A model with persistent vacuum

It is shown that there exists a selfadjoint Hamilton operator corresponding to the interactionH ₀ ^(a) +H ₀ ^(b) + _b ⁺ (x) _a (x) _b ^– (x)d ³ x, wherea andb denote two types of scalar particles. We discuss the scattering theory of this operator.Work partially supported by the Swiss National Science Foundation.This paper contains results from the author's Ph. D. Thesis [3].     

Spectral properties and bound-state scattering for weakly coupled λP(ϕ)2 models

We analyze the particle structure in weakly coupled λP(?)₂ models. Topics include existence of bound states and resonances, asymptotic expansions for bound-state masses, low-energy asymptotic completeness, and perturbation theory for scattering events involving bound states. The analysis is based on analyticity properties and perturbation theory for the Bethe-Salpeter kernel.     

Decay properties and borel summability for the Schwinger functions inP(Φ)2 theories

For the truncated Schwinger functions of theP(Φ)₂ field theories, we show strong decrease in the separation of points. This shows uniqueness of theories withP of degree four. We also extend the domain of analyticity in the coupling constant. For theories withP of degree four, the combination of these two results gives Borel summability.     

Liapunov Multipliers and Decay of Correlations in Dynamical Systems

The essential decorrelation rate of a hyperbolic dynamical system is the decay rate of time-correlations one expects to see stably for typical observables once resonances are projected out. We define and illustrate these notions and study the conjecture that for observables in $\mathcal{C}^1$ , the essential decorrelation rate is never faster than what is dictated by the smallest unstable Liapunov multiplier.     

A Rigorous Upper Bound on the Propagation Speed for the Swift–Hohenberg and Related Equations

We prove that if the initial condition of the Swift–Hohenberg equation $$\partial _t u(x,t) = (\varepsilon ^2 - (1 + \partial _x^2 )^2 ){\text{ }}u(x,t) - u^3 (x,t)$$ is bounded in modulus by Ce ^?βx as x→+∞, the solution cannot propagate to the right with a speed greater than $$\mathop {\sup }\limits_{0 < {\gamma } \leqslant \beta } {\gamma }^{ - 1} (\varepsilon ^2 + 4{\gamma }^2 + 8{\gamma }^4 ).$$ This settles a long-standing conjecture about the possible asymptotic propagation speed of the Swift–Hohenberg equation. The proof does not use the maximum principle and is simple enough to generalize easily to other equations. We illustrate this with an example of a modified Ginzburg–Landau equation, where the critical speed is not determined by the linearization alone.