Mehrfache Dispersionsrelationen für kurzreichweitige Potentiale,die sich nicht durch eine Überlagerung von Yukawa-Potentialen darstellen lassen

A triple dispersion relation is derived for the functionf(s, t, u) which becomes the scattering amplitudef(s, t) foru=4s?t. Besides the usual conditions which are needed for deriving a dispersion relation ins, the potential must decrease faster than exponentially at infinity. For this class of potentialsf(s, t, u) has essential singularities fort→∞ andu→∞. It is shown thatf(s, t, u) is bounded in the physical sheets of two independent Riemannian surfaces which are constructed by conformal mappings of thet- and theu-plane. In the new variables the conditions for the existence of dispersion relations are fulfilled.     

Ground state pairing correlation competes in the doped triangular lattice Hubbard model

By using the constrained path quantum Monte carlo method, we study the ground state paring correlations in the t ? U ? V Hubbard model on the triangular lattice. It is shown that pairings with various symmetries dominate in different electron filling regions. The pairing correlation with fn-wave symmetry dominates over other pairings around half fillings, and as the electron filling decreases away from the half filling, the d + id-wave pairing correlation tends to dominate. As the electron filling is bellow the Van Hove singularity, the f-wave pairing dominates. These crossovers are due to the interplay of electronic correlation and geometric frustration, associating with the competition between the antiferromagnetic correlations and ferromagnetic fluctuations. Our findings reveal the possible magnetic origin of superconductivity, and also provide useful information for the understanding of superconductivity in Na _x CoO₂·H₂O and the organic compounds.     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

Complex Wavelet Transform of the Two-mode Quantum States

By employing the bipartite entangled state representation and the technique of integration within an ordered product of operators, the classical complex wavelet transform of a complex signal function can be recast to a matrix element of the squeezing-displacing operator U ₂(μ, σ) between the mother wavelet vector 〈ψ| and the two-mode quantum state vector |f〉 to be transformed. 〈ψ|U ₂(μ, σ)|f〉 can be considered as the spectrum for analyzing the two-mode quantum state |f〉. In this way, for some typical two-mode quantum states, such as two-mode coherent state and two-mode Fock state, we derive the complex wavelet transform spectrum and carry out the numerical calculation. This kind of wavelet-transform spectrum can be used to recognize quantum states.     

Low-energyπK-scattering

A self-consistent calculation of thes- andp-wave resonance inπK-scattering is attempted using as input the exchanged resonances themselves and the exchange of a?-meson. While this approximation to the left-hand cut fails in thes-wave problem it produces ap-wave resonance but for a much too strong?-coupling. Position and width depend very sensitively on the inelastic region. Suppressing this region by a subtraction at threshold the subtraction constant can be adjusted to yield the observed position. The corresponding width is close to the experimental values for reasonable?-coupling.     

Meson Effect in the Proto Neutron Star PSR J0348+0432

The effect of mesons f ₀(975) (named as f), ?(1020) (named as ?) and δ on the moment of inertia of the PNS PSR J0348+0432 is examined in the framework of the relativistic mean field theory considering the baryon octet. It is found that the energy density ε and pressure p will increase considering the mesons δ whereas will decrease as the mesons f and ? being considered. When the mesons f,? and δ are considered, the energy density and pressure will all decrease. It is also found that the contribution of mesons f, ? and δ to the central energy density is only the central energy density’s 0.06 ～0.6% whereas the contribution of mesons f, ? and δ to the central pressure is the central pressure’s 4 ～7%. For the radius, it will decrease when the contributions of mesons f, ? and δ are considered. The moment of inertia I will increase considering the mesons δ whereas will decrease as the mesons f and ? being considered. When the mesons f, ? and δ are all considered, the moment of inertia will decrease. It is found that the contribution of mesons f and ? to moment of inertia is 4 ～9 times larger than that of mesons δ. Our results show that the mesons f, ? and δ contribute to the moment of inertia’s 2 ～5%.     

Kinetic Theory and Lax Equations for Shock Clustering and Burgers Turbulence

We study shock statistics in the scalar conservation law ? _t u+? _x f(u)=0, x∈?, t>0, with a convex flux f and spatially random initial data. We show that the Markov property (in x) is preserved for a large class of random initial data (Markov processes with downward jumps and derivatives of Lévy processes with downward jumps). The kinetics of shock clustering is then described completely by an evolution equation for the generator of the Markov process u(x,t), x∈?. We present four distinct derivations for this evolution equation, and show that it takes the form of a Lax pair. The Lax equation admits a spectral parameter as in Manakov (Funct. Anal. Appl. 10:328–329, 1976), and has remarkable exact solutions for Burgers equation (f(u)=u ²/2). This suggests the kinetic equations of shock clustering are completely integrable.     

Symmetry energy of the nucleus in the relativistic Thomas–Fermi approach with density-dependent parameters

We introduce an inhomogeneous term, f(t,x), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions f(t,x) which depend nontrivially on both t and x, we find that there is just one symmetry. If f is a function of only x, there are three symmetries with the algebra s l(2,R). When f is a function of only t, there are five symmetries with the algebra s l(2,R) ⊕ _s 2A ₁. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.     

Wavelet analysis of data in particle physics: Vector mesons in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilation

The advantages that wavelet analysis (WA) provides for resolving the structures in experimental data are demonstrated. Due to good scaling properties of the wavelets, one can consider data with various resolutions, which allows the resonances to be separated from the background and from each other. The WA is much less sensitive to noise than any other analysis and allows the role of statistical errors to be substantially reduced. The WA is applied to the e ⁺ e ^? annihilation into hadron states with quantum numbers of ρ and ω mesons, and to p-wave ππ scattering. Distinguishing the resonance structures from an experimental noise and the background allows us to make more reliable conclusions about the ρ′ and ω′ states. The WA yields a useful set of starting conditions for analysis of ω′ states with the multiresonance Breit-Wigner method preserving unitarity in the case of overlapping resonances. We also apply the WA for the ratio \(R_{e^ + e^ - } \).     

Signal velocity in oscillator arrays

We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. After describing necessary and sufficient conditions for asymptotic stability, we derive expressions for the phase velocity of propagation of disturbances in velocity through this system. We show that the high frequencies exhibit damping, which implies existence of well-defined signal velocitiesc₊ > 0 and c_? < 0 such that low frequency disturbances travel through the flock as f₊(x ? c₊t) in the direction of increasing agent numbers and f_?(x ? c_?t) in the other.     

Quantum Discord Behaviors in Two Qubits Spin Squeezing Model with Intrinsic Decoherence

By taking into account the intrinsic decoherence and the external magnetic field, quantum discord(QD) behaviors in two-qubit spin squeezing model are investigated in detail. It is found that the magnitude of quantum discord is strongly dependent on the initial states, the squeezing interaction μ, the magnetic field Ω and the purity r of initial states. With t → ∞, one can obtain the steady quantum discord (SQD) value, the environmental decoherence cannot entirely destroy the quantum correlation. Based on the analysis of the SQD, the conditions about the existence of SQD are obtained with different initial states. Varying the parameters μ, Ω and r not only can weaken the effects of decoherence but also can improve the magnitude of QD and SQD. The effects of the parameters μ and Ω on the QD and SQD display so different and complicated features that one cannot get an uniform law about them, while the values of QD and SQD are improved with increasing r. Properly tuning the parameters μ, Ω and r, one can obtain a larger value of QD or SQD.     

Role of qubit-cavity entanglement for switching dynamics of quantum interfaces in superconductor metamaterials

We study quantum effects of strong driving field applied to dissipative hybrid qubit-cavity system which are relevant for a realization of quantum gates in superconducting quantum metamaterials. We demonstrate that effects of strong and non-stationary drivings have significantly quantum nature and cannot be treated by means of mean-field approximation. This is shown from a comparison of steady state solution of the standard Maxwell–Bloch equations and numerical solution of Lindblad equation on a density matrix. We show that mean-field approach provides very good agreement with the density matrix solution at not very strong drivings f < f* but at f > f* a growing value of quantum correlations between fluctuations in qubit and photon sectors changes a behavior of the system. We show that in regime of non-adiabatic switching on of the driving such a quantum correlations influence a dynamics of qubit and photons even at weak f.     

Neutron single-particle structure of <Superscript>48</Superscript>Ca, <Superscript>50</Superscript>Ti, <Superscript>52</Superscript>Cr, <Superscript>54</Superscript>Fe,and <Superscript>56</Superscript>Ni nuclei

The change in the neutron single-particle structure of (1f?2p)-shell magic nuclei near the Fermi energy with an increase in the number of protons in the 1f _7/2 subshell from 0 for ⁴⁸Ca to 8 for ⁵⁶Ni has been investigated. Good agreement of the experimental and estimated values of the single-particle energies E _nlj of the bound states of neutrons in these nuclei with the results of calculations within the dispersive optical model is obtained.     

Einfluß der Pion-Pion-Wechselwirkung auf Pion-Nukleon-Streuphasen

The isospin dependent part of theS-wave pion-nucleon amplitude is calculated according to the CGLN approach, but recoil and projection on the partial waves are treated exactly. Then the difference against the experimental data is approximately a constant up to 100 MeV and amounts to 1/3 of the total value. It is shown, that at low energies the main corrections of the CGLN equations are taken into account by a subtraction of theπ+π→?+\(\overline \Re \),J=I=1 amplitudesf _± ¹ (t) as proposed byMandelstam andFrazer. Calculations have been done forS, P andD pion-nucleon amplitudes. The main result is a prediction of theS-wave amplitude obtained without adjusting free parameters up to 100 MeV. The relations of this method to the equations derived byBowcock, Cottingham andLurié according to the Cini-Fubini approach are discussed.     

On the derivation of the Boltzmann-Landau equation from the quantum mechanical hierarchy

The general solution of the equation of motion for the quantum mechanical distribu tion functionf ₂(r ₁ P ₁,r ₂ p ₂;t)in the two particle space is given by means of the Schrödinger scattering functions. A special initial condition leads to the usual Boltzmann equation plus density correction terms, which depend on the scattering matrixt(p′,p). In the long wavelength limit and in lowest order oft(p′,p) the Landau corrections to the simple Boltzmann streaming part are obtained.     

Background Independent Quantum Mechanics,Metric of Quantum States,and Gravity: A Comprehensive Perspective

This paper presents a comprehensive perspective of the metric of quantum states with a focus on the geometry in the background independent quantum mechanics. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the quantum state space and Kähler manifold. The metric of quantum states in the classical configuration space with the pseudo-Riemannian signature and its possible applications are explored. On contrary to the common perception that a metric for quantum state can yield a natural metric in the configuration space when the limit ?→0, we obtain the metric of quantum states in the configuration space without imposing the limiting condition ?→0. Here Planck’s constant ? is absorbed in the quantity like Bohr radii \(\frac{1}{2mZ\alpha}\sim a_{0}\). While exploring the metric structures associated with Hydrogen like atom, we witness another interesting finding that the invariant lengths appear in the multiple of Bohr’s radii as: ds ²=a ₀ ² (? Ψ)².     

Adaptive photodetectors based on charge gratings in the problems of frequency-modulated optical signal detection

Nonstationary photovoltage excitation by frequency-modulated light in an adaptive photodetector based on GaAs is studied. To observe the effect, the crystal is exposed to light beams with the relative frequency shift Δf(t). Linear frequency modulation Δf(t) = At is used in the experiments. As a result of such illumination, a pulsed electrical signal is induced in the crystal. The pulse appears at the deceleration of the interference pattern motion, and its duration is controlled by the frequency variation rate A and the time of the charge grating formation. The possibility of using the effect in the systems for measuring velocities and accelerations of moving objects is shown.     

Search for superheavy hydrogen isotopes <Superscript>4,5</Superscript>H in reactions of pion absorption by <Superscript>10,11</Superscript>B nuclei

The results of searching for production of superheavy hydrogen isotopes ^4,5H in reactions of absorption of stopped π^? mesons by ^10,11B nuclei are reported. A peak near 3 MeV was observed in the missing mass spectra measured in the reactions ^10,11B(π^?, t⁴He)X, ¹⁰B(π^?, d⁴He)X, and ¹⁰B(π^?, t³He)X. A structure caused by two ⁵H states with the resonance energies E _R = 5.2 and 10.4 MeV was observed in the missing mass spectra measured in the reactions ¹¹B(π^?, d⁴He)X, ¹¹B(π^?, t³He)X, and ¹⁰B(π^?, d³He)X.     

Glueballs of the <Emphasis Type="Italic">f</Emphasis><Subscript>0</Subscript> and <Emphasis Type="Italic">f</Emphasis><Subscript>2</Subscript> families,observed in processes with Pseudoscalar mesons

Within the approach based on analyticity and unitarity, the experimental data on the isoscalar S and D waves of the ππ → ππ, K\(\bar K\), ηη, ηη′ processes have been jointly analyzed for studying the status and quantum chromodynamics nature of the f ₀ andf ₂ mesons. Assignment of scalar and tensor mesons to lower nonets is proposed. Two states (f ₀ (1500) and f ₂ (2000)) are interpreted as glueballs.