Arbitrary External Field Research Articles

Calculation of electrostatic force between two charged dielectric spheres by the re-expansion method

In the calculation of the electrostatic force between two charged dielectric spheres, it is not easy to include the contribution of higher-order polarization which becomes very important when the spheres are closely located. We found that the re-expansion technique proposed by Washizu for the precise calculation of the dielectrophoretic force on a single sphere in an arbitrary external electrostatic field can be applied directly to a two-particle system. In this paper, the mathematical procedure for the application and some examples of the numerical calculation are presented. Comparison with existing methods, i.e., the method of successive images for conducting spheres and the bispherical coordinate method, shows the validity of the present approach. Convergence of the re-expansion method is poor if the ratio of the radii of the spheres is large and if the particles are closely spaced. Therefore, calculation of the force between a sphere and a dielectric plane wall is the hardest problem for the re-expansion method. Hence the electrostatic force on a small sphere resting on a large sphere is calculated to show that we can use the re-expansion method even for this case by substituting a large sphere for a plane wall in the force calculation.

Transmission and absorption properties of two-dimensional metallic photonic-band-gap materials

Using the multiple-scattering method, we study systematically the transmission and absorption properties of two-dimensional (2D) metallic photonic-band-gap (PBG) materials for a wide range of frequency and structure scales by adopting a realistic dielectric constant for metal cylinders. For both S and P waves, analytic expressions for the absorption power of a single metal cylinder under an arbitrary external field have been derived to explain the absorption behaviors of metallic PBG materials in a coherent way. The discussions and conclusions presented here can be generalized to 3D systems as well.

Calculation of AC losses in HTSC wires with arbitrary current voltage characteristics

A method for the calculation of magnetic field dynamics and AC losses in superconductors with smooth current–voltage characteristics is described. It is based on an integral equation for the current density, recently used by Brandt for magnetic relaxation. Brandt's equation is generalized to include arbitrary external magnetic fields and transport currents. One of the benefits of the integral equation formulation is that no boundary conditions `at infinity' are required, thus restricting the calculation region to the conductor cross section. The method is applied to superconducting tapes in oblique external fields. A further extension of the theory is shown to be applicable to the calculation of coupling losses in twisted multifilamentary superconductors.

One-loop finite temperature effective potential in QED in the worldline approach

The one-loop finite temperature effective potential of QED in an external electromagnetic field is obtained using the worldline method. The general structure of the temperature dependent part of the effective action in an arbitrary external inhomogeneous magnetic field is established. The two-derivative effective action of spinor and scalar QED in a static magnetic background at T≠0 is derived.

Electromagnetic response of charged bosons coupled to a Chern-Simons gauge field: A path-integral approach

We analyze the electromagnetic response of a system of charged bosons coupled to a Chern-Simons (CS) gauge field. Path-integral techniques are used to obtain an effective action for the particle density of the system dressed with quantum fluctuations of the CS gauge field. From the action thus obtained we compute the U(1) current of the theory for an arbitrary electromagnetic external field. For the particular case of a homogeneous external magnetic field, we show, neglecting the back reaction of density-current to electromagnetic fields, the quantization of the transverse conductivity, even in the presence of an arbitrary impurity distribution. The relevance of edge states in this context is analyzed. The propagator of density fluctuations is computed, and an effective action for the matter density in the presence of a vortex excitation is suggested.

Exact relations for the spin-correlation functions for an interacting electron gas in a nonuniform magnetic field

Without any approximation, exact relations for the spin-density correlation functions in an interacting electron gas under an arbitrary nonuniform external magnetic field are obtained by making use of the nonperturbative canonical formulation of quantum many-body theory [T. Toyoda, Ann. Phys. (N.Y.) 173, 226 (1987)]. The obtained results contain $f$-sum rules, a finite-temperature generalized Ward-Takahashi relation, as well as a finite-temperature version of the Nambu-Goldstone theorem with respect to the spontaneous symmetry breaking of the spin-rotational symmetry.

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

We present numerical and analytical results for the thermodynamical properties of the spin-1/2 Heisenberg chain at arbitrary external magnetic field. Special emphasis is placed on logarithmic corrections in the susceptibility and specific heat at very low temperatures ($T/J=10^{-24}$) and small fields. A longstanding controversy about the specific heat is resolved. At zero temperature the spin-Peierls exponent is calculated in dependence on the external magnetic field. This describes the energy response of the system to commensurate and incommensurate modulations of the lattice. The exponent for the spin gap in the incommensurate phase is given.

Generalized time-dependent density-functional theory including core polarization

A generalization of the time-dependent density-functional-theory for metal clusters which treats both valence and core polarization on the same microscopic basis is presented. The selfconsistency between valence and core responses is taken into account by means of a modified kernel and external field in the linearized response equations. The general case of an arbitrary external field and cluster structure, with given specific atomic positions, is presented.

