Theory of Open Quantum Systems
Theorie offener Quantensysteme
Course 0000000977 in WS 2023/4
|Semester Weekly Hours
|Chair of Angewandte Quantentheorie (Prof. Rabl)
Mon, 14:00–16:00, PH 3344
Courses are together with exams the building blocks for modules. Please keep in mind that information on the contents, learning outcomes and, especially examination conditions are given on the module level only – see section "Assignment to Modules" above.
|The Schrödinger equation, as taught in the introductory courses of quantum mechanics, describes the unitary evolution of an isolated quantum system. This situation, however, is hardly ever encountered in real experiments, where the system of interest typically interacts with a large number of uncontrolled degrees of freedom, for example, the quantized electromagnetic field, phonons in a solids, etc. The presence of this environment leads to irreversible, spontaneous decay and decoherence and a different mathematical formalism must be adopted in order to account for such phenomena. This lecture covers both basic and also more advanced techniques to describe the dynamics of such open quantum systems. A primary focus of this course will be placed on stochastic simulation methods and continuously monitored quantum systems, but it will also cover several special topics related to ongoing research directions in this field. The following main topics will be covered in this course:-) open quantum systems and the reduced density operator -) the quantum master equation-) stochastic processes and stochastic differential equations -) the stochastic Schrödinger equation -) Monte Carlo wave function simulations -) quantum measurement theory -) continuously observed quantum systems and quantum feedback theory-) phase-space methods-) the (discrete) truncated Wigner approximation-) phase transitions in driven-dissipative quantum systems -) strong-coupling and non-Markovian effects in waveguide QED-) the spin-boson modelThe main course will be complemented by an exercise course, where the students will learn how to apply the theoretical concepts introduced in the lecture by writing their own numerical programs for simulating open quantum systems in Python.
E-Learning course (e. g. Moodle)