Asymptotic Heat Kernel Expansion in the Semi-Classical Limit

Let H_(^h/2p) = (^h/_2p)²L +V{H_\hbar = \hbar^{2}L +V}, where L is a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold and V is a symmetric endomorphism field. We derive an asymptotic expansion for the heat kernel of H_(^h/2p){H_\hbar} as (^h/_2p) \searrow 0{\hbar \searrow 0}. As a consequence we get an asymptotic expansion for the quantum partition function and we see that it is asymptotic to the classical partition function. Moreover, we show how to bound the quantum partition function for positive (^h/_2p){\hbar} by the classical partition function.     

{\hbar}-adic Quantum Vertex Algebras and Their Modules

This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we study notions of (^h/_2p){\hbar}-adic nonlocal vertex algebra and (^h/_2p){\hbar}-adic (weak) quantum vertex algebra, slightly generalizing Etingof-Kazhdan’s notion of quantum vertex operator algebra. For any topologically free \mathbb C[[(^h/_2p)]]{{\mathbb C}\lbrack\lbrack{\hbar}\rbrack\rbrack}-module W, we study (^h/_2p){\hbar}-adically compatible subsets and (^h/_2p){\hbar}-adically S{\mathcal{S}}-local subsets of (End W)[[x, x ⁻¹]]. We prove that any (^h/_2p){\hbar}-adically compatible subset generates an (^h/_2p){\hbar}-adic nonlocal vertex algebra with W as a module and that any (^h/_2p){\hbar}-adically S{\mathcal{S}}-local subset generates an (^h/_2p){\hbar}-adic weak quantum vertex algebra with W as a module. A general construction theorem of (^h/_2p){\hbar}-adic nonlocal vertex algebras and (^h/_2p){\hbar}-adic quantum vertex algebras is obtained. As an application we associate the centrally extended double Yangian of \mathfrak s\mathfrak l₂{{\mathfrak s}{\mathfrak l}_{2}} to (^h/_2p){\hbar}-adic quantum vertex algebras.     

A semi-classical trace formula for Schrödinger operators

LetS _?=??Δ+V, withV smooth. If 0<E ²V(x), the spectrum ofS _? nearE ² consists (for ? small) of finitely-many eigenvalues,λ _j (?). We study the asymptotic distribution of these eigenvalues aboutE ² as ?→0; we obtain semi-classical asymptotics for $$\sum\limits_j {f\left( {\frac{{\sqrt {\lambda _j (\hbar )} - E}}{\hbar }} \right)} $$ with \(\hat f \in C_0^\infty \) , in terms of the periodic classical trajectories on the energy surface \(B_E = \left\{ {\left| \xi \right|^2 + V(x) = E^2 } \right\}\) . This in turn gives Weyl-type estimates for the counting function \(\# \left\{ {j;\left| {\sqrt {\lambda _j (\hbar )} - E} \right| \leqq c\hbar } \right\}\) . We make a detailed analysis of the case when the flow onB _E is periodic.     

Magnetoexciton absorption in coupled quantum wells

A Mott exciton in coupled quantum wells in a transverse magnetic field H is considered. An expression for the exciton spectrum in an arbitrary magnetic field for large separations D between quantum wells containing an electron (e) and a hole (h) is given. The exciton spectrum in a strong magnetic field for different Landau levels at arbitrary D has been calculated. Changes in the parameter D/l, where is the magnetic length, cause rearrangement of the magnetoexciton dispersion curves ℰ(P), where P is the conserved “magnetic” momentum, which is a function of the separation between the electron and hole in the plane of the quantum wells. Off-center (“roton”) extrema occur only for D/l,<(D/l)_cr, where (D/l)_cr is a function of the exciton quantum numbers n and m. The magnetoexciton effective mass in states with magnetic quantum number m=0 monotonically increases with H and D, while in states with m≠0 it is a nonmonotonic function of D/l. The probability of generating an exciton in coupled quantum wells increases with H. Absorption of electromagnetic radiation due to transitions between excitonic levels in coupled quantum wells is discussed. For an exciton containing a heavy hole the oscillator strengths increase with H and the oscillator strengths decrease. Zh. éksp. Teor. Fiz. 112, 1791–1808 (November 1997)     

