Related papers: Stability and correlations in dilute two-dimension…
Two-level boson systems displaying a quantum phase transition from a spherical (symmetric) to a deformed (broken) phase are studied. A formalism to diagonalize Hamiltonians with $O(2L+1)$ symmetry for large number of bosons is worked out.…
We construct spherically symmetric boson star solutions in $D \in \{4,5,6\}$ spacetime dimensions, considering the effects of both a quartic self-interaction term and a solitonic potential. We then perform a perturbative analysis,…
A class of two-species ({\it three-states}) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the…
The effect of decaying oscillatory perturbations on autonomous Hamiltonian systems in the plane with a stable equilibrium is investigated. It is assumed that perturbations preserve the equilibrium and satisfy a resonance condition. The…
We study the two-band Hubbard model in infinite dimensions by solving the dynamical mean-field equations with a strong coupling continuous-time quantum Monte Carlo method and show that an $s$-wave superconducting state can be stabilized in…
We study the stability of reaction-diffusion equations in presence of noise. The relationship of stability of solutions between the stochastic ordinary different equations and the corresponding stochastic reaction-diffusion equation is…
Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics.…
We study the out-of-equilibrium dynamics of the Bose-Hubbard model for two-component bosons using a strong-coupling approach within the closed-time-path formalism and develop an effective theory for the action of this problem. We obtain…
This paper study the hyperexponential stabilization for infinite-dimensional system on Hilbert space by a distributed time depending control law. The well-posedness of the closed loop for every time is obtained through the use of maximal…
The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic…
We study the dynamics of a symmetric two-level system strongly coupled to a broadened harmonic mode. Upon mapping the problem onto a spin-boson model with peaked spectral density, we show how analytic solutions can be obtained, at arbitrary…
The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
The quantum dynamics of interacting bosons in a one-dimensional system is investigated numerically. We consider dissipative and conservative two-particle interactions, and integrate the master equation describing the system dynamics via a…
We study the stability problem for a non-relativistic quantum system in dimension three composed by $ N \geq 2 $ identical fermions, with unit mass, interacting with a different particle, with mass $ m $, via a zero-range interaction of…
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential…
The exact solution for a system with two-particle annihilation and decoagulation has been studied. The spectrum of the Hamiltonian of the system is found. It is shown that the steady state is two-fold degenerate. The average number density…
We develop a mean-field model to examine the stability of a `quasi-2D suspension' of elongated particles embedded within a viscous membrane. This geometry represents several biological and synthetic settings, and we reveal mechanisms by…
The question of stability of steady spherical accretion has been studied for many years and, recently, the concept of spatial instability has been introduced. Here we study perturbations of steady spherical accretion flows (Bondi…
A variational basis set motivated by mean-field theory is utilized to describe the Bose-Einstein condensate within the adiabatic hyperspherical coordinate framework. The simplest single-orbital variant of this treatment reproduces many of…