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

@article{Nam2017NormAF, title={Norm approximation for many-body quantum dynamics: Focusing case in low dimensions}, author={Phan Th{\`a}nh Nam and Marcin Napi{\'o}rkowski}, journal={Advances in Mathematics}, year={2017} }

## 29 Citations

### 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…

### 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…

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

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

### On the Emergence of Quantum Boltzmann Fluctuation Dynamics near a Bose–Einstein Condensate

- Materials ScienceJournal of Statistical Physics
- 2023

In this work, we study the quantum fluctuation dynamics in a Bose gas on a torus $$\Lambda =(L{\mathbb {T}})^3$$ Λ = ( L T ) 3 that exhibits Bose–Einstein condensation, beyond the leading order…

### 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 the Fröhlich dynamics in the mean-field regime

- PhysicsJournal of Functional Analysis
- 2023

### Blow-up profile of rotating 2D focusing Bose gases

- Mathematics, Physics
- 2018

We consider the Gross-Pitaevskii equation describing an attractive Bose gas trapped to a quasi 2D layer by means of a purely harmonic potential, and which rotates at a fixed speed of rotation…

### Derivation of the Bogoliubov Time Evolution for a Large Volume Mean-Field Limit

- PhysicsAnnales Henri Poincaré
- 2019

The derivation of mean-field limits for quantum systems at zero temperature has attracted many researchers in the last decades. Recent developments are the consideration of pair correlations in the…

### The mean-field limit of the Lieb-Liniger model

- Computer ScienceDiscrete & Continuous Dynamical Systems
- 2022

It is shown that the time-dependent reduced density matrices of the system converge in trace norm to the pure states given by the solution to the one-dimensional cubic nonlinear Schrödinger equation (NLS) with an explict rate of convergence.

### Beyond Bogoliubov dynamics

- Mathematics, PhysicsPure and Applied Analysis
- 2021

We consider a quantum system of N interacting bosons in the mean field scaling regime. We construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to…

## 47 References

### Focusing Quantum Many-body Dynamics: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation

- Mathematics
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We consider the dynamics of N bosons in 1D. We assume that the pair interaction is attractive and given by $${N^{\beta-1}V(N^{\beta}.) where }$$Nβ-1V(Nβ). where $${\int V \leqslant 0}$$∫V⩽0. We…

### Rigorous Derivation of the Gross-Pitaevskii Equation with a Large Interaction Potential

- Mathematics
- 2008

Consider a system of $N$ bosons in three dimensions interacting via a repulsive short range pair potential $N^2V(N(x_i-x_j))$, where $\bx=(x_1, >..., x_N)$ denotes the positions of the particles. Let…

### A note on 2D focusing many-boson systems

- Physics
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We consider a 2D quantum system of $N$ bosons in a trapping potential $|x|^s$, interacting via a pair potential of the form $N^{2\beta-1} w(N^\beta x)$. We show that for all $0 \textless{} \beta…

### 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 Large Boson Systems with Attractive Interaction and a Derivation of the Cubic Focusing NLS in $\mathbb{R}^3$

- Mathematics
- 2016

Let us consider a many-body Boson system where the particles experience a short-range two-body interparticle interaction given by $v_N(x) = N^{3\beta}v(N^\beta x)$ with $v \in C^\infty_0$, without…

### 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…

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

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

### The Rigorous Derivation of the 2D Cubic Focusing NLS from Quantum Many-body Evolution

- Mathematics
- 2015

We consider a 2D time-dependent quantum system of $N$-bosons with harmonic external confining and \emph{attractive} interparticle interaction in the Gross-Pitaevskii scaling. We derive stability of…