Related papers: Mass operator and dynamical implementation of mass…
Koopman operator theory is a key tool in data assimilation of complex dynamical systems, with the potential to be applied to multimodal data. We formulate the problem of learning Koopman eigenfunctions from observations at arbitrary,…
The use of the mass term as a gauge fixing term has been studied by Zwanziger, Parrinello and Jona-Lasinio, which is related to the non-linear gauge $A_{\mu}^{2}=\lambda$ of Dirac and Nambu in the large mass limit. We have recently shown…
This paper presents an averaging method for nonlinear systems defined on Riemannian manifolds. We extend closeness of solutions results for ordinary differential equations on $R^{n}$ to dynamical systems defined on Riemannian manifolds by…
The Lewis and Riesenfeld method has been investigated, by Ramos et al in Ref.[1], for quantum systems governed by time-dependent PT symmetric Hamiltonians and particularly where the quantum system is a particle submitted to action of a…
Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
For dynamical systems involving decision making, the success of the system greatly depends on its ability to make good decisions with incomplete and uncertain information. By leveraging the Koopman operator and its adjoint property, we…
This paper extends the Madelung-Bohm formulation of quantum mechanics to describe the time-reversible interaction of classical and quantum systems. The symplectic geometry of the Madelung transform leads to identifying hybrid…
An effective theory is proposed, combining the standard gauge group $SU(3)_{C}\otimes SU(2)_{L}\otimes U(1)_{Y}$ with a horizontal discrete symmetry. By assigning appropriate charges under this discrete symmetry to the various fermion…
We propose efficient classical algorithms which (strongly) simulate the action of bosonic linear optics circuits applied to superpositions of Gaussian states. Our approach relies on an augmented covariance matrix formalism to keep track of…
The statistical tools needed to obtain a mass function from realistic collapse time estimates are presented. Collapse dynamics has been dealt with in paper I of this series by means of the powerful Lagrangian perturbation theory and the…
A set of N independent Gaussian linear time invariant systems is observed by M sensors whose task is to provide the best possible steady-state causal minimum mean square estimate of the state of the systems, in addition to minimizing a…
In statistical physics, the Nakajima-Mori-Zwanzig projection operator formalism is used to derive an integro-differential equation for observables in a Hilbert space, the generalized Langevin equation (GLE). This technique relies on the…
We construct effective field theories for gapped quantum Hall systems coupled to background geometries with local Galilean invariance i.e. Bargmann spacetimes. Along with an electromagnetic field, these backgrounds include the effects of…
Dynamics of non-Markovian systems is a classic problem yet it attracts an everlasting activity in physics and beyond. A powerful tool for modeling such setups is the Generalized Langevin Equation, however, its analysis typically poses a…
We want to select the best systems out of a given set of systems (or rank them) with respect to their expected performance. The systems allow random observations only and we assume that the joint observation of the systems has a…
It is shown how operator regularization can be used to obtain an expansion of the effective action in powers of derivatives of the background field. This is applied to massless scalar electrodynamics to find the one-loop corrections to the…
The time-dependent free Schr\"odinger operator is shown to be characterized as the only linear partial differential operator of the second order that is invariant under the Galilei group in the Euclidean space-time $\mathbb R\times\mathbb…
We present for the first time an explicit exposition of quantum corrections within the cubic Galileon theory including the effect of quantum gravity, in a background- and gauge-invariant manner, employing the field-reparametrisation…
We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine - either for prediction via probability estimation, or to compute a kernel via estimation of quantum states overlap. We design…