Empirical Master Equations. Part I: Numerical Properties

Numerical Analysis of Different Vibrational Relaxation Models for Master Equations

We present in this report two modelizations of vibrational relaxation processes in a gaz: the Landau-Teller (LT) model and the master equations (ME). We give diierent models for VT and VV rate constants. We propose an algorithm to solve the equations of vibrational relaxation (LT or ME) coupled with conservation equations of momentum and total energy. Both models are compared on the computation...

Numerical Methods and Stochastics Part I: Numerical Methods

Controllability properties for finite dimensional quantum Markovian master equations

Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of q...

Numerical Solution of Integral Equations with Finite Part Integrals

We obtain convergence rates for several algorithms that solve a class of Hadamard singular integral equations using the general theory of approximations for unbounded operators.

Generalized Lagrangian Master Equations

We discuss the geometry of the Lagrangian quantization scheme based on (generalized) Schwinger-Dyson BRST symmetries. When a certain set of ghost fields are integrated out of the path integral, we recover the Batalin-Vilkovisky formalism, now extended to arbitrary functional measures for the classical fields. Keeping the ghosts reveals the crucial role played by a natural connection on the spac...