Coherent state path integral for the interaction of spin with external magnetic fields

Linear canonical transformation and time transformation are used within the formalism of path integrals in coherent state representation to solve the problem of an interacting spin with arbitrary time-dependent external magnetic fields. The Factorization technique is used to solve the equation of motion. Examples of the calculation of the transition probability in terms of elementary functions and special functions for solvable systems are presented. For completeness Berry's phase is also derived under adiabatic expansion.

Semiclassical Form of the Relativistic Particle Propagator

A detailed derivation of the semiclassical form for the relativistic particle propagator in arbitrary external electromagnetic field is presented. To this end a path-integral representation is used. The final formula is a generalization of the Van Vleck–Pauli–Morette semiclassical representation in the nonrelativistic quantum mechanics. We demonstrate the efficiency of the former in the case of an arbitrary constant electromagnetic field.

Spin factor in the path integral representation for the Dirac propagator in external fields

We study the spin factor problem both in $3+1$ and $2+1$ dimensions which are essentially different for spin factor construction. Doing all Grassmann integrations in the corresponding path integral representations for Dirac propagator we get representations with spin factor in arbitrary external field. Thus, the propagator appears to be presented by means of bosonic path integral only. In $3+1$ dimensions we present a simple derivation of spin factor avoiding some unnecessary steps in the original brief letter (Gitman, Shvartsman, Phys. Lett. {\bf B318} (1993) 122) which themselves need some additional justification. In this way the meaning of the surprising possibility of complete integration over Grassmann variables gets clear. In $2+1$ dimensions the derivation of the spin factor is completely original. Then we use the representations with spin factor for calculations of the propagator in some configurations of external fields. Namely, in constant uniform electromagnetic field and in its combination with a plane wave field.

An Adaptive Hierarchical Particle‐Mesh Code With Isolated Boundary Conditions

This article describes a new, fully adaptive particle-multiple-mesh (PM2) numerical simulation code developed primarily for cosmological applications. The code integrates the equations of motion of a set of particles subject to their mutual gravitational interaction and to an optional, arbitrary external field. The interactions between particles are computed using a hierarchy of nested grids constructed anew at each integration step to enhance the spatial resolution in high-density regions of interest. As the code is aimed at simulations of relatively small volumes of space (not much larger than a single group of galaxies) with independent control over the external tidal fields, significant effort has gone into supporting isolated boundary conditions at the top grid level. This makes our method also applicable to noncosmological problems, at the cost of some complications, which we discuss. We point out the implications of some differences between our approach and those of other authors of similar codes, in particular with respect to the handling of the interface between regions of different spatial resolution. We present a selection of tests performed to verify the correctness and performance of our implementation. The conclusion suggests possible further improvements in the areas of independent time steps and particle softening lengths.

Transport Equations Including Many-Particle Correlations for an Arbitrary Quantum System: A General Formalism

We present a new method to derive transport equations for non-relativistic quantum many-particle systems. This method uses an equation-of-motion technique and is applicable to interacting fermions and (or) bosons in arbitrary time-dependent external fields. Using a cluster expansion of ther-particle density matrices the infinite hierarchy of equations of motion for many-particle expectation values is transposed into an equivalent one in terms of correlations. This new hierarchy permits a systematic breaking of the hierarchy at any order. Diagrams are derived for these transport equations. In a second paper the method is tested for exactly soluble electron-phonon models in one dimension.

The electrostatic problem for the SAW interdigital transducers in an external electric field. II. Periodic structures

For pt.I see ibid., vol.43, no.6, pp.1150-9 (1996). An exact solution of the electrostatic problem for calculating the surface charge and electric field distributions in an arbitrary periodic interdigital transducer (IDT) is given using the results of our companion paper. An arbitrary external electric field may be specified along the electrode structure with the unit cell containing one electrode, or several electrodes, of different widths. The potentials of the electrodes that may be specified are also arbitrary. It is shown that in the case without an external field, the solution includes all the known results as special cases. The case of shorted electrodes in the external electric field is investigated in detail. The surface charge and electric field distributions are calculated for a spatially harmonic external field with an arbitrary wavenumber. The results of the calculations are represented graphically for various ratios between the period of the electrode structure and the wavelength of the external field for the case of a unit cell containing one or two electrodes of different widths.

Proper time and path integral representations for the commutation function

On the example of the quantized spinor field, interacting with arbitrary external electromagnetic field, the commutation function is studied. It is shown that a proper time representation is available in any dimensions. Using it, all the light cone singularities of the function are found explicitly, generalizing the Fock formula in four dimensions, and a path integral representation is constructed.

