On Strong Superadditivity of the Entanglement of Formation

We employ a basic formalism from convex analysis to show a simple relation between the entanglement of formation E_F and the conjugate function E^* of the entanglement function E()=S(Tr_A). We then consider the conjectured strong superadditivity of the entanglement of formation E_F()E_F(_I)+E_F(_II), where _I and _II are the reductions of to the different Hilbert space copies, and prove that it is equivalent with subadditivity of E^*. Furthermore, we show that strong superadditivity would follow from multiplicativity of the maximal channel output purity for quantum filtering operations, when purity is measured by Schatten p-norms for p tending to 1.     

Total neutron multiplicities as a measure of the violence in heavy ion reactions

Energy spectra and multiplicities of neutrons from the reaction system 838 MeV³²S projectiles on¹⁹⁷Au have been measured in coincidence with binary fragmentations. Neutron detection was performed simultaneously in a 4 scintillator sphere and by time-of-flight. The linear momentum transfer (LMT) and the excitation energyE _CN ^* are deduced with the folding angle technique. Neutron multiplicities are compared for consistency and discussed as a measure of LMT andE _CN ^* . The saturation ofM ₄ (E _CN ^* ) beyondE _CN ^* 400 MeV seen for several systems of high fissility (x0.8) is attributed to the spreading of the folding angle distribution and the increasing competition of charged particle evaporation.     

Hyperthermal surface-collisions of water cluster cations

Size-selected, protonated water cluster cations (H₂O)_nH⁺, 4 n 32, are scattered at normal incidence from the surface of a diamond-coated silicon wafer at collision energies 0 E _coll 500 eV. The size distribution of collision-induced fragment-ions and the ion yield of scattered particles are analyzed, using a secondary time-of-flight mass spectrometer, as a function of the cluster size, n, and the collision energy, E _coll. Even at low impact energies only very small fragment-ions can be detected, with a maximum fragment size of 35% of the colliding parent cluster ions. For clusters consisting of more than 10 molecules, the protonated water dimer (H₂O)₂H⁺ becomes the predominant fragment-ion. The total charge survival yield obeys a nonlinear increase with cluster size; for the largest clusters investigated, more than 35% of the impacting ions survive the surface collision in the cationic charge state.     

Long-Time tails in a random diffusion model

Letw = {w(x)xZ^d} be a positive random field with i.i.d. distribution. Given its realization, letX _t be the position at timet of a particle starting at the origin and performing a simple random walk with jump rate w^–1(X_t). The processX={X _t:t0} combined withw on a common probability space is an example of random walk in random environment. We consider the quantities _t =(d/dt) E (X _t ² –M ^–1 t and _t(w) = (d/dt)E_w(X _t ² – M^– 1t). Here E_w. is expectation overX at fixedw and E = E_w (dw) is the expectation over bothX andw. We prove the following long-time tail results: (1) lim_t t^d/2_t= V²M^d/2–3(d/2)^d/2 and (2) lim_t t^d/4 _st(w)= Z_s weakly in path space, with {Z_s:s>0} the Gaussian process with EZ_s=0 and EZ_rZ_s= V²M^d/2–4(d)^d/2 (r + s)^–d/2. HereM and V² are the mean and variance of w(0) under . The main surprise is that fixingw changes the power of the long-time tail fromd/2 tod/4. Since , with ₀ the stationary measure for the environment process, our result (1) exhibits a long-time tail in an equilibrium autocorrelation function.     

Damping of second sound in the critical dynamics of liquid helium belowT λ

We calculate toO(=4 –d) the effect of the small ratiow ^* of the relaxation rates of the order parameter and the entropy on the damping of second sound in the hydrodynamic regime of liquid helium belowT . Forw ^* 1 we find a partial reduction of the previous discrepancy between theory and experiment on the amplitude of second sound damping.On leave from Universität Linz, Austria     

Heat transfer in unsteady MHD oscillatory flow

Heat transfer in unsteady MHD channel flow (of an incompressible viscous and electrically conducting fluid) under oscillatory pressure gradient when the channel surfaces are conducting and moving with time-dependent velocities has been analysed. The velocity, magnetic field and temperature distributions have been obtained and their numerical results are shown graphically.Symbols u velocity - H _o applied magnetic field - H _x induced magnetic field - T temperature - T ₁ ^* ,T ₂ ^* temperatures of the upper and lower planes - density - p pressure - kinematic viscosity - magnetic diffusivity - electrical conductivity of the fluid - A ^* characteristic velocity - L characteristic length - _e magnetic permeability of the fluid - C _p specific heat - coefficient of viscosity - k thermal conductivity - ₁, ₂ permeabilities of the planes - ₁, ₂ conductivities of the planes - ₁, ₂ conductance ratios of the planes - Pr Prandtl number (=C _p /k) - E Eckert number - M Hartmann number (= _e H _o L/) - R _e Reynolds number (=LA ^*/) - R _m magnetic Reynolds number (= _e LA ^*) - S Pr.E(=S)     

