Related papers: Equilibrium perturbations for stochastic interacti…
In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange…
We study the dissipation mechanism of a stochastic particle system for the Burgers equation. The velocity field of the viscous Burgers and Navier-Stokes equations can be expressed as an expected value of a stochastic process based on noisy…
When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the…
We consider critical one dimensional quantum systems initially prepared in their groundstate and perturbed by a smooth noise coupled to the energy density. By using conformal field theory, we deduce a universal description of the…
In Ref. [1, 2] a formalism to deal with high-order perturbations of a general spherical background was developed. In this article, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the…
We study the equilibrium fluctuations of an interacting particle system evolving on the discrete ring with $N\in\mathbb N$ points, denoted by $\mathbb T_N$, and with three species of particles that we name $A,B$ and $C$, but such that at…
A class of asymptotically autonomous systems on the plane with oscillatory coefficients is considered. It is assumed that the limiting system is Hamiltonian with a stable equilibrium. The effect of damped multiplicative stochastic…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new…
We study energy transport in a chain of quantum harmonic and anharmonic oscillators where the anharmonicity is induced by interaction between local vibrational states of the chain. Using adiabatic elimination and numerical simulations with…
We address the problem of constructing a non-equilibrium stationary state for a one-dimensional stochastic Klein-Gordon wave equation with non-linearity, using perturbation theory. The linear theory is reviewed, but with the linear…
Exact spectral truncations of the unforced, inviscid Burgers-Hopf equation are Hamiltonian systems with many degrees of freedom which exhibit intrinsic stochasticity and coherent scaling behavior. For this reason recent studies have…
Mackey-Glass equation arises in the leukemia model. We generalize this equation to include fractional-order derivatives in two directions. The first generalization contains one whereas the second contains two fractional derivatives. Such…
We study the effect of generic spatial anisotropies on the scaling behavior in the Kardar-Parisi-Zhang equation. In contrast to its "conserved" variants, anisotropic perturbations are found to be relevant in d > 2 dimensions, leading to…
The perturbation theory of operator semigroups is used to derive response formulas for a variety of combinations of acting forcings and reference background dynamics. In the case of background stochastic dynamics, we decompose the response…
Traditional finite element approaches are well-known to introduce spurious oscillations when applied to advection-dominated problems. We explore alleviation of this issue from the perspective of a generalized finite element formulation,…
The equilibrium properties of an open harmonic oscillator are considered in three steps: First the creation and destruction operators are generalized for open dynamics and the creation operator is used to construct coherent states. The…
A stability analysis is made for a non-singular pre-big-bang like cosmological model based on 1-loop corrected string effective action. Its homogeneous and isotropic solution realizes non-singular transition from de Sitter universe to…
Synchronization of coupled oscillators on a $d$-dimensional lattice with the power-law coupling $G(r) = g_0/r^\alpha$ and randomly distributed intrinsic frequency is analyzed. A systematic perturbation theory is developed to calculate the…
We study the evolution of linear perturbations in a Lema\^itre-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard…
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…