Abstract
In this paper, we consider a quantum Boltzmann equation, which describes the interaction between excited atoms and a condensate. The collision integrals are taken–over energy manifolds, having the full form of the Bogoliubov dispersion law for particle energy. We prove that nonnegative radially symmetric solutions of the quantum Boltzmann equation are bounded from below by a Gaussian distribution, uniformly in time.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 63-89 |
| Number of pages | 27 |
| Journal | Archive for Rational Mechanics and Analysis |
| Volume | 231 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 22 2019 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering
Cite this
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Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons. / Nguyen, Toan; Tran, Minh Binh.
In: Archive for Rational Mechanics and Analysis, Vol. 231, No. 1, 22.01.2019, p. 63-89.Research output: Contribution to journal › Article
TY - JOUR
T1 - Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons
AU - Nguyen, Toan
AU - Tran, Minh Binh
PY - 2019/1/22
Y1 - 2019/1/22
N2 - In this paper, we consider a quantum Boltzmann equation, which describes the interaction between excited atoms and a condensate. The collision integrals are taken–over energy manifolds, having the full form of the Bogoliubov dispersion law for particle energy. We prove that nonnegative radially symmetric solutions of the quantum Boltzmann equation are bounded from below by a Gaussian distribution, uniformly in time.
AB - In this paper, we consider a quantum Boltzmann equation, which describes the interaction between excited atoms and a condensate. The collision integrals are taken–over energy manifolds, having the full form of the Bogoliubov dispersion law for particle energy. We prove that nonnegative radially symmetric solutions of the quantum Boltzmann equation are bounded from below by a Gaussian distribution, uniformly in time.
UR - http://www.scopus.com/inward/record.url?scp=85049111337&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85049111337&partnerID=8YFLogxK
U2 - 10.1007/s00205-018-1271-z
DO - 10.1007/s00205-018-1271-z
M3 - Article
AN - SCOPUS:85049111337
VL - 231
SP - 63
EP - 89
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 1
ER -