## 35 Citations

Norm approximation for many-body quantum dynamics: Focusing case in low dimensions

- Physics, MathematicsAdvances in Mathematics
- 2019

Fluctuations of N-particle quantum dynamics around the nonlinear Schrödinger equation

- Physics, MathematicsAnnales de l'Institut Henri Poincaré C, Analyse non linéaire
- 2019

Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons

- Mathematics, Physics
- 2019

In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of N…

Dynamical Hartree–Fock–Bogoliubov Approximation of Interacting Bosons

- MathematicsAnnales Henri Poincaré
- 2021

We consider a many-body Bosonic system with pairwise particle interaction given by $$N^{3\beta -1}v(N^\beta x)$$ N 3 β - 1 v ( N β x ) where $$0<\beta <1$$ 0 < β < 1 and v a non-negative spherically…

Norm Approximation for Many-Body Quantum Dynamics and Bogoliubov Theory

- Physics, Mathematics
- 2017

We review some recent results on the norm approximation to the Schrodinger dynamics. We consider N bosons in \(\mathbb{R}^{3}\) with an interaction potential of the form N 3β−1 w(N β (x − y)) with 0…

Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model

- Mathematics
- 2021

We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quantized scalar field.…

Analysis of Fluctuations Around Non-linear Effective Dynamics

- Mathematics, Physics
- 2017

We consider the derivation of effective equations approximating the many-body quantum dynamics of a large system of N bosons in three dimensions, interacting through a two-body potential N3β−1V (N β…

Bogoliubov corrections and trace norm convergence for the Hartree dynamics

- MathematicsReviews in Mathematical Physics
- 2019

We consider the dynamics of a large number [Formula: see text] of nonrelativistic bosons in the mean field limit for a class of interaction potentials that includes Coulomb interaction. In order to…

Derivation of the Time Dependent Two Dimensional Focusing NLS Equation

- MathematicsJournal of Statistical Physics
- 2018

We present a microscopic derivation of the two-dimensional focusing cubic nonlinear Schrödinger equation starting from an interacting N-particle system of Bosons. The interaction potential we…

Dynamics of mean-field bosons at positive temperature

- Physics
- 2022

We study the time-evolution of an initially trapped weakly interacting Bose gas at positive temperature, after the trapping potential has been switched off. It has been recently shown in [24] that…

## References

SHOWING 1-10 OF 21 REFERENCES

Bogoliubov correction to the mean-field dynamics of interacting bosons

- Physics, Mathematics
- 2017

We consider the dynamics of a large quantum system of $N$ identical bosons in 3D interacting via a two-body potential of the form $N^{3\beta-1} w(N^\beta(x-y))$. For fixed $0\leq \beta <1/3$ and…

Quantum Many-Body Fluctuations Around Nonlinear Schrödinger Dynamics

- Physics, Mathematics
- 2017

We consider the many-body quantum dynamics of systems of bosons interacting through a two-body potential $${N^{3\beta-1} V (N^\beta x)}$$N3β-1V(Nβx), scaling with the number of particles N. For $${0…

Exact Evolution versus Mean Field with Second-order correction for Bosons Interacting via Short-range Two-body Potential

- Physics
- 2015

We consider the evolution of N bosons, where N is large, with two-body interactions of the form $N^{3\beta}v(N^\beta \cdot)$, $0\leq\beta\leq 1$. The parameter $\beta$ measures the strength of…

Second-Order Corrections to Mean Field Evolution of Weakly Interacting Bosons. I.

- Mathematics
- 2009

Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schrödinger equation that describes a second-order correction to the usual tensor product (mean-field)…

Fluctuations around Hartree states in the mean-field regime

- Physics
- 2013

We consider the dynamics of a large system of $N$ interacting bosons in the mean-field regime where the interaction is of order $1/N$. We prove that the fluctuations around the nonlinear Hartree…

Ground states of large bosonic systems: The gross-pitaevskii limit revisited

- Physics, Mathematics
- 2015

We study the ground state of a dilute Bose gas in a scaling limit where the Gross-Pitaevskii functional emerges. This is a repulsive non-linear Schr\"odinger functional whose quartic term is…

The time-dependent Hartree-Fock-Bogoliubov equations for Bosons

- Physics, Mathematics
- 2016

In this article, we use quasifree reduction to derive the time-dependent Hartree-Fock-Bogoliubov (HFB) equations describing the dynamics of quantum fluctuations around a Bose-Einstein condensate in…

Bogoliubov Spectrum of Interacting Bose Gases

- Physics
- 2012

We study the large‐N limit of a system of N bosons interacting with a potential of intensity 1/N. When the ground state energy is to the first order given by Hartree's theory, we study the next…

Collective Excitations of Bose Gases in the Mean-Field Regime

- Physics
- 2014

We study the spectrum of a large system of N identical bosons interacting via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov’s theory predicts that the spectrum of the…

Excitation Spectrum of Interacting Bosons in the Mean-Field Infinite-Volume Limit

- Physics
- 2014

We consider homogeneous Bose gas in a large cubic box with periodic boundary conditions, at zero temperature. We analyze its excitation spectrum in a certain kind of a mean-field infinite-volume…