Related papers: Variational approach for a class of cooperative sy…
The extraction of classical degrees of freedom in quantum mechanics is studied in the stochastic variational method. By using this classicalization, a hybrid model constructed from quantum and classical variables (quantum-classical hybrids)…
We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…
The behaviour of solutions for a non-linear diffusion problem is studied. A subordination principle is applied to obtain the variation of parameters formula in the sense of Volterra equations, which leads to the integral representation of a…
The mean-field dynamics of a collection of stochastic agents with local versus nonlocal interactions is studied via analytically soluble models. The nonlocal interactions result from a barycentric modulation of the observation range of the…
Most work on causality in machine learning assumes that causal relationships are driven by a constant underlying process. However, the flexibility of agents' actions or tipping points in the environmental process can change the qualitative…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
We present a novel generic framework to approximate the non-equilibrium steady states of dissipative quantum many-body systems. It is based on the variational minimization of a suitable norm of the quantum master equation describing the…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
Quantum cooperativity is evident in light-matter platforms where quantum emitter ensembles are interfaced with confined optical modes and are coupled via the ubiquitous electromagnetic quantum vacuum. Cooperative effects can find…
We introduce a novel method of efficiently simulating the non-equilibrium steady state of large many-body open quantum systems with highly non-local interactions, based on a variational Monte Carlo optimization of a matrix product operator…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…
Addressing both natural and societal challenges requires collective cooperation. Studies on collective-risk social dilemmas have shown that individual decisions are influenced by the perceived risk of collective failure. However, existing…
In the analysis of binary longitudinal data, it is of interest to model a dynamic relationship between a response and covariates as a function of time, while also investigating similar patterns of time-dependent interactions. We present a…
Applying techniques originally developed for systems lacking a variational structure, we establish conditions for the existence of solutions in systems that possess this property but their energy functional is unbounded both lower and…
In the paper we study a measure version of the evolutionary nonlinear Boltzmann-type equation in which we admit a random number of collisions of particles. We consider first a stationary model and use two methods to find its fixed points:…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
A class of generalized Schr\"{o}dinger problems in bounded domain is studied. A complete overview of the set of solutions is provided, depending on the values assumed by parameters involved in the problem. In order to obtain the results, we…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…