1,721,020 research outputs found
Large deviations for a stochastic model of heat flow
No full textWe investigate a one-dimensional chain of 2N harmonic oscillators in which
neighboring sites have their energies redistributed randomly. The sites −N and
N are in contact with thermal reservoirs at different temperature τ− and τ+.
Kipnis et al. (J. Statist. Phys., 27:65–74 (1982).) proved that this model satisfies
Fourier’s law and that in the hydrodynamical scaling limit, when N→∞, the
stationary state has a linear energy density profile ̄ θ(u), u ∈ [−1, 1]. We derive
the large deviation function S(θ(u)) for the probability of finding, in the stationary
state, a profile θ(u) different from ̄ θ(u). The function S(θ) has striking
similarities to, but also large differences from, the corresponding one of the
symmetric exclusion process. Like the latter it is nonlocal and satisfies a variational
equation. Unlike the latter it is not convex and the Gaussian normal
fluctuations are enhanced rather than suppressed compared to the local equilibrium
state. We also briefly discuss more general models and find the features
common in these two and other models whose S(θ) is know
Striped phases in two dimensional dipole systems
No full textWe prove that a system of discrete two-dimensional (2D) in-plane dipoles with four possible orientations, interacting via a three-dimensional (3D) dipole-dipole interaction plus a nearest neighbor ferromagnetic term, has periodic striped ground states. As the strength of the ferromagnetic term is increased, the size of the stripes in the ground state increases, becoming infinite, i.e., giving a ferromagnetic ground state, when the ferromagnetic interaction exceeds a certain critical value. We also give a rigorous proof of the reorientation transition in the ground state of a 2D system of discrete dipoles with six possible orientations, interacting via a 3D dipole-dipole interaction plus a nearest neighbor antiferromagnetic term. As the strength of the antiferromagnetic term is increased, the ground state flips from being striped and in plane to being staggered and out of plane. An example of a rotator model with a sinusoidal ground state is also discussed
Erratum to: Translation Invariant Extensions of Finite Volume Measures (Journal of Statistical Physics, (2017), 166, 3-4, (765-782), 10.1007/s10955-016-1595-8)
No full textIn the online published version the NSF grant number for JLL is incorrect. This has been corrected with this erratum. The correct statement is given below. The NSF grant JLL should be DMR 1104501 instead of DMR 1104500
Canonical Typicality
No full textIt is well known that a system, S, weakly coupled to a heat bath, B, is described by the canonical ensemble when the composite, S+B, is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true both for classical distributions on the phase space and for quantum density matrices. Here we show that a much stronger statement holds for quantum systems. Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced density matrix of the system is canonical, for the overwhelming majority of wave functions in the subspace corresponding to the energy interval encompassed by the microcanonical ensemble. This clarifies, expands and justifies remarks made by Schroedinger in 1952
Translation Invariant Extensions of Finite Volume Measures
No full textWe investigate the following questions: Given a measure μΛ on configurations on a subset Λ of a lattice L, where a configuration is an element of Ω Λ for some fixed set Ω , does there exist a measure μ on configurations on all of L, invariant under some specified symmetry group of L, such that μΛ is its marginal on configurations on Λ ? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which L= Zd and the symmetries are the translations. For the case in which Λ is an interval in Z we give a simple necessary and sufficient condition, local translation invariance (LTI), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which L is the Bethe lattice. On Z we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When Λ ⊂ Z is not an interval, or when Λ ⊂ Zd with d> 1 , the LTI condition is necessary but not sufficient for extendibility. For Zd with d> 1 , extendibility is in some sense undecidable
Point processes with specified low order correlations
No full textProceedings del convegno Inhomogeneous Rndom Systems, tenutosi a Parigi all IHP dil 25-26/1/200
Periodic Minimizers in 1D Local Mean Field Theory
No full textUsing reflection positivity techniques we prove the existence of minimizers for a class of mesoscopic free-energies representing 1D systems with competing interactions. All minimizers are either periodic, with zero average, or of constant sign. If the local term in the free energy satisfies a convexity condition, then all minimizers are either periodic or constant. Examples of both phenomena are given. This extends our previous work where such results were proved for the ground states of lattice systems with ferromagnetic nearest neighbor interactions and dipolar type antiferromagnetic long range interactions
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