Distribution function for systems far from thermal equilibrium

We present the general stationary solution of the Fokker-Planck equation for a system of interacting subsystems weakly coupled to reservoirs at different temperatures, T_j. For T_j = T, it reduces to the Boltzman distribution function.     

Scattering theory with different state spaces of perturbed and free system

A new method of the time-dependent approach to the scattering problem is presented. For the main initial objects we take a pair of nonnegative bilinear functionals β_j (j = 1,2) (instead of a pair of selfadjoint operators H_j). In the particular case β_j and H_j are connected by the Green's functions of the corresponding Schrödinger equations. In the general case β₂ may be rather arbitrary. The method proposed here can apply to the scattering problem with a non-operator perturbation. This method essentially uses a pair of different state spaces for the free and perturbed physical system respectively.     

Active suppression of narrowband noises in 3D sound fields

This paper presents a simple multiple-input-multiple-output (MIMO) controller for active suppression of narrowband noise in 3D sound fields. The controller only depends on a complex matrix H(jω₀) instead of an n × n transfer matrix to model the secondary paths. Unlike other available ANCs that obtain the controller transfer functions by adaptation, the proposed one solves its controller transfer matrix directly from H(jω₀); and tolerates some degrees of errors in H(jω₀). If necessary, the proposed system may be made adaptive to trace the drifting secondary path. Online identification of a matrix H(jω₀) is easier than that of a transfer matrix with many coefficient matrices. The estimate would be more accurate for H(jω₀) if other conditions remain the same. The proposed scheme can be modified to suppress narrowband noises with multiple bands by a moderate increase in complexity.     

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).     

Limits on the impact parameters occuring in specific K−p interactions at 8.25 GeV/c

We have determined a lower limit of the impact parameter for the reactions associated with the channels K^?p → K^?pπ⁺π^?K^?p → λπ⁺π^?π⁰. The limit was found to be highest for the diffractive parts of the first channel (～ 0.52 fm) and smallest for the forward Λ in the second channel (～0.21 fm).We have also examined the elements of the inverse correlation matrix for the transfer: the off-diagonal elements are small (consistent with zero) for n = 4?7 body products. The log 〈Q_i·Q_j〉 of the correlation matrix as a function of $\text{Гi?jГ}$ falls on a straight line and the eigenvalue λ₁ of the transverse momentum transfer eigenfunction was found to increase slightly from ～0.6 for 4-body to ～0.7 for 7-body products. The 〈cosφ_ij〉 of the Q_i, Q_j shows similar behaviour to the 〈Q_i·Q_j〉     

Possible explanation of magnetic dependence of the bragg peak intensity in the modulated phase of HoNo6S8

The possible explanation for the observed, by Lynn et al. [1], existence of the maximum in the magnetic field dependence of the Bragg peak intensity I_Q(H) in the modulated phase of HoMo₆S₈ is given. It is based on the so-called EX-model - the dominance of the exchange interaction between superconducting electrons and localized moments in the formation and destruction of the coexistence phase. In this approach the maximum in I_Q(H) results from the (zero wave-vector) electronic spin susceptibility dependence, in superconducting state, on the spin-orbit scattering time τ_So. The in [1] observed anisotropic character of I_Q(H), for H|Q and H⊥Q, is also explained.     

Effect of an external magnetic field and a trapped magnetic flux on the current-voltage characteristics of a granular high-temperature superconductor YBa2Cu3O7−δ

A comparative study of the current-voltage characteristics of the high-temperature ceramic superconductor YBa₂Cu₃O_～6.95 at T = 77.3 K is performed over wide ranges of external magnetic fields H _ext and “treatment” fields H _treat. It is found that the field dependences of the parameters a and j _c involved in the exponential equation E = a(j ? j _c)^v describing the current-voltage characteristics depend substantially on the method used for applying the magnetic field, whereas the exponent v ～ 2 depends on neither the method of application nor on the magnetic field strength. The field dependence of the trapped magnetic field H _trap is determined.     

Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q . The system of equations defining order parameters M _Q ^z , M _Q ^σ , M _z , and M ^σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ M _Q and H ⊥ M _Q (H _Z H ^σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T _M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ^σ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x _c and to a gapless state for x > x _c . In the immediate vicinity of the critical impurity concentration (x ～ x _c ), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.     

