Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics

The Rényi entropies R_p [ ρ], p> 0,≠ 1 of the highly-excited quantum states of the D-dimensional isotropicharmonic oscillator are analytically determined by use of the strong asymptotics of theorthogonal polynomials which control the wavefunctions of these states, the Laguerrepolynomials. This Rydberg energetic region is where the transition from classical toquantum correspondence takes place. We first realize that these entropies are closelyconnected to the entropic moments of the quantum-mechanical probability ρ_n(r)density of the Rydberg wavefunctions Ψ_{n,l, { μ}}(r); so, to the?_p-norms of the associated Laguerrepolynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques ofapproximation theory based on the strong Laguerre asymptotics. Finally, we determine thedominant term of the Rényi entropies of the Rydberg states explicitly in terms of thehyperquantum numbers (n,l), the parameter order p and the universedimensionality D for all possible cases D ≥ 1. We find that (a) theRényi entropy power decreases monotonically as the order p is increasing and (b) thedisequilibrium (closely related to the second order Rényi entropy), which quantifies theseparation of the electron distribution from equiprobability, has a quasi-Gaussianbehavior in terms of D.     

Almost mobility edges and the existence of critical regions in one-dimensional quasiperiodic lattices

We study a one-dimensional quasiperiodic system described by the Aubry–André model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry–André model are either extended or localized depending on the strength of incommensurate potential V being less or bigger than a critical value V _c , and thus no mobility edge exists. However, it was shown in a recent work that for the system with V < V _c and the wave vector α of the incommensurate potential is small, there exist almost mobility edges at the energy E _c±, which separate the robustly delocalized states from “almost localized” states. We find that, besides E _c±, there exist additionally another energy edges E _c′±, at which abrupt change of inverse participation ratio (IPR) occurs. By using the IPR and carrying out multifractal analyses, we identify the existence of critical regions among |E _c±|?≤?|E|?≤?|E _c′±| with the mobility edges E _c± and E _c′± separating the critical region from the extended and localized regions, respectively. We also study the system with V > V _c , for which all eigenstates are localized states, but can be divided into extended, critical and localized states in their dual space by utilizing the self-duality property of the Aubry–André model.     

Photoluminescence enhancement in double Ge/Si quantum dot structures

The luminescence properties of double Ge/Si quantum dot structures are studied at liquid helium temperature depending on the Si spacer thickness d in QD molecules. A seven-fold increase in the integrated photoluminescence intensity is obtained for the structures with optimal thickness d = 2 nm. This enhancement is explained by increasing the overlap integral of electron and hole wavefunctions. Two main factors promote this increasing. The first one is that the electrons are localized at the QD base edges and their wavefunctions are the linear combinations of the states of in-plane Δ valleys, which are perpendicular in k-space to the growth direction [001]. This results in the increasing probability of electron penetration into Ge barriers. The second factor is the arrangement of Ge nanoclusters in closely spaced QD groups. The strong tunnel coupling of QDs within these groups increases the probability of hole finding at the QD base edge, that also promotes the increase in the radiative recombination probability.     

Electronic transport in graphene nanoribbons with disorder look at the pseudo-spin polarization: Dirac versus tight-binding model

We have compared results of electronic transport using two different approaches: Dirac vs tight-binding (TB) Hamiltonians to assesses disorder-induced effects in graphene nanoribbons. We apply the proposed Hamiltonians to calculate the density of states, the transmission along the ribbon, and the pseudo-spin polarization (P(E)) in metallic armchair graphene nanoribbons. We clearly show differences between these two approaches in the interference processes, especially in the low-lying energy limit, when the systems are found in the presence of random impurities (disorder). This allows us to find fingerprints associated with each model used. As the disorder increases, more robust electronic transmission (through polarized states in a given sublattice) arises when one is dealing with the Dirac model only. We also find with this model unexpected peaks in the P(E) far from the Dirac point for wider nanoribbons. In the other hand, the model TB show the Dirac limit with disturbances of the hyperboloid subbands for certain potentials of the impurities. In general, our study is indicating that a P(E) spectroscopy (analyzing the line width and intensity) can be used to detect fingerprints of the increase of asymmetry in the scattering processes and the transport limits where hyperboloid subbands are important.     

Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of e ² / h, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate potential suppresses the current at finite voltage bias, and then narrows the linear response regime of the I-V curve which exhibits two plateaus corresponding to the superconducting gap and the band edge, respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value 2g _s + 2Δ with Δ the p-wave pairing amplitude and g _s the hopping between neighbor sites, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage also causes an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose I-V curve exhibits an exponential shape.     

Why <Emphasis Type="Italic">X</Emphasis>(3872) is not a molecule

We discuss the scenario where the X(3872) resonance is the \(c\bar c\) = χ_c1(2P) charmonium which “sits on” the D*⁰\({\bar D^0}\) threshold. We explain the shift of the mass of the X(3872) resonance with respect to the prediction of a potential model for the mass of the χ_c1(2P) charmonium by the contribution of the virtual D*\(\bar D\) + c.c. intermediate states into the self energy of the X(3872) resonance. This allows us to estimate the coupling constant of the X(3872) resonance with the D*⁰\({\bar D^0}\) channel, the branching ratio of the X(3872) → D*⁰\({\bar D^0}\) + c.c. decay, and the branching ratio of the X(3872) decay into all non-D*⁰\({\bar D^0}\) + c.c. states. We predict a significant number of unknown decays of X(3872) via two gluon: X(3872) → gluongluon → hadrons. We suggest a physically clear program of experimental researches for verification of our assumption.     

Testing the Distance-Duality Relation from Hubble,Galaxy Clusters and Type Ia Supernovae Data with Model Independent Methods

In this paper, we perform cosmological-model-independent tests for the distance-duality (DD) relation η(z)=D _L(1+z)^?2/D _A by combining the angular diameter distance D _A(or comoving distances D _c ) with the luminosity distance D _L. The D _A are provided by two galaxy clusters samples compiled by De Filippis et al. (the elliptical β model), Bonamente et al. (the spherical β model), the D _c are obtained from Hubble parameter data and D _L are given from the Union2.1 supernovae (SNe) Ia compilation. We employ two methods, i.e., method A: binning the SNe Ia data within the range Δz=|z?z _SNe|<0.005, and method B: reconstructing the D _L(z) by smoothing the noise of Union2.1 data set over redshift with the Gaussian smoothing function, to obtain D _L associated with the redshits of the observed D _A or D _c. Four parameterizations for η(z), i.e., η(z)=1+η ₀ z, η(z)=1+η ₀ z/(1+z), η(z)=1+η ₀ z/(1+z)² and η(z)=1?η ₀ ln(1+z), are adopted for the DD relation. We find that DD relation is consistent with the present observational data, and the results we obtained are not sensitive to the method and parameterization.     

Quantum interference effects induced by multiple magnetic impurities on a triangular lattice f-wave superconductor

The effects of multi-impurity quantum interference on triangular lattice f-wave superconductors are studied by self-consistently solving Bogoliubov-de Gennes equations within the t?t′?J?V model. An overall phase diagram is presented, which shows that f-wave superconductivity dominates near 0.3 doping. Rich phenomena are induced by quantum interference effects, such as periodic modulations in charge orders, pyramid frustum structures, and a magnetic moment reverse transition, which are qualitatively different from the single-impurity case. We also examine the local density of states to show how localized quasiparticle states are created at or near the impurity sites, which can be directly measured by scanning tunneling microscopy experiments.     

Killing the Hofstadter butterfly,one bond at a time

Electronic bands in a square lattice when subjected to a perpendicular magnetic field form the Hofstadter butterfly pattern. We study the evolution of this pattern as a function of bond percolation disorder (removal or dilution of lattice bonds). With increasing concentration of the bonds removed, the butterfly pattern gets smoothly decimated. However, in this process of decimation, bands develop interesting characteristics and features. For example, in the high disorder limit, some butterfly-like pattern still persists even as most of the states are localized. We also analyze, in the low disorder limit, the effect of percolation on wavefunctions (using inverse participation ratios) and on band gaps in the spectrum. We explain and provide the reasons behind many of the key features in our results by analyzing small clusters and finite size rings. Furthermore, we study the effect of bond dilution on transverse conductivity (σ _xy ). We show that starting from the clean limit, increasing disorder reduces σ _xy to zero, even though the strength of percolation is smaller than the classical percolation threshold. This shows that the system undergoes a direct transition from a integer quantum Hall state to a localized Anderson insulator beyond a critical value of bond dilution. We further find that the energy bands close to the band edge are more stable to disorder than at the band center. To arrive at these results we use the coupling matrix approach to calculate Chern numbers for disordered systems. We point out the relevance of these results to signatures in magneto-oscillations.     

