Quantum effects in an anharmonic crystal

• Дата: 2002
• Автор: Kozitsky, Yu.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут фізики конденсованих систем НАН України 2002
• Назва видання: Condensed Matter Physics
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/120681
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Quantum effects in an anharmonic crystal / Yu. Kozitsky // Condensed Matter Physics. — 2002. — Т. 5, № 4(32). — С. 601-616. — Бібліогр.: 41 назв. — англ.

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.