How chaotic is a state of a quantum system?

A concept related to the entropy is studied. Let A and B be two density matrices, with eigenvalues a₁, a₂,… and b₁, b₂,…, arranged in decreasing order and repeated according to multiplicity. Then A is said to be “more mixed”, or “more chaotic”, than B, if a₁?b₁, a₁+a₂?b₁+b₂,…,a₁+…+a_m?b₁+…+b_m,…; It turns out that if A is more mixed than B, then the entropy of A is larger than the entropy of B. However, more generally, let v be an arbitrary concave function, ?0, and vanishing at 0. Then, if A is more mixed than B, trv(A)?trv(B). It is shown that also the converse is true. Furthermore, a variety of other characterizations of the relation “A is more mixed than B” is obtained, and several applications to quantum statistical mechanics are given.     

Energy dependence of multiplicity in proton-nucleus collisions and models of multiparticle production

This is a continuation of our earlier investigation (Gurtuet al 1974Phys. Lett. 50 B 391) on multiparticle production in proton-nucleus collisions based on an exposure of emulsion stack to 200 GeV/c beam at the NAL. It is found that the ratioR _em = 〈n _s〉/〈n _ch〉, where 〈n _ch〉 is the charged particle multiplicity in pp-collisions, increases slowly from about 1 at 10 GeV/c to 1·6 at 68 GeV/c and attains a constant value of 1·71 ± 0·04 in the region 200 to 8000 GeV/c. Furthermore,R _em = 1·71 implies an effectiveA-dependence ofR _A =A ^0.18,i.e., a very weak dependence. Predictions ofR _em on various models are discussed and compared with the emulsion data. Data seem to favour models of hadron-nucleon collisions in which production of particles takes place through adouble step mechanism,e.g., diffractive excitation, hydrodynamical and energy flux cascade as opposed to models which envisage instantaneous production.     

Effects of low temperature irradiation with heavy ions on superconductor niobium

To study the effects of heavy ion irradiation at low temperature on type II superconductor Nb, the transition temperatureT _c , the normal state residual resistivityρ _B , the transition widthΔT _ph using oxygen ions of 25 MeV and subsequent thermal annealing were measured. The samples were held at temperatures <20 K during irradiation in a cryostat for in situ measurements. The maximum oxygen fluence was about 2·10¹⁵ cm^?2 corresponding a relatively high defect concentration. The heavy ion irradiation experiments are described. The critical temperatureT _c decreases with increasing residual resistivityρ _B . In agreement with the theory and experiments, the gap anisotropy parameter is 〈a ²〉=0.008, subsequent annealing shows a hysteresis ofT _c versusρ _B . The resistivity saturation value Δρ_BS = 2.55 μΩ cm was obtained and different recovery stages were found. Significant broadening of transition width during irradiation was observed.T _c andΔT _ph anneal to 60% in the temperature interval of (60–90) K. Oxygen induced effects as a simulation method of high neutron damage are compared with irradiation measurements using neutrons and deuterons.     

