407 research outputs found
The curious nonexistence of Gaussian 2-designs
2-designs -- ensembles of quantum pure states whose 2nd moments equal those
of the uniform Haar ensemble -- are optimal solutions for several tasks in
quantum information science, especially state and process tomography. We show
that Gaussian states cannot form a 2-design for the continuous-variable
(quantum optical) Hilbert space L2(R). This is surprising because the affine
symplectic group HWSp (the natural symmetry group of Gaussian states) is
irreducible on the symmetric subspace of two copies. In finite dimensional
Hilbert spaces, irreducibility guarantees that HWSp-covariant ensembles (such
as mutually unbiased bases in prime dimensions) are always 2-designs. This
property is violated by continuous variables, for a subtle reason: the
(well-defined) HWSp-invariant ensemble of Gaussian states does not have an
average state because the averaging integral does not converge. In fact, no
Gaussian ensemble is even close (in a precise sense) to being a 2-design. This
surprising difference between discrete and continuous quantum mechanics has
important implications for optical state and process tomography.Comment: 9 pages, no pretty figures (sorry!
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
Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories
We review theoretical aspects of unitary Fermi gas (UFG), which has been
realized in ultracold atom experiments. We first introduce the epsilon
expansion technique based on a systematic expansion in terms of the
dimensionality of space. We apply this technique to compute the thermodynamic
quantities, the quasiparticle spectrum, and the critical temperature of UFG. We
then discuss consequences of the scale and conformal invariance of UFG. We
prove a correspondence between primary operators in nonrelativistic conformal
field theories and energy eigenstates in a harmonic potential. We use this
correspondence to compute energies of fermions at unitarity in a harmonic
potential. The scale and conformal invariance together with the general
coordinate invariance constrains the properties of UFG. We show the vanishing
bulk viscosities of UFG and derive the low-energy effective Lagrangian for the
superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic
scaling and conformal symmetries that can be in principle realized in ultracold
atom experiments.Comment: 44 pages, 15 figures, contribution to Lecture Notes in Physics
"BCS-BEC crossover and the Unitary Fermi Gas" edited by W. Zwerge
Global persistence exponent of the two-dimensional Blume-Capel model
The global persistence exponent is calculated for the
two-dimensional Blume-Capel model following a quench to the critical point from
both disordered states and such with small initial magnetizations.
Estimates are obtained for the nonequilibrium critical dynamics on the
critical line and at the tricritical point.
Ising-like universality is observed along the critical line and a different
value is found at the tricritical point.Comment: 7 pages with 3 figure
Universality and scaling study of the critical behavior of the two-dimensional Blume-Capel model in short-time dynamics
In this paper we study the short-time behavior of the Blume-Capel model at
the tricritical point as well as along the second order critical line. Dynamic
and static exponents are estimated by exploring scaling relations for the
magnetization and its moments at early stage of the dynamic evolution. Our
estimates for the dynamic exponents, at the tricritical point, are and .Comment: 12 pages, 9 figure
Self-consistent model of ultracold atomic collisions and Feshbach resonances in tight harmonic traps
We consider the problem of cold atomic collisions in tight traps, where the
absolute scattering length may be larger than the trap size. As long as the
size of the trap ground state is larger than a characteristic length of the van
der Waals potential, the energy eigenvalues can be computed self-consistently
from the scattering amplitude for untrapped atoms. By comparing with the exact
numerical eigenvalues of the trapping plus interatomic potentials, we verify
that our model gives accurate eigenvalues up to milliKelvin energies for single
channel s-wave scattering of Na atoms in an isotropic harmonic trap,
even when outside the Wigner threshold regime. Our model works also for
multi-channel scattering, where the scattering length can be made large due to
a magnetically tunable Feshbach resonance.Comment: 7 pages, 4 figures (PostScript), submitted to Physical Review
Natural Orbitals and BEC in traps, a diffusion Monte Carlo analysis
We investigate the properties of hard core Bosons in harmonic traps over a
wide range of densities. Bose-Einstein condensation is formulated using the
one-body Density Matrix (OBDM) which is equally valid at low and high
densities. The OBDM is calculated using diffusion Monte Carlo methods and it is
diagonalized to obtain the "natural" single particle orbitals and their
occupation, including the condensate fraction. At low Boson density, , where and is the hard core diameter, the condensate is
localized at the center of the trap. As increases, the condensate moves
to the edges of the trap. At high density it is localized at the edges of the
trap. At the Gross-Pitaevskii theory of the condensate
describes the whole system within 1%. At corrections are
3% to the GP energy but 30% to the Bogoliubov prediction of the condensate
depletion. At , mean field theory fails. At , the Bosons behave more like a liquid He droplet than a trapped Boson
gas.Comment: 13 pages, 14 figures, submitted Phys. Rev.
Motion of influential players can support cooperation in Prisoner's Dilemma
We study a spatial Prisoner's dilemma game with two types (A and B) of
players located on a square lattice. Players following either cooperator or
defector strategies play Prisoner's Dilemma games with their 24 nearest
neighbors. The players are allowed to adopt one of their neighbor's strategy
with a probability dependent on the payoff difference and type of the given
neighbor. Players A and B have different efficiency in the transfer of their
own strategy therefore the strategy adoption probability is reduced by a
multiplicative factor (w < 1) from the players of type B. We report that the
motion of the influential payers (type A) can improve remarkably the
maintenance of cooperation even for their low densities.Comment: 7 pages, 7 figure
Quantum Corrections to Dilute Bose Liquids
It was recently shown (A. Bulgac. Phys. Rev. Lett. {\bf 89}, 050402 (2002))
that an entirely new class of quantum liquids with widely tunable properties
could be manufactured from bosons (boselets), fermions (fermilets) and their
mixtures (ferbolets) by controlling their interaction properties by the means
of a Feshbach resonance. We extend the previous mean--field analysis of these
quantum liquids by computing the lowest order quantum corrections to the ground
state energy and the depletion of the Bose--Einstein condensate and by
estimating higher order corrections as well. We show that the quantum
corrections are relatively small and controlled by the diluteness parameter
, even though strictly speaking in this case there is no
low density expansion.Comment: final published version, typos corrected, updated references and
added one referenc
Dynamical properties of the unitary Fermi gas: collective modes and shock waves
We discuss the unitary Fermi gas made of dilute and ultracold atoms with an
infinite s-wave inter-atomic scattering length. First we introduce an efficient
Thomas-Fermi-von Weizsacker density functional which describes accurately
various static properties of the unitary Fermi gas trapped by an external
potential. Then, the sound velocity and the collective frequencies of
oscillations in a harmonic trap are derived from extended superfluid
hydrodynamic equations which are the Euler-Lagrange equations of a
Thomas-Fermi-von Weizsacker action functional. Finally, we show that this
amazing Fermi gas supports supersonic and subsonic shock waves.Comment: 9 pages, 3 figures, invited talk at the International Workshop
"Critical Stability 2011" (Erice, October 2011), to be published in the
journal Few Body System
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