The action-angle coordinates for particle motion in magnetic mirror systems

In this paper the problem of the possibility of determining the cyclic Hamiltonian function of a particle moving about a magnetic vessel of the mirror type is discussed. From the Hamiltonian of the typeH=H(P ₁,P ₂,P ₃,Q ₃), derived by the author in a previous paper, the Hamiltonian functionH=H(J₁,J ₂,J ₃,w ₃) was determined whereP _i ,Q _i are the generalized impulses and coordinates andJ _i ,w _k is the action-angle coordinate system. The determination of the form H=H(J₁,J ₂,J ₃) depends on the possibility of solving the quadrature of the Hamilton-Jacobi equation leading to an open form in the general case. Some approximative expressions, suitably replacing the mirror system, are discussed. The solution has been extended to the range of relativistic velocities. The question of the uniqueness of the expression of the Hamiltonian function in cyclic variables is analyzed; it follows from this that the class of canonical transformations leaving the Hamiltonian in a cyclic form does not allow any great simplification of the relatively complicated transformation expressions.     

Some comments on the diffusion of particles in stochastic r.f. fields

The form of the distribution functionf (P _i, Q_i,t) is determined in terms of the integralW of the diffusion equation and of the initial distribution functionf ₀(P _i, Q_i, t).W gives the probability of the occurrence of a particle in the phase space P_i, Q_k.The Hamiltonian function of the particle and the distribution functionf obtained in the above way are used for establishing the value of the absorbed energy and the rate of absorption in the case of the homogeneous magnetostatic fields. We discuss the conservative r.f. field-particle system (also in the nonlinear approximation), the effect of the nonlinearity of the diffusion tensor and the meaning of the resonance for the rate of absorption. We discuss also shortly the effect of the external stochastic field on the stability of plasma, already mentioned in earlier literary sources.The author wishes to thank Dr. J. Lacina for valuable discussions.     

Algebras in higher-dimensional statistical mechanics - the exceptional partition (mean field) algebras

We determine the structure of the partition algebraP _n(Q) (a generalized Temperley-Lieb algebra) for specific values ofQ , focusing on the quotient which gives rise to the partition function ofn siteQ-state Potts models (in the continuousQ formulation) in arbitrarily high lattice dimensions (the mean field case). The algebra is nonsemisimple iffQ is a nonnegative integer less than 2n-1. We determine the dimension of the key irreducible representation in every specialization.Work supported by the Packard Foundation.     

A universal phase space for particles in Yang-Mills fields

Given a principal G-bundle P over M and a Hamiltonian G-space Q, one may construct the reduced symplectic manifold (T*P x Q)₀. When a connection on P is chosen, this manifold becomes a bundle over T*M with fibre Q. It is shown that this bundle is precisely the phase space constructed by Sternberg for a classical particle in a Yang-Mills field.Research partially supported by NSF Grant MCS 74-23180.A01.     

Optical behavior of composite carbonaceous aerosols: DDA and EMT approaches

Atmospheric particles may contain a small amount of black carbon (BC) that may affect their optical properties. These optical properties also depend strongly on the particle morphology and internal topology. The efficiency factors for scattering Q_sca, absorption Q_abs, extinction Q_ext, backscattering Q_bk, as well as the asymmetry parameter cos, linear polarization P, and scattering phase functions S₁₁ are analyzed in detail as functions of morphology and internal topology. Backscattering quantities (like Q_bk and P and S₁₁ at large scattering angles) are affected most significantly. The behavior of these quantities depends strongly on the internal mixing of the constituent materials making up the particle. Effective medium theories (EMTs), which assume that the particle is homogeneous and are applied frequently in radiative transfer studies, can underestimate Q_sca and S₁₁ especially when high carbon contents are considered. Contrarily, EMTs also tend to overestimate the values of the asymmetry parameter and Q_abs.     

