The Lieb-Wehrl entropy conjecture

Duration: 1 hour 14 mins 54 secs

About this item

Description:	Solovej, J P (University of Copenhagen) Tuesday 14 August 2012, 14:00-15:00


Created:	2012-08-16 15:59
Collection:	Spectral Theory of Relativistic Operators
Publisher:	Isaac Newton Institute
Copyright:	Solovej, J P
Language:	eng (English)


Abstract:	Using the coherent state transform Wehrl (1979) suggested a definition of the classical entropy of a quantum state. He conjectured that the classical entropy was minimized by coherent states, i.e., the states that also minimize the Heisenberg uncertainty inequality. Lieb (1978) proved this conjecture and at the same time conjectured that the same would be correct for the Bloch coherent states of all the irreducible SU(2) spin representations. This generalized Wehrl conjecture has been open for almost 35 years. I will present a short proof of the conjecture. This is joint work with E.H. Lieb.

Abstract:

Using the coherent state transform Wehrl (1979) suggested a definition of the classical entropy of a quantum state. He conjectured that the classical entropy was minimized by coherent states, i.e., the states that also minimize the Heisenberg uncertainty inequality. Lieb (1978) proved this conjecture and at the same time conjectured that the same would be correct for the Bloch coherent states of all the irreducible SU(2) spin representations. This generalized Wehrl conjecture has been open for almost 35 years. I will present a short proof of the conjecture. This is joint work with E.H. Lieb.

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