粒子的相互作用、极限环和相变

从各种相互作用的规范理论出发,讨论了规范场方程的某些新的解,并引入了势,然后探讨了它们与极限环、各种奇异点的关系,最后论述了这些结果可能具有的粒子性质和相变等物理意义．     

Nontrivial Phase Transition in a Continuum Mirror Model

We consider a Poisson point process on with intensity , and at each Poisson point we place a two sided mirror of random length and orientation. The length and orientation of a mirror is taken from a fixed distribution, and is independent of the lengths and orientations of the other mirrors. We ask if light shone from the origin will remain in a bounded region. We find that there exists a with 0 < < for which, if < , light leaving the origin in all but a countable number of directions will travel arbitrariliy far from the origin with positive probability. Also, if > , light from the origin will almost surely remain in a bounded region.     

Evidence for a Phase Transition in Three-Dimensional Lattice Models

It was recently discovered that an eigenvector structure of commutative families of layer-to-layer matrices in three-dimensional lattice models is described by a two-dimensional spin lattice generalizing the notion of one-dimensional spin chains. We conjecture the relations between the two-dimensional spin lattice in the thermodynamic limit and the phase structure of three-dimensional lattice models. We consider two simplest cases: the homogeneous spin lattice related to the Zamolodchikov–Bazhanov–Baxter model and a chess spin lattice related to the Stroganov–Mangazeev elliptic solution of the modified tetrahedron equation. Evidence for the phase transition is obtained in the second case.     

The Dynamics of a Conserved Phase Field System: Stefan-like, Hele-Shaw, and Cahn-Hilliard Models as Asymptotic Limits

The dynamics of a conserved phase field system for a free boundary,that is, are studied asymptotically.Many of the major macroscopic free-boundary problems arise aslimits in various scalings. Temperature, curvature, surfacetension, and velocity relations are derived, and compared withanalogous results for systems using a nonconserved order parameter.A single fourth-order equation which has been studied in spinodaldecomposition (Cahn-Hilliard) is obtained from this system ofequations by setting the latent heat to zero.     

Dynamical Phase Transition for a Quantum Particle Source

We analyze the time evolution describing a quantum source for non-interacting particles, either bosons or fermions. The growth behavior of the particle number (trace of the density matrix) is investigated, leading to spectral criteria for sublinear or linear growth in the fermionic case, but also establishing the possibility of exponential growth for bosons. We further study the local convergence of the density matrix in the long time limit and prove the semi-classical limit.     

Eigenvalue Degeneracy and Existence and Non-existence of a Phase Transition in One Dimension

We consider a one dimensional Ising chain with interaction potential J(k) such that J(k) = 0 when k > n. By a perturbation argument we show that long range order exists at sufficiently low temperatures if and only if This is consistent with Dyson's recent theorems and in addition predicts that when J(k) = k^?2 there is no long range order.     

Failure of Structural Material as a Nonequilibrium Phase Transition

The initial stage of instability in the failure of a structural material treated as a nonequilibrium phase transition is reconstructed. Its mechanism is based on spinodal decomposition (diffusion separation).     

Phase Transition Models in Atmospheric Dynamics

Abstract From both the theoretical and numerical viewpoints, we study a system of differential inclusions describing the evolution of the temperature and the specific humidity distributions in a system of moist air. We allow the so-called saturation concentration parameter to depend on the temperature, and thus we consider more general and interesting phase-change effects than the ones addressed in [2].     

Phase Transition and Eigenvalue Degeneracy of a One Dimensional Anharmonic Oscillator

For a one dimensional lattice model with long range exponential interaction the problem of deriving the thermodynamic properties of the system reduces to the problem of determining the spectrum of a differential equation for a one dimensional anharmonic oscillator with potential αx² + βγx⁴ where γ is the inverse of the range of the interaction and α is a function of temperature which is positive at high temperatures and negative at low temperatures. It is proved that at low temperatures, α < 0, and in the limit γ → 0, (corresponding to an infinitely long range interaction) the spectrum becomes asymptotically degenerate. The relation of degeneracy to the occurrence of a phase transition is discussed and the generalization to higher dimensions is mentioned briefly.     

Amenability and Phase Transition in the Ising Model

We consider the Ising model with external field h and coupling constant J on an infinite connected graph G with uniformly bounded degree. We prove that if G is nonamenable, then the Ising model exhibits phase transition for some h0 and some J<. On the other hand, if G is amenable and quasi-transitive, then phase transition cannot occur for h0. In particular, a group is nonamenable if and only if the Ising model on one (all) of its Cayley graphs exhibits a phase transition for some h0 and some J<.     

Possible Scenarios of a Phase Transition from Isotropic Liquid to a Hexatic Phase in the Theory of Melting in Two-Dimensional Systems

Theoretical and Mathematical Physics - A two-stage process consisting of two continuous Berezinskii-Kosterlitz-Thouless-type transitions with an intermediate anisotropic liquid, a hexatic phase, is...     

Quantum Phase Transition in an Interacting Fermionic Chain

We rigorously analyze the quantum phase transition between a metallic and an insulating phase in (non-solvable) interacting spin chains or one-dimensional fermionic systems. In particular, we prove the persistence of Luttinger liquid behavior in the presence of an interaction even arbitrarily close to the critical point, where the Fermi velocity vanishes and the two Fermi points coalesce. The analysis is based on two different multiscale analysis; the analysis of the first regime provides gain factors which compensate the small divisors due to the vanishing Fermi velocity.     

Fundamental Limits of Weak Recovery with Applications to Phase Retrieval

Foundations of Computational Mathematics - In phase retrieval, we want to recover an unknown signal $${{\varvec{x}}}\in {{\mathbb {C}}}^d$$ from n quadratic measurements of the form $$y_i =...     

Momentum Operators in Two Intervals: Spectra and Phase Transition

We study the momentum operator defined on the disjoint union of two intervals. Even in one dimension, the question of two non-empty open and non-overlapping intervals has not been worked out in a way that extends the cases of a single interval and gives a list of the selfadjoint extensions. Starting with zero boundary conditions at the four endpoints, we characterize the selfadjoint extensions and undertake a systematic and complete study of the spectral theory of the selfadjoint extensions. In an application of our extension theory to harmonic analysis, we offer a new family of spectral pairs. Compared to earlier studies, it yields a more direct link between spectrum and geometry.     

决策信息系统的变换及其变换规则形式化

传统的粗糙集分类、约简、规则挖掘方法处理的对象是某个时间点上的静态信息系统,因而获得的知识也是静态的.实际上信息系统通常表现为易变性和过程性,为了挖掘决策信息系统动态变换的趋势和规则,本文扩展了粗糙集中传统的分类、约简、规则挖掘的应用模式,提出决策信息系统基于时间序列单步和过程变换模型, 建立面向决策信息系统变化趋势的类划分机制和相应的语义,对条件属性变迁与决策属性变迁的相关性进行研究,并给出变换规则的形式化表示.