Superfluidity of indirect excitons vs quantum Hall correlation in double Hall systems: Different types of physical mechanisms of correlation organization in Hall bilayers

Bilayer Hall systems can be divided into two groups—with and without tunneling of carriers across the barrier between layers. We demonstrate that these both classes differ in topology sense which leads to the distinct quantum Hall hierarchy. In the case of forbidden interlayer carrier tunneling we developed the Metropolis Monte Carlo simulation for an energy competition of the reentrant integer quantum Hall state against the superfluid Bose Einstein condensate of indirect excitons in double-layer 2D Hall systems, GaAs/GaAlAs/GaAs and b-graphene/hBN/b-graphene, with complementary layer filling, ${\nu }_{bot}+{\nu }_{top}=1$. The resulted phase diagrams for both systems have been determined in consistence with the experimental data.     

p(x) and Tc(x) characteristics in the Y 1−b(Ca)bBa2Cu3O6+x cuprate family

A model has been proposed to calculate the $p\left(x\right)$ and $T_c\left(x\right)$ dependences in the Y _1?b(Ca)_bBa₂Cu₃O_6+x high-$T_c$ cuprate family and applied to $b=0$, $b=0.1$, and $b=0.2$ cases, for which experimental data exist in the literature. The results obtained imply that the Ca efficiency to provide holes is independent of the basal plane oxygen concentration, which is consistent with a view that electrons from CuO₂ layers would go primarily to Ca since it is twice closer than oxygen (in addition, the chain oxygen is screened by a layer made up of Ba and O(4) ions). It is shown that, in fully oxygenized compounds ($x=1$) the average efficiency, $\chi$, of a chain oxygen to attract an electron from the two nearby layers is reduced by the Ca insertion, though not because the charge transfer mechanism is in itself weakened by Ca, but because a part of electrons that are otherwise available in CuO${}_2$ layers has already been removed by the substitution of Y ³⁺ with Ca²⁺. It has been found that the $b$-dependence of the average oxygen doping efficiency can be fairly accurately described by the following relation: $\chi \left(b\right)=0.39\times (1?0.78b)$. The calculated $p\left(x\right)$ and $T_c\left(x\right)$ dependences are in very good agreement with the available experimental data.     

The second hyperpolarizability of systems described by the space-fractional Schrödinger equation

The static second hyperpolarizability is derived from the space-fractional Schrödinger equation in the particle-centric view. The Thomas–Reiche–Kuhn sum rule matrix elements and the three-level ansatz determines the maximum second hyperpolarizability for a space-fractional quantum system. The total oscillator strength is shown to decrease as the space-fractional parameter α decreases, which reduces the optical response of a quantum system in the presence of an external field. This damped response is caused by the wavefunction dependent position and momentum commutation relation. Although the maximum response is damped, we show that the one-dimensional quantum harmonic oscillator is no longer a linear system for $\alpha \ne 1$, where the second hyperpolarizability becomes negative before ultimately damping to zero at the lower fractional limit of $\alpha \to 1/2$.     

Radial position-momentum uncertainties for the infinite circular well and Fisher entropy

We show how the product of the radial position and momentum uncertainties can be obtained analytically for the infinite circular well potential. Some interesting features are found. First, the uncertainty Δr increases with the radius R and the quantum number n, the n-th root of the Bessel function. The variation of the Δr is almost independent of the quantum number n for $n>4$ and it will arrive to a constant for a large n, say $n>4$. Second, we find that the relative dispersion $\mathrm{\Delta }r/〈r〉$ is independent of the radius R. Moreover, the relative dispersion increases with the quantum number n but decreases with the azimuthal quantum number m. Third, the momentum uncertainty Δp decreases with the radius R and increases with the quantum numbers $m>1$ and n. Fourth, the product $\mathrm{\Delta }r\mathrm{\Delta }{p}_r$ of the position-momentum uncertainty relations is independent of the radius R and increases with the quantum numbers m and n. Finally, we present the analytical expression for the Fisher entropy. Notice that the Fisher entropy decreases with the radius R and it increases with the quantum numbers $m>0$ and n. Also, we find that the Cramer–Rao uncertainty relation is satisfied and it increases with the quantum numbers $m>0$ and n, too.     

On the Duffin–Kemmer–Petiau equation with linear potential in the presence of a minimal length

We point out an erroneous handling in the literature regarding solutions of the $(1+1)$-dimensional Duffin–Kemmer–Petiau equation with linear potentials in the context of quantum mechanics with minimal length. Furthermore, using Brau's approach, we present a perturbative treatment of the effect of the minimal length on bound-state solutions when a Lorentz-scalar linear potential is applied.     

Classification of “Real” Bloch-bundles: Topological quantum systems of type AI

We provide a classification of type AI topological quantum systems in dimension $d=1,2,3,4$ which is based on the equivariant homotopy properties of “Real” vector bundles. This allows us to produce a fine classification able to take care also of the non stable regime which is usually not accessible via $K$-theoretic techniques. We prove the absence of non-trivial phases for one-band AI free or periodic quantum particle systems in each spatial dimension by inspecting the second equivariant cohomology group which classifies “Real” line bundles. We also show that the classification of “Real” line bundles suffices for the complete classification of AI topological quantum systems in dimension $d⩽3$. In dimension $d=4$ the determination of different topological phases (for free or periodic systems) is fixed by the second “Real” Chern class which provides an even labeling identifiable with the degree of a suitable map. Finally, we provide explicit realizations of non trivial 4-dimensional free models for each given topological degree.     

On quantum symmetries of compact metric spaces

An action of a compact quantum group on a compact metric space $(X,d)$ is (D)-isometric if the distance function is preserved by a diagonal action on $X\times X$. In this study, we show that an isometric action in this sense has the following additional property: the corresponding action on the algebra of continuous functions on $X$ by the convolution semigroup of probability measures on the quantum group contracts Lipschitz constants. In other words, it is isometric in another sense due to Li, Quaegebeur, and Sabbe, which partially answers a question posed by Goswami. We also introduce other possible notions of isometric quantum actions in terms of the Wasserstein $p$-distances between probability measures on $X$ for $p\ge 1$, which are used extensively in optimal transportation. Indeed, all of these definitions of quantum isometry belong to a hierarchy of implications, where the two described above lie at the extreme ends of the hierarchy. We conjecture that they are all equivalent.     

The β-expansion of periodic dressed chain models

We revisit the method of calculating the $\beta$-expansion of the Helmholtz free energy of any one-dimensional (1D) Hamiltonian with invariance under space translations, presented in [O. Rojas, S.M. de Souza, M.T. Thomaz, J. Math. Phys. 43 (2002) 1390], extending this method to 1-D Hamiltonians that are invariant under translations along super-sites (sequences of $l$ sites). The method is applicable, for instance, to spin models and bosonic/fermionic versions of Hubbard models, either quantum or classical. As an example, we focus on the staggered spin-$S$ Ising model in the presence of a longitudinal magnetic field, comparing some of its thermodynamic functions to those of the standard Ising model. We show that for arbitrary values of spin ($S\in \{1,3/2,2,\dots \}$) but distinct values of the coupling constant and the magnetic field, the specific heat and the $z$-component of the staggered and usual magnetizations can be well approximated by their respective thermodynamic function of the spin-$1/2$ models in a suitable interval of temperature. These approximations are valid for the standard Ising model as well as for the staggered model, the thermodynamics of which are known exactly.