Linear and nonlinear liftings of states of quantum systems

In this paper, we study the representability of an arbitrary quantum state ?? ?? ??(H) as the reduction of a vector state r ?? ??(H) of the extended system. We extend the operation of lifting from the set of states ?? _n (H) to the set of generalized states ??(H). A method of constructing the Hilbert space H and the affine linear lifting ??(H) ?? ??(H) is studied. The construction of individual expansion H _?? of the space H for which the state ?? is a reduction of a vector state H _?? is of special interest.     

A model Hamiltonian for phonon energy transfer in gas—solid collisions

Using the formalism of second quantization in the occupation number representation, a model Hamiltonian of the form H = H_loc + H_nonloc + H_loc?nonloc is developed. H_loc describes the gas atom-phonon system when the gas atom is near the surface, and the phonon operators are only in this term. H_nonmloc describes the gas atom moving in a static potential with no bound states, and H_loc-nonloc couples these two parts of H. The method of solution is to diagonalize H_loc and then to embed it in the continuum of scattering states of H_nonloc. The model is designed so that this diagonalization can be performed essentially exactly for a large class of gas-metal systems. The procedure is illustrated with a simple example which nevertheless shows how multi-phonon processes can dominate in desorption.     

Destruction of order in nuclear spectra by a residual GOE interaction

We consider hamiltonians of the type H = H₀ + λV_GOE where H₀ is a fixed N × N matrix and V_GOE represents a gaussian orthogonal ensemble. The change as a function of λ of the average level density and of the eigenvector correlations is studied, and related to the distribution of branch points of H. It is shown that the GOE interaction completely dominates the spectral properties of H when its spectrum covers the spectrum of H₀.     

The ground state of an antiferromagnetic superconductor in the presence of a homogeneous magnetic field

The effect of a homogeneous magnetic field, H₀. on the ground state of an antiferromagnetic superconductor has been investigated. Assuming a one-dimensional like half-filled band, we have found a new state having gapless superconductivity and H₀-dependent order parameter. This state exists for H_Q/Δ₀>0.22 and when ∣Δ ? H_Q∣?H₀ < Δ + H_Q (H_Q is the staggered magnetic field, Δ is the superconducting order parameter and Δ₀ is Δ in the absence of H_Q and H₀).     

Quantization and confinement effects in superconducting nanostructures

The confinement of the flux lines by a lattice of submicron holes (‘antidots’) has been studied in nanostructured superconducting Pb/Ge multilayers. By introducing regular arrays of sufficiently large antidots, multi-quanta vortex lattices have been stabilized. Sharp cusp-like magnetization (M) anomalies, appearing at matching fieldsH_m=mφ₀/Sin superconducting films with the antidot lattices having a unit cell areaS, are successfully explained. These anomalies are, analogues of the well-knownM(H) cusp atH_c1, but for the onset of multi-quanta (m+1)φ₀-vortices penetration at each subsequent matching fieldH_m. It is shown that theM(H) curve between the matching fieldsH_m<H<H_m+1follows a simpleM∝ln(H−H_m) dependence. These experimental observations have revealed an unusual expansion of validity of the London limit in superconductors with lattices of relatively large antidots. The successful high quality fit of theM(H,T) curves convincingly demonstrates that a new type of the critical stateB=const (‘single-terrace critical state’) can be realized in superconductors with the antidot lattices.     