Black Hole Radiation and Volume Statistical Entropy

The simplest possible equation for Hawking radiation and other black hole radiated power is derived in terms of black hole density, ρ . Black hole density also leads to the simplest possible model of a gas of elementary constituents confined inside a gravitational bottle of Schwarzchild radius at tremendous pressure, which yields identically the same functional dependence as the traditional black hole entropy S _bh∝ (kAc ³)/ℏ G. Variations of S _bh can be obtained which depend on the occupancy of phase space cells. A relation is derived between the constituent momenta and the black hole radius R _H, p = which is similar tothe Compton wavelength relation.     

Magnetic-impurity states of electron in two-dimensional semiconductor structures

Electron states on an attractive center of small-radius r _c ? l (l = $\sqrt {\frac{{c\hbar }}{{eH}}} $ is the magnetic length) located in a two-dimensional structure are investigated in a uniform magnetic field H applied perpendicularly to the structure surface. The spectrum of magnetic-impurity (MI) particle states with an arbitrary moment projection on the direction H for Landau bands 0 ≤ N < l ²/r _c ² is derived in the approximation that mixing of Landau levels is weak. The dependence of the electron energy states on magnetic field, the layer thickness, and the impurity position are studied. It is shown that dimension lowering leads to a qualitatively different spectrum of MI states compared to the three-dimensional case [1]. A comparison of the obtained binding energy of the D ^? center with experimental data is performed.     

The Essence of Operators’ Weyl Ordering Scheme and New Operator Identities for Converting Q−P Ordering to Weyl Ordering

We find new operator formulas for converting Q?P and P?Q ordering to Weyl ordering, where Q and P are the coordinate and momentum operator. In this way we reveal the essence of operators’ Weyl ordering scheme, e.g., Weyl ordered operator polynomial ${_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}}$ , $$\begin{aligned} {_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}} =&\sum_{l=0}^{\min (m,n)} \biggl( \frac{-i\hbar }{2} \biggr) ^{l}l!\binom{m}{l}\binom{n}{l}Q^{m-l}P^{n-l} \\ =& \biggl( \frac{\hbar }{2} \biggr) ^{ ( m+n ) /2}i^{n}H_{m,n} \biggl( \frac{\sqrt{2}Q}{\sqrt{\hbar }},\frac{-i\sqrt{2}P}{\sqrt{\hbar }} \biggr) \bigg|_{Q_{\mathrm{before}}P} \end{aligned}$$ where ${}_{:}^{:}$ ${}_{:}^{:}$ denotes the Weyl ordering symbol, and H _m,n is the two-variable Hermite polynomial. This helps us to know the Weyl ordering more intuitively.     

Formation of a narrow baryon resonance with positive strangeness in K + collisions with Xe nuclei

The data on the charge-exchange reaction K ⁺Xe → K ⁰ pXe′, obtained with the bubble chamber DIANA, are reanalyzed using increased statistics and updated selections. Our previous evidence for formation of a narrow pK ⁰ resonance with mass near 1538 MeV is confirmed. The statistical significance of the signal reaches some 8 (6) standard deviations when estimated as $ {S \mathord{\left/ {\vphantom {S {\sqrt B \left( {{S \mathord{\left/ {\vphantom {S {\sqrt {B + S} }}} \right. \kern-0em} {\sqrt {B + S} }}} \right)}}} \right. \kern-0em} {\sqrt B \left( {{S \mathord{\left/ {\vphantom {S {\sqrt {B + S} }}} \right. \kern-0em} {\sqrt {B + S} }}} \right)}} $ . The mass and intrinsic width of the Θ⁺ baryon are measured as m = 1538 ± 2 MeV and Γ = 0.39 ± 0.10 MeV.     

