Open AccessAPPLICATION OF GEOMETROTHERMODYNAMICS TO THE SYSTEM WITH ZERO SOUND DESCRIBED BY THE METHOD OF HOLOGRAPHIC DUALITY
Author(s) -
Д.М. Зазулин,
С.Е. Кемелжанова,
П.Д. Эзау
Publication year - 2020
Publication title -
habaršy. fizika-matematika seriâsy
Language(s) - English
Resource type - Journals
ISSN - 1728-7901
DOI - 10.51889/2020-1.1728-7901.35
Subject(s) - phase transition , holography , scalar (mathematics) , zero (linguistics) , duality (order theory) , quantum , manifold (fluid mechanics) , speed of sound , work (physics) , zero sound , invariant (physics) , entropy (arrow of time) , physics , statistical physics , mathematics , thermodynamics , quantum mechanics , pure mathematics , geometry , mechanical engineering , linguistics , philosophy , fermi liquid theory , engineering , electron
In the framework of the method of geometrothermodynamics, in present work, we studied the properties of equilibrium manifold of the system with zero-sound predicted by the holographic duality method. The results are invariant under the Legendre transformations, i.e. independent of the choice of thermodynamic potential. For the systems under consideration, the corresponding metrics, determinants of metrics and scalar curvatures are calculated, and their properties are also described. Using the holographic approach, a new type of quantum liquid was discovered. The heat capacity of the liquid obtained in this work at low temperatures depends on the temperature ∼ T6. Entropy, which depends on temperature and baryom density, was taken as the thermodynamic potential. 3-dimensional obtained that clearly show at which values of thermodynamic variables scalar curvatures tend to infinity or to zero, which indicates possible phase transitions and possible compensation of interactions by quantum effects, respectively. It is shown that both variants of metrics in this case lead to the same conclusion regarding the location of possible phase transition lines in the considered holographic system with zero sound.