Related papers: The stable Derrida--Retaux system at criticality
We investigate the recently proposed dimensional reduction conjecture in driven disordered systems using a machine learning technique. The conjecture states that a static snapshot of a disordered system driven at a constant velocity is…
We reexamine the two-dimensional linear O(2) model ($\varphi^4$ theory) in the framework of the nonperturbative renormalization-group. From the flow equations obtained in the derivative expansion to second order and with optimization of the…
We present a controlled numerical study of the Berezinskii-Kosterlitz-Thouless (BKT) transition in the one-dimensional Bose-Hubbard model at unit filling, providing evidence of the characteristic logarithmic finite-size scaling of the BKT…
Derrick's theorem on the nonexistence of stable time-independent scalar field configurations [G. H. Derrick, J. Math. Phys. 5, 1252 (1964)] is generalized to finite systems of arbitrary dimension. It is shown that the "dilation" argument…
Many physical phenomena may be modelled by first order hyperbolic equations with degenerate dissipative or diffusive terms. This is the case for example in gas dynamics, where the mass is conserved during the evolution, but the momentum…
This paper is devoted to present a method of proving verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term. The value function is assumed to be continuous in…
We develop a Landau like theory to characterize the phase transitions in resetting systems. Restart can either accelerate or hinder the completion of a first passage process. The transition between these two phases is characterized by the…
We show that four-dimensional systems may exhibit a topological phase transition analogous to the well-known Berezinskii-Kosterlitz-Thouless vortex unbinding transition in two-dimensional systems. The realisation of an engineered quantum…
Lyapunov-Krasovskii approach is applied to parameter- and delay-robustness analysis of the feedback suggested by Manitius and Olbrot for a linear time-invariant system with distributed input delay. A functional is designed based on…
Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii--Kosterlitz--Thouless phase transitions of the two-dimensional (2D) classical $XY$ and the 2D generalized classical…
Recent experiments report that the long looked for thermotropic biaxial nematic phase has been finally detected in some thermotropic liquid crystalline systems. Inspired by these experimental observations we concentrate on some elementary…
Performativity means that the deployment of a predictive model incentivizes agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. Practitioners often repeatedly retrain the model on data…
In 1974, Harris proposed his celebrated criterion: Continuous phase transitions in $d$-dimensional systems are stable against quenched spatial randomness whenever $d\nu>2$, where $\nu$ is the clean critical exponent of the correlation…
In [1] Zhu and Rabitz presented a rapidly convergent iterative algorithm for optimal control of the expectation value of a positive definite observable in a pure-state quantum system. In this paper we generalize this algorithm to a quantum…
The Berezinskii-Kosterlitz-Thouless (BKT) phase transition is considered in the condition of lowest temperatures, when thermal fluctuations give place to quantum ones. For this goal, the critical dynamic of the Sine-Gordon model near the…
Several power-law critical properties involving different statistics in natural languages -- reminiscent of scaling properties of physical systems at or near phase transitions -- have been documented for decades. The recent rise of large…
We analyze the interplay of longitudinal and transverse fluctuations in a $U(1)$ symmetric two-dimensional $\phi^4$-theory. To this end, we derive coupled renormalization group equations for both types of fluctuations obtained from a linear…
We study the stability of a Markovian model of electricity production and consumption that incorporates production volatility due to renewables and uncertainty about actual demand versus planned production. We assume that the energy…
The work concentrates on relations, which are general and model independent in chaotic system, between time averages of a few (typically {\it very few}) observables. Equilibrium thermodynamics provides a guide and here is attempted to argue…
We consider the equilibrium behavior of fluids imbibed in disordered mesoporous media, including their gas-liquid critical point when present. Our starting points are on the one hand a description of the fluid/solid-matrix system as a…