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 $W$ we recover the well known weak levitation of the critical states, but we also reveal, for larger $W$, 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 ${\bf k}\cdot{\bf p}$ 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 $2^k$-pole boson states, $|N_kv_k\alpha_k I_kM_k>$ with $k=2,3$, realize the irreducible representation (IR) for the group reduction chains $SU(2k+1)\supset R_{2k+1}\supset R_3\supset R_2$. They have been analytically studied and widely used for the description of nuclear systems. However, no analytical expression for the degeneracy $d_v(I)$ of the $R_{2k+1}$'s IR, determined by the reduction $R_{2k+1}\supset R_3$, is available. Thus, the number of distinct values taken by $\alpha_k$ has been so far obtained by solving some complex equations. Here we derive analytical expressions for the degeneracy $d_v(I)$ 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 $2^k$-pole boson basis.Comment: 10page