Equilibrium points of the tilted perfect fluid Bianchi VI<Subscript><Emphasis Type="Italic">h</Emphasis></Subscript> state space

We present the full set of evolution equations for the spatially homogeneous cosmologies of type VI_h filled with a tilted perfect fluid and we provide the corresponding equilibrium points of the resulting dynamical state space. It is found that only when the group parameter satisfies h > –1 a self-similar solution exists. In particular we show that for h > – there exists a self-similar equilibrium point provided that whereas for h < – the state parameter belongs to the interval (1, . This family of new exact self-similar solutions belongs to the subclass n = 0 having non-zero vorticity. In both cases the equilibrium points have a six-dimensional stable manifold and may act as future attractors at least for the models satisfying n = 0. Also we give the exact form of the self-similar metrics in terms of the state and group parameter. As an illustrative example we provide the explicit form of the corresponding self-similar radiation model ( = ), parametrised by the group parameter h. Finally we show that there are no tilted self-similar models of type III and irrotational models of type VI_h.     

Electrodynamic Model of Initiation and Extinction of Emitting Sites Interacting Together in Cold Cathode Spots (Type A) in Air

From an electrodynamic and simple quantum-mechanical point of view a model is proposed which explains the phenomena of minimum arc current as well as the formation and extinction of tiny emitting sites interacting together in cold cathode spots (called type A) on the base of a specific coupling between the tunnelling “average” electrons and the metal bulk phonon field. The model seems to be especially applicable to such experimental conditions where typical trumpetlike microcraters with pronounced rims with diameters in the range 0.5—1 μm are left by microspot ensembles on the cathode surface. The model yields emitting-site lifetimes, currents, current densities and radii in the order of τ_p^s ? \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {3M/m} $\end{document} τ₀ ? 10^?11 sec, I_min = 4π ? \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {n/\mu _0 m} $\end{document}? 0.4 A, j = nev_s ? 4 · 10¹³ A/m² and r_a ? 2c/ω_Pl ? 30 nm (τ_p^s…lifetime of short wave phonons, M … atom mass, m … electron mass, τ₀ … mean free collision time of Fermi electrons at room temperature, n … conduction electron density in the metal bulk, v_s … metal bulk sound velocity, c … light velocity, ω_Pl … metal bulk plasma frequency (values for copper). The lifetime and the interaction diameter of an emitting site (event) ensemble are derived to τ_p^l ?(M/m) τ_p ? 3 nsec and Λ_p^l = ν_sτ_p^l ? 10 μ (τ_pΛ_p^l … lifetime and mean free path of long wave phonons).     

Deformation Quasi-Hopf Algebras of Non-semisimple Type from Cochain Twists

Given a symmetric decomposition ${\mathfrak g=\mathfrak h\oplus \mathfrak p}Given a symmetric decomposition \mathfrak g=\mathfrak h?\mathfrak p{\mathfrak g=\mathfrak h\oplus \mathfrak p} of a semisimple Lie algebra \mathfrak g{\mathfrak g}, we define the notion of a \mathfrak p{\mathfrak p}-contractible quantized universal enveloping algebra (QUEA): for these QUEAs the contraction \mathfrak g?\mathfrak g₀{\mathfrak g\rightarrow\mathfrak g_0} making \mathfrak p{\mathfrak p} abelian is nonsingular and yields a QUEA of \mathfrak g₀{\mathfrak g_0}. For a certain class of symmetric decompositions, we prove, by refining cohomological arguments due to Drinfel’d, that every QUEA of \mathfrak g₀{\mathfrak g_0} so obtained is isomorphic to a cochain twist of the undeformed envelope U(\mathfrak g₀){\mathcal U(\mathfrak g_0)}. To do so we introduce the \mathfrak p{\mathfrak p}-contractible Chevalley-Eilenberg complex and prove, for this class of symmetric decompositions, a version of Whitehead’s lemma for this complex. By virtue of the existence of the cochain twist, there exist triangular quasi-Hopf algebras based on these contracted QUEAs and, in the approach due to Beggs and Majid, the dual quantized coordinate algebras admit quasi-associative differential calculi of classical dimensions. As examples, we consider κ-Poincaré in 3 and 4 spacetime dimensions.     

