Ising model in a quasiperiodic transverse field,percolation, and contact processes in quasiperiodic environments

Quantum Ising models in a transverse field are related to continuous-time percolation processes whose oriented percolation versions are contact processes. We study such models in the presence of quasiperiodic disorder and prove localization in the ground state, no percolation, and extinction, respectively, for sufficiently large disorder.     

Direct evidence for quantum contact resistance effects in V-groove quantum wires

The effect of quantum contact resistance on one-dimensional (1D) electrical conductance was investigated in quantum wires (QWR) realized with V-shaped GaAs/AlGaAs heterostructure. The transition length between the electron reservoir and the QWR was controlled by employing an electric field. The required transition length is found to decrease with increasing overlap between the 2D states in the reservoir and the 1D states in the QWR.     

Critical Values in a Long-range Percolationon Spaces Like Fractals

On a certain class of general discrete spaces including fractals, we consider a model in which each pair of distinct points is connected by a random bond. The main question we are concerned is whether a connected component consisting of infinitely many points exists or not. This depends on the choice of parameters in the connecting probabilities, and the aim of this paper is to find thresholds of the parameters     

Auger relaxation processes in semiconductor nanocrystals and quantum wells

Auger recombination rates in mesoscopic semiconductor structures have been studied as a function of energy band parameters and heterostructure size. It is shown that nonthreshold Auger processes stimulated by the presence of heteroboundaries become the dominant nonradiative recombination channel in nanometer size semiconductor structures. The size dependence of luminescence quantum yields in nanostructures and microcrystals are discussed. Auger-like collisions of electrons and heavy holes are shown to serve as “accelerators” of thermalization processes in semiconductor quantum dots.     

Long-range quantum discord in critical spin systems

We show that quantum correlations as quantified by quantum discord can characterize quantum phase transitions by exhibiting nontrivial long-range decay as a function of distance in spin systems. This is rather different from the behavior of pairwise entanglement, which is typically short-ranged even in critical systems. In particular, we find a clear change in the decay rate of quantum discord as the system crosses a quantum critical point. We illustrate this phenomenon for first-order, second-order, and infinite-order quantum phase transitions, indicating that pairwise quantum discord is an appealing quantum correlation function for condensed matter systems.     

Macroscopic quantum tunneling in molecular magnets

Our present understanding of the phenomenon of quantum tunneling of magnetization (QTM), is reviewed in the light of the experiments performed on the molecular complex Mn₁₂-ac. This system, in which QTM was clearly shown for the first time, consists of molecules with mesoscopic spins in dipolar interactions. Both single and many-molecule effects are essential for the observation of QTM (crystal field, hyperfine and dipolar interactions), which allows one to make a link between mesoscopic physics and magnetism.     

Magnon bands in twisted bilayer honeycomb quantum magnets

We study the magnon bands of twisted bilayer honeycomb quantum magnets using linear spin wave theory. Although the interlayer coupling can be ferromagnetic or antiferromagnetic, we keep the intralayer one ferromagnetic to avoid possible frustration. For the interlayer ferromagnetic case, we find the magnon bands have similar features with the corresponding electronic energy spectrums. Although the linear dispersions near the Dirac points are preserved in the magnon bands of twisted bilayer magnets, their slopes are reduced with the decrease of the twist angles. On the other hand, the interlayer antiferromagnetic couplings generate quite different magnon spectra. The two single-layered magnon spectra are usually decoupled due to the opposite orientations of the spins in the two layers. We also develop a low-energy continuous theory for very small twist angles, which has been verified to fit well with the exact tight-binding calculations. Our results may be experimentally observed due to the rapid progress in two-dimensional magnetic materials.     

Long-range radiative interaction between semiconductor quantum dots

We model the resonant excitation transfer between semiconductor quantum dots, accounting for the radiative nature of the electromagnetic field. The model based on Maxwell equations and on a non-local linear susceptibility accounts both for the instantaneous dipole–dipole coupling, decaying as R⁻³, and for retardation effects, decaying as R⁻¹. The coupling is strongly resonant and its spatial range is of the order of the wavelength, due to the radiative nature of the retarded contribution.     

Inhomogeneous contact processes on trees

We consider an inhomogeneous contact process on a tree of degreek, where the infection rate at any site isλ, the death rate at any site in isδ (with 0 <δ ⩽ 1) and that at any site in is 1. Denote by the critical value for thehomogeneous model (i.e.,δ=1) on and byϑ(δ, λ) the survival probability of the inhomogeneous model on . We prove that whenk > 4, if , a subtree embedded in , with 1 ⩽σ ⩽ √k, then three existsδ _c ^σ strictly between ( ) and 1 such that ( ) whenδ >δ _c ^σ andϑ(δ, λ _c( ) > 0 whenδ <δ _c ^σ ; ifS={o}, the origin of , then for anyδ ε (0, 1).     

