On a Semiclassical Formula for Non-Diagonal Matrix Elements

Let H(?)=?? ²d²/dx ²+V(x) be a Schrödinger operator on the real line, W(x) be a bounded observable depending only on the coordinate and k be a fixed integer. Suppose that an energy level E intersects the potential V(x) in exactly two turning points and lies below V _∞=lim?inf?_|x|→∞ V(x). We consider the semiclassical limit n→∞, ?=? _n →0 and E _n =E where E _n is the nth eigenenergy of H(?). An asymptotic formula for 〈n|W(x)|n+k〉, the non-diagonal matrix elements of W(x) in the eigenbasis of H(?), has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.     

Mechanism of charge transfer in <Emphasis Type="Italic">n</Emphasis>-CdS/<Emphasis Type="Italic">p</Emphasis>-CdTe heterojunctions

The capacitance-voltage and current-voltage characteristics of the n-CdS/p-CdTe heterosystem are investigated. Analysis of these characteristics demonstrates that the CdTe_1?x S _x solid solution formed at the n-CdS/p-CdTe heterointerface is inhomogeneous in both the conductivity and composition. The thickness of solid solutions is estimated from the capacitance-voltage characteristics. It is shown that, for the n-CdS/p-CdTe heterosystem, the current-voltage characteristic in the current density range 10^?8-10^?5 A cm^?2 is governed by the thermal electron emission, whereas the current in the heterostructure at current densities in the range 10^?4-10^?2 A cm^?2 is limited by recombination of charge carriers in the electroneutral region of the CdTe_1?x S _x solid solution. The lifetime and the diffusion length of minority charge carriers in the CdTe_1?x S _x solid solution and the surface recombination rate at the interface between the CdS layer and the CdTe_1?x S _x solid solution are determined. It is demonstrated that the n-CdS/p-CdTe heterostructure operates as a p-i-n structure in which CdTe is a p layer, CdTe_1?x S _x is an i layer, and CdS is an n layer.     

Dynamical Characteristics of a Non-canonical Scalar-Torsion Model of Dark Energy

In this paper, we analyze the phase-space of a model of dark energy in which a non-canonical scalar field (tachyon) non-minimally coupled to torsion scalar in the framework of teleparallelism. Scalar field potential and non-minimal coupling function are chosen as V(?) = V₀?ⁿ and f(?) = ?^N, respectively. We obtain a critical point that behaves like a stable or saddle point depending on the values of N and n. Additionally we find an unstable critical line. We have shown such a behavior of critical points using numerical computations and phase-space trajectories explicitly.     

Multiple exchanges in lepton pair production in high-energy heavy ion collisions

As an archetype reaction for pQCD multigluon hard processes in collisions of ultrarelativistic nuclei, we analyze generic features of lepton pair production via multiphoton processes in peripheral heavy ion scattering. We report explicit results for collisions of two photons from one nucleus with two photons from the other nucleus, 2γ + 2γ → l⁺l^?. The results suggest that the familiar eikonalization of Coulomb distortions breaks down for oppositely moving Coulomb centers. The breaking of eikonalization in QED suggests that multigluon pQCD processes cannot be described in terms of collective nuclear gluon distributions. We discuss a logarithmic enhancement of the contribution from the 2γ + 2γ → l⁺l^? process to production of lepton pairs with large transverse momentum; similar enhancement is absent for the nγ + mγ → l⁺l^? processes with m, n > 2. We comment on the general structure of multiphoton collisions and properties of higher-order terms that cannot be eikonalized.     

Resonant multiphoton dissociation of the NO molecule

The multiphoton dissociation of an unexcited NO molecule involving intermediate Rydberg states n?σ(²∑⁺), n?π(²П), and n?δ(²Δ), which are populated by a weak probe field and decay owing to nonadiabatic transitions in the predissociation states of valence configurations B′²Δ, L ²П, I ²∑⁺, and B ²П, has been studied. The role of the ponderomotive interaction that occurs under the simultaneous action of an intensive electromagnetic monochromatic radiation on the studied system has been analyzed. A theory to describe the dynamics of the process has been described. The possibilities of laser stimulation of this process, which consist in the search for ranges of variation in the frequencies and intensities of laser radiation that provide the highest efficiency of the resonant photostimulated process, have been discussed.     