Instability of layered quantum liquids: 4. Intraplane and interplane correlations

We calculate the local-field correctionsG(q, q _z) f electron superlattices with interlayer distanced in order to describe many-body effects. A generalized Hubbard expression for the local-field correction is derived. The sum-rule version of the self-consistent approach for the local-field correction is developed and used to discuss the effects of exchange and correlation. The RPA-parameterr _s and the ratiod/a ^* determine the many-body effects.a ^* is the effective Bohr radius. The stability region for the Fermi liquid behavior of the layered electron gas is discussed: (i) forda ^* the critical RPA-parameterr _sc1 is determined by exchange andintraplane correlation effects, (ii) forda ^* withr _sc1 correlation effects are small and the instability point is mainly determined by exchange effects, (iii) forda ^* withr _sc<1 exchange andinterplane correlation effects are both important for the instability point. Our results are important for high-T _c superconductors, organic superconductors and semiconductor superlattices.     

Traces,Dispersions of States and Hidden Variables

No Heading The interplay between the tracial property and minimality of dispersions of states on projections of von Neumann algebras and C^*-algebras is investigated. Let be a state on a C^*-algebra A with the projection structure P(A). The dispersion () is defined as () = sup{(p) – (p)² | p P(A)}. It is proved that () 2/9 whenever is a state on a real rank zero C^*-algebra with no nonzero abelian representation. New characterization of traces in terms of dispersions is proved: A state on a von Neumann algebra without abelian and Type I₂ direct summands is a trace if and only if has the minimal dispersion on all 3x3 matrix substructures. A similar characterization of semifinite normal traces on von Neumann algebras is obtained. The connection between unitary invariance of states and minimal dispersion property on C^*-algebras is studied. Besides providing a new characterization of trace in terms of physically relevant properties, the existing results on hidden variables in W^*- and C^*-formalism of quantum mechanics are strengthen.     

Determination of the impurity concentration in heavily doped inhomogeneous semiconductors from the measurement of the low-temperature conductivity

A method has been developed for determining the effective concentration of shallow impuritiesN ^* reponsible for the low-temperature conductivity in the vicinity of the metal-insulator transition for inhomogeneous samples of n-Ge:As. The method is based on the measurement of two ratios of sample resistance -R(4.2 K)/R(300 K), =R(2.0 K)/R(4.2 K) and the conductivity (4.2 K). The next step consists of plotting and (4.2) vs . Assuming that is the most reliable parameter, one can calculate, after an averaging procedare, the corrected values of ^*, ^*(4.2) and the resistivity at room temperature ^*(300)=[ ^{* *}(4.2)]^–1. Finally, using the known dependence (300)=f(N) for homogeneous samples, one can obtain the values ofN ^*. The dependences ofN ^* on and on are plotted. The scaling behavior of the conductivity of the Ge:As samples with corrected values of ^*(4.2) andN ^* has been observed down toT=100 mK.     

Clusters,metastability, and nucleation: Kinetics of first-order phase transitions

We describe and interpret computer simulations of the time evolution of a binary alloy on a cubic lattice, with nearest neighbor interactions favoring like pairs of atoms. Initially the atoms are arranged at random; the time evolution proceeds by random interchanges of nearest neighbor pairs, using probabilities compatible with the equilibrium Gibbs distribution at temperatureT. For temperatures 0.59T_c, 0.81 T_c, and 0.89T _c, with density of A atoms equal to that in the B-rich phase at coexistence, the density C₁ of clusters ofl A atoms approximately satisfies the following empirical formulas: C₁ w(1 –)³ andC ₁, (1 –)⁴Q₁w¹ (2 l 10). Herew is a parameter and we defineQ _l = _K e ^–E(K) , where the sum goes over all translationally nonequivalentl-particle clusters andE(K) is the energy of formation of the clusterK. Forl > 10,Q ₁ is not known exactly; so we use an extrapolation formulaQ _l Aw _s ^–l l ^– exp(–bl ), wherew _s is the value ofw at coexistence. The same formula (withw > w _s) also fits the observed values of C, (for small values ofl) at densities greater than the coexistence density (forT=0.59T_c): When the supersaturation is small, the simulations show apparently metastable states, a theoretical estimate of whose lifetime is compatible with the observations. For higher supersaturation the system is observed to undergo a slow process of segregation into two coexisting phases (andw therefore changes slowly with time). These results may be interpreted as a more quantitative formulation (and confirmation) of ideas used in standard nucleation theory. No evidence for a spinodal transition is found.Supported by AFOSR Grant No. 73-2430D and by ERDA Contract No. EY-76-C-02-3077*000.     