Fundamental Entangling Operators in Quantum Mechanics and Their Properties

For the first time, we introduce so-called fundamental entangling operators \(e^{iQ_{1} P_{2}}\) and \(e^{iP_{1} Q_{2} }\) for composing bipartite entangled states of continuum variables, where Q_i and P_i (i = 1, 2) are coordinate and momentum operator, respectively. We then analyze how these entangling operators naturally appear in the quantum image of classical quadratic coordinate transformation (q₁, q₂) → (Aq₁ + Bq₂, Cq₁ + Dq₂), where AD?BC = 1, which means even the basic coordinate transformation (Q₁, Q₂) → (AQ₁ + BQ₂, CQ₁ + DQ₂) involves entangling mechanism. We also analyse their Lie algebraic properties and use the integration technique within an ordered product of operators to show they are also one- and two- mode combinatorial squeezing operators.     

Individual-collective crossover driven by particle size in dense assemblies of superparamagnetic nanoparticles

Prussian blue analogues (PBA) ferromagnetic nanoparticles Cs ^I _x Ni ^II [Cr ^III (CN)₆ ] _z ·3(H₂O) embedded in CTA⁺ (cetyltrimethylammonium) matrix have been investigated by magnetometry and magnetic small-angle neutron scattering (SANS). Choosing particle sizes (diameter D = 4.8 and 8.6 nm) well below the single-domain radius and comparable volume fraction of particle, we show that the expected superparamagnetic regime for weakly anisotropic isolated magnetic particles is drastically affected due to the interplay of surface/volume anisotropies and dipolar interactions. For the smallest particles (D = 4.8 nm), magnetocrystalline anisotropy is enhanced by surface spins and drives the system into a regime of ferromagnetically correlated clusters characterized by a temperature-dependent magnetic correlation length L _mag which is experimentally accessible using magnetic SANS. For D = 8.6 nm particles, a superparamagnetic regime is recovered in a wide temperature range. We propose a model of interacting single-domain particles with axial anisotropy that accounts quantitatively for the observed behaviors in both magnetic regimes.     

Collisional Broadening of CO<Subscript>2</Subscript> Transition Lines 10<Superscript>0</Superscript>0–00<Superscript>0</Superscript>1 by Inert Gas Atoms at 300–700 K

The spectrum of excitation of Rydberg states of thallium atoms has been investigated using a collimated atomic beam in a two-step isotope selective laser scheme 6²P_1/2 → 6²D_3/2 → Tl** in the presence of an electric field with a strength of up to 1.5 kV/cm near the level 16F_5/2. The optical transitions 6D_3/2 → 18D_3/2 and 6D_3/2 → 16G_7/2, which were induced by an external electric field and dipole-forbidden, have been studied experimentally. The values for the scalar polarizabilities (in units сm^–1/(kV/сm)²) α₀(16F_5/2) = 3.71 ± 0.3, α₀(18D_3/2) = 11.70 ± 0.25, and α₀(16G_7/2) = 44.1 ± 0.9, which are compared with the calculated one, have been obtained. The new values of energy parameters for the states 18D_3/2 and 16G_7/2 have been determined.     

Calculation of the diffusion coefficient in acoustic turbulence

The first (Born) approximation commonly used to calculate the diffusion coefficient D_T of a passive scalar in acoustic turbulence is shown to be insufficient. Even for a small main parameter—the Mach number, M?1—the next approximation gives a larger contribution to D_T than does the first approximation, but negative in sign. We present a procedure for correctly calculating D_T based on the solution of a nonlinear DIA (direct interaction approximation) equation for the mean Green’s function of the problem. We include an additional term in the general formula for D_T that directly describes the compressibility of acoustic turbulence. This term has not been known previously and has been disregarded even in the Born approximation. A positive value was obtained for D_T=CM³u₀/p₀. The spectrum E(x) was assumed to be smooth at distances Δ x～M²?1.     