Nonstationary phenomena in Si MOSFETs in the quantum hall effects regime

We report the observation of nonstationary hysteresis phenomena in charging of Si MOSFET at a quantizing magnetic field. In these experiments (Pudalovet al 1984; Pudalov and Semenchinsky 1985) the charging currentJ _g of the capacitance gate-2D-layer was measured while sweeping of the magnetic fieldH or a gate voltageV _g at a constant rate. The numerical integration of the measured valuesJ _g with respect to time gave the dependences of change inQ _s vsV _g or vsH. At low temperatureT<1 K there arise deviations from the linear dependenceQ _s(V _g) near those integer values of Landau level fillingν=n _s/n _H=2, 4, 6, 8, 12, which correspond to the most deep minima inρ _xx and flat plateaux inρ _xy. Heren _s is the 2D electron density,n _H being Landau level degeneracy number,ρ _xx andρ _xy —the resistivity tensor components. The inherent feature of the curveQ _s(V _g) is the hysteresis: at increasingV _g the chargeQ _s is less than the equilibrium value, while at decreasingV _g the charge exceeds the equilibrium one. The maximum difference of charges at an increase and decrease ofV _g grows-rapidly at loweringT and atT=0.42 K amounts to ～10% of the full charge confined by one Landau level (n _H.e.S). It is worth to note that such behaviour ofQ _s(V _g) does not influence the values ofρ _xy (with accuracy of ～ 10^?5) and the shape ofρ _xy plateaux andρ _xx-minima. Measurements at various sweep rates dV _g/dt demonstrated that if the sweep rate is lower, the hysteresis region is narrower and the deviation of chargesQ _s from its equilibrium value is smaller. By extrapolating the dependence of hysteresis loop width on dV _g/dt, the ultimate sweep rate may be estimated, for which a hysteresis will completely disappear. Thus, for instance, atT=0.42 K andν=4 it will occur when the time interval of one Landau level fillingτ _H will be equal to 100 years. A similar hysteresis in 2D-layer charge occurs in varying magnetic field also, when the gate voltage is disconnected with the battery and hence the charge in MOSFET is maintained constant. This hysteresis loop rapidly vanishes at temperatures >1 K. The long relaxation time of a nonequilibrium charge in 2D-layer can be connected phenomenologically with small drift velocities of electrons along the potential gradient due to a small value of conductivityσ _xx. This relaxation time may be estimated asτ～C/σ _xx whereC is the electrical capacitance of MOSFET area with a nonequilibrium charge. The value ofτ～10⁹ s givesσ _xx<10 _a ^?18 Ohm^?1/□, i.e.ρ _xx<10^?11 Ohm/□. Simultaneously with nonequilibrium charge relaxation in 2D-layer there arise circular Hall currents decaying with the same rate. In conclusion, we observed and investigated nonequilibrium charging of 2D-layer in quantum Hall effect regime. To explain the phenomenon we supposed that circular Hall currents is comparable to the eddy currents excited in a superconducting ring.     

2-[2-[4-[2-[2-[1,3-Dihydro-1,1-bis(4-hydroxyphenyl)-3-oxo-5-isobenzofuranthioureidyl]ethylaminocarbonyl]ethyl]phenyl] ethylamino]-5′-N-ethylcarboxamidoadenosine (FITC-APEC): A fluorescent ligand for A2a-adenosine receptors

The fluorescein conjugate, FITC-APEC (2-[2-[4-[2-[2-[1,3-dihydro-1,1-bis(4-hydroxyphenyl)-3-oxo-5-isobenzofuranthioureidyl]ethylaminocarbonyl]ethyl] phenyl]ethylamino]-5-N-ethylcarboxamidoadenosine), is a novel ligand derived from a series of functionalized congeners that act as selective A_2a-adenosine receptor agonists. The binding of FITC-APEC to bovine striatal A_2a-adenosine receptors measured by fluorescence techniques was saturable and of a high affinity, with aB _max of 2.3±0.3 pmol/mg protein andK _D of 57±2 nM. TheK _D value estimated by fluorescence was consistent with theK _i (11±0.3 nM) obtained by competition studies with [³H]CGS 21680. Additionally, theB _max value found by FITC-APEC measurement was in agreement withB _max values obtained using radioligand binding. FITC-APEC exhibited rapid and reversible binding to bovine striatum. The potencies of chemically diverse A_2a-adenosine receptor ligands estimated by inhibition of FITC-APEC binding were in good agreement with their potencies determined using radioligand binding techniques (r=0.97,P=0.0003). FITC-APEC binding was not altered by purine derivatives that do not recognize A_2a-adenosine receptors. These findings demonstrate that the novel fluorescent ligand FITC-APEC can be used in the quantitative characterization of ligand binding to A_2a-adenosine receptors.     

On the properties of asymmetric nuclear matter

The properties of asymmetric nuclear matter withα=(ρ _n-ρ _p)/ρ≦ 0.4 are studied within the framework of the lowest order Brueckner theory, atk _F =1.35fm^?1 (ρ=0.166 fm^?3). TheK-matrix is calculated self-consistently from the Reid soft core nucleon-nucleon interaction. In the case ofρ _n ≠ρ _p theK-matrix contains a term which does not conserve the total isospin of the interacting unlike-nucleon pair. At α=0.4 the relative magnitude of this term is of the order of 1 %. The symmetry energy is found equal to 23.1 MeV.     