Excitations in a quantum Hall ferromagnet with strong Coulomb interaction

A quantum Hall ferromagnet is considered at integer fillings ν, provided typical Coulomb interaction energy E _c is large compared to the cyclotron energy ω_H. Low-energy collective modes consist of a magnetoplasmon exciton and a gapless spin exciton. All charged excitations have a gap. The activation energy gap for a pair of charged topological excitations—skyrmion and antiskyrmion—is small, i.e., Δ< vω_H. The electric charge of a skyrmion is the multiple q=eνQ, where Q is the integer topological charge.     

Magnetoresistance of superconducting grains in ceramic YBa2Cu3O7 − δ high-temperature superconductors in weak magnetic fields

The current-voltage characteristics $E(j)_{H_{treat} } = const$ of ceramic (granular) YBa₂Cu₃O_6.95 samples preliminarily magnetized in different transverse magnetic fields H _treat have been measured in a zero field (H _ext = 0) at T = 77.3 K for elucidating specific features of dissipation in superconducting grains of high-temperature superconductors (HTSCs). The current-voltage curves measured in the range 0 ≤ H _trap ≤ H _c2J (where H _trap is the magnetic field trapped as a result of the pretreatment in H _treat and H _c2J is the upper critical field of the Josephson weak links) have been used to construct the field dependences of the magnetoresistance ρ_A(H _treat) _{j = const} of superconducting grains. It has been established that the magnetoresistance ρ_A of the superconducting grains is significantly lower than the magnetoresistance ρ_J for the Josephson medium. The dependence of ρ_A on H _treat and on the transport current density j has been investigated. It has been shown that the dependences ρ_A(H _treat) _{j = const} exhibit a clearly pronounced tendency to saturation, ρ_satur, and the value of ρ_satur increases with increasing j. It has been found that the lower critical field H _c1A of the superconducting grains strongly depends on the transport current density.     

Stable,metastable and unstable solutions of a spin-1 Ising system in the presence of magnetic fields due to the dipole and quadrupole moments

The spin-1 Ising model with bilinear (J) and biquadratic (K) interactions is studied for magnetic fields H_s and H_Q representing dipole and quadrupole moments, respectively, by using the lowest approximation of the cluster variation method. The influence of H_s, H_Q and α = J/K on metastable and unstable solutions, which are very important for many theoretical and experimental works, is investigated and it is found that metastable and unstable solutions occur at high temperatures when α and H_Q are increased. However if H_S is increased, metastable and unstable solutions can be found only at low temperatures.     

One-electron relativistic molecules with Coulomb interaction

As an approximation to a relativistic one-electron molecule, we study the operator \(H = ( - \Delta + m^2 )^{1/2} - e^2 \sum\limits_{j = 1}^K {Z_j } |x - R_j |^{ - 1}\) withZ _j ≧0,e ^?2=137.04.H is bounded below if and only ife ² Z _j ≦2/π allj. Assuming this condition, the system is unstable whene ²∑Z _j >2/π in the sense thatE ₀=inf spec(H)→?∞ as the R _j →0, allj. We prove that the nuclear Coulomb repulsion more than restores stability; namely \(E_0 + 0.069e^2 \sum\limits_{i< j} {Z_i Z_j } |R_i - R_j |^{ - 1} \geqq 0\) . We also show thatE ₀ is an increasing function of the internuclear distances |R _i ?R _j |.     

Multilevel systems and generalizations of the superalgebra

A new approach to constructing the various generalizations of the one-dimensional supersymmetric quantum mechanics is proposed, including the parasupersymmetric quantum mechanics constructed by Rubakov and Spiridonov as the special case. In particular, we derive the generalized superalgebra, which possesses the features both of the familiar superalgebra and of the parasuperalgebra. Namely, the generalized supercharges Q_i ^± and the Hamiltonian H forms the generalized superalgebra, where Q_i ^±2=0 (as for ordinary superalgebra), but the triple products of generalized supercharges obey the relations Q₁ ⁺Q_j ^–Q_j ⁺=Q_i ⁺H (i, j=1, 2) and Q_i ⁺Q_i ^–Q_j ⁺=(1/4)kQ_i ⁺, Q_i ⁺Q_i ^–Q_j ⁺=(1/4)kQ_i ⁺(i, j=1, 2; ij) (analogous to the parasuperalgebra). Furthermore, the generalized supercharges are conserved, i.e. [H, Q_i ^±]=0.Presented at the International Workshop on Squeezed and Correlated States, Moscow, December 3–7, 1990.     

