18,980 research outputs found
Parity-Time Symmetry Breaking beyond One Dimension: The Role of Degeneracy
We consider the role of degeneracy in Parity-Time (PT) symmetry breaking for
non-hermitian wave equations beyond one dimension. We show that if the spectrum
is degenerate in the absence of T-breaking, and T is broken in a generic manner
(without preserving other discrete symmetries), then the standard PT-symmetry
breaking transition does not occur, meaning that the spectrum is complex even
for infinitesimal strength of gain and loss. However the realness of the entire
spectrum can be preserved over a finite interval if additional discrete
symmetries X are imposed when T is broken, if X decouple all degenerate modes.
When this is true only for a subset of the degenerate spectrum, there can be a
partial PT transition in which this subset remains real over a finite interval
of T-breaking. If the spectrum has odd-degeneracy, a fraction of the degenerate
spectrum can remain in the symmetric phase even without imposing additional
discrete symmetries, and they are analogous to dark states in atomic physics.
These results are illustrated by the example of different T-breaking
perturbations of a uniform dielectric disk and sphere, and a group theoretical
analysis is given in the disk case. Finally, we show that multimode coupling is
capable of restoring the T-symmetric phase at finite T-breaking. We also
analyze these questions when the parity operator is replaced by another spatial
symmetry operator and find that the behavior can be qualitatively different.Comment: 8 pages, 6 figure
Buffer Sizing for 802.11 Based Networks
We consider the sizing of network buffers in 802.11 based networks. Wireless
networks face a number of fundamental issues that do not arise in wired
networks. We demonstrate that the use of fixed size buffers in 802.11 networks
inevitably leads to either undesirable channel under-utilization or unnecessary
high delays. We present two novel dynamic buffer sizing algorithms that achieve
high throughput while maintaining low delay across a wide range of network
conditions. Experimental measurements demonstrate the utility of the proposed
algorithms in a production WLAN and a lab testbed.Comment: 14 pages, to appear on IEEE/ACM Transactions on Networkin
Unconditional convergence and optimal error estimates of a Galerkin-mixed FEM for incompressible miscible flow in porous media
In this paper, we study the unconditional convergence and error estimates of
a Galerkin-mixed FEM with the linearized semi-implicit Euler time-discrete
scheme for the equations of incompressible miscible flow in porous media. We
prove that the optimal error estimates hold without any time-step
(convergence) condition, while all previous works require certain time-step
condition. Our theoretical results provide a new understanding on commonly-used
linearized schemes for nonlinear parabolic equations. The proof is based on a
splitting of the error function into two parts: the error from the time
discretization of the PDEs and the error from the finite element discretization
of corresponding time-discrete PDEs. The approach used in this paper is
applicable for more general nonlinear parabolic systems and many other
linearized (semi)-implicit time discretizations
Free Variables and the Two Matrix Model
We study the full set of planar Green's functions for a two-matrix model
using the language of functions of non-commuting variables. Both the standard
Schwinger-Dyson equations and equations determining connected Green's functions
can be efficiently discussed and solved. This solution determines the master
field for the model in the `-representation.'Comment: 8 pages, harvma
A generalization of a result of Häggkvist and Nicoghossian
Using a variation of the Bondy-Chvátal closure theorem the following result is proved: If G is a 2-connected graph with n vertices and connectivity κ such that d(x) + d(y) + d(z) ≥ n + κ for any triple of independent vertices x, y, z, then G is hamiltonian
PT-symmetry breaking and laser-absorber modes in optical scattering systems
Using a scattering matrix formalism, we derive the general scattering
properties of optical structures that are symmetric under a combination of
parity and time-reversal (PT). We demonstrate the existence of a transition
beween PT-symmetric scattering eigenstates, which are norm-preserving, and
symmetry-broken pairs of eigenstates exhibiting net amplification and loss. The
system proposed by Longhi, which can act simultaneously as a laser and coherent
perfect absorber, occurs at discrete points in the broken symmetry phase, when
a pole and zero of the S-matrix coincide.Comment: 4 pages, 4 figure
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