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粒子的相互作用、极限环和相变 总被引:6,自引:0,他引:6
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. 相似文献
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Matthew Harris 《Journal of Theoretical Probability》2001,14(2):299-317
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. 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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Colin J. Thompson 《Studies in Applied Mathematics》1969,48(4):299-309
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. 相似文献
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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). 相似文献
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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]. 相似文献
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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. 相似文献
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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<. 相似文献
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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... 相似文献
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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. 相似文献
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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 =... 相似文献
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Palle E. T. Jorgensen Steen Pedersen Feng Tian 《Complex Analysis and Operator Theory》2013,7(6):1735-1773
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. 相似文献