34,517 research outputs found
Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals
We investigate analytically and numerically the mean-field
superconducting-normal phase boundaries of two-dimensional superconducting wire
networks and Josephson junction arrays immersed in a transverse magnetic field.
The geometries we consider include square, honeycomb, triangular, and kagome'
lattices. Our approach is based on an analytical study of multiple-loop
Aharonov-Bohm effects: the quantum interference between different electron
closed paths where each one of them encloses a net magnetic flux. Specifically,
we compute exactly the sums of magnetic phase factors, i.e., the lattice path
integrals, on all closed lattice paths of different lengths. A very large
number, e.g., up to for the square lattice, exact lattice path
integrals are obtained. Analytic results of these lattice path integrals then
enable us to obtain the resistive transition temperature as a continuous
function of the field. In particular, we can analyze measurable effects on the
superconducting transition temperature, , as a function of the magnetic
filed , originating from electron trajectories over loops of various
lengths. In addition to systematically deriving previously observed features,
and understanding the physical origin of the dips in as a result of
multiple-loop quantum interference effects, we also find novel results. In
particular, we explicitly derive the self-similarity in the phase diagram of
square networks. Our approach allows us to analyze the complex structure
present in the phase boundaries from the viewpoint of quantum interference
effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure
Nested Lattice Codes for Gaussian Relay Networks with Interference
In this paper, a class of relay networks is considered. We assume that, at a
node, outgoing channels to its neighbors are orthogonal, while incoming signals
from neighbors can interfere with each other. We are interested in the
multicast capacity of these networks. As a subclass, we first focus on Gaussian
relay networks with interference and find an achievable rate using a lattice
coding scheme. It is shown that there is a constant gap between our achievable
rate and the information theoretic cut-set bound. This is similar to the recent
result by Avestimehr, Diggavi, and Tse, who showed such an approximate
characterization of the capacity of general Gaussian relay networks. However,
our achievability uses a structured code instead of a random one. Using the
same idea used in the Gaussian case, we also consider linear finite-field
symmetric networks with interference and characterize the capacity using a
linear coding scheme.Comment: 23 pages, 5 figures, submitted to IEEE Transactions on Information
Theor
Compute-and-Forward: Harnessing Interference through Structured Codes
Interference is usually viewed as an obstacle to communication in wireless
networks. This paper proposes a new strategy, compute-and-forward, that
exploits interference to obtain significantly higher rates between users in a
network. The key idea is that relays should decode linear functions of
transmitted messages according to their observed channel coefficients rather
than ignoring the interference as noise. After decoding these linear equations,
the relays simply send them towards the destinations, which given enough
equations, can recover their desired messages. The underlying codes are based
on nested lattices whose algebraic structure ensures that integer combinations
of codewords can be decoded reliably. Encoders map messages from a finite field
to a lattice and decoders recover equations of lattice points which are then
mapped back to equations over the finite field. This scheme is applicable even
if the transmitters lack channel state information.Comment: IEEE Trans. Info Theory, to appear. 23 pages, 13 figure
Observable Signature of the Berezinskii-Kosterlitz-Thouless Transition in a Planar Lattice of Bose-Einstein Condensates
We investigate the possibility that Bose-Einstein condensates (BECs), loaded
on a 2D optical lattice, undergo - at finite temperature - a
Berezinskii-Kosterlitz-Thouless (BKT) transition. We show that - in an
experimentally attainable range of parameters - a planar lattice of BECs is
described by the XY model at finite temperature. We demonstrate that the
interference pattern of the expanding condensates provides the experimental
signature of the BKT transition by showing that, near the critical temperature,
the k=0 component of the momentum distribution and the central peak of the
atomic density profile sharply decrease. The finite-temperature transition for
a 3D optical lattice is also discussed, and the analogies with superconducting
Josephson junction networks are stressed through the text
Quantum Interference on the Kagom\'e Lattice
We study quantum interference effects due to electron motion on the Kagom\'e
lattice in a perpendicular magnetic field. These effects arise from the
interference between phase factors associated with different electron
closed-paths. From these we compute, analytically and numerically, the
superconducting-normal phase boundary for Kagom\'e superconducting wire
networks and Josephson junction arrays. We use an analytical approach to
analyze the relationship between the interference and the complex structure
present in the phase boundary, including the origin of the overall and fine
structure. Our results are obtained by exactly summing over one thousand
billion billions () closed paths, each one weighted by its
corresponding phase factor representing the net flux enclosed by each path. We
expect our computed mean-field phase diagrams to compare well with several
proposed experiments.Comment: 9 pages, Revtex, 3 figures upon reques
Approaching Gaussian Relay Network Capacity in the High SNR Regime: End-to-End Lattice Codes
We present a natural and low-complexity technique for achieving the capacity
of the Gaussian relay network in the high SNR regime. Specifically, we propose
the use of end-to-end structured lattice codes with the amplify-and-forward
strategy, where the source uses a nested lattice code to encode the messages
and the destination decodes the messages by lattice decoding. All intermediate
relays simply amplify and forward the received signals over the network to the
destination. We show that the end-to-end lattice-coded amplify-and-forward
scheme approaches the capacity of the layered Gaussian relay network in the
high SNR regime. Next, we extend our scheme to non-layered Gaussian relay
networks under the amplify-and-forward scheme, which can be viewed as a
Gaussian intersymbol interference (ISI) channel. Compared with other schemes,
our approach is significantly simpler and requires only the end-to-end design
of the lattice precoding and decoding. It does not require any knowledge of the
network topology or the individual channel gains
Channel assignment and multicolouring of the induced subgraphs of the triangular lattice
AbstractA basic problem in the design of mobile telephone networks is to assign sets of radio frequency bands (colours) to transmitters (vertices) to avoid interference. Often the transmitters are laid out like vertices of a triangular lattice in the plane. We investigate the corresponding colouring problem of assigning sets of colours of given size k to vertices of the triangular lattice so that the sets of colours assigned to adjacent vertices are disjoint. We prove here that every triangle-free induced subgraph of the triangular lattice is ⌈7k/3⌉-[k]colourable. That means that it is possible to assign to each transmitter of such a network, k bands of a set of ⌈7k/3⌉, so that there is no interference
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