Spectroscopic Study of Porphyrin-Caffeine Interactions

The association between water-soluble porphyrins: 4,4′,4″,4?-(21?H,23?H-porphine-5,10,15,20-tetrayl)tetrakis-(benzoic acid) (H₂TCPP), 5,10,15,20-tetrakis(4-sulfonatophenyl)-21?H,23?H-porphine (H₂TPPS₄), 5,10,15,20-tetrakis[4-(trimethylammonio)phenyl]-21?H,23?H-porphine tetra-p-tosylate (H₂TTMePP), 5,10,15,20-tetrakis(1-methyl-4-pyridyl)-21?H,23?H-porphine tetra-p-tosylate (H₂TMePyP), the Cu(II) complexes of H₂TTMePP and H₂TMePyP, as well as chlorophyll a with caffeine (1,3,7-trimethylxanthine) has been studied analysing their absorption and emission spectra in aqueous (or acetone in case of chlorophyll a) solution. During the titration by caffeine the porphyrins absorption spectra undergo the evolution – the bathochromic effect can be observed as well as the hypochromicity of the Soret maximum. The association constants were calculated using curve-fitting procedure (K_AC of the order of magnitude of 10³?mol^-1). Whereas the emission spectra point at the presence of the fluorescence quenching effect testifying for the partial inactivation of the porphyrin molecule. The fluorescence quenching constants were calculated from Stern-Volmer plots. The results obtained show that caffeine can interact with water-soluble porphyrins and through formation of stacking complexes is able to quench their ability to emission.     

A new method for estimating the critical current density of a superconductor from its hysteresis loop

The critical current density J_c of some of the superconducting samples, calculated on the basis of the Bean’s model, shows negative curvature for low magnetic field with a downward bending near H = 0. To avoid this problem Kim’s expression of the critical current density, J_c = k/(H₀ + H), where J_c has positive curvature for all H, has been employed by connecting the positive constants k and H₀ with the features of the hysteresis loop of a superconductor. A relation between the full penetration field H_p and the magnetic field H_min, at which the magnetization is minimum, is obtained from the Kim’s theory. Taking the value of J_c at H = H_p according to the actual loop width, as in the Bean’s theory, and at H = 0 according to an enhanced loop width due to the local internal field, values of k and H₀ are obtained in terms of the magnetization values M⁺(?H_min), M^?(H_min), M⁺(H_p) and M^?(H_p). The resulting method of estimating J_c from the hysteresis loop turns out to be as simple as the Bean’s method.     

Polytypisme dans le systeme titane-soufre

Polytypism has been observed among non stoichiometric compounds. in the titanium-sulphur system. This phenomenon, studied at 800 and 900°C, appears near the composition TiS_1,70. Among a lot of varieties which commonly exhibit one-dimensional disorder, four structures have been worked out (12H, 48R, 8H, 10H) and four others identified (12H_a, 24H_b, 40H, 696R).A method is given for accurate evaluation of composition and z coordinates of sulphur atoms. Thus it appears that in these polytypes, atomic planes are equally spaced. Several modes of coexistence of two types present in a single crystal have been studied.     

Direct visualization of the vortex distributions in a superconducting film with a Penrose array of magnetic pinning centers: Symmetry induced giant vortex state

Using scanning Hall probe microscopy a direct visualization of the flux distribution in a Pb film covering a fivefold Penrose array of Co dots is obtained. We demonstrate that stable vortex configurations can be found for fields H ∼ 0.8H₁, H₁ and 1.6H₁, where H₁ corresponds to one flux quantum per pinning site. The vortex pattern at 0.8H₁ corresponds to one vacancy in one of the vertices of the thin tiles whereas at 1.6H₁ the vortex structure can be associated with one interstitial vortex inside each thick tile. Strikingly, for H = 1.6H₁ interstitial and pinned vortices arrange themselves in ring-like structures (“vortex corrals”) which favor the formation of a giant vortex state at their center.     

Thermal,magnetic and structural aspects of transitions in Mn0.63Cr0.37As. Thermodynamic properties from 10 to 350 K

Subambient crystallographic and magnetic structures and heat capacity on Mn_0.63Cr_0.37As are measured below 350 K. A complex first order magnetic (helimagnetic H_a^- to H_c-type) and structural (MnP- to MnP-type) transition, accompanied by a discontinuous unit cell volume change, and a second order magnetic [heli-(H_c) to paramagnetic] transition are observed at 165 and 219 K, respectively. The thermodynamic functions are derived and the thermodynamic characteristics of the transitions are discussed. The enthalpy and entropy of the combined MnP,H_a^- to MnP,H_c^- and MnP,H_c ⇌ MnP,P-type transitions are assessed to be 124.8R K and 0.749R, respectively. Two different models for the deconvolution of the magnetic heat-capacity envelope into contributions from the MnP,H_a^- to MnP,H_c^- and the MnP,H_c ⇌ MnP,P-type transitions are considered.     