A higher symmetry in the sol-gel transition at the consolute point

By methods of renormalized field theory we show that generically the multicritical behavior of the sol-gel transition at the consolute point is dominated by a fixed point symmetry which is higher than the symmetry of the original Hamiltonian. In general, this leads to Ising-like behavior of all fluctuations. We show in particular that the Fisher exponent _P of the percolation field coincides with the corresponding exponent _I of Ising fields. We perform a preliminary stability analysis which indicates that the higher symmetry is not broken in the physical 3-dimensional case.Dedicated to Professor Herbert Wagner on the occasion of his 60th birthday     

Thermodynamic functions of a two-sublattice ferrite in a magnetic field

This paper considers the effect of the magnetic field on the specific heat, entropy, and temperature behavior of the magnetization in a two-sublattice ferrite in the collinear phase. It is shown that the specific heat and entropy vary nonmonotonically with the magnetic field, while at low temperatures the magnetization increases with the temperature when the magnetic field takes values in the range H₁/2 < H h₁, where H₁ is the value of the magnetic field for which deviation from the collinear structure begins [1, 2].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 33–36, January, 1977.In conclusion, the author wishes to express his indebtedness to G. M. Nedlin and to thank him for his valuable appraisal of the work.     

Effective field theory approach to structure functions at small $x_{\mathrm{Bj}}$

We relate the structure functions of deep inelastic lepton-nucleon scattering to current-current correlation functions in a Euclidean field theory depending on a parameter r. The r-dependent Hamiltonian of the theory is P ⁰ -(1-r)P ³ , with P⁰ the usual Hamiltonian and P³ the third component of the momentum operator. We show that a small in the structure functions corresponds to the small r limit of the effective theory. We argue that for there is a critical regime of the theory where simple scaling relations should hold. We show that in this framework Regge behaviour of the structure functions obtained with the hard pomeron ansatz corresponds to a scaling behaviour of the matrix elements in the effective theory where the intercept of the hard pomeron appears as a critical index. Explicit expressions for various analytic continuations of the structure functions and matrix elements are given as well as path integral representations for the matrix elements in the effective theory. Our aim is to provide a framework for truly non-perturbative calculations of the structure functions at small for arbitrary Q². Received: 16 July 2002 / Published online: 9 December 2002 RID="a" ID="a" e-mail: O.Nachtmann@thphys.uni-heidelberg.de     

Approximate internal conversion coefficients for outer shell electrons

The recent extensive calculations of approximate internal conversion coefficients forN ₆-N ₇,O ₁-O ₇,P ₁-P ₅ andQ ₁ atomic subshells performed by the present authors are discussed. The used physical approximation (point nucleus—Coulomb field) together with the corrections for finite nuclear size and atomic screening are described in some detail. A comparison with previous calculation and experiments is presented. Possible improvements of the screening correction are given.Devoted to Professor V. Petrílka on his sixty-fifth birthday.Extended version of the invited paper presented at the International Conference on Radioactivity in Nuclear Spectroscopy, Vanderbilt University, Nashville, Tennessee, August, 1969.On leave from theNuclear Research Institute, e near Prague, Czechoslovakia.     

On retroactive occurrence and twin events in quantum mechanics

Bohr's well-known claim that only a registered phenomenon is a true phenomenon is further elaborated into occurrence in the past: If ideal occurrence of an eventP ((1–P)) is a state at a timet _i makes another eventQ ((1–Q))certain at a later timet _f, and, finallyU is the evolution operator fromt _i tot _f, then, it is proved that the final collapsed stateQ(U U ⁺)Q/TrQU U ⁺, which comes about in ideal occurrence ofQ att _f,equals the initial collapsed stateU(P P/TrP)U ⁺, which evolves from the state resulting from the ideal occurrence ofP in att _i. Utilizing the latter state is called theretroactive apparent ideal occurrence (RAIO) ofP in. A number of consequences, including the general notion of twin events (the case whent _f=t _i, andU=1) is derived. It is pointed out that RAIO is relevant in second-kind quantum measurement, in Wheeler's delayed-choice experiments in second-kind (or conditional) quantum preparators.     

