Related papers: The Relaxion Measure Problem
This work addresses the occupation measure relaxation of calculus of variations problems, which is an infinite-dimensional linear programming relaxation amenable to numerical approximation by a hierarchy of semidefinite optimization…
The relaxation mechanism, which solves the electroweak hierarchy problem without relying on TeV scale new physics, crucially depends on how a Higgs-dependent back-reaction potential is generated. In this paper, we suggest a new scenario in…
We introduce a vertical type relaxation for optimal control problems which only have $L^1$-coercivity for their controls. Usually such problems feature both concentration and oscillation effects at the same time. We propose relaxing to an…
The cosmological constant problem arises because the magnitude of vacuum energy density predicted by quantum mechanics is about 120 orders of magnitude larger than the value implied by cosmological observations of accelerating cosmic…
Optimization problems with stochastic dominance constraints provide a possibility to shape risk by selecting a benchmark random outcome with a desired distribution. The comparison of the relevant random outcomes to the respective benchmarks…
The collective behaviour of statistical systems close to critical points is characterized by an extremely slow dynamics which, in the thermodynamic limit, eventually prevents them from relaxing to an equilibrium state after a change in the…
One of the most frustrating issues in early universe cosmology centers on how to reconcile the vast choice of universes in string theory and in its most plausible high energy sibling, eternal inflation, that jointly generate the string…
Critical slowing down of the relaxation of the order parameter is relevant both in early the universe and in ultrarelativistic heavy ion collisions. We study the relaxation rate of the order parameter in an O(N) scalar theory near the…
An analytical prediction is established of how an isolated many-body quantum system relaxes towards its thermal long-time limit under the action of a time-independent perturbation, but still remaining sufficiently close to a reference case…
Relaxation effects impose fundamental limitations on our ability to coherently control quantum mechanical phenomena. In this letter, we establish physical limits on how closely can a quantum mechanical system be steered to a desired target…
We propose a novel explanation for the smallness of the observed cosmological constant (CC). Regions of space with a large CC are short lived and are dynamically driven to crunch soon after the end of inflation. Conversely, regions with a…
I present an analysis of the relaxation rate for long-wavelength fluctuations of the order parameter in an O(N) scalar theory near the critical point. Our motivation is to model the non-equilibrium dynamics of critical fluctuations near the…
Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on…
Volume is a natural geometric measure for comparing polyhedral relaxations of non-convex sets. Speakman and Lee gave volume formulae for comparing relaxations of trilinear monomials, quantifying the strength of various natural relaxations.…
In order to deal with a large cosmological constant a relaxation mechanism based on modified gravity has been proposed recently. By virtue of this mechanism the effect of the vacuum energy density of a given quantum field/string theory (no…
Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phe-nomena, by relaxing controls as Young measures. These semi-definite…
In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second…
Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this…
One of the general mechanisms that give rise to the slow cooperative relaxation characteristic of classical glasses is the presence of kinetic constraints in the dynamics. Here we show that dynamical constraints can similarly lead to slow…
We point out that the standard formulation of the cosmological constant problem itself is problematic since it is trying to apply the very large scale homogeneous cosmological model to very small (Planck) scale phenomenon. At small scales,…