Jets fromQ \bar Q P waves

We discuss angular distributions and some kinematic features for jets originating from the decay of orbitally excitedQ \(\bar Q\) states. These can be produced ine ⁺ e ^? storage rings via the radiative decay of the first radial excitedQ \(\bar Q\) vector meson. We further present the complete and explicit angular distribution for the cascade decaye ⁺ e ^? → 2³ S ₁ →γ ₁+³ P _j,³ P _j →γ ₂+1³ S ₁, 1³ S ₁ →μ ⁺ μ ^? in all casesj=0, 1, 2. These distributions serve as a test of the spinj of intermediate states inQ \(\bar Q\) systems. By the photon—gluon analogy they can successfully be applied to the jet process, too.     

Stress effect on the magnetoresistance of amorphous ferromagnets

To investigate the magnetization in amorphous ferromagnetic alloys we measured the change in the magnetoresistance (H⊥j and H 6j) simultaneously applying a tensile stress along the direction of the ribbons. With increasing stress we observed a complete alignment of the magnetic domain vectors M_s parallel andantiparallel (for λ_s > 0) or perpendicular (for λ_s < 0) to the stress axis. It is found that on average a value of σ_s = 10 kg/mm² is sufficient in all measured samples to produce this effect. The change in the magnetoresistance by stress annealing indicates that a preferred domain orientation in stress direction is induced.     

The spectral class of the quantum-mechanical harmonic oscillator

The purpose of this paper is to study the so-calledspectral class Q of anharmonic oscillatorsQ=?D ²+q having the same spectrum λ _n =2n (n≧0) as the harmonic oscillatorQ ⁰=?D ²+x ²?1. Thenorming constants \(t_n = \mathop {\lim }\limits_{x \uparrow \infty } \ell g[( - 1)^n {{e_n (x)} \mathord{\left/ {\vphantom {{e_n (x)} {e_n }}} \right. \kern-0em} {e_n }}( - x)]\) of the eigenfunctions ofQ form a complete set of coordinates inQ in terms of which the potential may be expressed asq=x ²?1?2D ² ?g? with $$\theta = \det \left[ {\delta _{ij} + (e^{ti} - 1)\int\limits_x^\infty {e_i^0 e_j^0 :0 \leqq i,j,< \infty } } \right],$$ e _n ⁰ being then ^th eigenfunctionQ ⁰. The spectrum and norming constants are canonically conjugate relative to the bracket [F, G]=∫ΔFDΔGdx,to wit: [λ _i , λj=0, [t _i, 2λ _j ]=1 or 0 according to whetheri=j or not, and [t _i,t _j]=0. This prompts an investigation of the symplectic geometry ofQ. The function ? is related to the theta function of a singular algebraic curve. Numerical results are also presented.     

Interplay between a homogeneous magnetic field and an antiferromagnetic field in one-dimensional superconductors

Mean-field theory applied to superconductors with one-dimensional band in the presence of both the homogeneous magnetic field H₀ and the antiferromagnetic field H_Q, the second-order phase transition temperature is investigated for the arbitrary angle θ between H₀ and H_Q. It is found that the remarkable superconducting region in the case of θ = 0 is retained only for small θ and that the spatially dependent order parameter coexists with the spatially uniform order parameter except for θ = τ/2.     

j3Δg state of the hydrogen molecule

The potential energy curve for the j³Δ_g state of the hydrogen molecule has been calculated in the Born-Oppenheimer approximation. Highly flexible wavefunctions depending explicitly on the interelectronic distance have been used. The vibrational Schrödinger equation for the j state has been solved for H₂, HD, and D₂. The results are compared with the available experimental data, and it is shown that the adiabatic and nonadiabatic effects are mainly responsible for the existing discrepancy. The singlet-triplet separation for the j-J pair of states is also discussed.     

Index of a family of Dirac operators on loop space

We use methods of constructive field theory to generalize index theory to an infinite-dimensional setting. We study a family of Dirac operatorsQ on loop space. These operators arise in the context of supersymmetric nonlinear quantum field models with HamiltoniansH=Q ². In these modelsQ is self-adjoint and Fredholm. A natural grading operator Γ exists such that ΓQ+QΓ=0. We studyQ ₊=P _? QP ₊, whereP _±=1/2 (1±Γ) are the orthogonal projections onto the eigenspaces of Γ. We calculate the indexi(Q ₊) for Wess-Zumino models defined by a superpotentialV(ω). HereV is a polynomial of degreen≧2. We establish thati(Q ₊)=n?1=degδV. In particular, the field theory models have unbroken supersymmetry, and (forn≧3) they have degenerate vacua. We believe that this is the first index theorem for a Dirac operator that couples infinitely many degrees of freedom.