Thermoelectric properties of layered ferrocuprates <Emphasis Type="Italic">Ln</Emphasis>BaCuFeO<Subscript>5 + δ</Subscript> (<Emphasis Type="Italic">Ln</Emphasis>= La,Pr, Nd,Sm, Gd-Lu)

The electrical resistivity ρ and the thermopower S of ceramic materials LnBaCuFeO_{5 + δ} (Ln= La, Pr, Nd, Sm, Gd-Lu) are measured in air at temperatures in the range from 300 to 1100 K. All the studied ferrocuprates are p-type semiconductors. The electrical resistivity ρ and the thermopower S of these compounds increase with a decrease in the radius of the Ln ³⁺ cation (with an increase in the number of 4f electrons n in Ln ³⁺). The nonmonotonic behavior of the dependences ρ=f(n) and S=f(n) indicates that the electrical properties of the layered ferrocuprates LnBaCuFeO_{5 + δ} depend on the electronic configuration of the Ln ³⁺ cation. The power factors P calculated for the LnBaCuFeO_{5 + δ} ceramic materials from the experimental values of ρ and S increase with increasing temperature and, at T = 1000 K, reach the maximum values P = 102.0 and 54.1 µW m^?1 K^?2 for Ln = Pr(4f ²) and Sm(4f ⁵), respectively, and become close to each other and equal to 30–35 µW m^?1 K^?2 for Ln = Gd(4f ⁷), Dy(4f ⁹), and Ho(4f ¹⁰).     

Proton-proton interaction with high multiplicity at energy of 70 GeV (proposal)

The goal of the proposed experiment is to investigate the collective behavior of particles in the process of multiple hadron production in pp interaction pp → n _π π + 2N at the beam energy E_lab = 70 GeV. The domain of high multiplicity n _π = 30–40, or z = n/\(\bar n\) = 4–6, will be studied. Near the threshold of reaction n _π → 69, z → z_th = 8.2, all particles acquire small relative momentum Δq < 1/R, where R is the dimension of the particle production region. As a consequence of multiboson interference, a number of collective effects may show up: (a) a drastic increase in the partial cross section σ(n) of production of n identical particles is expected, compared with commonly accepted extrapolation; (b) the formation of jets consisting of identical particles may occur as a result of the multiboson Bose-Einstein correlation (BEC) effect; (c) a large fluctuation of charged n(π⁺,π^?) and neutral n(π⁰) components and onset of centauros or chiral condensate effects are anticipated; (d) an increase in the rate of direct γ as a result of the bremsstrahlung in the partonic cascade and annihilation of π⁺π^? → nγ in dense and cold pionic gas or condensate is expected. In the domain of high multiplicity z ≥ 5, a major part of the c.m. energy \(\sqrt s = 11.6\) GeV is materialized, leading to a high-density thermalized hadronic system. Under this condition, a phase transition to cold quark-gluon plasma (QGP) may occur. The search for QGP signatures like large intermittency in the phase-space particle distribution and an enhanced rate of direct photons will be performed. The experimental setup is designed for detection of rare high-multiplicity events. The experiment is to be carried out at the extracted proton beam of the IHEP U-70 accelerator. The required beam intensity is ～10⁷ s^?1. Under the assumption that the partial cross section σ(n _π = 35) = 10-1 nb, the anticipated counting rate is 10-1 events/h. The multiboson BEC enhancement may drastically increase the counting rate.     

