Scaling Transform and Stretched States in Quantum Mechanics

We consider the Husimi Q(q, p)-functions which are quantum quasiprobability distributions on the phase space. It is known that, under a scaling transform (q; p) → (?q; ?p), the Husimi function of any physical state is converted into a function which is also the Husimi function of some physical state. More precisely, it has been proved that, if Q(q, p) is the Husimi function, the function ?² Q(?q; ?p) is also the Husimi function. We call a state with the Husimi function ?² Q(?q; ?p) the stretched state and investigate the properties of the stretched Fock states. These states can be obtained as a result of applying the scaling transform to the Fock states of the harmonic oscillator. The harmonic-oscillator Fock states are pure states, but the stretched Fock states are mixed states. We find the density matrices of stretched Fock states in an explicit form. Their structure can be described with the help of negative binomial distributions. We present the graphs of distributions of negative binomial coefficients for different stretched Fock states and show the von Neumann entropy of the simplest stretched Fock state.     

Der Grundzustand der Urfermionen im Gitterraum

The energy of the Dirac sea of interacting urfermions in a lattice space withZ ³ points is calculated using Heisenberg's Hamiltonian and a two-particle approximation which is a variational calculation with the test function ¦?〉=e ⁱη¦D ₀〉; ¦D ₀〉 is the Dirac sea without interaction,η=(ψ ^° ψ) a bilinear expression of the urfermion creation and annihilation operators. The same result is obtained by a BCS-calculation. Beyond that, we derive simple lower and upper bounds for the energy. Excited states are considered consisting of a particle-antiparticle pair with the energyE=2√ω ²+M ². The massM and the interaction constantW are connected by the equation (4W)^?1=Z ^?3∑(ω ²+M ²)^?1/2. For usual masses 4W～√Z/1 (1 a nuclear length). Methods are discussed to improve the results.     

Special features of the <Emphasis Type="Italic">K</Emphasis> = 0 channel in nuclear fission

The opinion that the K = 0 fission channel is completely closed if the spin J and the parity π of the nucleus undergoing fission do not satisfy the condition (?1) ^J = π is widespread. On the basis of a detailed analysis of quantum numbers characterizing the rotational states of deformed nuclei, it is shown that this opinion is erroneous. In fact, the K = 0 channel may be partly open. Its suppression is caused by special features of fission barriers in the state being considered. It is also shown that factors that suppress the K = 0channel may exist even in states characterized by J and π values such that they satisfy the condition (?1) ^J = π. More precise information about the contribution of the K = 0 channel may be obtained by measuring the hexadecapole component of the angular distribution of fragments originating from the slow-neutron-induced fission of aligned nuclei.     

New emission spectrum of the TeO molecule

The spectrum of Tellurium monoxide as excited in a heavy current arc run by a 2000 volt D.C. generator was studied in the visible and ultraviolet regions. Photographs of the spectrum revealed many new bands in the regionλ 6200 toλ 3300, which are clearly degraded to longer wavelengths. Some of the bands in the regionλ 3800 toλ 3300 were identified with those of the system in the regionλ 3800 toλ 3060 (here designated as system,B-X) observed and analysed byChoong Shin Piaw. The analysis of theB-X system was extended to include some of the new bands uptoλ 4500. In addition to those assigned toB-X system, a number of new bands in the regionλ 5000 toλ 3500 constitute another system designated asA-X system. The analysis of this system has led to the following quantum formula for the band heads.v=27835+408 (v′+1/2)?4·0(v′+1/2)² ?796 (v″+1/2)+3·5 (v″+1/2)². The lower state of the two systems is common and is identified as the ground state of the TeO molecule. Bands in the regionλ 6200 to 5000 were analysed as belonging to another brief system. This system appears to arise from a transition between two escited states of the TeO molecule. The nature and properties of electronic terms responsible for the observed electronic states of the TeO molecule were discussed along with those of the related molecules O₂, SO, and SeO from considerations of electron configurations.     

Monte Carlo Study of the Effect of Initial States and Structural Defects on Nonequilibrium Critical Behavior of the Three-Dimensional Ising Model

The effect of various initial magnetizations m₀ and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization m₀ These subclasses correspond to the system evolution from the high-temperature (m₀ = 0) and low-temperature (m₀ = 1) initial states with limit FDRs characteristic of these states.     

Untersuchungen an Zinn und Indium-Zinn-Legierungen im supraleitenden Zustand mit Hilfe des Mössbauer-Effekts

The recoilless nuclear resonance absorption of the 23.8 keV-γ-line of¹¹⁹Sn was measured in a transmission experiment. The measurements were performed with tin and tin-indium alloys, as a function of temperature above and below the transition points of superconductivity (2 ?K<T<6 ?K). The Lamb-Moessbauer-factors, the Debye-temperatures, and an upper limit of the quadrupol interaction were calculated from the data. Within the experimental accuracy there is no evidence for a difference of the quantities mentioned above in the normal and super-conducting state down toT=0.6T _c . The data for the isomeric shift yield a constants-electron density within the nucleus in the two states within 2·10^?4 down toT=0.8T _c .     