Dynamic (hyper)polarizability density analysis based on virtual excitation processes: visualization of the dynamic electron fluctuatability of systems under time-dependent external electric fields

A novel method for the analysis of dynamic (hyper)polarizabilities of systems in the presence of arbitrary time-dependent external electric fields is developed. By using a new concept the ‘dynamic (hyper)polarizability density’, we visualize the a ability of dynamic electron fluctuation (electron fluctuatability) of systems with relaxation processes under external electric fields with arbitrary intensities, frequencies and shape of amplitudes. The (hyper)polarizability density is partitioned into that for each virtual excitation process by the numerical Liouville approach.

Modification of a strong resonance radiation polarization in media with Doppler-broadened transitions of 0 to 1 and 1 to 0 types and in the presence of a DC electric field

For atomic media with resonant Doppler-broadened transitions of J=0 to J'=1 or J=1 to J'=0 type and taking into account the relaxation due to depolarizing collisions, a theory of non-linear optical polarization phenomena in the presence of a DC electric field is developed. The theory is valid in the case of both arbitrary resonance radiation intensity and arbitrary external DC electric field spatial orientation. The intensity-dependent contributions to variation of radiation polarization are analysed in detail in the Doppler limit. Special attention is paid to the case of linear polarization of incident radiation; in this case as well as in the presence of a DC electric field, the Doppler-enhanced non-linear optical contributions determining the emerging ellipticity and the rotation angle of polarization, respectively, are of the same order of magnitude (unlike the case of external magnetic field, in which the key effect is the rotation of polarization). It is shown, however, that in the case of the strictly transverse geometry and if the angle between the electric field direction and the initial polarization vector is equal to 45 degrees , the Doppler-enhanced non-linear optical contribution to the rotation angle becomes anomalously small. The effect of the presence of a longitudinal component of electric field on the non-linear optical polarization phenomena is investigated. In addition, although in the case of a purely longitudinal geometry for the considered transitions the electric field effect on radiation polarization modification is absent, some analytic results concerning self-rotation and deformation of a polarization ellipse in the Doppler limit for an intense initially elliptically polarized radiation are also presented.

Derivation of COM equations using the surface impedance method

The surface impedance method is used for the consistent derivation of coupling of modes equations which describe the interaction of SAW with a periodical system of electrodes of finite thickness. The exact analytic solution of the electrostatic problem in the presence of an arbitrary external electric field for a plane system of electrodes is applied to the calculation of the charge and electric field distributions. Mechanical perturbations are taken into account to first order of the thickness of the electrodes. As a result the scalar self-consistent equation for the electric potential of acoustic waves in the gratings is obtained. For the periodic structure this equation is reduced to the form of COM equations for slowly varying amplitudes. Analytical expressions for all coefficients of the COM equations connecting them with geometrical and material parameters are found. The NSPUDT effect can be considered. Dissipation and energy storage terms can be introduced empirically. The solution of the COM equations is represented in the form of a P matrix with elements written in a convenient form. A simple formula for calculating the location of maximum transducer frequency response is proposed, The balance of energy is considered. Some new relations among the elements of P matrix are found. >

Pseudoclassical Foldy-Wouthuysen transformation and canonical quantization of (D=2n)-dimensional relativistic particle with spin in an external electromagnetic field

The canonical quantization of a (D=2n)-dimensional Dirac particle with spin in an arbitrary external electromagnetic field is performed in a gauge that makes it possible to describe simultaneously particles and antiparticles (both massive and massiess) already at the classical level. A pseudoclassical Foldy-Wouthuysen transformation is used to find the canonical (Newton-Wigner) coordinates. The connection between this quantization scheme and Blount's picture describing the behavior of a Dirac particle in an external electromagnetic field is discussed.

Special variant of the Fradkin representation

The exact Fradkin representation of a Green's function ${\mathit{G}}_{\mathit{c}}$(x,y\ensuremath{\Vert}A) defined in the presence of an arbitrary external field A(z), is converted into a practical sequence of approximations whose first few terms should lead to a better-than-qualitative representation of those ${\mathit{G}}_{\mathit{c}}$[A] and closed-loop functionals L[A] needed in both potential theory and quantum field theory applications. The zeroth term of this approximation is the ``phase averaged'' (〈ph〉) form previously described, which generates a symmetrized version of the no-recoil (or eikonal) approximation; additional corrections correspond, in effect, to a proper-time rescaling of the 〈ph〉 approximation. An independent criterion exists to estimate the quality of the approximation obtained by retaining any finite number of corrections. The general construction is presented for scalar ${\mathit{G}}_{\mathit{c}}$[A] in 3+1 dimensions, and comparisons are made to the simplest, nontrivial, soluble examples in potential theory and in quantum field theory.