Sin t

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6. LOW-TEMPERATURE PROPERTIES OF NON-CRYSTALLINE
SOLIDS T lt 1 K TLS and the Tunneling Model
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Thermal conductivity
Specific heat
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(No Transcript)
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TUNNELING MODEL W.A. Phillips (1972) P.W.
Anderson, B. Halperin and C.M. Varma (1972)
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Thermal properties of dielectric glasses
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Acoustic properties of dielectric glasses
(res)
(rel)
(res rel)
Tco? ?1/3
Tco
Tco
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? T3
? ?2/T
DIELECTRIC PROPERTIES ?j ? E ?j ? p v ? ?
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Acoustic properties of metallic glasses
(res)
(rel)
(res rel)
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Universal Behavior of Glasses
(R. Pohl)
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(Freeman and Anderson)
C
B
?4
A
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(R. Pohl)
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? ? 102 - 1011 Hz !!!
(R. Pohl, X. Liu and E. J. Thompson, Rev. Mod.
Physics, 2002)
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Criticism to the Standard Tunneling Model ?
No direct experimental evidence that anything is
tunneling ? It does not explain universal
behavior ? Importance of interactions between the
TLS
(Yu and Leggett, 1988)
The effective interaction between 2 TLS
exchanging phonons is dipolar