Related papers: Stable interactions via proper deformations
We review the occurrence of negative energies in Pais-Uhlenbeck oscillator. We point out that in the absence of interactions negative energies are not problematic, neither in the classical nor in the quantized theory. However, in the…
We fulfill the detailed analysis of coupling the charged bosonic higher spin fields to external constant electromagnetic field in first order in external field strength. Cubic interaction vertex of arbitrary massive and massless bosonic…
Higher order derivative theories, generally suffer from instabilities, known as Ostrogradsky instabilities. This issue can be resolved by removing any existing degeneracy present in such theories. We consider a model involving at most…
The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…
We introduce and prove a novel linear response stability theory for spin glasses. The new stability under suitable perturbation of the equilibrium state implies the whole set of structural identities that characterize the spin glass phase.
We extend the method of controlled Lagrangians with kinetic shaping to those mechanical systems on semidirect product Lie groups with broken symmetry, more specifically to the Euler--Poincar\'e equations with advected parameters. We find a…
We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schr\"odinger equation in finite square lattices, modeling light propagation in two-dimensional nonlinear waveguide arrays. We…
We derive the most generic Carrollian higher derivative free scalar field theory intrinsically on a Carrollian manifold. The solutions to these theories are massless free particles propagating with speeds depending on the coupling constants…
We study the structure of stationary non equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non…
We address the stabilization of both classical and quantum systems modeled by jump-diffusion stochastic differential equations using a novel hysteresis switching strategy. Unlike traditional methods that depend on global Lyapunov functions…
This paper deals with an analysis and design of robust, state-feedback control law uniform-asymptotically stabilizing at origin the system consisting of coupled $n$th--order ordinary differential equations in the presence of a non-vanishing…
Boundedness properties of operators associated with non-degenerate symmetric $\alpha$-stable, $\alpha \in (1,2)$, probability measures on $\mathbb{R}^d$ are investigated on appropriate, Euclidean or otherwise, $L^p$-spaces, $p \in…
Within the framework of Lagrangian mechanics, the conservativeness of the hydrostatic forces acting on a floating rigid body is proved. The representation of the associated hydrostatic potential is explicitly worked out. The invariance of…
No quantum measurement can give full information on the state of a quantum system; hence any quantum feedback control problem is neccessarily one with partial observations, and can generally be converted into a completely observed control…
In this work, we develop a control-theoretic framework for constrained optimization problems with composite objective functions including non-differentiable terms. Building on the proximal augmented Lagrangian formulation, we construct a…
There is a close connection between stability and oscillation of delay differential equations. For the first-order equation $$ x^{\prime}(t)+c(t)x(\tau(t))=0,~~t\geq 0, $$ where $c$ is locally integrable of any sign, $\tau(t)\leq t$ is…
We introduce a simple spherical model whose structural properties are similar to the ones generated by models with directional interactions, by employing a binary mixture of large and small hard spheres, with a square-well attraction acting…
A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the…
We construct the free Lagrangian of the magnetic sector of Carrollian electrodynamics. The construction relies on Helmholtz integrability condition for differential equations in a self consistent algorithm, working hand in hand with…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…