Related papers: Second quantization for classical nonlinear dynami…
We propose a tensor network framework for approximating the evolution of observables of measure-preserving ergodic systems. Our approach is based on a spectrally-convergent approximation of the skew-adjoint Koopman generator by a…
The study of mathematical connections between operator-theoretic formulations of classical dynamics and quantum mechanics began at least as early as the 1930s in work of Koopman and von Neumann and was developed in later decades by many…
We continue the investigation of general geometric flows of $G_2$-structures initiated by the third author in "Flows of $G_2$-structures, I." Specifically, we determine the possible geometric flows (up to lower order terms) of…
We construct a 2-parameter family of unitarily equivalent irreducible representations of the triply extended group $\g$ of translations of $\mathbb{R}^{4}$ associated with a family of its 4-dimensional coadjoint orbits and show how a…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
Quantum many-body simulation provides a straightforward way to understand fundamental physics and connect with quantum information applications. However, suffering from exponentially growing Hilbert space size, characterization in terms of…
A correspondence is established between measure-preserving, ergodic dynamics of a classical harmonic oscillator and a quantum mechanical gauge theory on two-dimensional Minkowski space. This correspondence is realized through an isometric…
We study ergodic theoretical properties of flows on circle bundles over translation surfaces that arise via prequantization, generalizing the theory of Heisenberg nilflows to base surfaces more general than tori; these flows are among the…
Let $\Sigma$ be a compact manifold without boundary whose first homology is nontrivial. Hodge decomposition of the incompressible Euler's equation in terms of 1-forms yields a coupled PDE-ODE system. The $L^2$-orthogonal components are a…
This paper is a part of a series devoted to the Euclidean-hyperboloidal foliation method introduced by the authors for investigating the global existence problem associated with nonlinear systems of coupled wave-Klein-Gordon equations with…
This paper considers a nonlinear dynamical system on a complex, finite dimensional Banach space which has an asymptotically stable, hyperbolic fixed point. We investigate the connection between the so-called principle eigenfunctions of the…
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr\"odinger operators. In this paper we provide a formalism which also allows to study nonlinear systems. We start by defining…
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum…
A theoretic framework for dynamics is obtained by transferring dynamics from state space to its dual space. As a result, the linear structure where dynamics are analytically decomposed to subcomponents and invariant subspaces decomposition…
A framework for coherent pattern extraction and prediction of observables of measure-preserving, ergodic dynamical systems with both atomic and continuous spectral components is developed. It is based on an approximation of the generator of…
Well defined quantum field theory (QFT) for the electroweak force including quantum electrodynamics (QED) and the weak force is obtained by considering natural unitary representations of a group $K\subset U(2,2)$, where $K$ is locally…
We prove that the topological recursion formalism can be used to compute the WKB expansion of solutions of second order differential operators obtained by quantization of any hyper-elliptic curve. We express this quantum curve in terms of…
The Koopman framework is a popular approach to transform a finite dimensional nonlinear system into an infinite dimensional, but linear model through a lifting process, using so-called observable functions. While there is an extensive…
We develop methods for detecting and predicting the evolution of coherent spatiotemporal patterns in incompressible time-dependent fluid flows driven by ergodic dynamical systems. Our approach is based on representations of the generators…
We pose and solve the problem of quantum filtering based on continuous-in-time quadrature measurements (homodyning) for the case where the quantum process is in a thermal state. The standard construction of quantum filters involves the…