Callen-like method for the classical Heisenberg ferromagnet

A study of the d-dimensional classical Heisenberg ferromagnetic model in the presence of a magnetic field is performed within the two-time Green function’s framework in classical statistical physics. We extend the well known quantum Callen method to derive analytically a new formula for magnetization. Although this formula is valid for any dimensionality, we focus on one- and three- dimensional models and compare the predictions with those arising from a different expression suggested many years ago in the context of the classical spectral density method. Both frameworks give results in good agreement with the exact numerical transfer-matrix data for the one-dimensional case and with the exact high-temperature-series results for the three-dimensional one. In particular, for the ferromagnetic chain, the zero-field susceptibility results are found to be consistent with the exact analytical ones obtained by M.E. Fisher. However, the formula derived in the present paper provides more accurate predictions in a wide range of temperatures of experimental and numerical interest.     

An unexpected result in Einstein–Maxwell electrostatics

I examine a known exact static solution of the Einstein–Maxwell equations representing the exterior field of two charged masses. I find a property totally unexpected according to classical electrostatics: the electric field does not vanish between two like charges. The point where it does vanish (electrically neutral point) is found in the general case.     

Exterior and interior metrics with quadrupole moment

We present the Ernst potential and the line element of an exact solution of Einstein’s vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass distribution. We show that in the limiting case of slowly rotating and slightly deformed configuration, there exists a coordinate transformation that relates the exact solution with the approximate Hartle solution. It is shown that this approximate solution can be smoothly matched with an interior perfect fluid solution with physically reasonable properties. This opens the possibility of considering the quadrupole moment as an additional physical degree of freedom that could be used to search for a realistic exact solution, representing both the interior and exterior gravitational field generated by a self-gravitating axisymmetric distribution of mass of perfect fluid in stationary rotation.     

Electrodynamics of rotating planetary plasmaspheres in a dipole magnetic field

As a model of the actual structure of the planetary plasmasphere, we consider the electrodynamical problem of electric field and current generation by a planet with a dipole magnetic field corotating with the plasma envelope. The plasma envelope is characterized by the conductivity and angular velocity of the magnetospheric plasma as functions of the distance τ from the planet center and the angle ? measured from the rotation axis. The exact solutions of the Maxwell equations are obtained in the axially symmetric case within the framework of unipole electrodynamics when the rotational and magnetic axes coincide. These solutions describe the possible distributions of electric fields, currents, and charges in the rotating plasma envelope surrounding the magnetized planet. As an exmple, we constructed, using the theory proposed, the exact solution corresponding to the following structure of the plasmasphere:

1. the plasmasphere region corotating with the planet and located between L-shells (L=τ/Rsin ² ?, where R is the radius of the planet) from L=1 to L=L_*;
2. the polar region with differential, spherically symmetric rotation;
3. the transient region of the plasmasphere rotating differentially with the angular velocity dependent on the L-number and located between L-shells from L=L_* to L=L_*+L₀;
4. the external (vacuum) region.

Analysis of the multipole expansion of the electrostatic potential showed that the electric field potential is equal to zero in the external region (L>L_*+L₀), independently of the number of the boundary L-shell. This solution can serve as a basis for simulation of the plasmasphere formation processes, taking into account the actual conditions in the near-planetary plasma envelopes.     

Black hole solutions in heterotic string theory on a torus

We construct the general electrically charged, rotating black hole solution in the heterotic string theory compactified on a six-dimensional torus and study its classical properties. This black hole is characterized by its mass, angular momentum, and a 28-dimensional electric charge vector. We recover the axion-dilaton black holes and Kaluza-Klein black holes for special values of the charge vector. For a generic black hole of this kind, the 28-dimensional magnetic dipole moment vector is not proportional to the electric charge vector, and we need two different gyromagnetic ratios for specifying the relation between these two vectors. We also give an algorithm for constructing a 58 parameter rotating dyonic black hole solution in this theory, characterized by its mass, angular momentum, a 28-dimensional electric charge vector and a 28-dimensional magnetic charge vector. This is the most general asymptotically flat black hole solution in this theory consistent with the no-hair theorem.     

Influence of laser pulse on the autocorrelation function of H in a strong electric field

The autocorrelation function of electronic wave packet of hydrogen atom in a strong electric field below the zero-field ionization threshold is investigated in the formalism of semiclassical theory. It is found that the autocorrelation depends on the applied laser pulse significantly. In the case of narrow laser pulse, the reviving peaks in the autocorrelation can be attributed to the closed orbits of electrons, which are related to the classical dynamics of the system. But this correspondence is wiped out with increasing the laser width because of the interference among the adjacent reviving peaks.     