Positivity and complete positivity of differentiable quantum processes

We study quantum processes, as one parameter families of differentiable completely positive and trace preserving (CPTP) maps. Using different representations of the generator, and the Sylvester criterion for positive semi-definite matrices, we obtain conditions for the divisibility of the process into completely positive (CP-divisibility) and positive (P-divisibility) infinitesimal maps. Both concepts are directly related to the definition of quantum non-Markovianity. For the single qubit case we show that CP- and P-divisibility only depend on the dissipation matrix in the master equation form of the generator. We then discuss three classes of processes where the criteria for the different types of divisibility result in simple geometric inequalities, among these the class of non-unital anisotropic Pauli channels.     

Random quantum magnets with broad disorder distribution

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(ln J) ∼ | ln J|^{-1 - α}, α > 1, for large | ln J| (Lévy flight statistics). For sufficiently broad distributions, α < , the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the Lévy index, α. In one dimension, with = 2, we obtained several exact results through a mapping to surviving Riemann walks. In two dimensions the varying critical exponents have been calculated by a numerical implementation of the Ma-Dasgupta-Hu renormalization group method leading to ≈ 4.5. Thus in the region 2 < α < , where the central limit theorem holds for | ln J| the broadness of the distribution is relevant for the 2d quantum Ising model. Received 6 December 2000 and Received in final form 22 January 2001     

Maximally robust unravelings of quantum master equations

The stationary state of an open quantum system has infinitely many representations as an ensemble of pure states. We argue that the most natural ensemble is the most robust physically realizable ensemble. Robustness is quantified by the survival probability. Physical realization requires monitoring the environment to “unravel” the dissipative evolution.     

Multi-spin-subband structure of dilute magnetic semiconductor quantum wells: Feedback mechanism

Using a fully self-consistent envelope function approach, we focus on wide conduction band NMS (non-magnetic semiconductor)/DMS (dilute magnetic semiconductor)/NMS quantum wells, under weak external parallel magnetic field, where many spin-subbands are usually present. We concentrate on small values of the magnetic field because we want to investigate the influence of the feedback mechanism due to the difference of the concentrations of spin-up and spin-down carriers which could induce spontaneous spin-polarization i.e. in the absence of a magnetic field. We study the spin-subband structure, the spin-subband populations and the spin-polarization as functions of the sheet carrier concentration, _Ns$N_s$, for different values of the magnitude of the exchange interaction, |J|$\left|J\right|$, between the itinerant carriers and the magnetic impurities. Our calculations for 0.01 T show that at 20 K the values of |J|$\left|J\right|$ necessary to make this feedback mechanism sufficiently strong are too high compared to the |J|$\left|J\right|$ values of common Mn-doped systems in the conduction band. However, the feedback mechanism will be sufficiently strong at low enough temperatures below 20 K for realistic values of |J|$\left|J\right|$. Moreover, we explain how increasing the sheet carrier concentration the heterostructure is transformed from an almost square quantum well to a system of two coupled heterojunctions with an intermediate soft barrier.     

Long range order in the ground state of quantum interacting rotors in two dimensions

It has been rigorously proved that the ground state of interacting quantum rotors in two dimensions exhibits the magnetic long-range order in the ferromagnetic case. The assumptions are that the interaction is between nearest neighbors and it is strong enough, and that rotors are sufficiently heavy. The proof is based on the Reflection Positivity technique.     

Dynamic spin-glass behavior in a disorder-free,two-component model of quantum frustrated magnets

Motivated by the observation of a spin-glass transition in almost disorder-free Kagome antiferromagnets, and by the specific form of the effective low-energy model of the S = 1/2, trimerized Kagome antiferromagnet, we investigate the possibility to obtain a spin-glass behavior in two-component, disorder-free models. We concentrate on a toy-model, a modified Ashkin-Teller model in a magnetic field that couples only to one species of spins, for which we prove that a dynamic spin-glass behavior occurs. The dynamics of the magnetization is closely related to that of the underlying Ising model in zero field in which spins and pseudo-spins are intimately coupled. The spin-glass like history dependence of the magnetization is a consequence of the ageing of the underlying Ising model. Received 21 September 2001 and Received in final form 16 January 2002     

Analysis of a long-range random field quantum antiferromagnetic Ising model

We introduce a solvable quantum antiferromagnetic model. The model, with Ising spins in a transverse field, has infinite range antiferromagnetic interactions and random fields on each site following an arbitrary distribution. As is well-known, frustration in the random field Ising model gives rise to a many valley structure in the spin-configuration space. In addition, the antiferromagnetism also induces a regular frustration even for the ground state. In this paper, we investigate analytically the critical phenomena in the model, having both randomness and frustration and we report some analytical results for it.