Related papers: Renormalized oscillation theory for singular linea…
We propose an abstract framework describing energy-renormalized Hamiltonians in terms of local algebras. Within the framework, we examine the positivity improvingness of the semigroup generated by the renormalized Hamiltonian. As examples,…
This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity…
In this paper, we study and build the Hamiltonian system attached to any $\mathfrak{gl}_2(\mathbb{C})$ meromorphic connection with an arbitrary number of non-ramified poles of arbitrary degrees. In particular, we propose the Lax pairs and…
This chapter gives a self-contained review of the how standard open quantum system Hamiltonians can be mapped analytically onto representations in which the environments appear as one dimensional harmonic chains with nearest neighbour…
Renormalization of Hamiltonian field theory is usually a rather painful algebraic or numerical exercise. By combining a method based on the coupled cluster method, analysed in detail by Suzuki and Okamoto, with a Wilsonian approach to…
We use the recent theory of Spectral Submanifolds (SSM) for model reduction of nonlinear mechanical systems subject to parametric excitations. Specifically, we develop expressions for higher-order nonautonomous terms in the parameterization…
Hamiltonian Learning is a process of recovering system Hamiltonian from measurements, which is a fundamental problem in quantum information processing. In this study, we investigate the problem of learning the symmetric Hamiltonian from its…
We extend the definition of Lagrangian local bias proposed by Matsubara (2008) to include curvature and higher-derivative bias operators. Evolution of initially biased tracers using perturbation theory (PT) generates multivariate bias…
Following Part~I, we consider a class of reversible systems and study bifurcations of homoclinic orbits to hyperbolic saddle equilibria. Here we concentrate on the case in which homoclinic orbits are symmetric, so that only one control…
We present a generalized framework, renormalized density matrix downfolding (RDMD), to derive systematically improvable, highly accurate, and nonperturbative effective models from ab initio calculations. This framework moves beyond the…
Starting from a formal Hamiltonian as found in the physics literature -- omitting photons -- we define a renormalized Hamiltonian through charge and mass renormalization. We show that the restriction to the one-electron subspace is…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…
We propose a scheme for extending the model Hamiltonian method developed originally for studying the equilibrium properties of complex perovskite systems to include Langevin dynamics. The extension is based on Zwanzig's treatment of…
This paper is devoted to studying Hamiltonian oscillators in 1:1:1:1 resonance with symmetries, which include several models of perturbed Keplerian systems. Normal forms are computed in Poisson and symplectic formalisms, by mean of…
We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a…
We consider scenarios where the dynamics of a quantum system are partially determined by prior local measurements of some interacting environmental degrees of freedom. The resulting effective system dynamics are described by a disordered…
We consider integrable Hamiltonian systems in R^{2n} with integrals of motion F = (F_1,...,F_n) in involution. Nondegenerate singularities are critical points of F where rank dF = n-1 and which have definite linear stability. The set of…
In many practical applications, signals and environments are time- varying, which makes fixed filters unreliable. Adaptive filtering, on the other hand, updates in real time to suppress noise, track nonstationary signals, and identify…
This paper proposes Hamiltonian Learning, a novel unified framework for learning with neural networks "over time", i.e., from a possibly infinite stream of data, in an online manner, without having access to future information. Existing…