On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate

DOI10.1007/s10955-023-03082-xOpenAlexW4362540958MaRDI QIDQ2701137

Publication date: 27 April 2023

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.03825

zbMATH Keywords

Bose-Einstein condensate nonequilibrium quantum statistical mechanics thermal quantum fluctuations Boltzmann-Nordheim equations Boltzmann-Uhlenbeck-Uehling equations quantum Boltzmann equations

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Qxx) Time-dependent statistical mechanics (dynamic and nonequilibrium) (82Cxx) Applications of quantum theory to specific physical systems (81Vxx)

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An explicit coercivity estimate of the linearized quantum Boltzmann operator without angular cutoff ⋮ The derivation of the compressible Euler equation from quantum many-body dynamics

Cites Work

Dynamics of sound waves in an interacting Bose gas
The Gross-Pitaevskii hierarchy on general rectangular tori
Long time convergence of the Bose-Einstein condensation
Focusing quantum many-body dynamics: the rigorous derivation of the 1D focusing cubic nonlinear Schrödinger equation
On the Klainerman-Machedon conjecture for the quantum BBGKY hierarchy with self-interaction
Ground states of large bosonic systems: the Gross-Pitaevskii limit revisited
On the Cauchy problem for the homogeneous Boltzmann-Nordheim equation for bosons: local existence, uniqueness and creation of moments
On the rate of convergence for the mean field approximation of bosonic many-body quantum dynamics
Pair excitations and the mean field approximation of interacting Bosons. I
From Newton to Boltzmann: hard spheres and short-range potentials
Dynamical collapse of Boson stars
Smoothing effect of weak solutions for the spatially homogeneous Boltzmann equation without angular cutoff
The Hartree equation for infinitely many particles. II: Dispersion and scattering in 2D
Beyond mean field: on the role of pair excitations in the evolution of condensates
Quantum many-body fluctuations around nonlinear Schrödinger dynamics
The Boltzmann-Grad limit of a hard sphere system: analysis of the correlation error
Global well-posedness of the NLS system for infinitely many fermions
Analytical approach to relaxation dynamics of condensed Bose gases
Boltzmann limit for a homogeneous Fermi gas with dynamical Hartree-Fock interactions in a random medium
The mathematics of the Bose gas and its condensation.
Second-order corrections to mean field evolution of weakly interacting bosons. I
Weakly nonlinear Schrödinger equation with random initial data
Heisenberg picture of quantum kinetic evolution in mean-field limit
On the Boltzmann equation for 2D Bose-Einstein particles
The excitation spectrum for weakly interacting bosons
A simple derivation of mean field limits for quantum systems
On measure solutions of the Boltzmann equation. I: Moment production and stability estimates
The propagation of chaos for a rarefied gas of hard spheres in the whole space
The Boltzmann equation for Bose-Einstein particles: regularity and condensation
Intermolecular forces of infinite range and the Boltzmann equation
Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas
On the mean-field limit of bosons with Coulomb two-body interaction
Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with Integrable angular cross section
The phonon Boltzmann equation, properties and link to weakly anharmonic lattice dynamics
Some considerations on the derivation of the nonlinear quantum Boltzmann equation. II: The low density regime
On the Boltzmann equation for Fermi-Dirac particles with very soft potentials: averaging compactness of weak solutions
Global solutions to the Cauchy problem for the relativistic Boltzmann equation with near-vacuum data
Derivation of the cubic nonlinear Schrödinger equation from quantum dynamics of many-body systems
On the weak coupling limit of quantum many-body dynamics and the quantum Boltzmann equation
Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction
On the Cauchy problem for Boltzmann equations: Global existence and weak stability
On the Cauchy problem for the Boltzmann equation in the whole space: Global existence and uniform stability in \(L_{\xi}^{2}(H_{x}^{N})\)
On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
Boltzmann limit and quasifreeness for a homogeneous Fermi gas in a weakly disordered random medium
On the Boltzmann equation for Fermi-Dirac particles with very soft potentials: global existence of weak solutions
Kinetics of the Bose-Einstein condensation
On the Cauchy problem for focusing and defocusing Gross-Pitaevskii hierarchies
Derivation of the time dependent Gross-Pitaevskii equation without positivity condition on the interaction
Mean-field dynamics: Singular potentials and rate of convergence
Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate
Mean field limit for bosons and infinite dimensional phase-space analysis
Not to normal order-notes on the kinetic limit for weakly interacting quantum fluids
Quantum fluctuations and rate of convergence towards mean field dynamics
Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a Maxwellian gas
The Boltzmann equation: global existence for a rare gas in an infinite vacuum
Derivation of the Boltzmann equation from particle dynamics
On the nonlinear Boltzmann equation in unbounded domains
Global solution of the initial value problem for the Boltzmann equation near a local Maxwellian
The classical field limit of scattering theory for non-relativistic many- boson systems. II
The Boltzmann equation. I. Uniqueness and local existence
Renormalization group analysis of spectral problems in quantum field theory
On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
Fermi gas on a lattice in the van Hove limit
On Boltzmann equations and Fokker-Planck asymptotics: Influence of grazing collisions
Kinetic models and quantum effects: A modified Boltzmann equation for Fermi-Dirac particles
The mathematical theory of dilute gases
Smooth Feshbach map and operator-theoretic renormalization group methods.
On stability and strong convergence for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles
Classical solutions to the Boltzmann equation for molecules with an angular cutoff
A modified Boltzmann equation for Bose-Einstein particles: Isotropic solutions and long-time behavior
Weak coupling limit of the \(N\)-particle Schrödinger equation
Global existence of solutions of the Boltzmann equation for Bose-Einstein particles with anisotropic initial data
Mean field dynamics of a quantum tracer particle interacting with a boson gas
From hard sphere dynamics to the Stokes-Fourier equations: an \(L^2\) analysis of the Boltzmann-Grad limit
On the dynamics of finite temperature trapped Bose gases
Bogoliubov correction to the mean-field dynamics of interacting bosons
On the scattering problem for infinitely many fermions in dimensions \(d\geq 3\) at positive temperature
On the Cauchy problem with large data for a space-dependent Boltzmann-Nordheim boson equation
Derivation of the 1d Gross-Pitaevskii equation from the 3d quantum many-body dynamics of strongly confined bosons
The Dirac-Frenkel principle for reduced density matrices, and the Bogoliubov-de Gennes equations
Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
On coupling kinetic and Schrödinger equations
Uniform in time lower bound for solutions to a quantum Boltzmann equation of bosons
On the size of chaos in the mean field dynamics
Uniform in \(N\) global well-posedness of the time-dependent Hartree-Fock-Bogoliubov equations in \(\mathbb {R}^{1+1}\)
Compactness in Boltzmann's equation via Fourier integral operators and applications. III
Derivation of the nonlinear Schrödinger equation from a many body Coulomb system
Smoothing effects for the classical solutions to the Landau-Fermi-Dirac equation
Rate of convergence towards semi-relativistic Hartree dynamics
The Boltzmann equation for Bose-Einstein particles: condensation in finite time
A quantum Boltzmann equation for Haldane statistics and hard forces; the space-homogeneous initial value problem
Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature
Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime
Higher order corrections to the mean-field description of the dynamics of interacting bosons
Derivation of 3D energy-critical nonlinear Schrödinger equation and Bogoliubov excitations for Bose gases
The spatially homogeneous Boltzmann equation for Bose-Einstein particles: rate of strong convergence to equilibrium
On a system of equations for the normal fluid-condensate interaction in a Bose gas
Derivation of the time dependent Gross-Pitaevskii equation in two dimensions
Multivariate central limit theorem in quantum dynamics
The relativistic quantum Boltzmann equation near equilibrium
The Rigorous Derivation of the 2D Cubic Focusing NLS from Quantum Many-Body Evolution
Entropy maximisation problem for quantum relativistic particles
Transport Phenomena in Einstein-Bose and Fermi-Dirac Gases. I
On the Boltzmann equation for long-range interactions
Well-posedness for the spatially homogeneous Landau–Fermi–Dirac equation for hard potentials
Theorie cinétique d'un gaz de Bose dilué avec condensat
