相关论文: Completely Positive Bloch-Boltzmann Equations

In a large variety of spectroscopical applications Bloch-Boltzmann equations (BBE) play an essential role. They describe the evolution of the reduced density operator of an active atom which is coupled to radiation (Bloch part) and which…

A Multi-scale Boltzmann Equation (MBE) is found from the gas-kinetic theory and the direct modeling philosophy as a master equation for complex physical systems of neutral gases across all flow regimes, which locates between the continuum…

We investigate a kinetic model for interacting particles whose masses are integer multiples of an elementary mass. These particles undergo binary collisions which preserve momentum and energy but during which some number of elementary…

The relativistic Boltzmann equation for a single particle species generally implies a fixed, unchangeable equation of state that corresponds to that of an ideal gas. Real-world systems typically have more complicated equation of state which…

In this paper we show global well-posedness near vacuum for the binary-ternary Boltzmann equation. The binary-ternary Boltzmann equation provides a correction term to the classical Boltzmann equation, taking into account both binary and…

Experiments with ultracold Bose gases can already produce so strong atom--atom interactions that one can observe intriguing many-body dynamics between the Bose-Einstein condensate (BEC) and the normal component. The excitation picture is…

Master equations play a pivotal role in investigating open quantum systems. In particular, the Bloch-Redfield equation stands out due to its relation to a concrete physical environment. However, without further approximations it does not…

We develop an effective theory for biased tracers formulated at the level of the Boltzmann equation, providing a unified description of density and velocity bias. We introduce a general effective collision term in the tracer Boltzmann…

We propose a novel approach in the study of transport phenomena in dense systems or systems with long range interactions where multiple particle interactions must be taken into consideration. Within Boltzmann's kinetic formalism, we study…

The quantum Boltzmann-Bose equation describes a large system of Bose-Einstein particles in the weak-coupling regime. If the particle interaction is governed by the inverse power law, the corresponding collision kernel has angular…

Using the independent oscillator model with an arbitrary system potential, we derive a quantum Brownian equation assuming a correlated total initial state. Although not of Lindblad form, the equation preserves positivity of the density…

We consider complete positivity of dynamics regarding subsystems of an open composite quantum system, which is subject of a completely positive dynamics. By "completely positive dynamics", we assume the dynamical maps called the completely…

We consider the effect of non-reciprocity in a binary mixture of self-propelled particles with anti-aligning interactions, where a particle of type A reacts differently to a particle of type B than vice versa. Starting from a well-known…

The equation for the quantum motion of a Brownian particle in a gaseous environment is derived by means of S-matrix theory. This quantum version of the linear Boltzmann equation accounts non-perturbatively for the quantum effects of the…

We prove two equilibrium properties of a system of interacting atoms in three or higher dimensional continuous space. (i) If the particles interact via pair potentials of a nonnegative Fourier transform, their self-organization into…

In this paper we derive accurate numerical methods for the quantum Boltzmann equation for a gas of interacting bosons. The schemes preserve the main physical features of the continuous problem, namely conservation of mass and energy, the…

The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an…

We derive quantum Boltzmann equations for preheating by means of the density matrix formalism, which account for both the non-adiabatic particle production and the leading collisional processes between the produced particles. In so doing,…

In pre-Born-Oppenheimer (pre-BO) theory a molecule is considered as a quantum system as a whole, including the electrons and the atomic nuclei on the same footing. This approach is fundamentally different from the traditional quantum…

The linearized collision operator of the Boltzmann equation for single species can be written as a sum of a positive multiplication operator, the collision frequency, and a compact integral operator. This classical result has more recently,…