Related papers: Modifying the Dyson Series for Unstable Particles …
We propose a general strategy to discretize the Dyson series without applying direct numerical quadrature to high-dimensional integrals, and extend this framework to open quantum systems. The resulting discretization can also be interpreted…
We show how the state of an unstable particle can be defined in terms of stable asymptotic states. This general definition is used to discuss and to solve some old problems connected with the short-time and large-time behaviour of the…
We study inhomogeneous perturbations away from the strongly homogeneous background cosmology previously studied. The problem is greatly simplified by using the mapping on the inner Schwarzschild solution. The resulting linear perturbation…
Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…
Dyson's model is a one-dimensional system of Brownian motions with long-range repulsive forces acting between any pair of particles with strength proportional to the inverse of distances with proportionality constant $\beta/2$. We give…
The gravitation interaction between particles is taken into account in central configuration model. After that, the resonance perturbation of the particle of the central configuration by distant satellite is considered in the restricted…
Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard…
Recently we have introduced a lightweight, perturbative approach to quantum solitons. Thus far, our approach has been largely limited to configurations consisting of a single soliton plus a finite number of mesons, whose classical limit is…
We investigate unitarity within the Complex-Mass Scheme, a convenient universal scheme for perturbative calculations involving unstable particles in Quantum Field Theory which guarantees exact gauge invariance. Since this scheme requires to…
We present a perturbation method for determining the moment stability of linear ordinary differential equations with parametric forcing by colored noise. In particular, the forcing arises from passing white noise through an $n$th order…
Stochastic resonance is a well established phenomenon, which proves relevant for a wide range of applications, of broad trans-disciplinary breath. Consider a one dimensional bistable stochastic system, characterized by a deterministic…
We address the problem that the cross section for the collisions of unstable particles diverges, if calculated by standard methods. This problem is considered for beams much smaller than the decay length of the unstable particle, much…
We study the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for $\ell_2$ in the context of the Urysohn space $\Ur$. In particular, we show that this problem reduces to a purely combinatorial…
We develop a new approach to estimate the uncertainty due to missing higher orders in perturbative predictions (the perturbative "theory uncertainty"), which overcomes many inherent limitations of the currently prevalent methods based on…
We show how to convert divergent series, which typically occur in many applications in physics, into rapidly convergent inverse factorial series. This can be interpreted physically as a novel resummation of perturbative series. Being…
A few modified textbook Rayleigh-Schr\"{o}dinger perturbative representations of bound states are reviewed. They were all inspired by an adaptive re-split of the Hamiltonian, using nonstandard bases and the flexibility of normalization of…
We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case,…
This paper deals with the problem of predicting the future state of discrete-time input-delayed systems in the presence of unknown disturbances that can affect both the state and the output equations of the plant. Since the disturbance is…
A new two-step renormalization procedure is proposed. In the first step, the effects of high-energy states are considered in the conventional (Feynman) perturbation theory. In the second step, the coupling to many-body states is eliminated…
A new family of S-matrix theories with resonance poles is constructed and conjectured to correspond to the Homogeneous sine-Gordon theories associated with simply laced compact Lie groups, where some of the resonance poles can be traced to…