermion species are discussed. Prospects for future research are assessed.     

ALADIN热曲线的微正则系综分析

用微正则瞬时多碎裂统计模型分析了ALADIN热曲线.结果表明落在ALADIN热曲线温度平台(温度扭曲)附近的弹剩余核(热核)的理论代表点,并不落在相应弹剩余核热曲线的温度平台(扭曲)范围内,从而对ALADIN热曲线是否可作为核液气相变的证据提出质疑.     

Predictive kinetics for the thermal decomposition of RDX

The application of Variable Reaction Coordinate Transition State Theory for an energetic material is presented. The homolysis of the N–N bond in RDX is characterized using an embedding methodology in which key atoms in the bond-dissociation process are computed using CASPT2(10e,7o)/jun-cc-pVTZ, while the rest of the molecule is computed using M06-2X/jun-cc-pVTZ. Microcanonical rate theory is used to quantify the temperature and pressure dependent rate constants. The cleavage of the N–N bond is by far the dominant channel, with HONO elimination a distant second. The predicted rate constants are in excellent agreement with the experimental data. The computational approach can be used to provide accurate models for the combustion properties of novel energetic materials.     

超强激光的等离子体烧孔效应

针对激光聚变快速点火方案中的等离子体烧孔效应，用活塞模型研究了超强激光压缩等离子体并直接驱动激波的过程，给出了描述该过程的各物理参量的理论定标律。     

Velocity,temperature, and Reynolds-stress scaling in the wall region of turbulent boundary layer on a permeable surface

A finite total number of flow parameters in the wall region of a turbulent boundary layer points to universal behavior of turbulent shear stress as a function of mean-velocity gradient and turbulent heat flux as a function of both mean-velocity and mean-temperature gradients. Combined with dimensional arguments, this fact is used to reduce the momentum and heat equations to first-order ordinary differential equations for temperature and velocity profiles amenable to general analysis. Scaling laws for velocity and temperature in boundary layer flows with transpiration are obtained as generalizations of well-known logarithmic laws. Scaling relations are also established for shear stress and rms transverse velocity fluctuation. The proposed method has substantial advantages as compared to the classical approach (which does not rely on fluid-dynamics equations [1–3]). It can be applied to establish scaling laws for a broader class of near-wall turbulence problems without invoking closure hypotheses.     

Scaling in the neutrino mass matrix and the see-saw mechanism

Scaling is a highly predictive and fully reconstructible Ansatz for the structure of the neutrino Majorana mass matrix, which can be obtained in many models and scenarios. We summarize the phenomenology of scaling and discuss in particular its interesting aspects in the framework of the see-saw mechanism.     

时间分数阶Edwards-Wilkinson方程的标度行为研究

分别采用数值模拟和标度分析方法对1+1维时间分数阶Edwards-Wilkinson方程的标度行为进行研究.利用Caputo分数阶导数数值解求得的生长指数与采用直接标度分析方法得到的结果一致.     

Renormalized theory of magnetic field generation in resonance absorption

DC magnetic field generation in resonance absorption is studied, in a non-linear regime, when it becomes of sufficient order of magnitude to affect wave propagation, as well as electron-ion collisions or thermal dispersion do. It is shown that a simple expression obtained in the linear regime is still valid in the non-linear theory. Scaling laws are set up.     

Predicted power spectra for subordinated variables in periodic instabilities making use of a center manifold reduced floquet theory

A center manifold reduction is derived to analyze noise effects on periodic instabilities. Scaling and self-similarity relations are found among the autocorrelations of fast-relaxing degrees of freedom. In the infinite relaxation time limit for order parameters the power spectra converge to a single distribution in accord with previous findings.     

Restoration of Lorentz invariance in the lattice O(3) model with improved actions

Symanzik one-loop and block-spin renormalization group improved actions are studied by Monte Carlo simulation. Scaling sets in at small correlation length for the considered actions. The approach to the continuum relativistic energy-momentum dispersion is best for Symanzik one-loop improved action.     

Binding Three-Particles at the Edge of Stability

 The stability threshold for an Efimov state is determined as a function of the physical scales of the system. Light exotic nuclei and triatomic molecules are investigated. Scaling, universality, and renormalization-group invariance properties are discussed in this context. Received October 25, 2001; accepted for publication November 12, 2001     

Generation of gigawatt subnanosecond 1.06 μm pulses by regenerative amplification in Nd:Glass

A 0.1 μJ, 40 ps pulse, selected from a TEM₀₀ Nd:YAG master oscillator has been regeneratively amplified in a single 0.9 cm diameter gain module to the 100 mJ level while preserving both its temporal and spatial characteristics. Scaling of regenerative amplifiers to larger aperture 1.06 μm lasers is discussed.     

Extended Longitudinal Scaling: Direct evidence of saturation

Multiparticle production of charged particles at high energies exhibit the phenomenon of Limiting Fragmentation. Furthermore, the region in rapidity over which the production of particles appears to be independent of energy, increases with energy. It is argued that this phenomenon, known as Extended Longitudinal Scaling, is a direct manifestation of some kind of saturation, akin to that in the Color Glass Condensate picture of particle production.     

High power widely tunable infra-red generation from four-wave mixing in germanium

Tunable infra-red generation from 7–22 μm by non-collinear phase matched four-wave mixing in room temperature germanium is discussed and demonstrated for selected frequencies across this range. Scaling and optimization of the system should yield output powers of a few hundred kWs, particularly useful at ≈ 16 μm for isotopic enrichment of UF₆.     

Scaling inequalities for oriented percolation

We look at seven critical exponents associated with two-dimensional oriented percolation. Scaling theory implies that these quantities satisfy four equalities. We prove five related inequalitites.     

Complex-scaled spectrum completeness for pedestrians

The Complex Scaling Method (CSM) is rephrased in terms of a Hamiltonian containing an optical potential. Traditional theorems concerning Jost solutions, the Jost function, residues of a suitable Green’s function at its poles, and the resolution of the identity are extended. Elementary derivations of the completeness of the CSM spectrum are detailed for the one and the two channel cases.     

Scaling dynamics for a particle in a time-dependent potential well

Some dynamical properties for a classical particle confined in an infinitely deep box of potential containing a periodically oscillating square well are studied. The dynamics of the system is described by using a two-dimensional non-linear area-preserving map for the variables energy and time. The phase space is mixed and the chaotic sea is described using scaling arguments. Scaling exponents are obtained as a function of all the control parameters, extending the previous results obtained in the literature.     

Meson spectrum in quenched QCD on a 164 lattice

The masses of pseudoscalar and vector mesons and their radial excitations are measured in the quenched approximation to QCD by a 32nd-order numerical hopping-parameter expansion on a 16⁴ lattice. Scaling behaviour, finite-size effects and the influence of statistics are studied.