744 research outputs found
Quantum correlations from Brownian diffusion of chaotic level-spacings
Quantum chaos is linked to Brownian diffusion of the underlying quantum
energy level-spacing sequences. The level-spacings viewed as functions of their
order execute random walks which imply uncorrelated random increments of the
level-spacings while the integrability to chaos transition becomes a change
from Poisson to Gauss statistics for the level-spacing increments. This
universal nature of quantum chaotic spectral correlations is numerically
demonstrated for eigenvalues from random tight binding lattices and for zeros
of the Riemann zeta function.Comment: 4 pages, revtex file, 4 postscript file
Statistical distribution of quantum entanglement for a random bipartite state
We compute analytically the statistics of the Renyi and von Neumann entropies
(standard measures of entanglement), for a random pure state in a large
bipartite quantum system. The full probability distribution is computed by
first mapping the problem to a random matrix model and then using a Coulomb gas
method. We identify three different regimes in the entropy distribution, which
correspond to two phase transitions in the associated Coulomb gas. The two
critical points correspond to sudden changes in the shape of the Coulomb charge
density: the appearance of an integrable singularity at the origin for the
first critical point, and the detachement of the rightmost charge (largest
eigenvalue) from the sea of the other charges at the second critical point.
Analytical results are verified by Monte Carlo numerical simulations. A short
account of some of these results appeared recently in Phys. Rev. Lett. {\bf
104}, 110501 (2010).Comment: 7 figure
Electronic transport and vibrational modes in the smallest molecular bridge: H2 in Pt nanocontacts
We present a state-of-the-art first-principles analysis of electronic
transport in a Pt nanocontact in the presence of H2 which has been recently
reported by Smit et al. in Nature 419, 906 (2002). Our results indicate that at
the last stages of the breaking of the Pt nanocontact two basic forms of bridge
involving H can appear. Our claim is, in contrast to Smit et al.'s, that the
main conductance histogram peak at G approx 2e^2/h is not due to molecular H2,
but to a complex Pt2H2 where the H2 molecule dissociates. A first-principles
vibrational analysis that compares favorably with the experimental one also
supports our claim .Comment: 5 pages, 3 figure
Correlated N-boson systems for arbitrary scattering length
We investigate systems of identical bosons with the focus on two-body
correlations and attractive finite-range potentials. We use a hyperspherical
adiabatic method and apply a Faddeev type of decomposition of the wave
function. We discuss the structure of a condensate as function of particle
number and scattering length. We establish universal scaling relations for the
critical effective radial potentials for distances where the average distance
between particle pairs is larger than the interaction range. The correlations
in the wave function restore the large distance mean-field behaviour with the
correct two-body interaction. We discuss various processes limiting the
stability of condensates. With correlations we confirm that macroscopic
tunneling dominates when the trap length is about half of the particle number
times the scattering length.Comment: 15 pages (RevTeX4), 11 figures (LaTeX), submitted to Phys. Rev. A.
Second version includes an explicit comparison to N=3, a restructured
manuscript, and updated figure
Entanglement in the quantum Ising model
We study the asymptotic scaling of the entanglement of a block of spins for
the ground state of the one-dimensional quantum Ising model with transverse
field. When the field is sufficiently strong, the entanglement grows at most
logarithmically in the number of spins. The proof utilises a transformation to
a model of classical probability called the continuum random-cluster model, and
is based on a property of the latter model termed ratio weak-mixing. Our proof
applies equally to a large class of disordered interactions
Continuity of the Maximum-Entropy Inference
We study the inverse problem of inferring the state of a finite-level quantum
system from expected values of a fixed set of observables, by maximizing a
continuous ranking function. We have proved earlier that the maximum-entropy
inference can be a discontinuous map from the convex set of expected values to
the convex set of states because the image contains states of reduced support,
while this map restricts to a smooth parametrization of a Gibbsian family of
fully supported states. Here we prove for arbitrary ranking functions that the
inference is continuous up to boundary points. This follows from a continuity
condition in terms of the openness of the restricted linear map from states to
their expected values. The openness condition shows also that ranking functions
with a discontinuous inference are typical. Moreover it shows that the
inference is continuous in the restriction to any polytope which implies that a
discontinuity belongs to the quantum domain of non-commutative observables and
that a geodesic closure of a Gibbsian family equals the set of maximum-entropy
states. We discuss eight descriptions of the set of maximum-entropy states with
proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur
The role of Majorana CP phases in the bi-maximal mixing scheme -hierarchical Dirac mass case-
We discuss the energy scale profile of the bi-maximal mixing which is given
at the GUT energy scale in the minimal SUSY model, associated with an
assumption that Y_nu^dagger Y_nu is diagonal, where Y_nu is the neutrino-Yukawa
coupling matrix. In this model, the Dirac mass matrix which appears in the
seesaw neutrino mass matrix is determined by three neutrino masses, two
relative Majorana phases and three heavy Majorana masses. All CP phases are
related by two Majorana phases. We show that the requirement that the solar
mixing angle moves from the maximal mixing at GUT to the observed one as the
energy scale decreases by the renormalization effect. We discuss the
leptogenesis, and the lepton flavor violation process by assuming the universal
soft breaking terms.Comment: 19 pages, 2 figure
Approximating open quantum system dynamics in a controlled and efficient way: A microscopic approach to decoherence
We demonstrate that the dynamics of an open quantum system can be calculated
efficiently and with predefined error, provided a basis exists in which the
system-environment interactions are local and hence obey the Lieb-Robinson
bound. We show that this assumption can generally be made. Defining a dynamical
renormalization group transformation, we obtain an effective Hamiltonian for
the full system plus environment that comprises only those environmental
degrees of freedom that are within the effective light cone of the system. The
reduced system dynamics can therefore be simulated with a computational effort
that scales at most polynomially in the interaction time and the size of the
effective light cone. Our results hold for generic environments consisting of
either discrete or continuous degrees of freedom
Physics, Topology, Logic and Computation: A Rosetta Stone
In physics, Feynman diagrams are used to reason about quantum processes. In
the 1980s, it became clear that underlying these diagrams is a powerful analogy
between quantum physics and topology: namely, a linear operator behaves very
much like a "cobordism". Similar diagrams can be used to reason about logic,
where they represent proofs, and computation, where they represent programs.
With the rise of interest in quantum cryptography and quantum computation, it
became clear that there is extensive network of analogies between physics,
topology, logic and computation. In this expository paper, we make some of
these analogies precise using the concept of "closed symmetric monoidal
category". We assume no prior knowledge of category theory, proof theory or
computer science.Comment: 73 pages, 8 encapsulated postscript figure
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