16 research outputs found
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
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 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 , where increases
in the range , consistent with a crossover between
diffusive and hydrodynamic viscous, , 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 to in the scaled structure
function, which disappears when the dynamical scaling reasonably improves at
later times. This excludes noise as the cause for a 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