Layer stacking dependence on thermoelectric properties of massive Dirac fermions in bilayer graphene

We numerically study the thermoelectric transport in AB- and AA-stacked bilayer graphene in the presence of a strong magnetic field and disorder. In the AB-stacked case, we find that the thermoelectric conductivities display different asymptotic behaviors, depending on the ratio between the temperature and the width of the disorder-broadened Landau levels (LLs), similar to those of monolayer graphene. In the high temperature regime, the transverse thermoelectric conductivity α _xy saturates to a universal value 5.54k _B e/h at the center of each LL, and displays a linear temperature dependence at low temperatures. The calculated Nernst signal has a peak with a height of the order of k _B /e, and the thermopower changes sign at the central LL. We attribute this unique behavior to the coexistence of particle and hole LLs. In the AA-stacked bilayer case, it is found that the thermoelectric transport properties are consistent with the behavior of a band insulator. The obtained results demonstrate the sensitivity of the thermoelectric conductivity to the band gap near the Dirac point.     

Precision measurements of optical excitation functions for the mercury atom

We describe a computer-based facility for studying the excitation of atoms by ultramonochromatic electrons and give optical excitation functions for the 12 mercury spectral lines that originate from the n ¹ S ₀, n ¹ P ₁, n ¹ D ₂, n ³ S ₁, n ³ P _j , and n ³ D _j levels. We detected about 100 features in the energy dependences measured from the excitation threshold to 15.5 eV. The previously found positions of the features on the energy scale are in good agreement with our results. Most of the resonant features are shown to be mainly attributable to the decay of short-lived states of the negative mercury ion. We detected a postcollision interaction effect in the optical excitation functions of the lines that originate from the n ¹ S ₀ levels at energies of about 11 eV.     

Reflectance spectra and photonic band gaps of a one-dimensional photonic crystal based on a silicon-air periodic structure

The reflectance spectra of a one-dimensional photonic crystal based on a silicon-air periodic structure are calculated. A map of photonic band gaps is plotted, which makes it possible to deliberately choose the geometric parameters of the structure (the thickness of silicon partitions D _Si and the period A) for different ranges of the wavelength λ. To obtain structures with a photonic band gap in the range A/λ=0.15–0.5, the main region (as rule, corresponding to the lowest frequencies) can be used, and, taking into account the secondary photonic band gaps, the range A/λ can be extended to 1 and even more. In addition, it is found that, in the range D _Si/A=0.4–0.9, the secondary band gaps may be wider than the main ones (on the frequency scale). The influence of the filling factor D _Si/A on the formation of the edges of spectral bands is revealed.     

Dependence of the magnetic and superconducting characteristics of fine-grained HTSCs YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> on the degree of structural disorder and type of oxygen vacancy ordering in chain planes

The characteristics determining different contributions to the magnetic susceptibility at T > T _C (Pauli susceptibility, coherence length at T = 0, and Curie constant) as functions of the degree of structural disorder have been analyzed for high-temperature superconducting YBa₂Cu₃O _y samples ( y ≈ 6.92, T _C ≈ 92 K) with micrometer and submicron average grain sizes D _av. It is shown that the decrease in these characteristics, which is observed in fine-grained samples with a decrease in D _av, occurs in various ways, depending on the number and type of oxygen vacancy ordering in chain planes.     

Localization of weakly disordered flat band states

Certain tight binding lattices host macroscopically degenerate flat spectral bands. Their origin is rooted in local symmetries of the lattice, with destructive interference leading to the existence of compact localized eigenstates. We study the robustness of this localization to disorder in different classes of flat band lattices in one and two dimensions. Depending on the flat band class, the flat band states can either be robust, preserving their strong localization for weak disorder W, or they are destroyed and acquire large localization lengths ξ that diverge with a variety of unconventional exponents ν, ξ ~ 1 /W ^ν .     

Coulomb corrections to bremsstrahlung in the electric field of a heavy atom at high energies

We consider the differential and partially integrated cross sections for bremsstrahlung from high-energy electrons in an atomic field, with this field taken into account exactly. We use the semiclassical electron Green function and wavefunctions in an external electric field. It is shown that the Coulomb corrections to the differential cross section are very susceptible to screening. Nevertheless, the Coulomb corrections to the cross section summed over the final-electron states are independent of screening in the leading approximation in the small parameter 1/mr _scr (r _scr is the screening radius and m is the electron mass, ? = c = 1). We also consider bremsstrahlung from a finite-size electron beam on a heavy nucleus. The Coulomb corrections to the differential probability are also very susceptible to the beam shape, while the corrections to the probability integrated over momentum transfer are independent of it, apart from the trivial factor, which is the electron-beam density at zero impact parameter. For the Coulomb corrections to the bremsstrahlung spectrum, the next-to-leading terms with respect to the parameters mε (ε is the electron energy) and 1/mr _scr are obtained.