Energy scan of cross sections for <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>–</Superscript> annihilation into quarkonia and light hadrons in the Belle experiment

The cross sections of the reactions e⁺e^– → ?(nS)π⁺π^? (n = 1, 2,3) and e⁺e^– → h _b (nP)π⁺π^? (n = 1, 2) are measured as a function of the cms collision energy from their thresholds up to 11.02 GeV using the data of the Belle experiment operating at the KEKB e⁺e^– collider. The peaks of the ?(10 860) and ?(11020) resonances are observed in the cross sections with an insignificant contribution of the continuum. The decay ?(11020) → h _b (nP)π⁺π^? is found to fully proceed through intermediate isovector states Z _b (10610) and Z _b (10650).     

Nonexponential decay in the quantum dynamics of nanosystems

The quantum dynamical problem is solved for a system coupled to an equidistant-spectrum bath with the energy difference Ω between the neighboring levels n and n + 1 and the coupling matrix elements C _n ² = C ²(1 + Δ^?2 n ²)^?1 constraining the energy interval comprising the bath states interacting with the system. The evolution in the strong-coupling limit is determined by two parameters, Γ = πC ²/Ω ? 1 and α = Γ/Δ. If α ≠ 0, then the decrease in the population in the initial cycle with a period of 2π/Ω is not exponential and the effective rate constant increases with time. The results qualitatively explain the appearance of nonexponential relaxation regimes for a dense-spectrum nanosystem and predict the possibility of the multiple recovery of the initial-state population.     

Temperature Dependence of the Thermal Conductivity of a Trapped Dipolar Bose-Condensed Gas

The thermal conductivity of a trapped dipolar Bose condensed gas is calculated as a function of temperature in the framework of linear response theory. The contributions of the interactions between condensed and noncondensed atoms and between noncondensed atoms in the presence of both contact and dipole-dipole interactions are taken into account to the thermal relaxation time, by evaluating the self-energies of the system in the Beliaev approximation. We will show that above the Bose-Einstein condensation temperature (T?>?T _BEC ) in the absence of dipole-dipole interaction, the temperature dependence of the thermal conductivity reduces to that of an ideal Bose gas. In a trapped Bose-condensed gas for temperature interval k _B T?<<?n ₀ g _B , E _p ?<<?k _B T (n ₀ is the condensed density and g _B is the strength of the contact interaction), the relaxation rates due to dipolar and contact interactions between condensed and noncondensed atoms change as \( {\tau}_{dd12}^{-1}\propto {e}^{-E/{k}_BT} \) and τ _c12?∝?T ^?5, respectively, and the contact interaction plays the dominant role in the temperature dependence of the thermal conductivity, which leads to the T ^?3 behavior of the thermal conductivity. In the low-temperature limit, k _B T?<<?n ₀ g _B , E _p ?>>?k _B T, since the relaxation rate \( {\tau}_{c12}^{-1} \) is independent of temperature and the relaxation rate due to dipolar interaction goes to zero exponentially, the T ² temperature behavior for the thermal conductivity comes from the thermal mean velocity of the particles. We will also show that in the high-temperature limit (k _B T?>?n ₀ g _B ) and low momenta, the relaxation rates \( {\tau}_{c12}^{-1} \) and \( {\tau}_{dd12}^{-1} \) change linearly with temperature for both dipolar and contact interactions and the thermal conductivity scales linearly with temperature.     

Censored Glauber Dynamics for the Mean Field Ising Model

We study Glauber dynamics for the Ising model on the complete graph on n vertices, known as the Curie-Weiss Model. It is well known that at high temperature (β<1) the mixing time is Θ(nlog?n), whereas at low temperature (β>1) it is exp?(Θ(n)). Recently, Levin, Luczak and Peres considered a censored version of this dynamics, which is restricted to non-negative magnetization. They proved that for fixed β>1, the mixing-time of this model is Θ(nlog?n), analogous to the high-temperature regime of the original dynamics. Furthermore, they showed cutoff for the original dynamics for fixed β<1. The question whether the censored dynamics also exhibits cutoff remained unsettled.In a companion paper, we extended the results of Levin et al. into a complete characterization of the mixing-time for the Curie-Weiss model. Namely, we found a scaling window of order \(1/\sqrt{n}\) around the critical temperature β _c =1, beyond which there is cutoff at high temperature. However, determining the behavior of the censored dynamics outside this critical window seemed significantly more challenging.In this work we answer the above question in the affirmative, and establish the cutoff point and its window for the censored dynamics beyond the critical window, thus completing its analogy to the original dynamics at high temperature. Namely, if β=1+δ for some δ>0 with δ ² n→∞, then the mixing-time has order (n/δ)log?(δ ² n). The cutoff constant is (1/2+[2(ζ² β/δ?1)]^?1), where ζ is the unique positive root of g(x)=tanh?(β x)?x, and the cutoff window has order n/δ.     

