Details of Grant 

EPSRC Reference:	GR/R95586/01
Title:	Spectral Analysis of Partial Differential Equations and Applications in Quantum Mechanics
Principal Investigator:	Balinsky, Professor A
Other Investigators:	Evans, Professor WD
Researcher Co-Investigators:
Project Partners:
Department:	Sch of Mathematics
Organisation:	Cardiff University
Scheme:	Standard Research (Pre-FEC)
Starts:	01 June 2003	Ends:	31 May 2006	Value (£):	123,595
EPSRC Research Topic Classifications:	Mathematical Analysis Mathematical Physics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 30 May 2002 Mathematics Prioritisation Panel May 02 Deferred
Summary on Grant Application Form
Stability of matter is a statement, rooted in quantum mechanics and electrostatics, that the energy per particle has a lower bound which is independent of the state of matter and, in particular, of its amount. This fact is responsible for preventing matter from shrinking indefinitely in size, as well as for basic thermodynamical properties such as extensivity. It also explains why some molecules exists and other configurations of particles do not. The stability of matter problem concerns the question whether the minimal energy of a system of particles is bounded from below (stability of the first kind), and whether it is bounded from below by a constant times the number of particles (stability of the second kind).In the first, and main, part of the project we shall investigate stability problems for relativistic systems with and without magnetic fields; a magnetic field has important implications for stability. This will include a study of zero modes and Aharonov-Rohm type magnetic fields.In the second part we shall study spectral properties of operators and inequalities which are relevant to the first part.
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Organisation Website:	http://www.cf.ac.uk