Spectroscopy of alkali atoms and molecules attached to liquid He clusters

Large helium clusters, ranging in size from a few hundred to several thousand atoms, are produced in a nozzle expansion. Combining this source with a pick-up scattering cell in which the clusters can be seeded with chromophores allows us to probe the influence of the helium environment on the atoms and molecules attached to the clusters. Using an alkali as chromophore we recorded laser induced fluorescence spectra of Na atoms and molecules attached to helium clusters. Apart from the spectrum of the Na monomer, we have found spectroscopic bands which can unambiguous be assigned to two bound Na atoms. The first of this bands is due to 1^{1 +} (A) 1¹ _g ⁺ (X) excitations of the covalently bound singlet Na₂ molecule while the second is due to 1³ _g ⁺ 1^{3 +} excitations for the van der Waals bound triplet Na₂ dimer. Both bands have been vibrationally resolved. Furthermore we found very large fluorescence intensities in the region 605–635 nm which are likely due to the excitation of a species containing three Na atoms attached to a helium cluster.     

Symplectic Structures on Moduli Spaces of Parabolic Higgs Bundles and Hilbert Scheme

Parabolic triples of the form (E_*,,) are considered, where (E_*,) is a parabolic Higgs bundle on a given compact Riemann surface X with parabolic structure on a fixed divisor S, and is a nonzero section of the underlying vector bundle. Sending such a triple to the Higgs bundle (E_*,) a map from the moduli space of stable parabolic triples to the moduli space of stable parabolic Higgs bundles is obtained. The pull back, by this map, of the symplectic form on the moduli space of stable parabolic Higgs bundles will be denoted by d. On the other hand, there is a map from the moduli space of stable parabolic triples to a Hilbert scheme Hilb(Z), where Z denotes the total space of the line bundle K_{X X}(S), that sends a triple (E_*,,) to the divisor defined by the section on the spectral curve corresponding to the parabolic Higgs bundle (E_*,). Using this map and a meromorphic one–form on Hilb(Z), a natural two–form on the moduli space of stable parabolic triples is constructed. It is shown here that this form coincides with the above mentioned form d.     

Kinetic formulation of the isentropic gas dynamics andp-systems

We consider the 2×2 hyperbolic system of isentropic gas dynamics, in both Eulerian or Lagrangian variables (also called thep-system). We show that they can be reformulated as a kinetic equation, using an additional kinetic variable. Such a formulation was first obtained by the authors in the case of multidimensional scalar conservation laws. A new phenomenon occurs here, namely that the advection velocity is now a combination of the macroscopic and kinetic velocities. Various applications are given: we recover the invariant regions, deduce newL estimates using moments lemma and proveL –w* stability for 3.     

Trapping and cascading of eigenvalues in the large coupling limit

We consider eigenvaluesE of the HamiltonianH =–+V+W,W compactly supported, in the limit. ForW0 we find monotonic convergence ofE to the eigenvalues of a limiting operatorH (associated with an exterior Dirichlet problem), and we estimate the rate of convergence for 1-dimensional systems. In 1-dimensional systems withW0, or withW changing sign, we do not find convergence. Instead, we find a cascade phenomenon, in which, as , each eigenvalueE stays near a Dirichlet eigenvalue for a long interval (of lengthO( )) of the scaling range, quickly drops to the next lower Dirichlet eigenvalue, stays there for a long interval, drops again, and so on. As a result, for most large values of the discrete spectrum ofH is close to that ofE , but when reaches a transition region, the entire spectrum quickly shifts down by one. We also explore the behavior of several explicit models, as .Max Kade Foundation FellowPartially supported by USNSF under Grant DMS-8416049On leave of absence from Department of Mathematics and Statistics, Case Western Reserve University, Cleveland, OH 44106, USA. Partially supported by USNSF under Grant DMS-8620231 and the Case Institute of Technology, RIG     