Stationary cosmic jets as accelerators of ultrarelativistic cosmic ray particles

A model of a cosmic jet working in the mode of a magnetohydrodynamic nozzle and unipolar inductor is considered. It is shown that the “solid-state” rotation of screw magnetic field lines leads to acceleration of small fractions of plasma particles up to ultrarelativistic energies with the spectrum dq/d? ～ ? ^?n , the exponent n being close to the experimental value.     

Restricting Positive Energy Representations of Diff<Superscript>+</Superscript>(<Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>) to the Stabilizer of <Emphasis Type="Italic">n</Emphasis> Points

Let G _n ? Diff⁺(S ¹) be the stabilizer of n given points of S ¹. How much information do we lose if we restrict a positive energy representation \(U^c_h\) associated to an admissible pair (c, h) of the central charge and lowest energy, to the subgroup G _n ? The question, and a part of the answer originate in chiral conformal QFT. The value of c can be easily “recovered” from such a restriction; the hard question concerns the value of h. If c ≤ 1, then there is no loss of information, and accordingly, all of these restrictions are irreducible. In this work it is shown that \(U^c_{h}|_{G_n}\) is always irreducible for n =  1 and, if h =  0, it is irreducible at least up to n ≤  3. Moreover, an example is given for c >  2 and certain values of \(h \neq \tilde{h}\) such that \(U^c_{h}|_{G_1}\simeq U^c_{\tilde{h}}|_{G_1}\) . It is also concluded that for these values \(U^c_{h}|_{G_n}\) cannot be irreducible for n ≥  2. For further values of c, h and n, the question is left open. Nevertheless, the example already shows that, on the circle, there are conformal QFT models in which local and global intertwiners are not equivalent.     

Bestimmung der Kernmomente des Ho165 aus der Hyperfeinstruktur des Grundzustandes im Ho I-Spektrum

In an atomic beam magnetic resonance experiment, the hyperfine interaction constantsA andB of the⁴ I _2/15-groundstate of Ho¹⁶⁵ were found to beA=800,58389 (50) MHz,B=?1667,997 (50) MHz. Using an effective value for 〈r ^?3〉, the magnetic moment of the Ho¹⁶⁵ nucleus was calculated to beμ=4·1(4)μ _n . The quadrupolement was determined by use of the 〈r ^?3〉 given byWatson andFreeman. The result isQ=2·4·10^?24 cm².     

On the binding of atoms with antiatoms

The stability of X⁺Y⁺X^?Y^? Coulomb molecules consisting of X⁺Y^? atoms and X^?Y⁺ antiatoms to dissociation is studied. On the basis of multiparameter variational calculations, it is found that such molecules are stable to dissociation into X⁺X^? atoms and Y⁺Y^? antiatoms if the mass ratio of particles X and Y lies in the range 0.4710<m _X /m _Y <2.1231. The e⁺e⁺e^?e^?, π⁺μ⁺π^?μ^?, t⁺d⁺t^?d^?, p⁺K⁺p^?K^?, and d⁺p⁺d^?p^? molecules satisfy this condition.     

VUV-luminescence and excitation spectra of the heavy trivalent rare-earth ions in fluoride matrices

VUV 4f ⁿ → 4f^n?15d transitions of Gd³⁺, Er³⁺, Tm³⁺, and Lu³⁺ in fluoride matrices have been analyzed with high-resolution luminescence and excitation spectroscopy. In trifluorides, strong electron-phonon coupling has been found. In the other matrices, the luminescence spectra clearly yield zero-phonon lines and phonon replica, indicating intermediate coupling. The energies of the zero-phonon lines observed are compared with theoretical predictions. Near the threshold of f → d excitations, some of the excitation spectra yield sharp structures which cannot be explained with phonon replica but will be discussed in terms of the energy levels of the 4f^n?15d configuration.     

