Tunneling for spatially cut-off $P(ϕ)_2$-Hamiltonians

Gelfand-Shilov smoothing properties of the radially symmetric spatially homogeneous Boltzmann equation without angular cutoff

We prove that the Cauchy problem associated to the radially symmetric spatially homogeneous non-cutoff Boltzmann equation with Maxwellian molecules enjoys the same Gelfand-Shilov regularizing effect as the Cauchy problem defined by the evolution equation associated to a fractional harmonic oscillator.

Thermal Quantum Fields with Spatially Cut-off Interactions in 1+1 Space-time Dimensions

We construct interacting quantum fields in 1+1 space-time dimensions, representing charged or neutral scalar bosons at positive temperature and zero chemical potential. Our work is based on prior work by Klein and Landau and Hoegh-Krohn. Generalized path space methods are used to add a spatially cut-off interaction to the free system, which is described in the Araki-Woods representation. It is shown that the interacting KMS state is normal w.r.t. the Araki-Woods representation. The observable algebra and the modular conjugation of the interacting system are shown to be identical to the ones of…

空间截断 $\phi^4_2$ 中的序列指数-动机周期

Sequential exponential-motivic periods in spatially cut-off $ϕ^4_2$

本文研究空间截断 $\phi^4_2$ 的构造性积分，用指数-动机周期序列表示，分析伽罗瓦变换对配分周期发散和固定可观测量极限的影响，并给出无有界实现时极限不成比例的反例。

Stability and uniqueness for the spatially homogeneous Boltzmann equation with long-range interactions

In this paper, we prove some a priori stability estimates (in weighted Sobolev spaces) for the spatially homogeneous Boltzmann equation without angular cutoff (covering every physical collision kernels). These estimates are conditioned to some regularity estimates on the solutions, and therefore reduce the stability and uniqueness issue to the one of proving suitable regularity bounds on the solutions. We then prove such regularity bounds for a class of interactions including the so-called (non cutoff and non mollified) hard potentials and moderately soft potentials. In particular, we obtain t…

On exponential moments of the homogeneous Boltzmann equation for hard potentials without cutoff

We consider the spatially homogeneous Boltzmann equation for hard potentials without cutoff. We prove that an exponential moment of order $ρ=\min\{2γ/(2-ν),2\}$, with the usual notation, is immediately created. This is stronger than what happens in the case with cutoff. We also show that exponential moments of order $ρ\in (0,2]$ are propagated.

Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation

For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The main technique is based on a comparison principle that uses a certain dissipative property of the linear Boltzmann equation. Implications of the technique to propagation of upper Maxwellian bounds in the spatially-inhomogeneous case are discussed.