相关论文: Uniform in time lower bound for solutions to a qua…

We consider an approximation of the linearised equation of the homogeneous Boltzmann equation that describes the distribution of quasiparticles in a dilute gas of bosons at low temperature. The corresponding collision frequency is neither…

We consider the spatially inhomogeneous quantum Boltzmann equation for bosons with a singular collision kernel, the weak-coupling limit of a large system of Bose-Einstein particles interacting through inverse power law. Global…

The study of positivity of solutions to the Boltzmann equation goes back to Carleman (1933), and the initial argument of Carleman was developed byPulvirenti-Wennberg (1997), the second author and Briant (2015). The appearance of a lower…

The homogeneous bosonic Nordheim equation is a kinetic equation describing the dynamics of the distribution of particles in the space of moments for a homogeneous, weakly interacting, quantum gas of bosons. We show the existence of…

Inconsistencies are pointed out in the usual quantum versions of the classical linear Boltzmann equation constructed for a quantized test particle in a gas. These are related to the incorrect formal treatment of momentum decoherence. We…

Starting from the Bogoliubov diagonalization for the Hamiltonian of a weakly interacting Bose gas under the presence of a Bose-Enstein Condensate, we derive the kinetic equation for the Bogoliubov excitations. Without dropping any of the…

For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The…

In this paper, we prove the propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation. These $L^\infty$ bounds have been known to be a challenging open problem in relativistic kinetic theory. To…

A quantitative quantum field approach with non-local order parameters is presented for a very weakly interacting, dilute Bose gas. Within the presented model, which assumes the constraint of particle number conservation at constant average…

We consider the Bogoliubov approximation for the many-body quantum dynamics of weakly interacting Bose gases and establish a uniform-in-time validity of the Bogoliubov theory. The proof relies on a detailed analysis of the dispersive…

In this paper we prove the global in time existence and uniqueness of solutions of the spatially homogeneous Boltzmann equation for Bose-Einstein particles for the hard sphere model for bounded anisotropic initial data. The main idea of our…

We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal…

We formulate the time-dependent Bogoliubov dynamics of colliding Bose-Einstein condensates in terms of a positive-P representation of the Bogoliubov field. We obtain stochastic evolution equations for the field which converge to the full…

The relativistic quantum Boltzmann equation (or the relativistic Uehling-Uhlenbeck equation) describes the dynamics of single-species fast-moving quantum particles. With the recent development of the relativistic quantum mechanics, the…

The quantum instability of the mean-field theory for identical bosons is shown to be described by an appropriate Bogoliubov transformation. A connection between the quantum and classical linear stability theories is indicated. It is argued…

We investigate the phenomenon of Bose-Einstein condensation in ideal bosonic gases confined to axially-symmetric surfaces of revolution. The single-particle Schr\"odinger equation is formulated on a general surface and then explicitly…

We prove the appearance of an explicit lower bound on the solution to the full Boltzmann equation in the torus for a broad family of collision kernels including in particular long-range interaction models, under the assumption of some…

The Boltzmann-Nordheim equation is a modification of the Boltzmann equation, based on physical considerations, that describes the dynamics of the distribution of particles in a quantum gas composed of bosons or fermions. In this work we…

We study the time evolution of a quantum particle in a Gaussian random environment. We show that in the weak coupling limit the Wigner distribution of the wave function converges to a solution of a linear Boltzmann equation globally in…

We consider a Bose-Einstein condensate of bosons with repulsion, described by the Gross-Pitaevskii equation and restricted by an impenetrable "hard wall" (either rigid or flexible) which is intended to suppress the "snake instability"…