Spin-Dependent Bohmian Electronic Trajectories for Helium

We examine “de Broglie-Bohm” causal trajectories for the two electrons in a nonrelativistic helium atom, taking into account the spin-dependent momentum terms that arise from the Pauli current. Given that this many-body problem is not exactly solvable, we examine approximations to various helium eigenstates provided by a low-dimensional basis comprised of tensor products of one-particle hydrogenic eigenstates. First to be considered are the simplest approximations to the ground and first-excited electronic states found in every introductory quantum mechanics textbook. For example, the trajectories associated with the simple 1s(1)1s(2) approximation to the ground state are, to say the least, nontrivial and nonclassical. We then examine higher-dimensional approximations, i.e., eigenstates Ψ _α of the Hamiltonian in this truncated basis, and show that ∇ _i S _α =0 for both particles, implying that only the spin-dependent momentum term contributes to electronic motion. This result is independent of the size of the truncated basis set, implying that the qualitative features of the trajectories will be the same, regardless of the accuracy of the eigenfunction approximation. The electronic motion associated with these eigenstates is quite specialized due to the condition that the spins of the two electrons comprise a two-spin eigenfunction of the total spin operator. The electrons either (i) remain stationary or (ii) execute circular orbits around the z-axis with constant velocity.     

Cooper pairing and superfluidity in the Emery model

The energy E of the system as a function of the gauge phase Φ is calculated by exact diagonalization in a two-dimensional Cu₄O₈ cluster and by the slave-boson method for large systems. It is shown that motion of carriers with charge 2e, i.e., Cooper pairs, is observed for certain values of the parameters in the Hamiltonian. This motion is identified from the onset of a characteristic maximum of E(Φ) at Φ≈Φ₀/2, where Φ₀ is the flux quantum. The phase diagram is constructed and the range of values of the model parameters where the effect is observed is determined. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 78–82 (25 January 1996)     

Energy and pressure dependence of the CO2 laser induced dissociation of sulfur hexafluoride

Low pressure SF₆ with its isotopes in natural abundance was irradiated by a pulsed CO₂ laser operated on theP20 line (10.6 μm band). Dissociation yields of³²SF₆ and³⁴SF₆ were measured separately. If the radiation is focussed into the cell, the dissociation yield is proportional to the 3/2 power of the laser energy, as was derived under general conditions and confirmed experimentally. The reaction probabilityP(Φ), the fraction of molecules dissociated by an energy flux Φ, was measured using parallel light. For both isotopes,P(Φ) saturates at high energy flux close toP=1. At a lower flux (2 J cm⁻²), the dissociation probability of³²SF₆ displays a threshold, whereas the dissociation probability of³⁴SF₆ is a very steep function of Φ over the whole range of fluxes.P(Φ) at the higher energy flux was measured in a cavity absorption cell, in which up to 80% of the molecules were dissociated by a single pulse. Below 0.2 mbar SF₆ the dissociation yields for both isotopes are pressure independent. Above 2 mbar the isotopic selectivity is completely lost. Addition of hydrogen always decreases the dissociation yields.     

Ionization of hydrogen and helium atoms by highly charged fast ions in collisions with small momentum transfer

Ionization of hydrogen and helium atoms is studied for the case of “soft” collisions with highly charged fast ions with v≲Z≪v² and v≫v ₀, where Z is the ion charge, v is the collision velocity, and v ₀∼1 is the characteristic velocity of the electron in the ground state of the atom. Analytical expressions are derived for the singly and doubly differential cross section for ionization of a hydrogen atom accompanied by the ejection of a slow electron v _e≲v ₀, where v _e is the velocity of the ejected electron with respect to the recoil ion). The results are generalized to the case of single ionization of helium. It is shown that soft collisions provide the main contribution to the hydrogen ionization cross section and for all practical purposes determine the cross section for single ionization of helium. The asymmetry in the angular distribution of the ejected slow electrons and the properties of momentum exchange in such collisions are discussed. Finally, a formula for the cross section for single ionization of helium is proposed. Zh. éksp. Teor. Fiz. 112, 1966–1977 (December 1997)     

Spin polarization and spin-dependent transmittance in II–VI diluted magnetic semiconductorheterostructure

In this work, we carried out detailed investigation of a Cd_1?xMn_xTe/CdTe/Cd_1?xMn_xTe diluted magnetic semiconductor based quantum well. Our theoretical results are based on an accurate self-consistent resolution of the one-dimension Schrödinger and Poisson’s equations in the framework of the mean-field approximation for spin-up and spin-down orientations of carriers coupled via the sp–d exchange interaction. From the calculation of spin-dependent carrier densities for ferromagnetic and anti-ferromagnetic coupling, we evidence the spin-up and spin-down space separation for holes in quantum well for different values of band offsets. From deduced spin polarizations, we show that the CdTe region acts as a layer of spin rearrangement and spin reversal, respectively, in the ferromagnetic and anti-ferromagnetic coupling. The transmittance coefficients T₊ and T_? of injected spin-up and spin-down carriers are evaluated as a preliminary work to assess the spin-dependent currents in devices consisting of alternatively layers of non-magnetic and diluted magnetic semiconductors.     

