$370K Funding

1 People

External

The subject of this research is mathematical problems of physics of open systems--the systems that exchange energy with the environment. The questions to be addressed range from general and theoretical to study of specific systems, designed with applications in mind. An example of a theoretical (and, indeed, foundational) problem, studied by the PI, is a systematic approach to quantum mechanics, using quantum stochastic calculus. This project aims at elucidating well-known problems with interpretation of quantum theory, including state reduction and the measurement problem. At the same time, the PI will collaborate with experimental physics groups on design and explanation of laboratory experiments. One project of this type is concerned with the emergent behavior in motion of interacting agents. In this project, aggregation and separation of light-sensitive robots is studied, emphasizing the role of sensorial delay. A new project, in which sophisticated mathematical methods meet with laboratory experiments, addresses electrical conductivity of graphene sheets and of active carbon. The latter topic is important for the design of quantum devices and thus is immediately aligned with Quantum Leap, one of the NSF's 10 Big Ideas. Noise and disorder are ubiquitous phenomena, particularly important in the study of open systems. Their mathematical models use several tools of probability theory. The most important one is stochastic analysis, studying differential equations with noise; this is one of the principal topics to be investigated in this project. Other methods include ergodic theory, functional analysis and dynamical systems. The PI will continue training graduate students and junior researchers: a major part of this research will be done in collaboration with junior researchers mentored by the PI. Collaboration with three physics groups--experimental as well as theoretical--will be a crucial part of the project, determining the particular research directions. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.