Influence of dephasing on the entanglement teleportation via a two-qubit Heisenberg XYZ system

We study the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system in the presence of intrinsic decoherence. The usefulness of such a system for performance of the quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation protocol T₁\mathcal{T}_1 is also investigated. The results depend on the initial conditions and the parameters of the system. The roles of system parameters such as the inhomogeneity of the magnetic field b and the spin-orbit interaction parameter D, in entanglement dynamics and fidelity of teleportation, are studied for both product and maximally entangled initial states of the resource. We show that for the product and maximally entangled initial states, increasing D amplifies the effects of dephasing and hence decreases the asymptotic entanglement and fidelity of the teleportation. For a product initial state and specific interval of the magnetic field B, the asymptotic entanglement and hence the fidelity of teleportation can be improved by increasing B. The XY and XYZ Heisenberg systems provide a minimal resource entanglement, required for realizing efficient teleportation. Also, in the absence of the magnetic field, the degree of entanglement is preserved for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.. The same is true for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right., in the absence of spin-orbit interaction D and the inhomogeneity parameter b. Therefore, it is possible to perform quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation T₁\mathcal{T}_1, with perfect quality, by choosing a proper set of parameters and employing one of these maximally entangled robust states as the initial state of the resource.     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-Restriction Bounds for Eigenfunctions Along Curves in the Quantum Completely Integrable Case

We show that for a quantum completely integrable system in two dimensions, the L ²-normalized joint eigenfunctions of the commuting semiclassical pseudodifferential operators satisfy restriction bounds of the form for generic curves γ on the surface. We also prove that the maximal restriction bounds of Burq-Gerard-Tzvetkov [BGT] are generically attained for certain exceptional subsequences of eigenfunctions. The author was supported by a William Dawson Fellowship and NSERC Grant OGP0170280.     

Absorption of solar radiation by solar neutrinos

We calculate the absorption probability of photons radiated from the surface of the Sun by a left-handed neutrino with definite mass and a typical momentum for which we choose |p₁| = 0.2 MeV, producing a heavier right-handed antineutrino. Considering the two transitions and we obtain the two oscillation lengths L₁₂ = 4960.8 m, L₂₃ = 198.4 m, the two absorption probabilities P₁₂^abs. = 2.5 x 10^-67, P₂₃^abs. = 1.2 x 10^-58 and the two absorption ranges au, au, using a neutrino mass differences of meV, meV and associated transition dipole moments. We collect all necessary theoretical ingredients, i.e. neutrino mass and mixing scheme, induced electromagnetic transition dipole moments, quadratic charged lepton mass asymmetries and their interdependence.Received: 4 November 2003, Revised: 23 March 2004, Published online: 5 May 2004     

Stability of One-Electron Molecules in the Brown–Ravenhall Model

In appropriate units, the Brown-Ravenhall Hamiltonian for a system of 1 electron relativistic molecules with K fixed nuclei having charge and position Zk, R_k, k=1,2, ?,Kk=1,2, \ldots,K, is of the form \bB_1,K = L₊ ( D₀ + aV_c) L₊ \bB_{1,K}= \Lambda_+ \bigl( D_0 + \alpha V_c\bigr) \Lambda_+ , where v₊ is the projection onto the positive spectral subspace of the free Dirac operator D₀ and V_c = - ?_k=1^K \fracaZ_k\lmod \bx-R_k \rmod + ?_{k < l,  k,l=1}^K \fracaZ_k Z_l\lmod R_k-R_l \rmod V_c= - \sum_{k=1}^K \frac{\alpha Z_k}{\lmod \bx-R_k \rmod} + \sum_{kZ_k ￡ aZ_c = \frac2p/2 + 2/ p\alpha Z_k \leq \alpha Z_c = \frac{2}{\pi /2 + 2/ \pi}, k=1,2, ?,Kk=1,2, \ldots,K, and a ￡ \frac2 p(p²+4)(2+?{1+ p/2})\alpha \leq \frac{2 \pi}{(\pi^2+4)(2+\sqrt{1+ \pi /2})}, \ \bB_1,K 3 \operatornameconst \cdotp K\bB_{1,K} \geq \operatorname{const} \cdotp K.     