Spin-dependent photoabsorption at theL-edges of ferromagnetic Gd and Tb metal

The spin-dependent absorption of circularly polarized x-rays is studied at theL-edges of ferromagnetic Gd and Tb metal. At theL ₁-edge a spin-dependent part of the absorption coefficient of 10^–3–10^–2 is observed. Strong resonance absorption known as white line occurs at theL ₂- andL ₃-absorption onset. Correlated with it one finds large spin-dependent absorption effects with amplitudes of a few percent. The spin-dependent absorption spectra reflect the profiles of the spin densities of the states populated in the absorption process. Thep-states show spin densities correlated with the first two flat bands above the Fermi level. The spin density of thed-like states is concentrated in the energy range of the white line. In Gd a splitting of (0.5–0.6) eV of the unoccupied 5d spin up and spin down bands is indicated for both spin-orbit partners. In Tb a large dependence of the 5d spin density on the spin-orbit configuration is observed. The experimental results on the spin densities in Gd are compared with band structure calculations for the ferromagnetic ground-state. The theoretical and experimental spin density profiles agree well for thep-states but not for thed-states. The discrepancy concerning thed-states may be attributed to core-hole polarization effects in the absorption process.     

Calculation of VLEED spectra with the extended linear augmented plane wave kp method

We describe a new method to calculate the VLEED (very low energy electron diffraction) spectra within the Bloch waves approach. The method is based on the variational solution of the Schr?dinger equation for a semi-infinite crystal. Inside the solid the trial LEED functionΦ is a linear combination of propagating and evanescent Bloch waves, which are generated by the inverse ELAPW (extended linear augmented plane waves)-kp method. The trial function is smoothly continuous over the whole space, and it satisfies by construction the equation (Ĥ − E)Φ=0 both in the crystal and in the vacuum half-spaces. In the surface layer the equation δ‖(Ĥ − E)Φ‖=0 is solved. To illustrate the properties of the method we discuss its application to the 1D case. We have performed a self-consistent band structure calculation of the 1T chalcogenide VSe₂ and obtained from the first principles the normal-incidence target current spectrum (TCS) for its (0001) surface. Presented at the VIII-th Symposium on Surface Physics, Třešt’ Castle, Czech Republic, June 28 – July 2, 1999.     

Influence of local spin polarization to the Kondo effect

We use the spin non-degenerate single impurity Anderson model to investigate the influence of the local spin polarization to the Kondo effect. By using the Schrieffer-Wolff transformation, we obtain a generalized s-d exchange Hamiltonian, which describes the interaction between a polarized local spin and conduction electrons. In this case, the singlet is no longer an eigenstate as shown by variational calculations where the splitting of the local energy Δ = ɛ _d↑ − ɛ _d↓ can be arbitrarily small. The local spin polarization generates the instability of the singlet ground state of the S = 1/2 s-d exchange model.      

Interactions of charmed mesons with nucleons in the ¯<Emphasis Type="Italic">p</Emphasis><Emphasis Type="Italic">d</Emphasis> reaction

We study the possibility to measure the elastic ΦN (Φ≡J/ψ,ψ(2S), ψ(3770), χ_2c) scattering cross section in the reaction ˉp+d→Φ+n _sp and the elastic D(ˉD)N scattering cross section in the reaction ˉp+d→D ⁻ D ⁰ p _sp. Our studies indicate that the elastic scattering cross sections can be determined for Φ momenta about 4–6 GeV/c and D/ˉD momenta 2–5 GeV/c by selecting events with p _t≥ 0.4 GeV/c for Φ's and p _t(p _sp) ≥ 0.5 GeV/c for D/ˉD-meson production. Received: 8 November 1999     

Evaluation of the <Superscript>52</Superscript>Cr–<Superscript>52</Superscript> Cr Interaction via Spin-Flip Scattering

In order to evaluate g ₀, the interaction strength of a pair of ⁵²Cr atoms with total spin S = 0, a specially designed s-wave scattering of the pair has been studied theoretically. Both the incident atom and the target atom trapped by a potential are polarized previously but in reverse directions. Due to spin-flips, the outgoing atom may have spin component μ ranging from −3 to 3. The outgoing channels are classified by μ. The effect of g ₀ on the s-wave cross sections of each of these μ- channels has been predicted. In particular, when the parameters of the trapping potential are given around their optimal values so that the cross sections can be maximized, distinguished features of the dependence of the cross sections on g ₀ are found. These features are helpful for evaluating g ₀.     