Universe Described by Variable Modified Chaplygin Gas with Statefinder Diagnostic in General Relativity

The universe filled with variable modified Chaplygin gas having the equation of state p=Aρ?B/ρ ^α , where 0≤α≤1, A is a positive constant and B is a positive function of the average scale factor a(t) of the universe (i.e. B=B(a)) is studied within the framework of general relativity. The new class of exact solutions of Einstein’s field equations is derived by using a time dependent deceleration parameter. The cosmic jerk parameter in our derived model is in good agreement with the recent data of astrophysical observations under appropriate condition. It is observed that the universe starts from an asymptotic Einstein static era and reaches to the ΛCDM model. So from recently developed statefinder parameters, the behavior of different stages of the universe is studied. The physical and kinematical properties of cosmological models are also discussed.     

Spectral properties of chlorines and electron transfer with their participation in the photosynthetic reaction center of photosystem II

Structural factors that provide localization of excited states and determine the properties of primary donor and acceptor of electron in the reaction center of photosystem II (PSII RC) are studied. The results of calculations using stationary and time-dependent density functional theory indicate an important role of protein environments of chlorophylls P_A, P_B, B_A, and B_B and pheophytins H_A and H_B in the area with a radius of no greater than ≤10 Å in the formation of excitonic states of PSII RC. When the neighboring elements are taken into account, the wavelength of long-wavelength Q _y transition of chlorophyll molecules is varied by about 10 nm. The effect is less developed for pheophytin molecules (Δλ ? 2 nm). The following elements strongly affect energy of the transition: His^A198 and His^D197 amino-acid residues that serve as ligands of magnesium atoms affect P_A and P_B, respectively; Met^A183 affects P_A; Met^A172 and Met^D198 affect B_A; water molecules that are located above the planes of the B_A and B_B macrocycles form H bonds with carbonyl groups; and phytol chains of P_A and P_B affect B_A, B_B, H_A, and H_B. The analysis of excitonic states, mutual positions of molecular orbitals of electron donors and acceptors, and matrix elements of electron transfer reaction shows that (i) charge separation between B_A and H_A and P_B and B_A is possible in the active A branch of cofactors of PSII RC and (ii) electron transfer is blocked at the B_B - H_B fragment in inactive B branch of PSII RC.     

Generalized Trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems

New systematic approximants are proposed for exponential functions, operators and inner derivation δ _H . Remainders of systematic approximants are evaluated explicitly, which give degrees of convergence of approximants. The first approximant corresponds to Trotter's formula [1]: exp(A+B)= \(\mathop {\lim }\limits_{n \to \infty } \) [exp(A/n) exp(B/n)] ⁿ . Some applications to physics are also discussed.     

Determination of coupling constants from superconvergence sum rules in vector meson — Vector meson scattering

Dynamical relations between masses and coupling constants have been studied using the superconvergent sum rule technique in vector meson — vector meson scattering. Unessential complications due to the spin have been removed by defining a set of 25 KSF invariant amplitudes. Commonly accepted analyticity properties and asymptotics estimated arguing along the line of unitarity then lead to superconvergent sum rules for three amplitudes. Their saturation by one-intermediate-particle contributions in the processesωρ→ ωρ, ωB→ωB andωA ₁→ωA ₁ results in a system of nine coupled equations which have been approximately solved for coupling constants and aρ-ω-B- A ₁ mass sum rule.     

Levelcrossing experiments in the first excited1 P 1 states of the alkaline earths

The hyperfine structure of the lowest¹P₁ state of²⁵Mg,⁴³Ca,⁸⁷Sr,¹³⁵Ba and¹³⁷Ba have been measured by the level-crossing and anticrossing technique. The magnetic dipole and electric quadrupole coupling constants determined by these measurements are²⁵Mg(3s3p¹P₁):A=? 7.7(5) MHz; 16 MHz>B>0 MHz,⁴³Ca(4s4p¹P₁):A=? 15.3(4) MHz; ¦B¦<12 MHz,⁸⁷Sr (5s5p¹P₁:A=? 3.4(4) MHz;B=39(4) MHz,¹³⁵Ba(6s6p¹P₁):A=? 97.5(1.0) MHz;B=31(9)MHz,¹³⁷Ba(6s6p¹P₁):A=?109.2(1.2) MHz;B=51(12)MHz. The results have been compared with the predictions of the Breit-Wills theory of the two-electron hyperfine structure using the experimental data on the³P states. Large discrepancies have been observed which are due to different radial wave functions of thes andp electron in the triplet and singlet system. This effect has been taken into account by fitting the data with the aid of two additional parameters. That this procedure is justified is shown by an analysis of the fine structure splitting, the life times, and the isotopic shifts in thesp configurations of group II elements.     

