Specific heat oscillations in quasi-periodic structures |
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| Affiliation: | 1. Departamento de Fı́sica, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN, Brazil;2. Instituto de Fı́sica, Universidade do Estado do Rio de Janeiro, R. São Francisco Xavier 524, 20559-900 Rio de Janeiro-RJ, Brazil;3. Departamento de Fı́sica, Universidade Estadual de Maringá, Av. Colombo 5790, 87020-900 Maringá-PR, Brazil;1. Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal;2. Departamento de Matemáticas, Facultad de Ciencias de la Universidad de Oviedo, Federico García Lorca, 18, 33007 Oviedo, Spain;1. Institute for Technical Physics and Materials Science, Centre for Energy Research, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary;2. Budapest University of Technology and Economics, Budafoki út 8, H-1111 Budapest, Hungary;1. Theory Department, H.A.S. Wigner RCP, Budapest, Hungary;2. Department of Physics, Babeş-Bolyai University, Cluj-Napoca, Romania |
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| Abstract: | Most models on quasi-crystals, as well as the related experimental results, exhibit fractal energy spectra. We discuss the relevant thermodynamic implications of this feature by performing both analytical and numerical calculations of the specific heats associated with successive hierarchical approximations to fractal energy spectra. Instructive anomalies are displayed, namely the specific heat exhibits an infinite number of small-amplitude oscillations symmetrically disposed around a characteristic dimension of the spectrum. We also analyse a multifractal spectrum generated dynamically by the logistic map and conjecture a possible connection with Tsallis' generalized thermostatics. |
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