85,658 research outputs found
Novel discrete symmetries in the general N = 2 supersymmetric quantum mechanical model
In addition to the usual supersymmetric (SUSY) continuous symmetry
transformations for the general N = 2 SUSY quantum mechanical model, we show
the existence of a set of novel discrete symmetry transformations for the
Lagrangian of the above SUSY quantum mechanical model. Out of all these
discrete symmetry transformations, a unique discrete transformation corresponds
to the Hodge duality operation of differential geometry and the above SUSY
continuous symmetry transformations (and their anticommutator) provide the
physical realizations of the de Rham cohomological operators of differential
geometry. Thus, we provide a concrete proof of our earlier conjecture that any
arbitrary N= 2 SUSY quantum mechanical model is an example of a Hodge theory
where the cohomological operators find their physical realizations in the
language of symmetry transformations of this theory. Possible physical
implications of our present study are pointed out, too.Comment: LaTeX file, 9 pages, EPJC format, To appear in EPJ
A digital interface for Gaussian relay networks: lifting codes from the discrete superposition model to Gaussian relay networks
For every Gaussian relay network with a single source-destination pair, it is
known that there exists a corresponding deterministic network called the
discrete superposition network that approximates its capacity uniformly over
all SNR's to within a bounded number of bits. The next step in this program of
rigorous approximation is to determine whether coding schemes for discrete
superposition models can be lifted to Gaussian relay networks with a bounded
rate loss independent of SNR. We establish precisely this property and show
that the superposition model can thus serve as a strong surrogate for designing
codes for Gaussian relay networks.
We show that a code for a Gaussian relay network, with a single
source-destination pair and multiple relay nodes, can be designed from any code
for the corresponding discrete superposition network simply by pruning it. In
comparison to the rate of the discrete superposition network's code, the rate
of the Gaussian network's code only reduces at most by a constant that is a
function only of the number of nodes in the network and independent of channel
gains.
This result is also applicable for coding schemes for MIMO Gaussian relay
networks, with the reduction depending additionally on the number of antennas.
Hence, the discrete superposition model can serve as a digital interface for
operating Gaussian relay networks.Comment: 5 pages, 2010 IEEE Information Theory Workshop, Cair
- …