2,591 research outputs found
Reconfiguration of quantum states in -symmetric quasi-one dimensional lattices
We demonstrate mesoscopic transport through quantum states in quasi-1D
lattices maintaining the combination of parity and time-reversal symmetries by
controlling energy gain and loss. We investigate the phase diagram of the
non-Hermitian system where transitions take place between unbroken and broken
-symmetric phases via exceptional points. Quantum transport in
the lattice is measured only in the unbroken phases in the energy band-but not
in the broken phases. The broken phase allows for spontaneous symmetry-broken
states where the cross-stitch lattice is separated into two identical single
lattices corresponding to conditionally degenerate eigenstates. These
degeneracies show a lift-up in the complex energy plane, caused by the
non-Hermiticity with -symmetry.Comment: 12 pages, 7 figure
Antiresonance induced by symmetry-broken contacts in quasi-one-dimensional lattices
We report the effect of symmetry-broken contacts on quantum transport in
quasi-one-dimensional lattices. In contrast to 1D chains, transport in
quasi-one-dimensional lattices, which are made up of a finite number of 1D
chain layers, is strongly influenced by contacts. Contact symmetry depends on
whether the contacts maintain or break the parity symmetry between the layers.
With balanced on-site potential, a flat band can be detected by asymmetric
contacts, but not by symmetric contacts. In the case of asymmetric contacts
with imbalanced on-site potential, transmission is suppressed at certain
energies. We elucidate these energies of transmission suppression related to
antiresonance using reduced lattice models and Feynman paths. These results
provide a nondestructive measurement of flat band energy which it is difficult
to detect.Comment: 8 pages, 5 figure
Flat-band localization and self-collimation of light in photonic crystals
We investigate the optical properties of a photonic crystal composed of a
quasi-one-dimensional flat-band lattice array through finite-difference
time-domain simulations. The photonic bands contain flat bands (FBs) at
specific frequencies, which correspond to compact localized states as a
consequence of destructive interference. The FBs are shown to be nondispersive
along the line, but dispersive along the
line. The FB localization of light in a single direction
only results in a self-collimation of light propagation throughout the photonic
crystal at the FB frequency.Comment: 18 single-column pages, 7 figures including graphical to
Emergent localized states at the interface of a twofold -symmetric lattice
We consider the role of non-triviality resulting from a non-Hermitian
Hamiltonian that conserves twofold PT-symmetry assembled by interconnections
between a PT-symmetric lattice and its time reversal partner. Twofold
PT-symmetry in the lattice produces additional surface exceptional points that
play the role of new critical points, along with the bulk exceptional point. We
show that there are two distinct regimes possessing symmetry-protected
localized states, of which localization lengths are robust against external
gain and loss. The states are demonstrated by numerical calculation of a
quasi-1D ladder lattice and a 2D bilayered square lattice.Comment: 10 pages, 7 figure
Non-orientability induced PT phase transition in Moebius ladder lattices
We study parity-time (PT) phase transitions in the energy spectra of ladder
lattices caused by the interplay between non-orientability and non-Hermitian PT
symmetry. The energy spectra show level crossings in circular ladder lattices
with increasing on-site energy gain-loss because of the orientability of a
normal strip. However, the energy levels show PT phase transitions in
PT-symmetric Moebius ladder lattices due to the non-orientability of a Moebius
strip. In order to understand the level crossings of PT symmetric phases, we
generalize the rotational transformation using a complex rotation angle. We
also study the modification of resonant tunneling induced by a sharply twisted
interface in PT-symmetric ladder lattices. Finally, we find that the perfect
transmissions at the zero energy are recovered at the exceptional points of the
PT-symmetric system due to the self-orthogonal states.Comment: 9 pages, 6 figure
Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus
We report the realization of novel symmetry-protected Dirac fermions in a
surface-doped two-dimensional (2D) semiconductor, black phosphorus. The widely
tunable band gap of black phosphorus by the surface Stark effect is employed to
achieve a surprisingly large band inversion up to ~0.6 eV. High-resolution
angle-resolved photoemission spectra directly reveal the pair creation of Dirac
points and their moving along the axis of the glide-mirror symmetry. Unlike
graphene, the Dirac point of black phosphorus is stable, as protected by
spacetime inversion symmetry, even in the presence of spin-orbit coupling. Our
results establish black phosphorus in the inverted regime as a simple model
system of 2D symmetry-protected (topological) Dirac semimetals, offering an
unprecedented opportunity for the discovery of 2D Weyl semimetals
Symmetry-protected flatband condition for Hamiltonians with local symmetry
We derive symmetry-based conditions for tight-binding Hamiltonians with
flatbands to have compact localized eigenstates occupying a single unit cell.
The conditions are based on unitary operators commuting with the Hamiltonian
and associated with local symmetries that guarantee compact localized states
and a flatband. We illustrate the conditions for compact localized states and
flatbands with simple Hamiltonians with given symmetries. We also apply these
results to general cases such as the Hamiltonian with long-range hoppings and
higher-dimensional Hamiltonian.Comment: 7 pages, 2 figure
Cryptanalysis of the New CLT Multilinear Maps
Multilinear maps have many cryptographic applications. The first
candidate construction of multilinear maps was proposed by Garg,
Gentry, and Halevi (GGH13) in 2013, and soon afterwards, another
candidate was suggested by Coron, Lepoint, and Tibouchi (CLT13)
that works over the integers. However, both of these were found to
be insecure in the face of a so-called zeroizing attack (HJ15,
CHL+15). To improve on CLT13, Coron, Lepoint, and Tibouchi
proposed another candidate of new multilinear maps over the
integers (CLT15).
In this paper, we describe an attack against CLT15. Our attack
shares the essence of the cryptanalysis of CLT13 and exploits low
level encodings of zero, as well as other public parameters. As in
CHL+15, this leads to finding all the secret parameters of
\kappa-multilinear maps
in polynomial time of the security parameter
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