Related papers: Variational Principle of Bogoliubov and Generalize…
We consider $N$ bosons in a box in $\mathbb {R}^d$ with volume $N/\rho$ under the influence of a mutually repellent pair potential. The particle density $\rho\in (0,\infty)$ is kept fixed. Our main result is the identification of the…
This paper promotes the differential method as a new fruitful strategy for estimating a ground-state energy of a many-body system. The case of an arbitrary number of attractive Coulombian particles is specifically studied and we make some…
We develop a variational approach at finite temperature that incorporates many-body correlation self-consistently. The grand potential is constructed in terms of Green's function expressed by the variational parameters. We apply this…
A novel Rayleigh-Schr\"odinger many-body perturbation theory (MBPT) approach is introduced by making use of a particle-number-breaking Bogoliubov reference state to tackle (near-)degenerate open-shell fermionic systems. By choosing a…
The mean-field approximations of many-boson dynamics are known to be effective in many physical relevant situations. The mathematical justifications of such approximations rely generally on specific considerations which depend too much on…
We present a time-dependent variational approach with the multiple Davydov $D_2$ trial state to simulate the dynamics of light-matter systems when the field is in a coherent state with an arbitrary finite mean photon number. The variational…
We develop a variational method for interacting surface systems with higher-form global symmetries. As a natural extension of the conventional second-quantized Hamiltonian of interacting bosons, we explicitly construct a second-quantized…
Systems of interest in physics are usually composed by a very large number of interacting particles. At equilibrium, these systems are described by stationary states of the many-body Hamiltonian (at zero temperature, by the ground state).…
We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure…
The main goal of the present article is to extend the Bogolyubov method for deriving kinetic equations to dissipative many-body systems. The basic conjecture underlying the Bogolyubov approach is the functional hypothesis, according to…
We present a novel generic framework to approximate the non-equilibrium steady states of dissipative quantum many-body systems. It is based on the variational minimization of a suitable norm of the quantum master equation describing the…
We generalise the two-sided Bogoliubov inequality for classical particles from [L. Delle Site et al., J.Stat.Mech.Th.Exp. 083201 (2017)] to systems of quantum particles. As in the classical set-up, the inequality leads to upper and lower…
We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of…
We develop a framework to systematically investigate the influence of many-particle interference on the dynamics of generic $-$ possibly interacting $-$ bosonic systems. We consider mixtures of bosons which belong to several distinguishable…
A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number…
We review recent results about the derivation of the Gross-Pitaevskii equation and of the Bogoliubov excitation spectrum, starting from many-body quantum mechanics. We focus on the mean-field regime, where the interaction is multiplied by a…
We consider a system of N interacting bosons in the mean-field scaling regime and construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to arbitrary precision. The N-independent corrections are…
In this work we develop a complete variational many-body theory for a system of $N$ trapped bosons interacting via a general two-body potential. In this theory both the many-body basis functions {\em and} the respective expansion…
Many quantal many-body methods that aim at the description of self-bound nuclear or mesoscopic electronic systems make use of auxiliary wave functions that break one or several of the symmetries of the Hamiltonian in order to include…
Bose-Einstein condensates made of ultracold trapped bosonic atoms have become a central venue in which interacting many-body quantum systems are studied. The ground state of a trapped Bose-Einstein condensate has been proven to be 100%…