Susceptibility,hysteresis and magnetization states in the CuMn spin glass

AC susceptibilities have been measured at T ⪡ T_f on a quenched Cu-8.25 at% Mn sample along the hysteresis curve and especially in remanent magnetization states. Along the M(H)-curve _ϰ∥ starts to decrease already below the S-point field H_w, when dM/dM is still increasing. After reduction of the external field from H ⪢ H_w to zero ϰ_⊥ by far exceeds ϰ _∥, which itself is a little increased above its starting (ZFC) value. Reversing the external field ϰ_∥ develops distinct maxima at the step fields H_st. A model is developed considering the spin glass at M_r to consist of magnetic moments bound by different anisotropies to preferential directions which are oriented partly at random (anisotropy field H¹_w), partly along M_r (anisotropy field H H¹_st ⪡ H¹_w). The model connects both susceptibilities with characteristic parameters of the hysteresis and quantitatively explains the data.     

On the nonrelativistic limit of the Dirac theory

The relation between a “nonrelativistic” Hamiltonian of the formH ^∞=(A+B)²+C and a corresponding family of “Dirac-Hamiltonians”H(c) in the limitc → ∞ is investigated. It is shown that the resolvent (z ?H(c))^?1 and the relativistic perturbation of isolated eigenvalues ofH ^∞ are analytic in 1/c for sufficiently large |c|.     

An YBCO film as a Josephson medium near T c : Frequency and field dependences and scaling relationships

The diamagnetic response of a laser-deposited YBCO film was studied in weak exciting magnetic fields H _ac =H ₀sinωt (H ₀=2–500 mOe, ω/2π=1–30 kHz). An analysis of the experimentally measured diamagnetic response showed evidence of a ring character of the electric field flowing in the sample at small H ₀ values. The plots of T _m (the temperature of maximum dissipative losses χ″₁) versus H ₀ measured at various frequencies showed the existence of a certain critical field strength H*(ω) at which the (1?T _m /T _c ) versus H ₀ ^2/3 plots exhibit a break. A logarithmic dependence of T _m on the frequency ω of the exciting field H _ac is reliably valid only in the region of (ω/2π)>5 kHz. Verification of the scaling relationship showed that this relationship is valid (to within the experimental accuracy) for the frequencies ω above 5 kHz and the field amplitudes H ₀>H*(ω). However, the exponent n in the scaling relationship under consideration is not correlated with the exponent n in the power relationship describing the current-voltage characteristic.     

Regression analysis for deflection magnetic field parameters measured by the dual-coil method

In this study, the magnetic field-parameters of a typical saddle-shaped deflection yoke were measured using the dual-coil method developed by the group. The measurement data was processed and analyzed using two methods: 2-variable regression analysis method and 3-variable regression analysis method. The two results were compared with the analytically calculated results, which was used as the reference. It was shown that the data collection range has large impact to the results of H₂, H₄, and the further away from the central axis the probe is placed, the larger the error is. The errors of H₂ and H₄ are smaller using the 3-variable regression analysis method as compared with the ones using 2-variable regression method. The 3-variable regression analysis method uses H₆ in the process of calculating H₂ and H₄, which is coincident with the definition of them in the formula of H_y = H₀ + H₂X² + H₄X⁴ + H₆X⁶ +?.     

Lattice coupling strength of electron-induced-irradiated defects in InP

Optical properties of some Electron-Induced-Irradiated defects in InP, hole traps H₇, H₅, H₄ and electron trap E₁₁, are investigated by means of Deep-Level-Optical-Spectroscopy.Both majority and minority photoionisation cross-sections measurements of E₁₁ and H₅ are performed, together with direct measurements of the hole capture cross section of H₅. In case of levels H₇ and H₄ the only majority photoionisation cross section could be obtained.Interpretation is made on the basis of one dimensional configuration coordinate diagrams. From these it is concluded that levels H₄ and E₁₁ are weakly relaxed while levels H₅ and H₇ are strongly coupled to the lattice. This is a new indication that EII defects in InP can be at least classified into two groups, owing to their microscopic origin and to their physical properties.     

