Related papers: A Note on Perturbations During a Regular Bounce
Faddeev and Jackiw's method for constrained systems is used to derive a gauge invariant formulation of cosmological perturbations in the one bubble inflationary universe. For scalar perturbations in a flat universe, reduction of the action…
We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability…
In the present work we present the full treatment of scalar and vector cosmological perturbations in a non-singular bouncing universe in the context of metric $f(R)$ cosmology. Scalar metric perturbations in $f(R)$ cosmology were previously…
The controversial problem of an isolated system with an internal adiabatic wall is investigated with the use of a simple microscopic model and the Boltzmann equation. In the case of two infinite volume one-dimensional ideal fluids separated…
We consider linear perturbation equations for long-wavelength scalar metric perturbations in generalised gravity, applicable to non-singular cosmological models including a bounce from collapse to expansion in the very early universe. We…
We develop perturbative methods to study and control dynamical phenomena related to exceptional points in Non-Hermitian systems. In particular, we show how to find perturbative solutions based on the Magnus expansion that accurately…
We perform a detailed investigation of the simplest possible cosmological model in which a bounce can occur, namely that where the dynamics is led by a simple massive scalar field in a general self-interacting potential and a background…
We investigate singular geometries which can be associated with warped branes in arbitrary dimensions. If the brane tension is allowed to be variable, the extremum condition for the action requires additional constraints beyond the solution…
The derivation of a Moving Boundary Approximation or of the response of a coherent structure like a front, vortex or pulse to external forces and noise, is generally valid under two conditions: the existence of a separation of time scales…
We restate the adiabatic elimination approximation as the first term in a singular perturbation expansion. We use the invariant manifold formalism for singular perturbations in dynamical systems to identify systematic improvements on…
In general, to avoid a singularity in cosmological models involves the introduction of exotic kind of matter fields, for example, a scalar field with negative energy density. In order to have a bouncing solution in classical General…
It is shown that perturbation theory in $2D$ nonlinear $\sigma$-models as well gauge theories in dimension $D\geq 2$ produces answers that depend on boundary conditions even after the infinite volume limit has been taken. This unphysical…
A self-gravitating sphere of polytropic gas (polytrope) is considered. The system of equations describing radial motions of this sphere in Lagrangian variables reduces to the only nonlinear PDE of the second order in both variables…
We introduce a method where successive coordinate transformations are applied to decrease the error in the adiabatic master equation resulting from truncation in the local adiabatic parameter. Our method reduces the nonphysical behaviour…
We show that disordered boundaries destroy bulk phase separation in scalar active systems in dimension $d<d_c=3$. This is in strong contrast with the equilibrium case where boundaries have no impact on the bulk of phase-separated systems.…
We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. We present results for this system, and argue that it offers lessons for real molecular collisions in…
Cavitation and bubble dynamics are central concepts in engineering, the natural sciences, and the mathematics of fluid mechanics. Due to the nonlinear nature of their dynamics, the governing equations are not fully solvable. Here, the…
We describe a non-perturbative method for computing the energy band structures of one-dimensional models with general point potentials sitting at equally spaced sites. This is done thanks to a Bethe ansatz approach and the method is…
Quantum adiabatic evolutions find a broad range of applications in quantum physics and quantum technologies. The traditional form of the quantum adiabatic theorem limits the speed of adiabatic evolution by the minimum energy gaps of the…
Physical systems with loss or gain feature resonant modes that are decaying or growing exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, a so-called "exceptional…