The Einstein specific heat model for finite systems

• Autor(a) principal: Boscheto, E.
• Data de Publicação: 2016
• Outros Autores: De Souza, M. [UNESP], López-Castillo, A.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1016/j.physa.2016.02.010; http://hdl.handle.net/11449/172867
• topic: Einstein model; Finite size systems; Specific heat

The theoretical model proposed by Einstein to describe the phononic specific heat of solids as a function of temperature consists of the very first application of the concept of energy quantization to describe the physical properties of a real system. Its central assumption lies in the consideration of a total energy distribution among N (in the thermodynamic limit N → ∞) non-interacting oscillators vibrating at the same frequency (ω). Nowadays, it is well-known that most materials behave differently at the nanoscale, having thus some cases physical properties with potential technological applications. Here, a version of the Einstein model composed of a finite number of particles/oscillators is proposed. The main findings obtained in the frame of the present work are: (i) a qualitative description of the specific heat in the limit of low-temperatures for systems with nano-metric dimensions; (ii) the observation that the corresponding chemical potential function for finite solids becomes null at finite temperatures as observed in the Bose-Einstein condensation and; (iii) emergence of a first-order like phase transition driven by varying N.