Surfing and generation of cosmic rays in relativistic shock waves

We consider the problem of cosmic-ray generation through the surfing acceleration of charged particles in relativistic magnetosonic shock waves (the branch of fast magnetic sound) propagating in magnetized space plasmas. The dependence of the particle surfing acceleration efficiency on the angle θ _Bn between the normal to the shock front plane and the magnetic field vector in the plasma upstream of the shock is analyzed in detail. We show that for angles satisfying the condition χ = βΓ tan θ _Bn ⩾ 1, where β = U/c, Γ = (1 − β)^{2 −1/2}, U is the shock velocity, and c is the speed of light, the particles can theoretically be accelerated through surfing for an unlimited time and can gain an unlimited energy. For angles satisfying the condition χ < 1, the kinetic energy ℰ of the particles is limited by ℰ = 2mc ²χ²/(1 − χ²) (m is the particle rest mass). Our main conclusion is that the generation of cosmic rays through the surfing acceleration of particles in the front of a relativistic shock wave for Γ ≫ 1 is also efficient when the angle θ _Bn is very small, i.e., it differs significantly from a right angle. Estimates for the energies of particles accelerated through surfing in relativistic jets are provided.     

New Quantum Private Comparison Protocol Using χ-Type State

We present a new quantum private comparison protocol based on the four-particle χ-type states. Different from previous protocols using the four-particle χ-type states, our protocol have some advantages. Without using the entangled character, we only need to prepare one type of χ-type state and N χ-type states. And we use the Pauli local unitary operation on particles to encode the information and to extract information by measurement. We also discuss that our protocol can withstand all various kinds of outside attacks and participant attacks.     

Qudit-type entanglement of continuous variables via weak cross-Kerr non linearity

We propose a protocol for creating arbitrary qudit state (including entangled states) with arbitrary dimensionality in continuous variable system using weak cross-Kerr nonlinearity, linear beamsplitters, detectors not resolving photon numbers, and sources of coherent states. The equation for unique determination of the used coherent states amplitudes is found. The protocol is applicable for creating entangled states at distances of 100 km using cross-Kerr nonlinearity χ ≥ χ _min ≃ 0.01 and optical fiber quantum channel.     

Chiral symmetry and charmonium decays to two pseudoscalars

We apply hard pion Chiral Perturbation Theory to charmonium decays to ππ, KK and ηη. We first discuss why we expect to be able to provide results for the chiral logarithms in χc0 and χc2 decays to two pseudoscalars while for the decays from J/ψ, ψ(nS) and χc1 no simple prediction is possible. The leading chiral logarithm turns out to be absent for χc0, χc2 → PP. This result is true for all fully chiral singlet states of spin zero and two.     

Finite-size scaling of the level compressibility at the Anderson transition

We compute the number level variance Σ ₂ and the level compressibility χ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With N, W, and L denoting, respectively, linear system size, disorder strength, and the average number of levels in units of the mean level spacing, we find that both χ(N, W) and the integrated Σ ₂ obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder given by a box distribution of width W/2. We compute the critical exponent as ν≈ 1.45±0.12 and the critical disorder as W _c≈ 8.59±0.05 in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find χ≈ 0.28±0.06 at the metal-insulator transition in very close agreement with previous results. Received 1st November 2001 and Received in final form 8 March 2002 Published online 6 June 2002     

Quantum Fisher Information in Two-Qubit Pure States

In terms of quantum Fisher information (QFI), a quantity χ ² was introduced by Pezzé and Smerzi (Phys. Rev. Lett. 102 100401, 2009). They pointed out that the inequality χ ²<1 was a sufficient condition for multiparticle entanglement. For the two-qubit symmetric states, we found that the inequality χ ²<1 is a necessary and sufficient condition for entanglement and spin squeezing, and that χ ² is equal to the second kind of spin squeezing parameter x₂²\xi _{2}^{2}. For the two-qubit asymmetric states, it is only a sufficient condition. In order to make it a necessary and sufficient condition, we extend the concept of the QFI and χ ², and generalize the relations among the entanglement measurement, the spin squeezing parameters and χ ² in symmetric pure states to arbitrary pure states.     

Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia

Earlier by the authors (Yad. Fiz. 70, 68 (2007)), the bƃ states were treated in the framework of the spectral integral equation, together with simultaneous calculations of radiative decays of the considered bottomonia. In the present paper, such a study is carried out for the charmonium states. We reconstruct the interaction in the c-c sector on the basis of the data for the charmonium levels with J _PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺, 1⁺⁻ and radiative transitions ψ(2S) → γχ _c0(1P), γχ _c1(1P), γχ _c2(1P), γχ _c(1S) and χ _c0(1P), χ _c1(1P), χ _c2(1P) → γJ/ψ. The c-c levels and their wave functions are calculated for the radial excitations with n ≤ 6. Also, we determine the c-c component of the photon wave function using the e ⁺ e ⁻-annihilation data: e ⁺ e ⁻ → J/ψ(3097), ψ(3686), ψ(3770), ψ(4040), ψ(4160), ψ(4415) and perform the calculations of the partial widths of the two-photon decays for the n = 1 states η _c0(1S), χ _c0(1P), χ _c2(1P) → γγ and n = 2 states η _c0(2S) → γγ, χ _c0(2P) → γγ. We discuss the status of the recently observed c-c states X(3872) and Y(3941): according to our results, the X(3872) can be either χ _c1(2P) or η _c2(1D), while Y(3941) is χ _c2(2P). The text was submitted by the authors in English.     

Elimination of Rotational Degrees of Freedom in Expansion Methods for Three Nucleons

 Euler angles determining rotations of a system as a whole are conveniently separated in three-particle basis functions. Analytic integration of matrix elements over Euler angles is done in a general form. Results for the Euler angle integrated matrix elements of a realistic NN interaction are listed. The partial wave decomposition of correlated three-body states is considered. E-mail address: efros@mbslab.kiae.ru Received May 4, 2002; accepted July 26, 2002     

Search for theχ′ c charmonium states as solution to the CDFψ′ puzzle

The efforts of Roy-Sridhar-Close-Cho-Wise-Trivedi to resolve the CDFψ′ anomaly with cascades from above-thresholdχ′ _c states require well defined signatures [a small total width and a large branching fraction forχ′ _cJ →γ+ψ′] for the solution to be viable. Here we estimate the production of such states from BR(B→χ′ _cJ +X)BR(χ′ _cJ →γψ′) andγγ production ofχ′ _c2 at CLEO II, and comment on the feasibility of testing the hypothesis in terms of current experimental capabilities.     

Central exclusive quarkonium production with tagged forward protons at RHIC

We study the Central Exclusive Production (CEP) of χ _cJ and η _c mesons at RHIC in proton–proton collisions. We consider the χ _cJ →J/ψ + γ decay channels and, recalling that the J _z =0 suppression of the J=1,2 states can be compensated by their larger branchings to J/ψ + γ, present predictions of rates and distributions for χ _c(0,1,2) production. Particular attention is paid to the impact of p _⊥ cuts applied to the outgoing protons, which can influence the relative rates significantly. The distribution in the azimuthal angle difference between the outgoing protons and the proton p_^²p_{\perp}^{2} is also studied, and shown to depend sensitively on the spin and parity of the centrally produced meson, as well as being affected by the soft-survival factors, S ². Two- and four-body decays, which are particularly relevant for χ _c0 production, are also considered. We show that in the two-body case, backgrounds from ‘direct’ QCD production based on both perturbative and non-perturbative models are expected to be under control.     

Quantum Key Distribution Using a <Emphasis Type="Italic">χ</Emphasis>-Type State

By swapping the entanglement of χ-type state, we propose a quantum key distribution protocol, in which only Alice needs to prepare χ-type states and transmit a particle sequence. Both Alice and Bob need to perform χ-type state measurements.     