Two regimes of vortex penetration into platelet-shaped type-II superconductors

Vortex penetration into a thin superconducting strip of a rectangular cross section is considered at an increasing applied magnetic field H _a , taking an interplay between the Bean-Livingston and the geometric barriers in the sample into account. We calculate the magnetic field H _p at which the penetration begins and show that two regimes of vortex penetration are possible. In the first regime, vortices appearing at the corners of the strip at H _a = H _p immediately move to its center, where a vortex dome starts to develop. In the second regime, the penetration occurs in two stages. In the first stage, at H _a < H _p , tilted vortices penetrate into the edge regions of the strip, where novel domes are shown to be formed at the top, bottom, and lateral surfaces. In the second stage, at H _a = H _p , the vortex propagation to the center becomes possible. The difference between the regimes manifests itself in slightly different dependences of the magnetic moment of the strip on H _a .     

The ground state of two-dimensional electrons in a nonuniform magnetic field

An exact solution to the Schrödinger equation for the ground state of two-dimensional Pauli electrons in a nonuniform transverse magnetic field H is presented for two cases. In the first case, the field H depends on a single variable, H = H(y), while in the second case, the field is axially symmetric, H = H(ρ), ρ²=x ²+y ². The electron density distributions n = n(y) and n = n(ρ) that correspond to a completely filled lower level are found. For quasiuniform fields of fixed sign, the functions n(y) and n(ρ) are locally related to the magnetic field: n(y) = H(y)/?₀ and n(ρ) = H(ρ)/?₀, where ?₀ = hc/|e| is a magnetic flux quantum. Magnetic fields are considered that are periodic, singular, and bounded in the plane xy. Finite electron objects in a nonuniform magnetic field are analyzed.     

Particle size dependence of exchange-bias and coercivity in CuO nanoparticles

For CuO nanocrystals of size 6.6-37 nm, the exchange bias H_eb and coercivity H_c are measured at 5 K in zero-field-cooled (ZFC) and field-cooled (FC at 50 kOe) samples and their variations investigated as a function of particle size D. The similar 1/D variations observed for the difference coercivity ΔH_c=H_c(FC)−H_c(ZFC) and the interfacial exchange energy Δσ=H_ebM_fD are discussed in terms of the ferromagnetic magnetization M_f being produced by the uncompensated surface Cu²⁺ spins in the otherwise antiferromagnetically ordered CuO nanoparticles. This leads to the observation that the experimentally measured ΔH_c provides a good measure of Δσ in nanoparticle systems, with H_eb/ΔH_c varying as 1/M_fD.     

Comment on “Remarks on the structure of states of composite quantum systems and envariance” [Phys. Lett. A 355 (2006) 180]

Let ρ∈S(H₁⊗H₂) with dim(H₁⊗H₂)=∞. Suppose that L:S(H₁⊗H₂)→S(H₁) is a map. It is asserted in [1] that if L satisfies the condition Tr(PL(ρ))=Tr((P⊗I₂)ρ) for all rank-one orthogonal projectors P∈B(H₁), then L is given by L(ρ)=Tr₂(ρ). However the proof in Blanchard and Bruning (2006) [1] is not correct. The purpose of this short Letter is to give a proof of this result.     

Anomalous specific heat of dipolar spin glasses and ferroelectrics

We show that for a random Ising model with 1/R³ interactions, the probability distribution of molecular field p(H) goes to zero as H tends to zero. We suggest that p(H) ～ H^{$\text{1}\text{2}$} for small H. Monte Carlo calculations of p(H) for the model are performed with results consistent with this suggestion. These results are used to explain the anomalous T^{$\text{3}\text{2}$} specific heat observed in alkali halides containing off-center ions, and in ferroelectrics.