Quenching Evolution in a Quantum-Classical Hybrid System

The adiabatic theorem, an important theory in quantum mechanics, tells that a quantum system subjected to gradually changing external conditions remains to the same instantaneous eigenstate of its Hamiltonian as it initially in. In this paper, we study the quench evolution that is another extreme circumstance where the external conditions vary rapidly such that the quantum system can not follow the change and remains in its initial state (or wavefunction). We examine the matter-wave pressure and derive the requirement for such an evolution. The study is conducted by considering a quantum particle in an infinitely deep potential, the potential width Q is assumed to be change rapidly. We show that the total energy of the quantum subsystem decreases as Q increases, and this rapidly change exerts a force on the wall which plays the role of boundary of the potential. For Q < Q₀ (Q₀ is the initial width of the potential), the force is repulsive, and for Q > Q₀, the force is positive. The condition for the quenching evolution evolution is given via a spin-\( \frac{1}{2} \) in a rotating magnetic field.

     

Galvano- and Thermomagnetic phenomena in thin films with nonidentical surfaces

A theory of galvano- and thermomagnetic phenomena in thin films with nonidentical surfaces is presented. The kinetic equation is solved with consideration of boundary conditions in films with nonidentical surfaces in the presence of a magnetic field perpendicular to the film plane, and an electric field and temperature gradient within the film plane. General expressions are found for the components of the galvano- and thermomagnetic tensors _ik, _ik, _ik which are oscillating functions of film thickness and magnetic field. A detailed analysis is performed of the dependence of magnetic resistance(d, H), the Nernst — Ettingshausen(N-E) coefficient Q(d, H), the electron component of thermal conductivity(d, H), and the thermo-emf(d, H) on film thickness and magnetic field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 86–91, October, 1977.In conclusion, the authors express their gratitude to B. M. Askerov for his constant interest in the study and fruitful evaluation of the results.     

An algebraic approach to quantum field theory and commutation relations for energy momentum in the framework of general relativity

We present a consistent set of commutation relations (C.R.) for a quantum system immersed in a classical gravitational field. The gravity field is described by metric tensorg _ik (x) andg ₀₀(x) with coordinate gaugeg _i0=0. The Hamiltonian of the system is found to be a linear function of [–g ₀₀(x)]^1/2. Its properties we define by C.R. avoiding explicit expression in terms of fields, as well as its splitting into free and interaction parts. In this way a consistent set of C.R., which are equally simple for a flat and curvilinear space, can be established. To stress the main idea of our approach, we consider the simple but still nontrivial example of a scalar electrodynamics immersed in a gravity field. The electromagnetic current operator we define by its C.R. and not explicitly. An interesting feature of this approach is that the Poisson equation follows from the consistency of the C.R. The C.R. for the energy and momentum operators of the system in a gravity field are established which generalize the usual Poincare group generators C.R. For example, we find (i/hc ²)[H _(x) ,H _(x) ]=P _– , whereH _(x) is the Hamiltonian of the system, which is a linear functional of (x)[–g ₀₀(x)]^1/2 andP _s(x) represents the momentum-density operator [averaged with the classical functions(x)].     

Theory of Raman scattering and infrared absorption by interacting phonon-magnon states in FeF2

It is shown theoretically that, in the presence of a strong magnetic field, effects due to the interaction betweenB _1g ,E _g,TA phonons and magnons should be important in the Raman and infrared absorption spectrum of FeF₂. As a result the two magnon line should split. A microscopic Hamiltonian for the interactions has been derived. The calculated values of theE _g phonon-one magnon interaction, 9.9 cm^–1, and of theB _1g phonon-two magnon coupling, 6.3 cm^–1, are comparable to those in FeCl₂2H₂O metamagnet, in which C phonon-magnon hybrydization has been observed [1]. It is shown that hybridization between two magnon andB _1g orTA phonon can occur in FeF₂ if the magnon energy approaches the phonon energy due to increasing magnetic field or increasing temperature.On the leave from Technical University, Pozna, Institute of Physics, Pozna 61–138 Piotrowo 3, Poland     