The potts glass in uniform and random fields: a monte carlo investigation

As a simple model of an anisotropic orientational glass with short range forces, the 3-state Potts model on the simple cubic lattice with nearest neighbor interactions drawn from a Gaussian distribution is considered. With Monte Carlo methods we study the response of the system to a uniform “field” which favors one of the states. This is motivated by experiments which apply stress that favors one molecular orientation of the quadrupolar glass. The responsem to that fieldh=H/k _BT is analyzed in terms of an expansionm= χ₁ h+χ₁ h ²+χ₁ h ³+..., where χ₁ is the linear susceptibility, and χ₂,χ₁₃ are nonlinear susceptibilities. Unlike the case of spin glasses, where the spin inversion symmetry of the system in the absence of fields implies χ₂≡0,χ₂ is nonzero here and diverges to −∞ at the zero temperature transition of the model, while χ₃ diverges to +∞ as in spin glasses. At inifinite temperature, however, χ₁=1/3, χ₂=1/18 and χ₃=-1/54, i.e. the nonlinear susceptibilities have a different sign as at low temperature. In contrast, a random field does not induce a uniform order parameterm but only a glass order parameterq. The temperature dependence of this glass order parameterq(T) shows for intermediate field strength order parameterq(T) shows for intermediate field strength a maximum of the slopedq(T)/dT very similar to corresponding experiments.     

Quark-Antiquark states and their radiative transitions in terms of the spectral integral equation: Bottomonia

In the framework of the spectral integral equation, we consider the states and their radiative transitions. We reconstruct the interaction on the basis of data for the levels of the bottomonium states with J ^PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺ as well as the data for the radiative transitions γ (3S) → _γχbJ(2P) and γ(2S) → _γχbJ(1P) with J = 0, 1, 2. We calculate bottomonium levels with the radial quantum numbers n ≤ 6, their wave functions, and corresponding radiative transitions. The ratios Br[_χbJ(2P) → _γγ(2S)]/Br[_χbJ(2P) → _γγ(1S)] for J = 0, 1, 2 are found to be in agreement with data. We determine the component of the photon wave function using the data for the e ⁺ e ⁻ annihilation, e ⁺ e ⁻ → γ(9460), γ(10 023), γ(10 036), γ(10 580), γ(10 865), γ(11 019), and predict partial widths of the two-photon decays ηb0 → γγ, χb0 → γγ, χb2 → γγ for the radial excitation states below the threshold (n ≤ 3). The text was submitted by the authors in English.     

Level Density of the Hénon-Heiles System Above the Critical Barrier Energy

We discuss the coarse-grained level density of the Hénon-Heiles system above the barrier energy, where the system is nearly chaotic. We use periodic orbit theory to approximate its oscillating part semiclassically via Gutzwiller’s semiclassical trace formula (extended by uniform approximations for the contributions of bifurcating orbits). Including only a few stable and unstable orbits, we reproduce the quantum-mechanical density of states very accurately. We also present a perturbative calculation of the stabilities of two infinite series of orbits (R_n and L_m), emanating from the shortest librating straight-line orbit (A) in a bifurcation cascade just below the barrier, which at the barrier have two common asymptotic Lyapunov exponents χ_R and χ_L.     

Spatial distribution of transition radiation of relativistic particles in the dihedral angle formed by perfectly conductive planes

Spatial distributions of transition radiation intensity of particles entering the dihedral angle and escaping from it are calculated. It was shown that radiation of escaping charge at any opening of the dihedral angle ?? is concentrated near the motion direction. If the particle enters the angle, the radiation distribution is defined by the opening angle. At opening angles ?? = ??/n, radiation is concentrated near the direction of actual charge motion when n is an even number and near the direction of image charge motion when n is an odd number. At other opening angles, the spatial distribution of entering particle radiation has two maxima whose positions are defined by the injection angle.     

