Quantum effects in an anharmonic crystal
A model of quantum particles performing D -dimensional anharmonic oscillations around their equilibrium positions which form the d -dimensional simple cubic lattice Zd is considered. The model undergoes a structural phase transition when the fluctuations of displacements of particles become macr...
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| Datum: | 2002 |
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| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут фізики конденсованих систем НАН України
2002
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| Schriftenreihe: | Condensed Matter Physics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/120681 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Quantum effects in an anharmonic crystal / Yu. Kozitsky // Condensed Matter Physics. — 2002. — Т. 5, № 4(32). — С. 601-616. — Бібліогр.: 41 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | A model of quantum particles performing D -dimensional anharmonic oscillations
around their equilibrium positions which form the d -dimensional
simple cubic lattice Zd is considered. The model undergoes a structural
phase transition when the fluctuations of displacements of particles become
macroscopic. This phenomenon is described by susceptibilities depending
on Matsubara frequencies ωn , n ∈ Z . We prove two theorems
concerning the thermodynamic limits of these susceptibilities. The first theorem
states that the susceptibilities with nonzero ωn remain bounded at all
temperatures, which means that the macroscopic fluctuations in the model
are always non-quantum. The second theorem gives a sufficient condition
for the static susceptibility (i.e. corresponding to ωn = 0 ) to be bounded
at all temperatures. This condition involves the particle mass, the anharmonicity
parameters and the interaction intensity. The physical meaning of
this result is that, for all D and all values of the temperature, strong quantum
effects suppress critical points and the long range order. The proof
is performed in the approach where the susceptibilities are represented as
functional integrals. A brief description of the main features of this approach
is delivered. |
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