Ion dynamics in methylcellulose–LiBOB solid polymer electrolytes

A polymer electrolyte system comprising methylcellulose (MC) as the host polymer and lithium bis(oxalato) borate (LiBOB) as the lithium ion source has been prepared via the solution cast technique. The electrolyte with the highest conductivity of 2.79 μS cm^?1 has a composition of 75 wt% MC–25 wt% LiBOB. The mobile ion concentration (n) in this sample was estimated to be 5.70?×?10²⁰ cm^?3. A good correlation between ionic conductivity, dielectric constant, and free ion concentration has been observed. The ratio of mobile ion number density (n) at a particular temperature to the concentration n ₀ of free ions at T?=?∞ (n/n ₀) and the power law exponents (s) exhibit opposite trends when varied with salt concentration.     

The electron energy spectrum and superconducting transition temperature of strongly correlated fermions with three-center interactions

The renormalizations of the fermionic spectrum are considered within the framework of the t-J* model taking into account three-center interactions (H₍₃₎) and magnetic fluctuations. Self-consistent spin dynamics equations for strongly correlated fermions with three-center interactions were obtained to calculate quasi-spin correlators. A numerical self-consistent solution to a system of ten equations was obtained to show that, in the nearest-neighbor approximation, simultaneously including H₍₃₎ and magnetic fluctuations at n>n₁ (n₁ ≈ 0.72 for 2t/U = 0.25) caused qualitative changes in the structure of the energy spectrum. A new Van Hove singularity is then induced in the density of states, and an additional maximum appears in the T_c(n) concentration dependence of the temperature of the transition to the superconducting phase with order parameter symmetry of the d _x ²?y² type.     

Production of exotic Λ hypernuclei via mesonic beams

We study the production of neutron-rich hypernuclei _Λ ¹² Be, _Λ ¹⁶ C, and _Λ ¹⁰ Li by the (π^?, K⁺) and (K^?, π⁺) reactions in flight and treat two different mechanisms of production. The first mechanism is a two-step process with meson charge exchange (e.g., π^?p → π⁰n, π⁰p → K⁺Λ). The other mechanism is one-step production (π^?p → K⁺Σ^?) proceeding via a small Σ^? component, arising in Λ hypernuclei due to ΛN–ΣN coupling, as a doorway state. Typically, the two-step mechanism is more productive. The forward differential cross section of the ¹⁰B(π^?,K⁺) reaction is about 70 nb/sr at an incident momentum of 1.05 GeV/c. On the other hand, the one-step process can serve as a direct measurement of the Σ admixture if the two-step contribution is suppressed by a suitable choice of the reaction kinematics.     

A More Efficient Contextuality Distillation Protocol

Based on the fact that both nonlocality and contextuality are resource theories, it is natural to ask how to amplify them more efficiently. In this paper, we present a contextuality distillation protocol which produces an n-cycle box B ? B ^′ from two given n-cycle boxes B and B ^′. It works efficiently for a class of contextual n-cycle (n ≥?4) boxes which we termed as “the generalized correlated contextual n-cycle boxes”. For any two generalized correlated contextual n-cycle boxes B and B ^′, B ? B ^′ is more contextual than both B and B ^′. Moreover, they can be distilled toward to the maximally contextual box C H _n as the times of iteration goes to infinity. Among the known protocols, our protocol has the strongest approximate ability and is optimal in terms of its distillation rate. What is worth noting is that our protocol can witness a larger set of nonlocal boxes that make communication complexity trivial than the protocol in Brunner and Skrzypczyk (Phys. Rev. Lett. 102, 160403 2009), this might be helpful for exploring the problem that why quantum nonlocality is limited.