A simple example of "Quantum Darwinism": Redundant information storage in many-spin environments

As quantum information science approaches the goal of constructing quantum computers, understanding loss of information through decoherence becomes increasingly important. The information about a system that can be obtained from its environment can facilitate quantum control and error correction. Moreover, observers gain most of their information indirectly, by monitoring (primarily photon) environments of the "objects of interest." Exactly how this information is inscribed in the environment is essential for the emergence of "the classical" from the quantum substrate. In this paper, we examine how many-qubit (or many-spin) environments can store information about a single system. The information lost to the environment can be stored redundantly, or it can be encoded in entangled modes of the environment. We go on to show that randomly chosen states of the environment almost always encode the information so that an observer must capture a majority of the environment to deduce the system's state. Conversely, in the states produced by a typical decoherence process, information about a particular observable of the system is stored redundantly. This selective proliferation of "the fittest information" (known as Quantum Darwinism) plays a key role in choosing the preferred, effectively classical observables of macroscopic systems. The developing appreciation that the environment functions not just as a garbage dump, but as a communication channel, is extending our understanding of the environment's role in the quantum-classical transition beyond the traditional paradigm of decoherence.Comment: 21 pages, 6 figures, RevTex 4. Submitted to Foundations of Physics (Asher Peres Festschrift

Lattice Boltzmann for Binary Fluids with Suspended Colloids

A new description of the binary fluid problem via the lattice Boltzmann method is presented which highlights the use of the moments in constructing two equilibrium distribution functions. This offers a number of benefits, including better isotropy, and a more natural route to the inclusion of multiple relaxation times for the binary fluid problem. In addition, the implementation of solid colloidal particles suspended in the binary mixture is addressed, which extends the solid-fluid boundary conditions for mass and momentum to include a single conserved compositional order parameter. A number of simple benchmark problems involving a single particle at or near a fluid-fluid interface are undertaken and show good agreement with available theoretical or numerical results.Comment: 10 pages, 4 figures, ICMMES 200

A scaling theory of 3D spinodal turbulence

A new scaling theory for spinodal decomposition in the inertial hydrodynamic regime is presented. The scaling involves three relevant length scales, the domain size, the Taylor microscale and the Kolmogorov dissipation scale. This allows for the presence of an inertial "energy cascade", familiar from theories of turbulence, and improves on earlier scaling treatments based on a single length: these, it is shown, cannot be reconciled with energy conservation. The new theory reconciles the t^{2/3} scaling of the domain size, predicted by simple scaling, with the physical expectation of a saturating Reynolds number at late times.Comment: 5 pages, no figures, revised version submitted to Phys Rev E Rapp Comm. Minor changes and clarification

Quantum algorithm for smoothed particle hydrodynamics

We present a quantum computing algorithm for the smoothed particle hydrodynamics (SPH) method. We use a normalization procedure to encode the SPH operators and domain discretization in a quantum register. We then perform the SPH summation via an inner product of quantum registers. Using a one-dimensional function, we test the approach in a classical sense for the kernel sum and first and second derivatives of a one-dimensional function, using both the Gaussian and Wendland kernel functions, and compare various register sizes against analytical results. Error convergence is exponentially fast in the number of qubits. We extend the method to solve the one-dimensional advection and diffusion partial differential equations, which are commonly encountered in fluids simulations. This work provides a foundation for a more general SPH algorithm, eventually leading to highly efficient simulations of complex engineering problems on gate-based quantum computers

Role of inertia in two-dimensional deformation and breakup of a droplet

We investigate by Lattice Boltzmann methods the effect of inertia on the deformation and break-up of a two-dimensional fluid droplet surrounded by fluid of equal viscosity (in a confined geometry) whose shear rate is increased very slowly. We give evidence that in two dimensions inertia is {\em necessary} for break-up, so that at zero Reynolds number the droplet deforms indefinitely without breaking. We identify two different routes to breakup via two-lobed and three-lobed structures respectively, and give evidence for a sharp transition between these routes as parameters are varied.Comment: 4 pages, 4 figure

Phase separating binary fluids under oscillatory shear

We apply lattice Boltzmann methods to study the segregation of binary fluid mixtures under oscillatory shear flow in two dimensions. The algorithm allows to simulate systems whose dynamics is described by the Navier-Stokes and the convection-diffusion equations. The interplay between several time scales produces a rich and complex phenomenology. We investigate the effects of different oscillation frequencies and viscosities on the morphology of the phase separating domains. We find that at high frequencies the evolution is almost isotropic with growth exponents 2/3 and 1/3 in the inertial (low viscosity) and diffusive (high viscosity) regimes, respectively. When the period of the applied shear flow becomes of the same order of the relaxation time $T_R$ of the shear velocity profile, anisotropic effects are clearly observable. In correspondence with non-linear patterns for the velocity profiles, we find configurations where lamellar order close to the walls coexists with isotropic domains in the middle of the system. For particular values of frequency and viscosity it can also happen that the convective effects induced by the oscillations cause an interruption or a slowing of the segregation process, as found in some experiments. Finally, at very low frequencies, the morphology of domains is characterized by lamellar order everywhere in the system resembling what happens in the case with steady shear.Comment: 1 table and 12 figures in .gif forma

Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids

We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and homogeneous mixture into a two-phase configuration. We find the average domain size growing with time as $t^\gamma$, where $\gamma$ increases in the range $0.545 < \gamma < 0.717$, consistent with a crossover between diffusive $t^{1/3}$ and hydrodynamic viscous, $t^{1.0}$, behaviour. We find good collapse onto a single scaling function, yet the domain growth exponents differ from others' works' for similar values of the unique characteristic length and time that can be constructed out of the fluid's parameters. This rebuts claims of universality for the dynamical scaling hypothesis. At early times, we also find a crossover from $q^2$ to $q^4$ in the scaled structure function, which disappears when the dynamical scaling reasonably improves at later times. This excludes noise as the cause for a $q^2$ behaviour, as proposed by others. We also observe exponential temporal growth of the structure function during the initial stages of the dynamics and for wavenumbers less than a threshold value.Comment: 45 pages, 18 figures. Accepted for publication in Physical Review

Ghost-patterning and non-patterning in a draining film model

Patterns can form when the uniform state of any system is unstable so that some non-uniform motif grows in amplitude. Here, we identify an alternative way to form non-trivial structures, which we call “ghost-patterns”. Ghost-patterns emerge from noisy initial conditions when all non-uniform modes decay in amplitude except for one non-trivial motif which fails to decay. Hence, in seeking structured states, it is not necessary to find positive growth rates. We demonstrate ghost-patterns in an idealized non-equilibrium model intended to emulate draining thin-film suspensions