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Register a new userOne-dimensional Janus fluids. Exact solution and mapping from the quenched to the annealed system
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The equilibrium properties of a Janus fluid confined to a one-dimensional channel are exactly derived. The fluid is made of particles with two faces (active and passive), so that the pair interaction is that of hard spheres, except if the two active faces are in front of each other, in which case the interaction has a square-well attractive tail. Our exact solution refers to quenched systems (i.e., each particle has a fixed face orientation), but we argue by means of statistical-mechanical tools that the results also apply to annealed systems (i.e., each particle can flip its orientation) in the thermodynamic limit. Comparison between theoretical results and Monte Carlo simulations for quenched and annealed systems, respectively, shows an excellent agreement.
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The equilibrium properties of a Janus fluid made of two-face particles confined to a one-dimensional channel are revisited. The exact Gibbs free energy for a finite number of particles $N$ is exactly derived for both quenched and annealed realizations. It is proved that the results for both classes of systems tend in the thermodynamic limit ($Ntoinfty$) to a common expression recently derived (Maestre M A G and Santos A 2020 J Stat Mech 063217). The theoretical finite-size results are particularized to the Kern--Frenkel model and confirmed by Monte Carlo simulations for quenched and (both biased and unbiased) annealed systems.
Structural and thermodynamic properties of multicomponent hard-sphere fluids at odd dimensions have recently been derived in the framework of the rational function approximation (RFA) [Rohrmann and Santos, Phys. Rev. E textbf{83}, 011201 (2011)]. It is demonstrated here that the RFA technique yields the exact solution of the Percus-Yevick (PY) closure to the Ornstein-Zernike (OZ) equation for binary mixtures at arbitrary odd dimensions. The proof relies mainly on the Fourier transforms $hat{c}_{ij}(k)$ of the direct correlation functions defined by the OZ relation. From the analysis of the poles of $hat{c}_{ij}(k)$ we show that the direct correlation functions evaluated by the RFA method vanish outside the hard core, as required by the PY theory.
We discuss the exact solution for the properties of the recently introduced ``necklace model for reptation. The solution gives the drift velocity, diffusion constant and renewal time for asymptotically long chains. Its properties are also related to a special case of the Rubinstein-Duke model in one dimension.
We study the real time evolution of the correlation functions in a globally quenched interacting one dimensional lattice system by means of time adaptive density matrix renormalization group. We find a clear light-cone behavior quenching the repulsive interaction from the gapped density wave regime. The spreading velocity increases with the final values of the interaction and then saturates at a certain finite value. In the case of a Luttinger liquid phase as the initial state, for strong repulsive interaction quenches, a more complex dynamics occurs as a result of bound state formations. From the other side in the attractive regime, depending on where connected correlation functions are measured, one can observe a delay in the starting time evolution and a coexistence of ballistic and localized signals.
We present a driven diffusive model which we call the Bus Route Model. The model is defined on a one-dimensional lattice, with each lattice site having two binary variables, one of which is conserved (``buses) and one of which is non-conserved (``passengers). The buses are driven in a preferred direction and are slowed down by the presence of passengers who arrive with rate lambda. We study the model by simulation, heuristic argument and a mean-field theory. All these approaches provide strong evidence of a transition between an inhomogeneous ``jammed phase (where the buses bunch together) and a homogeneous phase as the bus density is increased. However, we argue that a strict phase transition is present only in the limit lambda -> 0. For small lambda, we argue that the transition is replaced by an abrupt crossover which is exponentially sharp in 1/lambda. We also study the coarsening of gaps between buses in the jammed regime. An alternative interpretation of the model is given in which the spaces between ``buses and the buses themselves are interchanged. This describes a system of particles whose mobility decreases the longer they have been stationary and could provide a model for, say, the flow of a gelling or sticky material along a pipe.
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