Zur Frage des Grundzustandes im Tb I-Spektrum

In an atomic beam magnetic resonance experiment on Tb¹⁵⁹ ΔF=0 transitions in several hfs-levels of thermally excited fine structure states have been observed. Detailed analysis of data showed twoJ=15/2 states, oneJ=13/2, oneJ=11/2, and, probably, oneJ=9/2 state to be present. For these levelsg _J-values are given. It was concluded that the ground state of neutral terbium is 4f ⁸ 5d 6s ^{2 8} G _15/2. The 4f ⁹ 6s ^{2 6} H _15/2-level lies not more than 1000 cm^?1 higher.     

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.     

Measurement of the spin structure function <Emphasis Type="Italic">g</Emphasis><Subscript>1</Subscript> at HERMES

New, preliminary results are presented for the deuteron structure function g ₁ ^d , where the kinematic range has been extended to 0.0021<x<0.85 and Q ²>0.1 GeV², to include 7 new data points at low x with respect to previously released results. Within the present statistics, the structure function ratio g ₁ ^d /F ₁ ^d is found to be independent of Q ².     

Measurement of the Lamb shift 42S1/2-42P1/2 of the helium ion

Helium ions were produced in then=4 states by electron collisions with ground state atoms, resulting in simultaneous ionization and excitation. Dipole transitions between the Zeeman levels of the states 4² S _1/2 and 4² P _1/2 were induced by a microwave electric field. The intensity of the emitted Fowlerα line 4686 Å, corresponding to transitions from then=4 to then=3 states was then reduced by about 3%. From the measurements, a value of the Lamb shiftδ=1751±25 MHz was obtained, compared with the theoretical valueδ=1768.23±0.55 MHz, and the results ofLea, Leventhal andLamb ofδ=1765±20 MHz.     

Potential of quasielastic meson knockout from a nucleon by high-energy electrons and pions for studying the structure of exotic excited states of a final-state baryon

The possibility of studying q ⁴ \(\bar q\) exotic baryon states by means of N(e, e’M)B reactions proceeding via an extremely simple mechanism and involving the quasielastic knockout of various mesons from a nucleon by electrons of energy in the few-GeV region is considered as a development of the previous investigations of our group. A quark microscopic formalism based on the cluster model of q ⁴ \(\bar q\) states, which makes it possible to determine momentum distributions of mesons in various channels of B → N + M virtual decays (in principle, these distributions can be compared with experimental data), is expounded by considering the example of the pentaquark (B = Θ⁺). The decay widths of the q ⁴ \(\bar q\) baryon states being discussed are governed by the degree of separation of quark clusters (this is a parameter of the model used). The electroproduction cross sections prove to be small because of kinematical constraints requiring that physically admissible values of the momentum ‖k‖ of the virtual meson M lie in the region where relevant amplitudes are suppressed substantially by form factors in pentaquark vertices. In particular, N (e, e′π ^±)B reactions involving pion knockout furnish direct information about nonstrange components of baryon B; however, the expected cross sections for such reactions are an order of magnitude smaller than their counterparts for analogous reactions leading to the production of a pentaquark Θ⁺. Because of the smallness of the electroproduction cross sections, it is reasonable to consider the production of a pentaquark and other q ⁴ \(\bar q\) exotic states in reactions characterized by quasielastic kinematics and initiated by pions of energy in the range between about 1 and 5 GeV and in similar stripping and pickup nuclear reactions.     

Generalized Drude scattering rate from the memory function formalism: an independent verification of the Sharapov-Carbotte result

An explicit perturbative computation of the Mori’s memory function was performed by Götzeand Wölfle (GW) to calculate generalized Drude scattering (GDS) rate for the case ofelectron-impurity and electron-phonon scattering in metals by assuming constant electronicdensity of states at the Fermi energy. In the present investigation, we go beyond thisassumption and extend the GW formalism to the case in which there is a gap around theFermi surface in electron density of states. The resulting GDS is compared with a recentone by Sharapov and Carbotte (SC) obtained through a different route. We find goodagreement between the two at finite frequencies. However, we find discrepancies in the dcscattering rate. These are due to a crucial assumption made in SC namely ω ? | Σ(?+ ω) ? Σ^?(?)|. No such high frequency assumption is made in the memory functionbased technique.     