Measurement of the diffractive structure function in deep inelastic scattering at HERA

This paper presents an analysis of the inclusive properties of diffractive deep inelastic scattering events produced inep interactions at HERA. The events are characterised by a rapidity gap between the outgoing proton system and the remaining hadronic system. Inclusive distributions are presented and compared with Monte Carlo models for diffractive processes. The data are consistent with models where the pomeron structure function has a hard and a soft contribution. The diffractive structure function is measured as a function ofx , the momentum fraction lost by the proton, of , the momentum fraction of the struck quark with respect tox , and ofQ ² in the range 6.3·10^–4x <>^–2, 0.1<0.8 and=">Q ²<100>². The dependence is consistent with the formx wherea=1.30±0.08(stat) _–0.14 ^+0.08 (sys) in all bins of andQ ². In the measuredQ ² range, the diffractive structure function approximately scales withQ ² at fixed . In an Ingelman-Schlein type model, where commonly used pomeron flux factor normalisations are assumed, it is found that the quarks within the pomeron do not saturate the momentum sum rule.supported by Worldlab, Lausanne, Switzerland     

Magnetoexciton absorption in coupled quantum wells

A Mott exciton in coupled quantum wells in a transverse magnetic field H is considered. An expression for the exciton spectrum in an arbitrary magnetic field for large separations D between quantum wells containing an electron (e) and a hole (h) is given. The exciton spectrum in a strong magnetic field for different Landau levels at arbitrary D has been calculated. Changes in the parameter D/l, where is the magnetic length, cause rearrangement of the magnetoexciton dispersion curves ℰ(P), where P is the conserved “magnetic” momentum, which is a function of the separation between the electron and hole in the plane of the quantum wells. Off-center (“roton”) extrema occur only for D/l,<(D/l)_cr, where (D/l)_cr is a function of the exciton quantum numbers n and m. The magnetoexciton effective mass in states with magnetic quantum number m=0 monotonically increases with H and D, while in states with m≠0 it is a nonmonotonic function of D/l. The probability of generating an exciton in coupled quantum wells increases with H. Absorption of electromagnetic radiation due to transitions between excitonic levels in coupled quantum wells is discussed. For an exciton containing a heavy hole the oscillator strengths increase with H and the oscillator strengths decrease. Zh. éksp. Teor. Fiz. 112, 1791–1808 (November 1997)     

Retrieval and chaos in layeredQ-Ising neural networks

Using a probabilistic approach, we study the parallel dynamics of theQ-Ising layered networks for arbitraryQ. By introducing auxiliary thermal fields, we express the stochastic dynamics within the gain function formulation of the deterministic dynamics. Evolution equations are derived for arbitraryQ at both zero and finite temperatures. An explicit analysis of the fixed-point equations is carried out for bothQ=3 andQ. The retrieval properties are discussed in terms of the gain parameter, the storage capacity, and the temperature. Using the time evolution of the distance between two network configurations, we investigate the possibility of microscopic chaos. Chaotic behavior is always present for arbitrary finiteQ. However, in the limitQ the existence of chaos depends on the parameters of the system.     

Zur Hyperfeinstruktur des 62P3/2-Terms von Rb87

The hyperfine structure of the 6² P _3/2 state of Rb⁸⁷ has been reinvestigated with optical double resonance in zero magnetic field. The results for the hfs-splitting constants areA(6² P _3/2, Rb⁸⁷)=27.70 (2) Mc/s andB(6² P _3/2, Rb⁸⁷)=3.94 (4) Mc/s. From these constants one obtains a value for the nuclear quadrupole moment uncorrected for shielding effects ofQ=+0.138 (1)·10^?24 cm².