The Green-Kubo Formula for the Spin-Fermion System

The spin-fermion model describes a two level quantum system (spin 1/2) coupled to finitely many free Fermi gas reservoirs which are in thermal equilibrium at inverse temperatures β _j . We consider non-equilibrium initial conditions where not all β _j are the same. It is known that, at small coupling, the combined system has a unique non-equilibrium steady state (NESS) characterized by strictly sitive entropy production. In this paper we study linear response in this NESS and prove the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes generated by temperature differentials. Dedicated to Jean Michel Combes on the occasion of his sixtyfifth birthday     

Spin-Dependent Bohm Trajectories for Pauli and Dirac Eigenstates of Hydrogen

The de Broglie-Bohm causal theory of quantum mechanics is applied to the hydrogen atom in the fully spin-dependent and relativistic framework of the Dirac equation, and in the nonrelativistic but spin-dependent framework of the Pauli equation. Eigenstates are chosen which are simultaneous eigenstates of the energy H, total angular momentum M, and z component of the total angular momentum M _z. We find the trajectories of the electron, and show that in these eigenstates, motion is circular about the z-axis, with constant angular velocity. We compute the rates of revolution for the ground (n=1) state and the n=2 states, and show that there is agreement in the relevant cases between the Dirac and Pauli results, and with earlier results on the Schrödinger equation.     

Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result

We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ₁₂) − S(γ₁) is restricted to states of the form . We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L ₁ → L _p for L _p spaces defined by the Schatten p-norm on matrices, and give another proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L ₁ → L _p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.     

Molecular magnetism in closo-azadodecaborane supericosahedrons

ABSTRACT

The connection of 12 s = ½ closo-azadodecaborane radical units (NB₁₁H₁₁?), where a hydrogen atom is removed from the nitrogen atom, produces a supericosahedron [(NB₁₁H₆?)₁₂]^(S), S being the total spin of the system. This work describes the study of the low-lying energy spin-projected states of this supericosahedron with two different geometrical arrangements, each nitrogen atom pointing (1) inwards or (2) outwards with respect to radial axes. These spin-projected states are mapped into a Heisenberg spin Hamiltonian, thus allowing the determination of coupling constants between magnetic sites. The eigenvalues of this model Hamiltonian then predict the ground spin state and the corresponding combinations of spin orientations of the magnetic centres. We show that the energy minimum in the [(N_in/outB₁₁H₆?)₁₂]^(S) systems corresponds to a high-spin S = 6 state.     

Spin susceptibility of neutron-irradiation-disordered YBa2Cu3O6.9 in the normal and superconducting states

The spin-spin relaxation rate ⁶³ T ₂ ⁻¹ of ⁶³Cu nuclei in CuO₂ layers is measured in the normal and superconducting states of the compound YBa₂Cu₃O_6.9 (T _c ^onset =94 K) subjected to radiation-induced disordering by a fast-neutron flux Φ to T _c ^onset =68 K (Φ=7×10¹⁸ cm⁻²) and T _c ^onset <4 K (Φ=12×10¹⁸ cm⁻²). It is found that as the structural disorder increases, the contribution of the indirect spin-spin interaction ⁶³ T _2G ⁻¹ , which is related to the value of the spin susceptibility at the boundary of the Brillouin zone of the copper planes χ_s(q={π/a; π/a}), decreases slightly at the transition to the superconducting state for the initial sample and remains unchanged for the weakly disordered sample. This behavior of the short-wavelength contribution to the spin susceptibility attests to the stability of the x ²−y ² symmetry of the energy gap against structural disorder, in accordance with proposed theoretical models of Cooper pairing for high-T _c cuprates. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 3, 172–177 (10 February 1998)     

Vacuum Nodes and Anomalies in Quantum Theories

We show that nodal points of ground states of some quantum systems with magnetic interactions can be identified in simple geometric terms. We analyse in detail two different archetypical systems: i) the planar rotor with a non-trivial magnetic flux Φ and ii) the Hall effect on a torus. In the case of the planar rotor we show that the level repulsion generated by any reflection invariant potential V is encoded in the nodal structure of the unique vacuum for θ=π. In the second case we prove that the nodes of the first Landau level for unit magnetic charge appear at the crossing of the two non-contractible circles α₋, β₋ with holonomies h _α-(A)=h _β-(A)=−1 for any reflection invariant potential V. This property illustrates the geometric origin of the quantum translation anomaly. Received: 6 April 1999 / Accepted: 21 October 2000     

Three-dimensional vortex visualization in stratified spin-up

Abstract  

We present the results of three-dimensional time-dependent numerical simulations of incremental spin-up of a thermally stratified fluid. The fluid inside a vertical cylindrical container of radius R and height 2H is water characterized by the kinematic viscosity ν and thermal diffusivity κ. Initially, its density (temperature) varies linearly with height and is characterized by a constant buoyancy frequency N, which is proportional to the density gradient. The system undergoes an abrupt change in the rotation rate from its initial value Ω_i, when the fluid is in a solid-body rotation state, to the final value Ω_f. The aim of this contribution is to show the formation of columnar vortices in a high Rossby number spin-up flow.