Nonlinear Reformulation of Heisenberg's Dynamics

A structural similarity between Classical Mechanics (CM) and Quantum Mechanics (QM) was revealed by P.A.M. Dirac in terms of Lie Algebras: while in CM the dynamics is determined by the Lie algebra of Poisson brackets on the manifold of scalar fields for classical position/momentum observables Q/P, QM evolves (in Heisenberg's picture) according to the formally similar Lie algebra of commutator brackets of the corresponding operators:

Quenching of the E1 strength in <Superscript>149</Superscript>Nd

Lifetime measurements of excited states in ¹⁴⁹Nd have been performed using the advanced time-delayed b \beta g \gamma g \gamma(t) method. Half-lives of 14 excited states in ¹⁴⁹Nd have been determined for the first time or measured with higher precision. Twelve new g \gamma -lines and 5 new levels have been introduced into the decay scheme of ¹⁴⁹Pr based on results of the g \gamma g \gamma coincidence measurements. Reduced transition probabilities have been determined for 40 g \gamma -transitions in ¹⁴⁹Nd . Configuration assignments for 6 rotational bands in ¹⁴⁹Nd are proposed. Enhanced E1 transitions indicate that the ground-state band and the band built on the 332.9keV level constitute a pair of the K^p = 5/2^±\ensuremath K^{\pi} = 5/2^{\pm} parity doublet bands. Potential energy surfaces on the (b₂,b₃)\ensuremath (\beta_{2},\beta_{3}) -plane have been calculated for the lowest single quasi-particle configurations in ¹⁴⁹Nd using the Strutinski method and the axially deformed Woods-Saxon potential. The predicted occurrence of the octupole-deformed K = 5/2 configuration is in agreement with experiment. Unexpectedly low |D₀|\ensuremath \vert D_0\vert values obtained for the K^p = 5/2^±\ensuremath K^{\pi} = 5/2^{\pm} parity doublet bands may result from cancellation between the proton and neutron shell correction contributions to |D₀|\ensuremath \vert D_0\vert .     

Small-x behaviour of the polarized photon structure function F_3^\gamma(x,Q^2)

We study the small-x behaviour of the polarized photon structure function F₃^gF_3^{\gamma}, measuring the gluon transversity distribution, in the leading logarithmic approximation of perturbative QCD. There are two contributions, both arising from two-gluon exchange. The leading contribution to small-x is related to the BFKL pomeron and behaves like x^-1-w₂x^{-1-\omega_2}, w₂ = O(a_S)\omega_2 ={\cal O}(\alpha_S). The other contribution includes in particular the ones summed by the DGLAP equation and behaves like x^1-w₀(+)x^{1-\omega_0^{(+)}}, w₀⁽⁺⁾ = O(?{a_S})\omega_0^{(+)} = {\cal O}(\sqrt{\alpha_S}).     

标定X射线粉末照相指数的新图解法,推广于正交晶系与单斜晶系

本文叙述了X射线粉末照相指数的新图解法在正交晶系与单斜晶系中的应用。由于在这两个晶系中所须确定的原始参量多于2,所以不可能像在四方晶系或六角晶系的情形,一次用图解法在平面上求得晶胞的所有初基参量。本文分析了正交晶系与单斜晶系的一些特殊情形,可用新图解法对粉末照相上一些特殊情形下的衍射线指数进行标定。为方便起见,图解法是尽量用线坐标进行的。