Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-04-27
Publ. Math. IHES 113 (2011), no. 1, 39 - 67
Physics
Condensed Matter
Strongly Correlated Electrons
23 pages
Scientific paper
We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N\geq 2 polarons. Fr\"ohlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling \sqrt\alpha, and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U<2\alpha, stability of matter does hold for U>2\alpha, that is, the ground state energy per particle has a finite limit as N\to\infty. (ii) There is no binding of any kind if U exceeds a critical value that depends on \alpha but not on N. The same results are shown to hold for the Pekar-Tomasevich model.
Frank Rupert L.
Lieb Elliott H.
Seiringer Robert
Thomas Lawrence E.
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