2 research outputs found
Thermodynamics and structure of simple liquids in the hyperbolic plane
We provide a consistent statistical-mechanical treatment for describing the
thermodynamics and the structure of fluids embedded in the hyperbolic plane. In
particular, we derive a generalization of the virial equation relating the bulk
thermodynamic pressure to the pair correlation function and we develop the
appropriate setting for extending the integral-equation approach of
liquid-state theory in order to describe the fluid structure. We apply the
formalism and study the influence of negative space curvature on two types of
systems that have been recently considered: Coulombic systems, such as the one-
and two-component plasma models, and fluids interacting through short-range
pair potentials, such as the hard-disk and the Lennard-Jones models.Comment: 25 pages, 10 Figure
Periodic boundary conditions on the pseudosphere
We provide a framework to build periodic boundary conditions on the
pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian
space of constant negative curvature. Starting from the common case of periodic
boundary conditions in the Euclidean plane, we introduce all the needed
mathematical notions and sketch a classification of periodic boundary
conditions on the hyperbolic plane. We stress the possible applications in
statistical mechanics for studying the bulk behavior of physical systems and we
illustrate how to implement such periodic boundary conditions in two examples,
the dynamics of particles on the pseudosphere and the study of classical spins
on hyperbolic lattices.Comment: 30 pages, minor corrections, accepted to J. Phys.