Peculiarities of the spectral-angular distribution of transition radiation from a relativistic particle in a dihedral angle

The spatial distributions of transition radiation from relativistic particles entering and exiting the edge of a dihedral angle formed by perfectly conducting flat surfaces have been investigated. The angular distributions of the radiation intensity in dihedral angles with various opening angles have been calculated. The angular distributions of forward radiation (when the particle exits the dihedral angle) and backward radiation (when the particle enters the dihedral angle) are shown to differ significantly.     

The molecular structures and electron distributions of the 1,8-bis-(dimethylamino)-naphthalenes,studied by density functional and ab initio MP2 calculations

The equilibrium structure of 1,8-bis-(dimethylamino)-naphthalene (DMAN), has been investigated in some detail; only one minimum energy conformer was found, although a saddle point, close to the structure of a previously claimed second conformer (J. Am. Chem. Soc., 120, 4840 (1998)), was also identified. Alternative apparent minima are attributed to artefacts when small bases are used. Equilibrium structures of members of the DMAN series with chloro-, bromo-, nitro- and methoxy-substituents in the ortho(2,7-) and para(4,5-) positions, as well as 4-nitro-DMAN were also determined, and compared with crystallographic and previous theoretical data. There are close correlations between calculated and observed values for bond lengths, angles and dihedral angles across the known compounds, and this enables additional correlation with other members of the series where no experimental data so far exists. The MP2 and DFT methods used, with a triple zeta basis set including polarization (TZVP), lead to very similar results but the dihedral angles in particular show more variation. Substituent effects on the bond lengths and angles in the ring geometry are relatively small, and the intrinsic pattern of short αβ-bonds in the naphthalene system is largely preserved, but the C₃C₄ bond is shorter than that for C₁C₂. Steric effects arising from interaction of 1,8- and 2,7-substituents on the naphthalene ring leads to significant twisting of the naphthalene skeleton. In addition, considerable in-plane and out-of-plane bending of the substituents from the naphthalene ring system is apparent. The effect of adjacent substituents upon the dihedral angle between the dimethylamino-groups and the ring is also apparent. The ground state molecular electronic properties have been determined and compared with experiment. The electron distribution in the B3LYP methods lead to markedly higher dipole moments than the MP2 ones, and the latter are regarded as more reliable.     

Bilinear optical susceptibilities of potassium dihydrogen phosphate and of III–V,II–VI and I–VII semiconductors

The approximate orbital-approach of Jha and Bloembergen is used to calculate the non-dispersive part of the bilinear optical susceptibility,χ ⁽²⁾, for various compounds. Using bonding and antibonding states of the molecular orbital theory it is shown thatχ ⁽²⁾ satisfies a simple relation in terms of other measurable physical quantities. This relation is used to calculateχ ⁽²⁾ for various III–V, II–VI and I–VII semiconductors, both with cubic zinc blende structure and with hexagonal wurtzite structure. The same procedure is used to obtainχ ⁽²⁾ for potassium dihydrogen phosphate (KDP). The calculated values are compared with the experimentally observed values and it is found that the present model gives excellent results for II–VI compounds and for KDP.     

A Kind Tripartite Entangled State Representation and?Its Application in Quantum Teleportation

We discuss entanglement for a tripartite system by setting up a new state vector representation |p,χ ₁,χ ₂〉 in three-mode Fock space. The Schmidt decomposition of |p,χ ₁,χ ₂〉 is presented and its application in teleporting a bipartite entangled state or a two-mode squeezed state to a pair of receivers is analyzed.     

The phase diagram of (NH4I)x(KI)1−x

The χ,T phase diagram of (NH₄I)_x(KI)_1−x has been determined using neutron diffraction experiments and dielectric spectroscopy. At low temperatures and with decreasing χ, the sequence γ, β, ε and glass phase has been detected. The critical concentration χ_c≈0.55 separates the glassy phase with frozen-in orientational disorder from the ε phase which reveals long-range orientational order. Close to χ_c our experiments reveal evidence for two subsequent glass transitions.