# Beyond Bogoliubov dynamics

@article{Bomann2019BeyondBD, title={Beyond Bogoliubov dynamics}, author={Lea Bo{\ss}mann and Soren Petrat and Peter Pickl and Avy Soffer}, journal={Pure and Applied Analysis}, year={2019} }

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 arbitrary precision. The corrections are such that they can be explicitly computed in an N-independent way from the solutions of the Bogoliubov and Hartree equations and satisfy a generalized form of Wick's theorem. We determine the n-point correlation functions of the excitations around the mean field, as…

## 14 Citations

### Low-energy spectrum and dynamics of the weakly interacting Bose gas

- PhysicsJournal of Mathematical Physics
- 2022

We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates, and dynamics, which provides…

### Asymptotic expansion of low-energy excitations for weakly interacting bosons

- PhysicsForum of Mathematics, Sigma
- 2021

Abstract We consider a system of N bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy…

### Edgeworth expansion for the weakly interacting Bose gas

- Mathematics, Physics
- 2022

We consider the ground state and the low-energy excited states of a system of N identical bosons with interactions in the mean-ﬁeld scaling regime. For the ground state, we derive an Edgeworth…

### Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron

- Physics
- 2022

We consider the large polaron described by the Fr¨ohlich Hamiltonian and study its energy-momentum relation deﬁned as the lowest possible energy as a function of the total momentum. Using a suitable…

### Large Deviation Estimates for Weakly Interacting Bosons

- MathematicsJournal of Statistical Physics
- 2022

We study the many-body dynamics of an initially factorized bosonic wave function in the mean-field regime. We prove large deviation estimates for the fluctuations around the condensate. We derive an…

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

- MathematicsReviews in Mathematical Physics
- 2022

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.…

### Dynamics of a Tracer Particle Interacting with Excitations of a Bose–Einstein Condensate

- PhysicsAnnales Henri Poincaré
- 2022

We consider the quantum dynamics of a large number N of interacting bosons coupled a tracer particle, i.e. a particle of another kind, on a torus. We assume that in the initial state the bosons…

### Dynamics of interacting bosons: a compact review

- Physics
- 2021

The success of the Gross–Pitaevskii and Bogoliubov theories in the description of large systems of interacting bosons led to a substantial eﬀort into rigorously deriving these eﬀective theories. In…

### A Large Deviation Principle in Many-Body Quantum Dynamics

- Physics, MathematicsAnnales Henri Poincaré
- 2021

It is shown that fluctuations around the limiting Hartree dynamics satisfy large deviation estimates that are consistent with central limit theorems that have been established in the last years.

### Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas

- Physics, MathematicsCalculus of Variations and Partial Differential Equations
- 2021

We consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of…

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