Determining theCP-violating phase γ

The weak phase γ is conventionally probed by theB _s→ρ ⁰ mode. The predicted rate is tiny. Even if aB _s→ρ ⁰ K _s rate difference could be established, it would not be clear that sin 2γ had been measured, because amplitudes with other weak phases may contribute significantly. Non-CP eigenstates, such asB _s →D _s ^± K ^?, have a two-fold advantage overB _s→ρ ⁰ K _s. Their rates are orders of magnitude above that forB _s→ρ ⁰ K _s, and they probe theCP-violating phase γ, without any contamination from other weak phases. Detailed time-dependent studies of non-CP eigenstates remove possible final-state phases and extract the weak phase γ.     

Minimal number of operators for observability ofN-level quantum systems

This paper discusses the minimal numbern _min of operatorsA ₁,...,A _n , whose expectation values at some instants determine the statistical state of anN-level quantum system. We assume that the macroscopic information about the system in question is given by the mean values Tr[ρ(t _j )A _i ]=m _i (t _j ) ofn self-adjoint operatorsA ₁,...,A _n at some instantst ₁<t ₂t _s , wheres ²?1.     

The two particle-phonon multiplet πh 11/2 νf 7/2 × 3− and higher-lying four-nucleon yrast states in the doubly-odd nucleus 146 63 Eu83

The isotopes¹⁵B,¹⁸C,^19,20N,^34,35Al and³⁹P have been produced as projectile-like fragments from the interaction of a⁸⁶Kr beam of 45 MeV/u from GANIL with a¹⁸¹Ta target. Separated by the 0° magnetic analyser LISE, the nuclei are identified by means of aΔE- E semiconductor telescope. It is surrounded, in a geometry close to 4π, by a thin plastic scintillator (NE 102) and a large volume liquid scintillator (NE 213) for the detection of betas and neutrons, respectively, from the decay of the implanted nuclei. By observation of theβ-delayed neutrons, the half-livesT _1/2 and neutron emission probabilitiesP _n have been measured. TheT _1/2 of¹⁸C,²⁰N,³⁵Al,³⁹P and P_n of¹⁸C,^19,20N,^34,35Al and³⁹P are determined for the first time. For the isotopes¹⁷C,^36,37Si and³⁸P upper limits of P_n are deduced.     

Analysis of experiments on the measurement of the pion electromagnetic formfactor

We analyse the experiments [1–3] on the measurement of the pion electromagnetic formfactor in the time-like and space-like region using an expression with correct analytical properties and with the asymptotics predicted by QCD. The best fit values for the physical quantities (1) electromagnetic radius of the pion:r _π ² =0.466±0.002 fm², (2) the mass and width of the ρ (770) and the ρ′ (1600) meson:m _ρ=768±1 MeV,Г _ρ=138±1 MeV,m _ρ′=1546±26 MeV,Г _ρ'=620±60 MeV; (3) the residuesg _ρ m _ρ ² =0.676±0.003,g _ρ′ m _ρ′ ² =?(0.644±0.009); (4) the ππ-scattering lengtha ₁ ¹ =(0.1±0.01)m _π ^?3 .     

Hopping conductivity of Ni-doped p-CdSb in strong magnetic fields

Magnetoresistance (MR) of oriented single crystals of the anisotropic semiconductor p-CdSb doped with 2 at% of Ni is investigated between T=1.5 and 300 K in transversal pulsed magnetic fields up to B=30 T. In fields B∼4-15 T at T below 4.2 K, the resistivity obeys the law ln ρ∼η[B?(B)]^1/2 with ?(B)=a(0)/a(B), where a is the carrier localization radius and parameter η depends on a(0), on the acceptor concentration N_A and on the direction of the magnetic field with respect to the crystallographic axes, but does not depend on T. Such behavior gives evidence for MR realized by hopping charge transfer over the nearest-neighbor sites in strong magnetic field. The analysis of the experimental data yields the values of η, agreeing with calculated ones within an error of 10%, taking into account the effects of the anisotropy of the acceptor states and of the explicit dependence of a(B) due to the increase in the activation energy of shallow acceptors in magnetic field and the sensitivity of the metal-insulator transition to B.     

