Pith. sign in

REVIEW 4 cited by

The Cauchy problem and BEC stability for the quantum Boltzmann-Condensation system for bosons at very low temperature

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1609.07467 v3 pith:R6YMTZCS submitted 2016-09-23 math.AP

The Cauchy problem and BEC stability for the quantum Boltzmann-Condensation system for bosons at very low temperature

Ricardo Alonso , Irene M. Gamba , Minh-Binh Tran This is my paper
classification math.AP
keywords systemboltzmann-condensationcondensateinitialkineticproblemquantumstability
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

We study a quantum Boltzmann-Condensation system that describes the evolution of the interaction between a well formed Bose-Einstein condensate and the quasi-particles cloud. The kinetic model is valid for a dilute regime at which the temperature of the gas is very low compared to the Bose-Einstein condensation critical temperature. In particular, our system couples the density of the condensate from a Gross-Pitaevskii type equation to the kinetic equation through the dispersion relation in the kinetic model and the corresponding transition probability rate from pre to post collision momentum states. We rigorously show the following three properties (1) the well-posedness of the Cauchy problem for the system in the case of a radially symmetric initial configuration, (2) find qualitative properties of the solution such as instantaneous creation of exponential tails and, (3) prove the uniform condensate stability related to the initial mass ratio between condensed particles and quasi-particles. The stability result from (3) leads to global in time existence of the initial value problem for the quantum Boltzmann-Condensation system.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Entropy Structures and Long-Time Relaxation for 3-Wave Kinetic Equations

    math.AP 2026-05 conditional novelty 8.0

    For a broad class of 3-wave kinetic equations, a new one-sided entropy mechanism yields global L^1_loc weak solutions and forces local relaxation to zero as t tends to infinity.

  2. Entropy Structures and Long-Time Relaxation for 3-Wave Kinetic Equations

    math.AP 2026-05 unverdicted novelty 7.0

    New entropy structures from one-sided balance conditions on interaction weights yield global weak L1_loc solutions to 3-wave kinetic equations and prove their local relaxation to zero equilibrium.

  3. Global time-analytic strong solutions for a class of 3-wave kinetic equations

    math-ph 2026-07 accept novelty 6.0

    For radial nonnegative data, a regularized 3-wave kinetic equation has a unique global strong solution that stays nonnegative and is time-analytic.

  4. Local existence of strong solutions to the capillary wave kinetic equation

    math.AP 2026-07 accept novelty 5.0

    Local strong solutions exist for the capillary wave kinetic equation in L^∞ weighted spaces without assuming radial symmetry.