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A research proposal in Mathematical Physics

Applicant Graf Gian Michele
Number 131837
Funding scheme Project funding (Div. I-III)
Research institution Institut für Theoretische Physik ETH Zürich
Institution of higher education ETH Zurich - ETHZ
Main discipline Theoretical Physics
Start/End 01.11.2010 - 31.10.2012
Approved amount 196'852.00
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All Disciplines (2)

Theoretical Physics

Keywords (7)

statistical mechanics; quantum field theory; scattering theory; topological insulators; Quantum Mechanics; Open Systems; Transport Theory

Lay Summary (English)

Lay summary
Transport of current, heat or spin are among the most visible features of large quantum system. Sometimes they are characterized by a striking stability with respect to variations of external conditions, such as in topological insulators. Some transport properties appear to be insensitive not only in regard to conservative forces, but even to some forms of friction.The project is a research effort in Mathematical Physics. It aims at unraveling the mathematical structures underlying these and similar transport properties. Despite the complexity and variety of the considered systems at a fundamental level, they display - at a more abstract level - fairly universal geometrical concepts, like curvature and topological indices. Nevertheless such descriptions are often not unique. One aim is to relate some of those different geometric concepts. Another, and more extensive one, is to extend the "geometrization of transport" to open quantum system. This involves a careful and extensive study of their dynamics, which is quite different from that of the more conventional isolated systems. We intendend to develop some new views on quantum transport which are mathematically transparent and of lasting value.
Direct link to Lay Summary Last update: 21.02.2013

Responsible applicant and co-applicants


Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Statistical Mechanics Seminar 08.11.2012 Warwick
IX International Conference of Mathematical Physics in Armenia 03.09.2012 Yerevan
Seminar in Mathematischer Physik 14.06.2012 Erlangen
Mathematical Aspects of Quantum Mechanics and Quantum Transport Theory 23.04.2012 Bielefeld

Associated projects

Number Title Start Funding scheme
143222 A research proposal in Mathematical Physics 01.11.2012 Project funding (Div. I-III)


The applicant proposes a research plan in Mathematical Physics suited to make best use of the joint expertise of a new postdoc and of his own. The intended postdoc, to be employed at ETH beginning Fall 2010, is Marcello Porta, a PhD graduate from the University of Rome 1, advised by G. Gallavotti. The research to be performed is about one or several of the following topics,as further detailed in Section 2.2: (i) fluctuation theorems in non-equilibrium statistical mechanics, (ii) constructive quantum field theory,(iii) scattering in quantum field theory,(iv) topological insulators.