538,330 research outputs found
Entanglement in quantum critical phenomena
Quantum phase transitions occur at zero temperature and involve the
appearance of long-range correlations. These correlations are not due to
thermal fluctuations but to the intricate structure of a strongly entangled
ground state of the system. We present a microscopic computation of the scaling
properties of the ground-state entanglement in several 1D spin chain models
both near and at the quantum critical regimes. We quantify entanglement by
using the entropy of the ground state when the system is traced down to
spins. This entropy is seen to scale logarithmically with , with a
coefficient that corresponds to the central charge associated to the conformal
theory that describes the universal properties of the quantum phase transition.
Thus we show that entanglement, a key concept of quantum information science,
obeys universal scaling laws as dictated by the representations of the
conformal group and its classification motivated by string theory. This
connection unveils a monotonicity law for ground-state entanglement along the
renormalization group flow. We also identify a majorization rule possibly
associated to conformal invariance and apply the present results to interpret
the breakdown of density matrix renormalization group techniques near a
critical point.Comment: 5 pages, 2 figure
Displaced workers, early leavers, and re-employment wages
When receiving information about an imminent plant closure or mass layoffs, workers search for new jobs. This has been the premise of advance notice legislation, but has been difficult to verify using survey data. In this paper, we lay out a search model that takes explicitly into account the information flow prior to a mass layoff. Using universal wage data files that allow us to identify individuals working with healthy and displacing firms both at the time of displacement as well as any other time period, we test the predictions of the model on re-employment wages. Controlling for worker quality and unobservable firm characteristics, workers leaving a "distressed" firm have higher re-employment wages than workers who stay with the distressed firm until displacement.Displaced workers, search theory, advance notice, linked firm-worker data sets
Large Scale Cross-Correlations in Internet Traffic
The Internet is a complex network of interconnected routers and the existence
of collective behavior such as congestion suggests that the correlations
between different connections play a crucial role. It is thus critical to
measure and quantify these correlations. We use methods of random matrix theory
(RMT) to analyze the cross-correlation matrix C of information flow changes of
650 connections between 26 routers of the French scientific network `Renater'.
We find that C has the universal properties of the Gaussian orthogonal ensemble
of random matrices: The distribution of eigenvalues--up to a rescaling which
exhibits a typical correlation time of the order 10 minutes--and the spacing
distribution follow the predictions of RMT. There are some deviations for large
eigenvalues which contain network-specific information and which identify
genuine correlations between connections. The study of the most correlated
connections reveals the existence of `active centers' which are exchanging
information with a large number of routers thereby inducing correlations
between the corresponding connections. These strong correlations could be a
reason for the observed self-similarity in the WWW traffic.Comment: 7 pages, 6 figures, final versio
Universal proofs of entropic continuity bounds via majorization flow
We introduce a notion of majorization flow, and demonstrate it to be a
powerful tool for deriving simple and universal proofs of continuity bounds for
entropic functions relevant in information theory. In particular, for the case
of the alpha-R\'enyi entropy, whose connections to thermodynamics are discussed
in this article, majorization flow yields a Lipschitz continuity bound for the
case alpha > 1, thus resolving an open problem and providing a substantial
improvement over previously known bounds.Comment: 29 pages; v2: added Cor. 3.2, Section 7, shortened some proofs, minor
fixes; v3: added Section 6.2, minor fixe
Wireless Network Information Flow: A Deterministic Approach
In a wireless network with a single source and a single destination and an
arbitrary number of relay nodes, what is the maximum rate of information flow
achievable? We make progress on this long standing problem through a two-step
approach. First we propose a deterministic channel model which captures the key
wireless properties of signal strength, broadcast and superposition. We obtain
an exact characterization of the capacity of a network with nodes connected by
such deterministic channels. This result is a natural generalization of the
celebrated max-flow min-cut theorem for wired networks. Second, we use the
insights obtained from the deterministic analysis to design a new
quantize-map-and-forward scheme for Gaussian networks. In this scheme, each
relay quantizes the received signal at the noise level and maps it to a random
Gaussian codeword for forwarding, and the final destination decodes the
source's message based on the received signal. We show that, in contrast to
existing schemes, this scheme can achieve the cut-set upper bound to within a
gap which is independent of the channel parameters. In the case of the relay
channel with a single relay as well as the two-relay Gaussian diamond network,
the gap is 1 bit/s/Hz. Moreover, the scheme is universal in the sense that the
relays need no knowledge of the values of the channel parameters to
(approximately) achieve the rate supportable by the network. We also present
extensions of the results to multicast networks, half-duplex networks and
ergodic networks.Comment: To appear in IEEE transactions on Information Theory, Vol 57, No 4,
April 201
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