Related papers: Second random-phase approximation, Thouless' theor…
Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature…
Numerical and analytical studies of "final states" of two-dimensional (2D) decaying turbulence are reported. The first part of this work is trying to give a definition for final states of 2D decaying turbulence. Although the functional…
The direct ring coupled-cluster doubles (drCCD)-based random phase approximation (RPA) has provided an attractive framework for the development and application of RPA-related methods. However, a potential unphysical solution issue recently…
The principle of stationary phase (PSP) is re-examined in the context of linear time-frequency (TF) decomposition using Gaussian, gammatone and gammachirp filters at uniform, logarithmic and cochlear spacings in frequency. This necessitates…
Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the…
The formalism of the continuum random-phase approximation theory which treats, without ap- proximations, the continuum part of the single-particle spectrum, is extended to describe charge- exchange excitations. Our approach is…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
In this work we address the open problem of high Reynolds number limit in hydrodynamic turbulence, which we modify by considering a vanishing random (instead of deterministic) viscosity. In this formulation, a small-scale noise propagates…
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…
Some general features of the spectrum of the Hartree-Fock-Bogoliubov equations are examined. Special attention is paid to the asymptotic behavior of the single quasiparticle wave functions (s.qp.w.fs.), matter density distribution and…
Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy system, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values.…
We consider here variational solutions in the Hartree-Fock approximation upon breaking time reversal and axial symmetries. When decomposed on axial harmonic oscillator functions, the corresponding single particle triaxial eigenstates as…
A proof of the relativistic $H$-theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics…
Self-consistent random phase approximation (SCRPA) is applied to the exactly solvable model with fermion boson coupling proposed by Sch\"utte and Da-Providencia. Very encouraging results in comparison with the exact solution of the model…
The asymptotic behaviour of the Hartree equation is studied near translation-invariant steady states. For short-range interaction kernels satisfying a uniform Penrose stability condition, including the screened Coulomb interaction,…
When a Hamiltonian density is bounded by below, we know that the lowest-energy state must be stable. One is often tempted to reverse the theorem and therefore believe that an unbounded Hamiltonian density always implies an instability. The…
We show that the invariant measure of point vortices, when conditioning the Hamiltonian to a finite interval, converges weakly to the enstrophy measure by conditioning the renormalized energy to the same interval. We also prove the…
The steady-state approximation (hereafter abbreviated as SSA) consists in setting $dy/dt=0$, where $y$ denotes the concentration of a short-lived intermediate subject to first-order decay with a rate constant $k$. The sole reason for…
We present a technique which allows us to solve the Random Phase Approximation equations with finite-range interactions and treats the continuum part of the excitation spectrum without approximations. The interaction used in the…
In this note, which is of general stability theory interest, we discuss some of the key assertions usually stated in the context of the transition to turbulence problem. In particular, the two main points made here in the setting of the…