Dynamics of large boson systems with attractive interaction and a derivation of the cubic focusing NLS equation in R3
Another proof of BEC in the GP-limit
On the derivation of the wave kinetic equation for NLS
Convergence rate towards the fractional Hartree equation with singular potentials in higher Sobolev trace norms
Excitation spectrum of Bose gases beyond the Gross–Pitaevskii regime
The excitation spectrum of the Bose gas in the Gross–Pitaevskii regime
Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics
Bogoliubov Spectrum of Interacting Bose Gases
On the Cauchy problem for the nonlinear Boltzmann equation global existence uniqueness and asymptotic stability
Transport of a quantum particle in a time-dependent white-noise potential
Bogoliubov corrections and trace norm convergence for the Hartree dynamics
Statistical Physics of Non Equilibrium Quantum Phenomena
Bogoliubov theory for dilute Bose gases: The Gross-Pitaevskii regime
A kinetic equation for ultra-low temperature Bose–Einstein condensates
Book Review: From Newton to Boltzmann: hard spheres and short-range potentials
Blow-up rate estimates for the solutions of the bosonic Boltzmann-Nordheim equation
Global existence and stability of mild solutions to the Boltzmann system for gas mixtures
Existence of global solutions to the Cauchy problem for the inelastic Boltzmann equation with near-vacuum data
Derivation of the Hartree equation for compound Bose gases in the mean field limit
Derivation of the 1d nonlinear Schrödinger equation from the 3d quantum many-body dynamics of strongly confined bosons
On the validity of the Boltzmann equation for short range potentials
Singular solutions for the Uehling–Uhlenbeck equation
Quantum-mechanical perturbations giving rise to a statistical transport equation
Asymptotic expansion of low-energy excitations for weakly interacting bosons
Cluster expansion for a dilute hard sphere gas dynamics
Mean-field evolution of fermionic systems
Mathematical concepts of quantum mechanics.
Derivation of the transport equation for electrons moving through random impurities
On a model Boltzmann equation without angular cutoff
Dynamical formation of a Bose-Einstein condensate
On spatially homogeneous solutions of a modified Boltzmann equation for Fermi-Dirac particles.
A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas
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Unnamed Item
Unnamed Item
About the use of entropy production for the Landau-Fermi-Dirac equation
Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons
On semi-classical limit of spatially homogeneous quantum Boltzmann equation: weak convergence
Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation
Correlation energy of a weakly interacting Fermi gas
Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime
Bose-Einstein condensation with optimal rate for trapped bosons in the Gross-Pitaevskii regime
The time-dependent Hartree-Fock-Bogoliubov equations for bosons
Optimal local well-posedness theory for the kinetic wave equation
On well-posedness for general hierarchy equations of Gross-Pitaevskii and Hartree type
Fluctuation theory in the Boltzmann-Grad limit
Long time dynamics for the Landau-Fermi-Dirac equation with hard potentials
The rigorous derivation of the \(\mathbb{T}^2\) focusing cubic NLS from 3D
Rigorous derivation of a ternary Boltzmann equation for a classical system of particles
On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy
Collective excitations of Bose gases in the mean-field regime
The Hartree equation for infinitely many particles. I: Well-posedness theory
Vector partitions, multi-dimensional Faà di Bruno formulae and generating algorithms
Derivation of the Bogoliubov time evolution for a large volume mean-field limit
On existence and uniqueness to homogeneous Boltzmann flows of monatomic gas mixtures
On the time dependence of the rate of convergence towards Hartree dynamics for interacting bosons
The derivation of the \(\mathbb{T}^{3}\) energy-critical NLS from quantum many-body dynamics
On a Boltzmann equation for Haldane statistics
Finite time blow-up and condensation for the bosonic Nordheim equation
On the transfer of energy towards infinity in the theory of weak turbulence for the nonlinear Schrödinger equation
On the mean-field approximation of many-boson dynamics
Exact evolution versus mean field with second-order correction for bosons interacting via short-range two-body potential.
Mean-field- and classical limit of many-body Schrödinger dynamics for bosons
On the quantum Boltzmann equation
Some considerations on the derivation of the nonlinear quantum Boltzmann equation
