Freiburg 2008 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 5: Vielteilchentheorie

MP 5.2: Vortrag

Dienstag, 4. März 2008, 17:20–17:40, KGI-HS 1023

The zero-entropy-density conjecture — •Zoltán Zimborás¹ and Szilárd Farkas² — ¹Theoretische Physik, Universität des Saarlandes, Saarbrücken 66041 Campus 1, Germany — ²Department of Physics, University of Chicago, Chicago, Illinois 60637

A natural and long-standing conjecture in mathematical quantum statistical physic is that the entropy density vanishes for all translation-invariant pure states on a quantum spin-chain. Or equivalently, S(N), the von Neumann entropy of such a state restricted to N consecutive spins, is sublinear. We report on a new result about this conjecture. We have shown that this conjecture cannot be sharpened, i.e., translation-invariant states give rise to arbitrary fast sublinear entropy growth. The proof is constructive, and is based on a class of states derived from quasifree states on a CAR algebra. We will also discuss the d-dimensional case, and a general lower-bound on the entropy asymptotics of pure shift-invariant quasifree states will be given.
References:
1) S. Farkas and Z. Zimborás, J. Math. Phys. 48, 102110 (2007).
2) S. Farkas and Z. Zimborás, J. Math. Phys. 46, 123301 (2005).