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Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…
The aim of the paper is to present various asymptotic behaviors of skew-evolution semiflows in Banach spaces, as exponential decay, instability, exponential in- stability and integral instability. Relations between these asymptotic…
We analyse the long-time evolution of the three-dimensional flow in a closed cubic turbulent Rayleigh-B\'{e}nard convection cell via a Koopman eigenfunction analysis. A data-driven basis derived from diffusion kernels known in machine…
We study spherical evolution in scalar-Gauss-Bonnet gravity with additional Ricci coupling and use the gauge-invariant approach of Ref.~\cite{Reall:2021voz} to track well-posedness. Our results show that loss of hyperbolicity when it…
We construct physical semi-classical states annihilated by the Hamiltonian constraint operator in the framework of loop quantum cosmology as a method of systematically determining the regime and validity of the semi-classical limit of the…
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest…
For an atom in an externally driven cavity, we show that special initial states lead to near-disentangled atom-field evolution, and superpositions of these can lead to near maximally-entangled states. Somewhat counterintutively, we find…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
We investigate ultraviolet fixed points in the real-time evolution of non-Abelian gauge fields. Classical-statistical lattice simulations reveal equal-time correlation functions with a spectral index 3/2. Analytical understanding of this…
We study the quantum correlation and classical correlation dynamics in a spin-boson model. For two different forms of spectral density, we obtain analytical results and show that the evolutions of both correlations depend closely on the…
We develop a model of string dynamics with back-reaction from both scaling and non-scaling loops taken into account. The evolution of a string network is described by the distribution functions of coherence segments and kinks. We derive two…
Entanglement or entanglement generating interactions permit to achieve the maximum allowed speed in the dynamical evolution of a composite system, when the energy resources are distributed among subsystems. The cases of pre-existing…
We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the…
We construct the time evolution of Kawasaki dynamics for a spatial infinite particle system in terms of generating functionals. This is carried out by an Ovsjannikov-type result in a scale of Banach spaces, which leads to a local (in time)…
We provide regularity of solutions to a large class of evolution equations on Banach spaces where the generator is composed of a static principal part plus a non-autonomous perturbation. Regularity is examined with respect to the graph norm…
We present a local framework for investigating non-unitary evolution groups pertinent to effective field theories in general semi-classical spacetimes. Our approach is based on a rigorous local stability analysis of the algebra of…
In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…
The evolution of degenerate matter out of equilibrium is a topic of interest in fields such as condensed matter, nuclear and atomic physics, and increasingly cosmology, including inflaton physics prior to reheating. This follow-up paper…
In the context of interacting particle systems, we study the influence of the action of the semigroup on the concentration property of Lipschitz functions. As an application, this gives a new approach to estimate the relaxation speed to…