Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange ± J: A Monte Carlo study

,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor -interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function, , while a power law prefactor cannot be distinguished. The Kohlrausch exponent y ( T ) decreases from at [0pt] to at [0pt] however. The relaxation time is compatible with the exponential divergence postulated by McMillan for spin glasses at their lower critical dimension, but the exponent that can be extracted still differs significantly from the theoretical value, . Thus the present results support the conclusion that the Potts spin glass in d = 3 dimensions differs qualitatively from the Ising spin glass. Received: 8 October 1997 / Accepted: 27 November 1997     

Nonequilibrium Measurements of Free Energy Differences for Microscopically Reversible Markovian Systems

An equality has recently been shown relating the free energy difference between two equilibrium ensembles of a system and an ensemble average of the work required to switch between these two configurations. In the present paper it is shown that this result can be derived under the assumption that the system's dynamics is Markovian and microscopically reversible.     

Nonlocality in the Expanding Infinite Well

According to D. Bohm's interpretation of quantum mechanics, a particle always has a well-defined spatial trajectory. A change in boundary conditions can nonlocally change that trajectory. In this note we point out a striking instance of this phenomenon that is easy to understand qualitatively.     

关于本科生量子力学教学的一些体会

简要介绍几年来我给北京大学物理学院三年级本科生讲授"量子力学A"课程的一些经验和体会.为了使学生们能够较为容易地理解量子力学的基本概念和原则,我尝试着从科学史的角度进行讲述,取得了较好的效果.同时,恰当地打一些比喻,对于学生们深刻领会某些相对来说抽象的概念也有很大帮助.     

Computational performance of Free Mesh Method applied to continuum mechanics problems

The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics.     

A new conserved quantity of mechanical systems with differential constraints

A new conserved quantity of non-Noether symmetry for the mechanical systems with differential constraints is studied. First, the differential equations of motion of the systems are established. Then, the determining equations and restriction equations of the non-Noether symmetry are obtained and a new conserved quantity is given. Finally, an example is given to illustrate the application of the results.     

Time-dependent harmonic oscillator in a magnetic field and an electric field on the non-commutative plane

In the non-commutative space, wave functions and geometric phases are derived for the time-dependent harmonic oscillator in external time-dependent magnetic and electric field. Explicit forms of the coherent states are also given, which are not the minimum uncertainty states for the coordinates and momenta.     

John Bell and the Identical Twins

I present a biographical profile of John S. Bell based upon extensive interviews I had with him. I present Bell‘s views on the quantum theory along with a simple explanation of his identity. Jeremy Bernstein is Professor Emeritus of Physics at the Stevens Institute of Technology and a former staff writer for The New Yorker.     

$${f(\mathcal R)}$$ quantum cosmology

We have quantized a flat cosmological model in the context of the metric models, using the causal Bohmian quantum theory. The equations are solved and then we have obtained how the quantum corrections influence the classical equations.     

Quantum Mechanics and Imprecise Probability

An extension of the Born rule, the quantum typicality rule, has recently been proposed [B. Galvan in Found. Phys. 37:1540–1562 (2007)]. Roughly speaking, this rule states that if the wave function of a particle is split into non-overlapping wave packets, the particle stays approximately inside the support of one of the wave packets, without jumping to the others. In this paper a formal definition of this rule is given in terms of imprecise probability. An imprecise probability space is a measurable space endowed with a set of probability measures ℘. The quantum formalism and the quantum typicality rule allow us to define a set of probabilities on (X ^T ,ℱ), where X is the configuration space of a quantum system, T is a time interval and ℱ is the σ-algebra generated by the cylinder sets. Thus, it is proposed that a quantum system can be represented as the imprecise stochastic process , which is a canonical stochastic process in which the single probability measure is replaced by a set of measures. It is argued that this mathematical model, when used to represent macroscopic systems, has sufficient predictive power to explain both the results of the statistical experiments and the quasi-classical structure of the macroscopic evolution.