Project Details
Projekt
Stochastic Quantum Scattering --- New Tools, New Aspects
Applicant
Professor Dr. Karl Thomas Guhr
Subject Area
Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
Term
since 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 540160740
It is very difficult to measure the physical processes in molecules, atoms, atomic nuclei or in the quantum world in general. Scattering experiments that map these processes onto macroscopic scales are highly important. To this end, one bombards the "target", that is, the tiny object of interest in the quantum world with even tinier particles. The acting forces change the particle and possibly also the target. An example: atomic nuclei are bombarded with protons, protons or neutrons or even other particles leave the (modified) target area. These are then measured in macroscopic detectors. In general, the different incoming and outgoing particles with distinct properties that are relevant and used in the experiment are called "scattering channels" or "channels" for short. In the quantum world, particles are described by waves. The scattering by the target changes amplitude and phase of the incoming wave. The scattering matrix contains all the information on how the incoming wave is mapped onto the outgoing wave, possibly in a different channel. However, it is seldom possible to measure the scattering matrix, only the moduli squared of the scattering matrix elements, the cross sections, are experimentally accessible. From those one can infer the properties of the target, that is, in the example above, how the atomic nucleus is composed, which are the acting forces and so on. All this is very generally applicable, because scattering experiments are carried out in all areas of the quantum world. Actually, even certain experiments with classical waves, such as electromagnetic or acoustic ones, can be described in this way. Moreover, in wireless communication such as cell phone networks similar modeling is applied. Often the target is chaotic in a very general sense, that is, the physics is so complex that one has to work with statistical methods. This is what is known as stochastic quantum scattering, which is the subject of the proposed project. We succeeded some time ago in developing a modern mathematical procedure even further and thus to solve a longstanding problem: we calculated exactly the previously unknown statistical distributions of the scattering matrix elements and of the cross sections between different channels. There are three cases which differ in their behavior under time reversal. This new mathematical tool we now want to exploit further. In the project we want to: first, exactly calculate the one of the three cases that we have not yet addressed, and second, to use our knowledge of the distributions to precisely answer a whole series of still unsolved questions, and third, to perform comparisons with experimental data.
DFG Programme
Research Grants
International Connection
France, India, Mexico, Poland, South Korea
