EPSRC Reference: 
EP/P007155/1 
Title: 
Fermionic Exchange Symmetry: Consequences for the 1 and 2Fermion Picture 
Principal Investigator: 
Schilling, Dr CS 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Oxford Physics 
Organisation: 
University of Oxford 
Scheme: 
EPSRC Fellowship 
Starts: 
01 December 2016 
Ends: 
06 September 2019 
Value (£): 
269,465

EPSRC Research Topic Classifications: 
Condensed Matter Physics 
Mathematical Physics 
Quantum Optics & Information 


EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
The Pauli exclusion principle (PEP) is one of most prominent principles in Physics and Chemistry. It is not only fundamentally relevant but also very elegant and can therefore easily be taught already at the high school level: Each energy shell in atoms cannot be occupied by more than two electrons. This significant restriction on occupation numbers manifests itself in the Aufbau principle explaining the structure of atoms and is consequently at the heart of our periodic table. PEP is not only relevant on this atomic scale but also on much larger scales. For instance, it is responsible for the stability of neutron stars, built up from billions of billions of neutrons: All those neutrons would like in principle to collapse to a tiny spatial region due to their attractive gravitational attraction which, however, is prohibited by the PEP not allowing more than two electrons to sit at the same place.
Despite success as an isolated concept, PEP as a restriction on the way how electrons occupy energy shells is de facto a consequence of the more substantial fermionic exchange symmetry. This mathematical property of the many electron system follows from the quantum character of electrons: They are identical and the swapping of any two of them must not change the theoretical description of that physical system. In in a groundbreaking work by the geometer Alexander Klyachko it was recently shown that this more substantial fermionic exchange symmetry implies further restrictions on occupation numbers. These socalled generalized Pauli constraints (GPC) are more restrictive than the famous PEP and make the latter one obsolete.
Now, with all these GPC at hand it is possible and timely as well to develop a comprehensive understanding of the influence of the more abstract fermionic exchange symmetry on the behaviour of electrons occupying energy shells. This is particularly important for our understanding of Quantum Physics since the description of physical effects is made much easier by exploiting an occupation number picture rather than studying the full mathematical properties of the complex manyelectron wave function.
In my proposed project I will study and eventually confirm the physical relevance of these generalized Pauli constraints. Since the electrons are `fighting' for the lowest energy shells these GPC are expected to be relevant: At least some electrons need to occupy less preferable (i.e. higher) energy shells to not violate any GPC. This expected conflict between electrons shall be explored and quantified in my project. In particular, I will develop a heuristically motivated principle, the `Pauli pressure', explaining how some electrons are pressed into the lowest few energy shells and how some other electrons desperately try to occupy lower shells. Besides these more fundamental and mathematically concise concepts I will study concrete systems of a few electrons to test my proposed concept. For which systems is this `Pauli pressure' particularly dominant and how does it simplify the theoretical description of quantum systems? How can we measure the `Pauli pressure' and can we find an elegant way to even visualize it in experiments?
The GPC and their potential relevance described in the form of an emerging `Pauli pressure' will also affect our understanding of entanglement. This concept of a spooky action between quantum particles describes some additional correlations between different electrons even if they are spatially wellseparated. Yet, if the `Pauli pressure' is sufficiently strong it can freeze electrons in specific energy shells and therefore reduce the total entanglement. This shall be studied and eventually be understood by concise mathematical means.

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Organisation Website: 
http://www.ox.ac.uk 