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- Kroon, Lars, et al.
(författare)
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Renormalization of aperiodic model lattices: spectral properties
- 2003
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Ingår i: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 1751-8113 .- 1751-8121 .- 0305-4470 .- 1361-6447. ; 36, s. 4519-4532
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Tidskriftsartikel (refereegranskat)abstract
- Many of the published results for one-dimensional deterministic aperiodic systems treat rather simplified electron models with either a constant site energy or a constant hopping integral. Here we present some rigorous results for more realistic mixed tight-binding systems with both the site energies and the hopping integrals having an aperiodic spatial variation. It is shown that the mixed Thue–Morse, period-doubling and Rudin–Shapiro lattices can be transformed to on-site models on renormalized lattices maintaining the individual order between the site energies. The character of the energy spectra for these mixed models is therefore the same as for the corresponding on-site models. Furthermore, since the study of electrons on a lattice governed by the Schrödinger tight-binding equation maps onto the study of elastic vibrations on a harmonic chain, we have proved that the vibrational spectra of aperiodic harmonic chains with distributions of masses determined by the Thue–Morse sequence and the period-doubling sequence are purely singular continuous.
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| 2. |
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| 3. |
- Sisman, Altug
(författare)
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Surface dependence in thermodynamics of ideal gases
- 2004
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Ingår i: Journal of Physics A. - 1751-8113 .- 1751-8121. ; 37, s. 11353-11361
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Tidskriftsartikel (refereegranskat)abstract
- The Casimir-like size effect rises in ideal gases confined in a finite domain due to the wave character of atoms. By considering this effect, thermodynamic properties of an ideal gas confined in spherical and cylindrical geometries are derived and compared with those in rectangular geometry. It is seen that anideal gas exhibits an unavoidable quantum surface free energy and surface over volume ratio becomes a control variable on thermodynamic state functions in microscale. Thermodynamics turns into non-extensive thermodynamics and geometry difference becomes a driving force since the surface over volumeratio depends on the geometry.
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