Random Curves by Conformal Welding

We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle given in terms of the exponential of Gaussian Free Field. We conjecture that our curves are locally related to SLE$(\kappa)$ for $\kappa<4$.Comment: 5 page

Fourier's Law from Closure Equations

We give a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is proportional to the temperature gradient with a temperature dependent heat conductivity and the stationary temperature exhibits a nonlinear profile

Statistical Mechanics of Logarithmic REM: Duality, Freezing and Extreme Value Statistics of 1/f1/f Noises generated by Gaussian Free Fields

We compute the distribution of the partition functions for a class of one-dimensional Random Energy Models (REM) with logarithmically correlated random potential, above and at the glass transition temperature. The random potential sequences represent various versions of the 1/f noise generated by sampling the two-dimensional Gaussian Free Field (2dGFF) along various planar curves. Our method extends the recent analysis of Fyodorov Bouchaud from the circular case to an interval and is based on an analytical continuation of the Selberg integral. In particular, we unveil a {\it duality relation} satisfied by the suitable generating function of free energy cumulants in the high-temperature phase. It reinforces the freezing scenario hypothesis for that generating function, from which we derive the distribution of extrema for the 2dGFF on the $[0,1]$ interval. We provide numerical checks of the circular and the interval case and discuss universality and various extensions. Relevance to the distribution of length of a segment in Liouville quantum gravity is noted.Comment: 25 pages, 12 figures Published version. Misprint corrected, references and note adde

Approach to ground state and time-independent photon bound for massless spin-boson models

It is widely believed that an atom interacting with the electromagnetic field (with total initial energy well-below the ionization threshold) relaxes to its ground state while its excess energy is emitted as radiation. Hence, for large times, the state of the atom+field system should consist of the atom in its ground state, and a few free photons that travel off to spatial infinity. Mathematically, this picture is captured by the notion of asymptotic completeness. Despite some recent progress on the spectral theory of such systems, a proof of relaxation to the ground state and asymptotic completeness was/is still missing, except in some special cases (massive photons, small perturbations of harmonic potentials). In this paper, we partially fill this gap by proving relaxation to an invariant state in the case where the atom is modelled by a finite-level system. If the coupling to the field is sufficiently infrared-regular so that the coupled system admits a ground state, then this invariant state necessarily corresponds to the ground state. Assuming slightly more infrared regularity, we show that the number of emitted photons remains bounded in time. We hope that these results bring a proof of asymptotic completeness within reach.Comment: 45 pages, published in Annales Henri Poincare. This archived version differs from the journal version because we corrected an inconsequential mistake in Section 3.5.1: to do this, a new paragraph was added after Lemma 3.

High Temperature Expansions and Dynamical Systems

We develop a resummed high-temperature expansion for lattice spin systems with long range interactions, in models where the free energy is not, in general, analytic. We establish uniqueness of the Gibbs state and exponential decay of the correlation functions. Then, we apply this expansion to the Perron-Frobenius operator of weakly coupled map lattices.Comment: 33 pages, Latex; [email protected]; [email protected]

Agile in the Era of Digitalization : A Finnish Survey Study

This paper was a Candidate for the Best Full Paper.Peer reviewe

Kurt Symanzik - a stable fixed point beyond triviality

In 1970 Kurt Symanzik proposed a "precarious" phi**4-theory with a negative quartic coupling constant as a valid candidate for an asymptotically free theory of strong interactions. Symanzik's deep insight in the non-trivial properties of this theory has been overruled since then by the Hermitian intuition of generations of scientists, who considered or consider this actually non-Hermitian highly important theory to be unstable. This short - certainly controversial - communication tries to shed some light on the historical and formalistic context of Symanzik's theory in order to sharpen our (quantum) intuition about non-perturbative theoretical physics between (non)triviality and asymptotic freedom.Comment: 6 pages, no figures, new style files, revised for typos, improved discussion, new references adde