Universal Features of the Time Evolution of Evanescent Modes in a Left-Handed Perfect Lens

The time evolution of evanescent modes in Pendry's perfect lens proposal for ideally lossless and homogeneous, left-handed materials is analyzed. We show that time development of sub-wavelength resolution exhibits universal features, independent of model details. This is due to the unavoidable near-degeneracy of surface electromagnetic modes in the deep sub-wavelength region. By means of a mechanical analog, it is shown that an intrinsic time scale (missed in stationary studies) has to be associated with any desired lateral resolution. A time-dependent cut-off length emerges, removing the problem of divergences claimed to invalidate Pendry's proposal.Comment: 4 pages, 3 figures, title slightly changed, reference added, minor correction

DSMC evaluation of the Navier-Stokes shear viscosity of a granular fluid

A method based on the simple shear flow modified by the introduction of a deterministic non-conservative force and a stochastic process is proposed to measure the Navier-Stokes shear viscosity in a granular fluid described by the Enskog equation. The method is implemented in DSMC simulations for a wide range of values of dissipation and density. It is observed that, after a certain transient period, the system reaches a hydrodynamic stage which tends to the Navier-Stokes regime for long times. The results are compared with theoretical predictions obtained from the Chapman-Enskog method in the leading Sonine approximation, showing quite a good agreement, even for strong dissipation.Comment: 6 pages, 4 figures; to appear in Rarefied Gas Dynamics: 24th International Symposium (AIP Conference Proceedings

Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres

The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, $\Delta s$, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), $s_\text{ex}$, and the pair-correlation contribution, $s_2$. Thus, the RMPE represents the net contribution to $s_\text{ex}$ due to spatial correlations involving three, four, or more particles. A heuristic `ordering' criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension $1<d<3$ has been proposed [Santos, A.; L\'opez de Haro, M. \emph{Phys. Rev. E} \textbf{2016}, \emph{93}, 062126]. The aim of this work is to use this approach to evaluate the RMPE as a function of both $d$ and the packing fraction $\phi$. It is observed that, for any given dimensionality $d$, the RMPE takes negative values for small densities, reaches a negative minimum $\Delta s_{\text{min}}$ at a packing fraction $\phi_{\text{min}}$, and then rapidly increases, becoming positive beyond a certain packing fraction $\phi_0$. Interestingly, while both $\phi_{\text{min}}$ and $\phi_0$ monotonically decrease as dimensionality increases, the value of $\Delta s_{\text{min}}$ exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality $d\simeq 2.38$. A plot of the scaled RMPE $\Delta s/|\Delta s_{\text{min}}|$ shows a quasiuniversal behavior in the region $-0.14\lesssim\phi-\phi_0\lesssim 0.02$.Comment: 10 pages, 3 figures; v2: minor change

Vapor-liquid equilibrium and equation of state of two-dimensional fluids from a discrete perturbation theory

The interest in the description of the properties of fluids of restricted dimensionality is growing for theoretical and practical reasons. In this work, we have firstly developed an analytical expression for the Helmholtz free energy of the two-dimensional square-well fluid in the Barker--Henderson framework. This equation of state is based on an approximate analytical radial distribution function for $d$-dimensional hard-sphere fluids ($1\leq d\leq 3$) and is validated against existing and new simulation results. The so-obtained equation of state is implemented in a discrete perturbation theory able to account for general potential shapes. The prototypical Lennard-Jones and Yukawa fluids are tested in its two-dimensional version against available and new simulation data with semi-quantitative agreement.Comment: 9 pages, 6 figures; v2: new references adde

Negativity for two blocks in the one dimensional Spin 1 AKLT model

In this paper we compute the entanglement, as quantified by negativity, between two blocks of length $L_A$ and $L_B$, separated by $L$ sites in the one dimensional spin-1 AKLT model. We took the model with two different boundary conditions. We consider the case of $N$ spins 1 in the bulk and one spin 1/2 at each boundary which constitute an unique ground state, and the case of just spins 1, even at the end of the chain, where the degeneracy of the ground state is four. In both scenarios we made a partition consisting of two blocks $A$ and $B$, containing $L_A$ and $L_B$ sites respectively. The separation of these two blocks is $L$. In both cases we explicitly obtain the reduced density matrix of the blocks $A$ and $B$. We prove that the negativity in the first case vanishes identically for $L\geq 1$ while in the second scenario it may approach a constant value $N=1/2$ for each degenerate eigenstate depending on the way one constructs these eigenstates. However, as there is some freedom in constructing these eigenstates, vanishing entanglement is also possible in the latter case. Additionally, we also compute the entanglement between non-complementary blocks in the case of periodic boundary conditions for the spin-1 AKLT model for which there is a unique ground state. Even in this case, we find that the negativity of separated blocks of spins is zero.Comment: 7 pages, 3 figure