Structural properties and reactivity of bimetallic silver-gold clusters

Bimetallic silver-gold clusters are well suited to study changes in metallic versus ionic properties involving charge transfer as a function of the size and the composition. We present structures, ionization potentials (IP) and vertical detachment energies (VDE) for neutral and charged bimetallic Au_nAg_m ( 2(n + m)5) clusters obtained from density functional level of theory. In the stable structures of these clusters Au atoms assume positions which favor charge transfer from Ag atoms. In clusters with equal numbers of hetero atoms (n = m = 1- 4) heteronuclear bonding is preferred to homonuclear bonding, giving rise to large values of ionization potentials. For larger clusters (n=m=5, 10) stable structures do not favor neither hetero bonding nor segregation into the single components, although they exhibit more metallic than ionic features. This remains valid also for Au₈Ag₁₂ cluster characterized by strong charge transfer to gold subunit. The influence of doping of pure gold clusters with silver atoms on VDE and IP values is discussed in context of their reactivity towards O₂ and CO molecules. As a starting point we consider reactivity towards CO and O₂ molecules on the example of AgAu^- dimer. The results show that the catalytic cycle can be fullfilled.     

The role of excited species in UV-laser materials ablation

UV-laser ablation is described in terms of a two-level system in which the excitation energy is dissipated via stimulated emission, thermal relaxation, and activated desorption of excited species. For thermal relaxation times t _T>10^–9 s and E* E (activation energies for excited-state and ground-state species) the model predicts high ablation rates at moderate surface temperatures, typically below 2000° C.On leave from General Physics Institute, Russian Academy of Sciences, 117942 Moscow, RussiaOn leave from Institute of Applied Physics, Russian Academy of Sciences, 603600 Nizhnii Novgorod, RussiaOn leave from L.D. Landau Theoretical Physics Institute, Russian Academy of Sciences, 142432 Chernogolovka, Moscow region, Russia     

Discretization of the thermal excitation in highly excited matter

In this paper the thermal energy diffusion for quantum particles is described. The quantum heat transport equation is obtained. It is shown that, for a short-time thermal excitation (of the order of the relaxation time), the excited matter response is quantized on the different levels (atomic, nuclear, quark) with quantum thermal energy equalE ^atomic 9 eV,E ^nuclear 7 MeV, andE ^quark 139 MeV.     

Lyapunov Exponent and Density of States of a One-Dimensional Non-Hermitian Schrödinger Equation

We calculate, using numerical methods, the Lyapunov exponent (E) and the density of states (E) at energy E of a one-dimensional non-Hermitian Schrödinger equation with off-diagonal disorder. For the particular case we consider, both (E) and (E) depend only on the modulus of E. We find a pronounced maximum of (|E|) at energy E=2/ , which seems to be linked to the fixed point structure of an associated random map. We show how the density of states (E) can be expanded in powers of E. We find (|E|)=(1/ ²)+(4/3 ³) |E|²+. This expansion, which seems to be asymptotic, can be carried out to an arbitrarily high order.     

Selectively dopedn-AlxGa1−xAs/GaAs heterostructures with high-mobility two-dimensional electron gas for field effect transistors

The transport properties of warm and hot electrons in selectively dopedn-Al _x Ga_1–x As/GaAs heterostructures created by electric fields up to 500 V/cm were studied by Hall effect, conductivity, and Shubnikov-de Haas measurements at lattice temperatures from 4.2 to 300 K. Hall measurements revealed a substantial decrease of electron mobility and also of sheet electron concentration at 77 K with enhanced electric field. The accelerated 2D electrons are partly scattered into the low-mobility first excited (E ₁) subband, and they are partly trapped in immobile states located in the Al_xGa_1–xAs near the interface. Consequently, two differentv(E) characteristics were obtained at 77 K. The 2D electrons populating only the lowest (E ₀) subband exhibit a velocity of v-2×10⁷ cm/s at 500 V/cm, while the averaged velocity due to all electrons reaches a value of v-1.5×10⁷cm/s at 500 V/cm. The analysis of the Shubnikov-de Haas oscillations and Fast Fourier transformation of the data manifested that the 2D electrons are very rapidly accelerated at 4.2 K and achieve electron temperatures much higher than the lattice temperature at electric fields as low as 1 V/cm. The major cooling process for these electrons is scattering into the low-mobilityE ₁ subband.     

Hearing the zero locus of a magnetic field

We investigate the ground state of a two-dimensional quantum particle in a magnetic field where the field vanishes nondegenerately along a closed curve. We show that the ground state concentrates on this curve ase/h tends to infinity, wheree is the charge, and that the ground state energy grows like (e/h)^2/3. These statements are true for any energy level, the level being fixed as the charge tends to infinity. If the magnitude of the gradient of the magnetic field is a constantb ₀ along its zero locus, then we get the precise asymptotics(e/h) ^2/3 (b ₀) ^2/3 E _* +O(1) for every energy level. The constantE _* .5698 is the infimum of the ground state energiesE() of the anharmonic oscillator family .