12,948 research outputs found
Quantum Hall Effect on the Hofstadter Butterfly
Motivated by recent experimental attempts to detect the Hofstadter butterfly,
we numerically calculate the Hall conductivity in a modulated two-dimensional
electron system with disorder in the quantum Hall regime. We identify the
critical energies where the states are extended for each of butterfly subbands,
and obtain the trajectory as a function of the disorder. Remarkably, we find
that when the modulation becomes anisotropic, the critical energy branches
accompanying a change of the Hall conductivity.Comment: 4 pages, 6 figure
Influence of Homeotropic Anchoring Walls upon Nematic and Smectic Phases
McMillan liquid crystal model sandwiched between strong homeotropic anchoring
walls is studied. Phase transitions between isotropic, nematic, and smectic A
phases are investigated for wide ranges of an interaction parameter and of the
system thickness. It is confirmed that the anchoring walls induce an increase
in transition temperatures, dissappearance of phase transitions, and an
appearance of non-spontaneous nematic phase. The similarity between influence
of anchoring walls and that of external fields is discussed.Comment: 5 pages, 6 figure
Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment
The exact quantum dynamics of the reduced density matrix of two coupled spin
qubits in a quantum Heisenberg XY spin star environment in the thermodynamic
limit at arbitrarily finite temperatures is obtained using a novel operator
technique. In this approach, the transformed Hamiltonian becomes effectively
Jaynes-Cumming like and thus the analysis is also relevant to cavity quantum
electrodynamics. This special operator technique is mathematically simple and
physically clear, and allows us to treat systems and environments that could
all be strongly coupled mutually and internally. To study their entanglement
evolution, the concurrence of the reduced density matrix of the two coupled
central spins is also obtained exactly. It is shown that the dynamics of the
entanglement depends on the initial state of the system and the coupling
strength between the two coupled central spins, the thermal temperature of the
spin environment and the interaction between the constituents of the spin
environment. We also investigate the effect of detuning which in our model can
be controlled by the strength of a locally applied external magnetic field. It
is found that the detuning has a significant effect on the entanglement
generation between the two spin qubits.Comment: 9 pages (two-coulumn), 6 figures. To appear in Phys. Rev.
Non-Markovian dynamics of a nanomechanical resonator measured by a quantum point contact
We study the dynamics of a nanomechanical resonator (NMR) subject to a
measurement by a low transparency quantum point contact (QPC) or tunnel
junction in the non-Markovian domain. We derive the non-Markovian
number-resolved (conditional) and unconditional master equations valid to
second order in the tunneling Hamiltonian without making the rotating-wave
approximation and the Markovian approximation, generally made for systems in
quantum optics. Our non-Markovian master equation reduces, in appropriate
limits, to various Markovian versions of master equations in the literature. We
find considerable difference in dynamics between the non-Markovian cases and
its Markovian counterparts. We also calculate the time-dependent transport
current through the QPC which contains information about the measured NMR
system. We find an extra transient current term proportional to the expectation
value of the symmetrized product of the position and momentum operators of the
NMR. This extra current term, with a coefficient coming from the combination of
the imaginary parts of the QPC reservoir correlation functions, has a
substantial contribution to the total transient current in the non-Markovian
case, but was generally ignored in the studies of the same problem in the
literature. Considering the contribution of this extra term, we show that a
significantly qualitative and quantitative difference in the total transient
current between the non-Markovian and the Markovian wide-band-limit cases can
be observed. Thus, it may serve as a witness or signature of the non-Markovian
features in the coupled NMR-QPC system.Comment: Accepted for publication in Physical Review B (20 pages, 13 figures
Levitation of quantum Hall critical states in a lattice model with spatially correlated disorder
The fate of the current carrying states of a quantum Hall system is
considered in the situation when the disorder strength is increased and the
transition from the quantum Hall liquid to the Hall insulator takes place. We
investigate a two-dimensional lattice model with spatially correlated disorder
potentials and calculate the density of states and the localization length
either by using a recursive Green function method or by direct diagonalization
in connection with the procedure of level statistics. From the knowledge of the
energy and disorder dependence of the localization length and the density of
states (DOS) of the corresponding Landau bands, the movement of the current
carrying states in the disorder--energy and disorder--filling-factor plane can
be traced by tuning the disorder strength.
We show results for all sub-bands, particularly the traces of the Chern and
anti-Chern states as well as the peak positions of the DOS. For small disorder
strength we recover the well known weak levitation of the critical states,
but we also reveal, for larger , the strong levitation of these states
across the Landau gaps without merging. We find the behavior to be similar for
exponentially, Gaussian, and Lorentzian correlated disorder potentials. Our
study resolves the discrepancies of previously published work in demonstrating
the conflicting results to be only special cases of a general lattice model
with spatially correlated disorder potentials.
To test whether the mixing between consecutive Landau bands is the origin of
the observed floating, we truncate the Hilbert space of our model Hamiltonian
and calculate the behavior of the current carrying states under these
restricted conditions.Comment: 10 pages, incl. 13 figures, accepted for publication in PR
Squeezing out predictions with leptogenesis from SO(10)
We consider the see-saw mechanism within a non-supersymmetric SO(10) model.
By assuming the SO(10) quark-lepton symmetry, and after imposing suitable
conditions that ensure that the right-handed (RH) neutrino masses are at most
mildly hierarchical (compact RH spectrum) we obtain a surprisingly predictive
scenario. The absolute neutrino mass scale, the Dirac and the two Majorana
phases of the neutrino mixing matrix remain determined in terms of the set of
already measured low energy observables, modulo a discrete ambiguity in the
signs of two neutrino mixing angles and of the Dirac phase. The RH neutrinos
mass spectrum is also predicted, as well as the size and sign of the
leptogenesis CP asymmetries. We compute the cosmological baryon asymmetry
generated through leptogenesis and obtain the correct sign and a size
compatible with observations.Comment: 18 pages, 2 figures; minor changes, version accepted for publication
in PR
Anomalous quantum confined Stark effects in stacked InAs/GaAs self-assembled quantum dots
Vertically stacked and coupled InAs/GaAs self-assembled quantum dots (SADs)
are predicted to exhibit a strong non-parabolic dependence of the interband
transition energy on the electric field, which is not encountered in single SAD
structures nor in other types of quantum structures. Our study based on an
eight-band strain-dependent Hamiltonian indicates that
this anomalous quantum confined Stark effect is caused by the three-dimensional
strain field distribution which influences drastically the hole states in the
stacked SAD structures.Comment: 4 pages, 4 figure
New results for the missing quantum numbers labeling the quadrupole and octupole boson basis
The many -pole boson states, with ,
realize the irreducible representation (IR) for the group reduction chains
. They have been analytically
studied and widely used for the description of nuclear systems. However, no
analytical expression for the degeneracy of the 's IR,
determined by the reduction , is available. Thus, the
number of distinct values taken by has been so far obtained by
solving some complex equations. Here we derive analytical expressions for the
degeneracy characterizing the octupole and quadrupole boson states,
respectively. The merit of this work consists of the fact that it completes the
analytical expressions for the -pole boson basis.Comment: 10page
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