Maxwell construction

Abstract: We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit area on a bounding wall, to bulk correlation functions evaluated far away from the wall. It shows that (i) P(ρ) is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to P, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; and (iii) P is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles and show that the densities at coexistence do not satisfy a Maxwell construction on P.

Abstract: We present a mesoscopic model, based on the Boltzmann equation, for the interaction between a solid wall and a nonideal fluid. We present an analytic derivation of the contact angle in terms of the surface tension between the liquid-gas, the liquid-solid, and the gas-solid phases. We study the dependency of the contact angle on the two free parameters of the model, which determine the interaction between the fluid and the boundaries, i.e. the equivalent of the wall density and of the wall-fluid potential in molecular dynamics studies. We compare the analytical results obtained in the hydrodynamical limit for the density profile and for the surface tension expression with the numerical simulations. We compare also our two-phase approach with some exact results obtained by E. Lauga and H. Stone [J. Fluid. Mech. 489, 55 (2003)] and J. Philip [Z. Angew. Math. Phys. 23, 960 (1972)] for a pure hydrodynamical incompressible fluid based on Navier-Stokes equations with boundary conditions made up of alternating slip and no-slip strips. Finally, we show how to overcome some theoretical limitations connected with the discretized Boltzmann scheme proposed by X. Shan and H. Chen [Phys. Rev. E 49, 2941 (1994)] and we discuss the equivalence between the surface tension defined in terms of the mechanical equilibrium and in terms of the Maxwell construction.

Abstract: We study quantum phase transitions in the ground state of the two dimensional hard-core boson Hubbard Hamiltonian. Recent work on this and related models has suggested ``supersolid'' phases with simultaneous diagonal and off-diagonal long range order. We show numerically that, contrary to the generally held belief, the most commonly discussed ``checkerboard'' supersolid is thermodynamically unstable. Furthermore, this supersolid cannot be stabilized by next-near-neighbor interaction. We obtain the correct phase diagram using the Maxwell construction. We demonstrate that the ``striped'' supersolid is thermodynamically stable and is separated from the superfluid phase by a continuous phase transition.

Abstract: The precise measurements of the high masses of the pulsars PSR $\mathrm{J}1614\ensuremath{-}2230$ (${M}_{1614}=1.97\ifmmode\pm\else\textpm\fi{}0.04{M}_{\ensuremath{\bigodot}}$) and PSR $\mathrm{J}0348\ensuremath{-}0432$ (${M}_{0348}=2.01\ifmmode\pm\else\textpm\fi{}0.04{M}_{\ensuremath{\bigodot}}$) provide an important constraint for the equation of state of cold, dense matter and are suited to give interesting insights regarding the nature and existence of the possible phase transition to deconfined quark matter in the cores of neutron stars. We analyze the stability and composition of compact star sequences for a class of hybrid nuclear--quark-matter equations of state. The quark matter phase is described in the framework of a standard color superconducting 3-flavor Nambu--Jona-Lasinio model, and the hadronic phase is given by the Dirac--Brueckner--Hartree--Fock equation of state for the Bonn-A potential. The phase transition is obtained by a Maxwell construction. Within this model setup, we aim to constrain otherwise not strictly fixed parameters of the Nambu--Jona-Lasinio model, namely, the coupling strengths in the vector meson and diquark interaction channels. We perform this investigation for two different parametrizations characterized by a different scalar coupling constant. The analysis of flow data obtained in heavy-ion collisions resulted in a further constraint that we account for in our discussion. Massive hybrid stars with extended quark matter cores can be obtained in accordance with all of the considered constraints.