A note on the validity of Bogoliubov correction to mean-field dynamics
Mean field evolution of fermions with Coulomb interaction
Local well-posedness for Boltzmann's equation and the Boltzmann hierarchy via Wigner transform
Bose-Einstein condensation in a dilute, trapped gas at positive temperature
Norm approximation for many-body quantum dynamics: Focusing case in low dimensions
On the rigorous derivation of the 2D cubic nonlinear Schrödinger equation from 3D quantum many-body dynamics
Derivation of Hartree's theory for generic mean-field Bose systems
Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in \(d=3\) based on spacetime norms
From the \(N\)-body Schrödinger equation to the quantum Boltzmann equation: a term-by-term convergence result in the weak coupling regime
Localization lengths and Boltzmann limit for the Anderson model at small disorders in dimension 3
On isotropic distributional solutions to the Boltzmann equation for Bose-Einstein particles
Moment inequalities and high-energy tails for Boltzmann equations with inelastic interactions
On the blow up and condensation of supercritical solutions of the Nordheim equation for bosons
Talbot effect for the cubic non-linear Schröedinger equation on the torus
Bose condensates in interaction with excitations: a two-component space-dependent model close to equilibrium
The Boltzmann equation for Bose-Einstein particles: velocity concentration and convergence to equilibrium
Rigorous derivation of the cubic NLS in dimension one
Small data global well-posedness for a Boltzmann equation via bilinear spacetime estimates
Beyond Bogoliubov dynamics
On the quantum Boltzmann equation near Maxwellian and vacuum
Uniqueness of solutions to the spectral hierarchy in kinetic wave turbulence theory
Derivation of the linear Boltzmann equation from the damped quantum Lorentz gas with a general scatterer configuration
Global well-posedness of a binary-ternary Boltzmann equation
Nonlinear aspects of the theory of Bose-Einstein condensates
Mean-field quantum dynamics with magnetic fields
Derivation of a matrix-valued Boltzmann equation for the Hubbard model
The Hartree limit of Born's ensemble for the ground state of a bosonic atom or ion
Derivation in Strong Topology and Global Well-Posedness of Solutions to the Gross-Pitaevskii Hierarchy
The Exponentially Convergent Trapezoidal Rule
Unconditional Uniqueness of the cubic Gross--Pitaevskii Hierarchy with Low Regularity
Unconditional Uniqueness for the Cubic Gross-Pitaevskii Hierarchy via Quantum de Finetti
Effective Evolution Equations from Quantum Dynamics
A simple proof of convergence to the Hartree dynamics in Sobolev trace norms
Pair excitations and the mean field approximation of interacting Bosons, II
THE BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF IN THE WHOLE SPACE: II, GLOBAL EXISTENCE FOR HARD POTENTIAL
Global classical solutions of the Boltzmann equation without angular cut-off
Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential
A description of the evolution of quantum states by means of the kinetic equation
Global existence and stability of mild solutions to the inelastic Boltzmann system for gas mixtures
Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics
Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff
ON THE WEAK-COUPLING LIMIT FOR BOSONS AND FERMIONS
A reaction network approach to the convergence to equilibrium of quantum Boltzmann equations for Bose gases
Gibbs Measures of Nonlinear Schrödinger Equations as Limits of Quantum Many-Body States in Dimension d ≤ 3
Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensate
Atomism and quantization
Fluctuations around Hartree states in the mean-field regime
Well-Posedness of the Cauchy Problem for a Space-Dependent Anyon Boltzmann Equation
Rate of Convergence to Mean Field for Interacting Bosons
A derivation of a new set of equations at the onset of the Bose–Einstein condensation
Bose-Condensed Gases at Finite Temperatures
On the Vlasov hierarchy
On the Boltzmann equation for rigid spheres
On the existence of global solutions of mixed problem for non-linear Boltzmann equation
ON THE WEAK COUPLING LIMIT FOR A FERMI GAS IN A RANDOM POTENTIAL
On moments and uniqueness for solutions to the space homogeneous Boltzmann equation
Boltzmann Equation with Infinite Energy: Renormalized Solutions and Distributional Solutions for Small Initial Data and Initial Data Close to a Maxwellian
Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
Correlation Structures, Many-Body Scattering Processes, and the Derivation of the Gross–Pitaevskii Hierarchy
On Mittag-Leffler Moments for the Boltzmann Equation for Hard Potentials Without Cutoff