Functional properties of quantum logics

A quantum logic is defined as a setL of functions from the set of all statesS into [0, 1] satisfying the orthogonality postulate: for any sequencea ₁,a ₂, ... of members ofL satisfyinga _i+a _j≤1 fori≠j there isb∈L such thatb+a ₁+a ₂+...=1. Every logicL is in a natural way an orthomodular σ-orthocomplemented partially ordered set (L, ≤, ′) with members ofS inducing a full set of measures onL. It is shown that a logicL is quite full if and only if (L,≤,′) is isomorphic to an orthocomplemented set lattice of subsets ofS. Sufficient conditions are given in order that a quite full logic be representable in the set of projection quadratic formsf(u)=(Pu, u) on a complex Hilbert space, or in the set of trace functionsf(A)=Trace (AP) generated by projectionsP, where the domain off is the set of non-negative self-adjoint trace operators of trace 1 in a complex Hilbert space.     

Mechanism by which a single water molecule affects primary charge separation kinetics in a bacterial photosynthetic reaction center of Rhodobacter sphaeroides

Using quantum-chemical methods, we have studied the role played by water molecules W-A and W-B that are bound by hydrogen bonds to accessory bacteriochlorophyll molecules B _A and B _B in the process of primary charge separation in the reaction center of Rhodobacter Sphaeroides. We have found that the occurrence of a rotational mode of the W-A molecule at 32 cm^?1 and/or its harmonics in stimulated emission of an electron donor P* and the dynamics of population of the states P⁺B _A ^? and P⁺H _A ^? may be related to the structural heterogeneity of the reaction center and the existence of a conformation in which the W-A molecule is predominantly involved in one hydrogen bond (with BA). Based on the calculated redox potentials B _A and P, it has been shown that the appearance of the W-A molecule in the reaction center reduces the energy of the P⁺B _A ^? state by ??600 cm^?1. This is somewhat smaller than the influence of the amino-acid residue Tyr^M210 (??870 cm^?1) and correlates well with a substantial decrease in the electron transfer rate in mutant forms of reaction centers GM203L (which do not contain W-A molecules) and YM210F (in which Tyr^M210 is replaced with Phe). The data obtained allow us to suggest that rotation of the water molecule with a fixed position of its H atom that is involved in a hydrogen bond with the keto carbonyl group of B _A is initiated due to the charge separation between the halves of special pair P and the formation of the state P _A ⁺ P _B ^? . The large effect of this rotation on the kinetics of population of the states P⁺B _A ^? and P⁺H _A ^? after the excitation of P is quite consistent with its influence on the energy of the state P⁺B _A ^? .     

Ecological interaction and phylogeny, studying functionality on composed networks

We study a class of composed networks that are formed by two tree networks, T_P and T_A, whose end points touch each other through a bipartite network B_PA. We explore this network using a functional approach. We are interested in how much the topology, or the structure, of T_X (X=A or P) determines the links of B_PA. This composed structure is a useful model in evolutionary biology, where T_P and T_A are the phylogenetic trees of plants and animals that interact in an ecological community. We make use of ecological networks of dispersion of fruits, which are formed by frugivorous animals and plants with fruits; the animals, usually birds, eat fruits and disperse their seeds. We analyse how the phylogeny of T_X determines or is correlated with B_PA using a Monte Carlo approach. We use the phylogenetic distance among elements that interact with a given species to construct an index κ that quantifies the influence of T_X over B_PA. The algorithm is based on the assumption that interaction matrices that follows a phylogeny of T_X have a total phylogenetic distance smaller than the average distance of an ensemble of Monte Carlo realisations. We find that the effect of phylogeny of animal species is more pronounced in the ecological matrix than plant phylogeny.     

Distinguishability ofSU(2)×U(1)×U′(1) andSO(10) gauge models from the Weinberg-Salam model

The predictions ofSU(2)×U(1)×U′(1) andSO(10) gauge models for the asymmetry parametersA-,B-,C _L andC _R in the deep inelastic scattering of polarized electrons and positrons by unpolarized protons and deuterons are compared with those calculated in the Weinberg Salam model for different values ofy. The model based on,SU(2)×U(1)×U′(1) group has been found almost indistinguishable from the Weinberg Salam model with regard to the parametersA-,B- andC _L (except forB- in the region 0≦y≦0.2) althoughC _R exhibits marked distinguishability. TheSO(10) model, for certain choice of its model parameters, can be distinguished from the Weinberg Salam model through measurement of the asymmetry parameters for different values ofy.