Precision measurements of optical excitation functions for the cadmium atom

An experimental setup and a technique for the investigation of excitation of atoms by ultramonoenergetic electrons are described. The optical excitation functions are given for 14 spectral lines of the cadmium atom originating from the n ¹ S ₀, 5¹ P ₁, n ³ S ₁, 5³ P ₁, and n ³ D _j levels. More than 150 specific features are found in the energy dependences of the effective excitation cross sections measured from the excitation threshold to 16 eV. The most pronounced of these features are in good agreement with the fine structure observed previously. The main mechanisms of the initial-level population, namely, the direct transition of an electron from the ground atomic state to the initial level of a spectral line, the population of the initial levels due to the decay of short-lived states of a negative ion, and the cascade population, are separated. In the excitation functions of the lines originating from the n ¹ S ₀ levels, in the energy range from 10.9 to 12.4 eV, we observed for the first time an effect of postcollision interactions of emitted and scattered electrons in the vicinity of the thresholds of four autoionization states of the cadmium atom.     

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 \(R_{e^ + e^ - } \).     

Charmonium 2007: New experimental results

The most important experimental results in charmonium physics in the energy region above the threshold for open-charm production that were obtained in recent years are surveyed. The first measurements of the exclusive cross sections for e ⁺ e ^? → D \(\bar D\), D \(\bar D\)*, and D* \(\bar D\)* processes are discussed along with the discovered decay ψ(4415) → \(\bar D_2^* \)(2460). The properties of charmonium-like states, including the group of states Y (4260), Y (4325), and Y (4660) with quantum numbers of J ^PC = 1^??; the X(3940) and X(4160) states discovered in the process of double charmonium production in e ⁺ e ^? annihilation; and the X(3872), Y(3940), and Z ^±(4430) states found in B-meson decays, are presented.     

Efficient Nonlocal <Emphasis Type="Italic">M</Emphasis>-Control and <Emphasis Type="Italic">N</Emphasis>-Target Controlled Unitary Gate Using Non-symmetric GHZ States

Efficient local implementation of a nonlocal M-control and N-target controlled unitary gate is considered. We first show that with the assistance of two non-symmetric qubit⁽¹⁾-qutrit^(N) Greenberger-Horne-Zeilinger (GHZ) states, a nonlocal 2-control and N-target controlled unitary gate can be constructed from 2 local two-qubit CNOT gates, 2N local two-qutrit conditional SWAP gates, N local qutrit-qubit controlled unitary gates, and 2N single-qutrit gates. At each target node, the two third levels of the two GHZ target qutrits are used to expose one and only one initial computational state to the local qutrit-qubit controlled unitary gate, instead of being used to hide certain states from the conditional dynamics. This scheme can be generalized straightforwardly to implement a higher-order nonlocal M-control and N-target controlled unitary gate by using M non-symmetric qubit⁽¹⁾-qutrit^(N) GHZ states as quantum channels. Neither the number of the additional levels of each GHZ target particle nor that of single-qutrit gates needs to increase with M. For certain realistic physical systems, the total gate time may be reduced compared with that required in previous schemes.     

Structure of the Gamow-Teller resonance in <Superscript>58</Superscript>Cu studied via the proton-and <Emphasis Type="Italic">γ</Emphasis>-decay measurements

The Gamow-Teller (GT) states in ⁵⁸Cu have been studied by ⁵⁸Ni(³He, t + p) and ⁵⁸Ni(³He, t + γ) coincidence experiments at E(³He)=450 MeV and θ=0°. Proton emissions from the GT states in ⁵⁸Cu to the hole states in ⁵⁷Ni have been observed with solid-state detectors in coincidence with high-energy tritons measured with a magnetic spectrometer. For the first time, γ-ray emissions from the excited states in ⁵⁸Cu and in ⁵⁷Ni, following the ⁵⁸Ni(³He, t + p) reaction at intermediate energies, have also been observed in coincidence with tritons. The wave functions of the T=1 and T=2 GT states with the f ₇ ^2/?1 neutron-hole configuration are inferred to be strongly coupled to 2p-2h configurations, making fragmented GT strengths in ⁵⁸Cu.     

Study of postcollision interaction upon electron-impact excitation of the magnesium atom

The excitation functions of the spectral lines of the MgI principal series in the VUV region (for the principal quantum numbers n = 4–7) are studied in experiments on collisions of electrons with magnesium atoms in the range of electron energies from the excitation thresholds to ～25 eV. The scatter in the electron energy was ～0.7 eV. Above the ionization potential, some singularities attributed to autodetachment and autoionization states were found in excitation functions. Shifts to higher energies with increasing n, which take place for the most significant singularity (maximum) relative to the autoionization state 3p4s ¹ P ₁ ^o , are explained by the important role played by this state in the population of the initial levels through the mechanism of post-collision interaction. The theoretical analysis of the experimental results based on the classical model of the postcollision interaction estimates the width of the autoionization state as ～0.45 eV, which is close to the data of other researchers.     

Finite-size scaling of correlation functions in finite systems

We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional finite system of size L,the correlation function can be written as the product of|r|~(-(d-2+η))and a finite-size scaling function of the variables r/L and tL~(1/ν),where t=(T-T_c)/T_c,ηis the critical exponent of correlation function,andνis the critical exponent of correlation length.The correlation function only has a sigificant directional dependence when|r|is compariable to L.We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations.We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponentη.