Relaxation of finite, closed systems

On a semi-finite W^*-algebra together with a faithful normal semi-finite trace τ and a one-parameter group of trace preserving ^*-automorphism α_t, we study the limit as t → ∞ of α^*_tψ of a normal state ψ. It is shown that the existence of this limit in the weak sense is determined by the spectral properties of the evolution operator. These results are specialized to finite classical and quantum mechanical systems.     

An energy law preserving C finite element scheme for simulating the kinematic effects in liquid crystal dynamics

In this paper, we use finite element methods to simulate the hydrodynamical systems governing the motions of nematic liquid crystals in a bounded domain Ω. We reformulate the original model in the weak form which is consistent with the continuous dissipative energy law for the flow and director fields in W^1,2+σ(Ω) (σ > 0 is an arbitrarily small number). This enables us to use convenient conformal C⁰ finite elements in solving the problem. Moreover, a discrete energy law is derived for a modified midpoint time discretization scheme. A fixed iterative method is used to solve the resulted nonlinear system so that a matrix free time evolution may be achieved and velocity and director variables may be solved separately. A number of hydrodynamical liquid crystal examples are computed to demonstrate the effects of the parameters and the performance of the method.     

Electronic properties of a large quantum dot at a finite temperature

The physical properties of a two-dimensional parabolic quantum dot composed of large number of interacting electrons are numerically determined by the Thomas–Fermi (TF) method at a finite temperature. Analytical solutions are given for zero temperature for comparative purposes. The exact solution of the TF equation is obtained for the non-interacting system at finite temperatures. The effect of the number of particles and temperature on the properties are investigated both for interacting and non-interacting cases. The results indicate that the effect of e–e interaction on the density profile shows different temperature dependencies above and below a certain temperature T_c.     

A model study of quark-number susceptibility at finite chemical potential and temperature

In this Letter, we try to give a direct method for calculating the quark-number susceptibility (QNS) at finite chemical potential and temperature. In our approach the QNS is given by a formula which solely involves (the dressed quark propagator at finite chemical potential μ and temperature T). From this the QNS at finite chemical potential and temperature is calculated in the framework of rainbow-ladder approximation of the Dyson–Schwinger approach using the meromorphic quark propagator proposed in [M.S. Bhagwat, M.A. Pichowsky, P.C. Tandy, Phys. Rev. D 67 (2003) 054019]. It is found that the QNS χ(μ,T) has a singularity when μ comes close to a critical value μ₀, and the susceptibility as a function of T becomes discontinuous at some values of T when μ is near μ₀. At high temperature the QNS approaches the ideal quark gas result, while at very small temperature (T<40 MeV) the susceptibility equals zero. For all values of μ we studied, the susceptibility shows a rapid increase near T=120–140 MeV, which could be regarded as the signal of a crossover.     

On the Discrete Spectrum of a Spatial Quantum Waveguide with a Disc Window

In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width d. We impose the Neumann boundary condition on a disc window of radius a and Dirichlet boundary conditions on the remained part of the boundary of the strip. We prove that such system exhibits discrete eigenvalues below the essential spectrum for any a > 0. We give also a numeric estimation of the number of discrete eigenvalue as a function of \fracad\frac{a}{d}. When a tends to the infinity, the asymptotic of the eigenvalue is given.     

Isotope effects on vibronic coupling of pyrazine

The vibronic couplings of pyrazine-d₀ and pyrazine-d₄ between the lowest electronic excited states ¹B_3u(n, π^*) and ¹B_2u(π, π^*) through the out-of-plane CH bending vibration ν_10a(b_1g) have been studied from the Raman, electronic absorption and fluorescence spectra. The isotope effects on the scattering cross section of the ν_10a Raman line, the vibrational potential in the ¹B_3u(n, π^*) state and on the frequency change of the ν_10a vibration between the ground and the lowest electronic excited states are well explained by conventional Herzberg-Teller coupling mechanism. However, the intensities of the vibronic bands in the electronic absorption and fluorescence spectra are hardly explained with this coupling mechanism.     

Resonances in at rest

Data on at rest show two resonant processes: (a) f₀(1370)η,f₀(1370)→σσ and ρρ, (b) η(1440)σ, η(1440)→ηπ⁺π⁻. The branching ratio BR[f₀(1370)→ρρ]/BR[f₀(1370)→σσ]=0.98±0.25 in the mass range available here. Using data on , the ratio Γ_4π/Γ_2π5 for f₀(1370). The effects of the strongly s-dependent width of f₀(1370) are discussed in some detail.The η(1440) is observed decaying to ησ and a₀(980)π, with strong destructive interference between them. In its decay to a₀(980)π, a narrow peak appears in the ηπ mass spectrum, but 30–50 MeV above that usually attributed to a₀(980) and significantly above the KK threshold. This effect is explained naturally by a two-step process: η(1440)→K^*(890)K followed by rescattering of the two kaons through a₀(980) to ηπ above the KK threshold.     

Effect of localized spins in coherent transport through quantum dots

The effect of localized spins on the quantum coherence in solids is discussed. A quantum dot with an odd number of electrons can be a model system for a localized spin. It is experimentally shown that a spin flip scattering by a quantum dot pulls the trigger of quantum decoherence. On the other hand, spin flip scattering is the basic process to construct the Kondo singlet state around a magnetic impurity. Through an interference effect of the Kondo state (the Fano–Kondo effect) in a side-coupled dot system, we show experimentally that the Kondo singlet state is quantum mechanically coherent. The analysis of the Fano–Kondo lineshape indicates the locking of the phase shift to π/2, which is in agreement with theoretical predictions. The Fano–Kondo effect is also observed in an Aharonov–Bohm ring, in which a quantum dot is embedded, and also indicates the phase shift locking to π/2.     

Frequency-dependent Hall effect in spintronic systems under zero magnetic field

It is shown that in an electronic system with finite Rashba coupling and in the absence of external magnetic field, the Hall resistivity (ρ_xy) is finite at both zero and finite frequencies. This Hall resistivity is determined by the reactive part (real part) of the inverse dielectric functions. This allows us to probe the real part of the dielectric function in a spintronic system by using a transport measurement.     

Study of in flight

An analysis of data on is presented at beam momenta 600 to 1940 MeV/c. There is evidence for an I=1, J^PC=2⁻⁺ resonance in ηηπ⁰ with mass M=1880±20 MeV and width 255±45 MeV, decaying strongly to a₂(1320)η; it is too strong to be explained as the high mass tail of π₂(1670)→a₂(1320)η. There is tentative evidence also for weak decays to f₀(1500)π. It makes a natural partner to the η₂(1860).     

On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass μ≠0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy–momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form g_μ,νρ with ρ>0, thus providing a concrete quantum field theoretic model of the cosmological constant. This ρ represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p0.     

Extending the Fast Multipole Method for Charges inside a Dielectric Sphere in an Ionic Solvent: High Order Image Approximations for Reaction Fields

As a sequel to our previous paper on extending the Fast Multipole Method (FMM) for charges inside a dielectric sphere [J. Comput. Phys. 223 (2007) 846–864], this paper further extends the FMM to the electrostatic calculation for charges inside a dielectric sphere immersed in an ionic solvent, a scenery with more relevance in biological applications. The key findings include two fourth-order multiple discrete image approximations in terms of u = λa to the reaction field induced by the ionic solvent, provided that u = λa < 1 where λ is the inverse Debye screening length of the ionic solvent and a is the radius of the dielectric sphere. A 10⁻⁴ relative accuracy in the reaction field of a source charge within the sphere can be achieved with only 3–4 point image charges. Together with the image charges, the FMM can be used to speed up the calculation of electrostatic interactions of charges in a dielectric sphere immersed in an ionic solvent.     

Dipolar Coupling Information in Multispin Systems: Application of a Compensated REDOR NMR Approach to Inorganic Phosphates

Anexperimental strategy has been developed for measuring multiple dipole–dipole interactions in inorganic compounds using the technique of rotational echo double resonance (REDOR) NMR. Geometry-independent information about the dipole couplings between the observe nuclear species S (arbitrary quantum number) and the heteronuclear species I (spin- ) can be conveniently obtained from the experimental curve of ΔS/S₀ versus dipolar evolution time by limiting the analysis to the initial data range 0 < ΔS/S₀ < 0.30. Numerical simulations have been carried out on a three-spin system of type SI₂ in order to assess the effect of the I–I homonuclear dipole–dipole coupling and the influence of experimental imperfections such as finite pulse length and misadjustments of the 180° pulses applied to the I-spin species. The simulations show further that within the initial data range the effects of such misadjustments can be internally compensated by a modified sequence having an additional 180° pulse on the I channel in the middle of the dipolar evolution periods. Experimental ²⁷Al{³¹P} REDOR results on the multispin systems Al(PO₃)₃, AlPO₄, [AlPO₄]₁₂(C₃H₇)₄NF, and Na₃PO₄ confirm the general utility of this approach. Thus, for applications to unknown systems the compensation strategy obviates calibration procedures with model compounds.     

The limitimg behaviour of the well width of a quantum two-dimensional metal–insulator transition

Metal–Insulator transition using an exact two-dimensional (2D) dielectric function is investigated for a shallow donor in an isolated well of a GaAs/Ga_1−xAl_sAs superlattice system within the effective mass approximation. Vanishing of the donor ionization energy as a function of well width and the donor concentration suggests that a phase transition is not possible even below a well width of 10 Å, supporting the scaling theory of localization. The effects of Anderson localization, exchange and correlation in the Hubbard model are included in a simple way. The relationship between the present model and the Mott criterion in terms of Hubbard model is also brought out. The critical concentration appears to be enhanced when a random distribution of impurities is considered. The limiting behaviour of the well width for a quantum 2D well is brought out. A simple expression is derived for a Mott constant in 2D, a*N_c^1/2 exp (9.86 exp (−L/a*))=0.123, where N_c is the critical concentration per area. Results are compared with the existing data available and discussed in the light of existing literature.     

Surface reaction kinetics in oxygen nonstoichiometry re-equilibration of BaTiO3−δ

We report the (bare) surface redox-reaction rate constant that was determined, along with the chemical diffusivity , by a conductivity relaxation technique on Al-doped single crystal and undoped polycrystal BaTiO_3−δ as a function of oxygen activity in its range of −16≤log a_O2≤0 at elevated temperatures of 800–1100 °C. It takes a value in the range of −4<log( /cm s⁻¹)≤−1, which is even larger than that of the oxides that are considered best as oxygen membranes. It has been found that the surface reaction step grows more rate controlling as the electronic transference number gets smaller or the electronic stoichiometric composition (δ≈0) is approached. The oxygen potential drop due to the surface reaction was estimated by an oxygen concentration cell technique. The oxygen potential drop grows larger as the stoichiometric composition is approached, that is in accord with the variation of against oxygen activity.     

Entanglement evolution of a two-qubit system interacting with a quantum spin environment

We investigate the entanglement dynamics and decoherence of a two-qubit system under a quantum spin environment at finite temperature in the thermodynamics limit. For the case under study, we find different initial states will result in different entanglement evolution, what deserves mentioning here is that the state |Ψ=cosα|01+sinα|10 is most robust than other states when π/2<α<π, since the entanglement remains unchanged or increased under the spin environment. In addition, we also find the anisotropy parameter Δ can suppress the destruction of decoherence induced by the environment, and the undesirable entanglement sudden death arising from the process of entanglement evolution can be efficiently controlled by the inhomogeneous magnetic field ζ.     

Single-particle distribution function of a quantum dot system at finite temperature

In the present paper, we shall rigorously re-establish the result of the single-particle function of a quantum dot system at finite temperature. Unlike the proof given in our previous work (Phys. Rev. B 74 195414 (2006)), we take a different approach, which does not exploit the explicit expression of the Gibbs distribution function. Instead, we only assume that the statistical distribution function of the quantum dot system is thermodynamically stable. As a result, we are able to show clearly that the electronic structure in the quantum dot system is completely determined by its thermodynamic stability. Furthermore, the weaker requirements on the statistical distribution function also make it possible to apply the same method to the quantum dot systems in non-equilibrium states.     

Parameter-dependent resonant third-order susceptibility contributed by inter-band transitions in quantum wells

The resonance enhancement of the third-order nonlinear optical susceptibility χ⁽³⁾ for degenerated four-wave mixing, due to the transition between valence band and conduction band, in InGaN/GaN multi-quantum wells have been calculated. The band structures of valence bands and conduction bands and the wave functions are calculated by the theory of effective mass. The contributions of the subbands of holes (heavy holes, light holes and the spin-orbit split-off bands) to χ⁽³⁾ in the different directions are discussed. The correlations between χ⁽³⁾ in the different directions and the width of the quantum wells, and the constituents of the quantum wells are obtained.     

Link invariants of finite type and perturbation theory

The Vassiliev-Gusarov link invariants of finite type are known to be closely related to perturbation theory for Chern-Simons theory. In order to clarify the perturbative nature of such link invariants, we introduce an algebra V _x containing elements g _i satisfying the usual braid group relations and elements a _i satisfying g _i–g _infi ^sup-1 =a _i, where is a formal variable that may be regarded as measuring the failure of g _infi ^sup2 to equal 1. Topologically, the elements a _i signify intersections. We show that a large class of link invariants of finite type are in one-to-one correspondence with homogeneous Markov traces on V _x. We sketch a possible application of link invariants of finite type to a manifestly diffeomorphisminvariant perturbation theory for quantum gravity in the loop representation.     

Magnetische zustände in den kfz legierungen der 3d-übergangsmetalle

By representing the critical temperatures for magnetic order according to the number of outer (s + d) electrons per atom e/a, a systematic connection of the magnetic states in fcc alloys of the 3d-transition metals may be recognized. There exist two distinct groups of alloys exhibiting antiferromagnetic and ferromagnetic order, respectively. The transition from antiferromagnetism to ferromagnetism proceeds in the range 8.0 < e/a < 8.4. In the transition range magnetically heterogeneous states will appear.