Zur Theorie der Bewegung geladener Teilchen in richtungskonstanten Magnetfeldern exponentieller Zeitabhängigkeit. I. Allgemeine Theorie und Einschaltvorgang

The general solution of the equations of motion for a charged particle in a magnetic field is given for the following case: the spatially homogeneous magnetic field having a constant direction is a superposition of a field constant in time and one decreasing exponentially in time; taken into account is the influence of the electric field induced by the time dependent magnetic field and a friction force proportional to the particle velocity. The higher transcendental functions appearing in the exact solution are approximated in various ways in dependence on the values of the argument and parameters. The important case of a switching process without a friction force is investigated in detail. The higher transcendential functions can be approximated by simplier functions in such a way, that the solutions for the switching process, valid for all times, differ from the solutions in the case of a linear increasing magnetic field only by factors consisting of elementary functions. Approximated formulae of a very simple form are obtained for position, velocity, kinetic energy and magnetic moment of the particle. The particle orbits are classified and their dependence on the initial values and parameters of the magnetic fields is studied. A comparison between our results and a rectangular variation of the field shows that the latter is not a good approximation for a really exponential increasing field. Finally a detailed investigation shows that the electric field induced by the time dependent magnetic field has an important influence on the particle motion.     

On the role of combined static hyperfine interactions for the interpretation of in-beam nuclear Larmor-precession measurements

Differential perturbed angular-distribution measurements have been performed for¹⁰⁷Cd and¹⁰⁹Cd in silver hosts. The data have been obtained at various target temperatures with and wthout applied magnetic fields. The theory of static, combined electric and magnetic hyperfine interaction has been applied for comparison of the zero-field quadrupole data and the external field Larmor-precession data.It is concluded that this combined interaction of the external magnetic field and the damage-induced, electric field gradients quantitatively accounts for the observed dependence of Larmor-precession amplitudes on time, temperature and field strength. The significance of the experimental time range for the appearance and thus for the interpretation of this dependence is demonstrated.     

Space-time structure and bound-charge fields

Together with a “postulate of equivalent situations,” the exact solution for the field of a charge in a uniformly accelerated noninertial frame of reference (NFR) makes it possible to find the space-time structure and fields of charged conductors of arbitrary shape without using the Einstein equations. The energy of the electric field outside of a charged plane, which is equal to the rest energy of the masses of the charges creating the field, is determined. The space-time metric outside of the charged plane is established; it could also have been found from the exact solution of the Einstein-Maxwell equations. This solution describes the equilibrium of charged dust in parallel electric and gravitational fields. The field and metric are found outside of a charged conducting sphere. While it eliminates the self-energy divergence, the proposed method renders the classical electrodynamics internally consistent on transition to any short distance. All-Russian Scientific Research Institute of Opticophysical Measurements. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 63–74, October, 1997.     

Electronic states and the Stark shift in narrow band InSb quantum spherical layer

Electron states and the Stark shift in narrow band quantum spherical InSb layers are considered in frameworks of Kane model with respect to non-parabolicity of the dispersion law. An exact analytical solution of the corresponding Klein–Gordon equation for the model of impenetrable walls is obtained, and in addition to that a transcendent equation for determination of electron energetic spectrum is derived as well. The influence of the electric field is considered in frames of the perturbation theory, it is also shown that the value of the Stark shift is proportional to the second power degree of the field. Dependences of the electron energy versus the internal field values, external radius, and electric field are presented. The obtained results are compared with results obtained for the case with standard dispersion.     

A generalization of the fluctuation-dissipation theorem for the case of excess noise

Electrical fluctuations proportional to the square of the external field are investigated in the case of quasi-equilibrium conditions. The binary correlation function, proportional to the square of the external field, is expressed in terms of the zero-field quaternary correlation function for both quantum and classical cases. This result can be considered as a generalization of the fluctuation-dissipation theorem. The 1/f spectrum is obtained as a consequence of the symmetry properties of the quaternary correlation function without consideration of the physical mechanisms responsible for the noise. The method of investigation of the 1/f spectrum through zero-field quaternary correlation function is discussed.     

Drift theory of charged-particle motion for a strong electric field in a weakly relativistic approximation

Drift equations of motion are derived for a charged particle in the case of a strong electric field with allowance for relativistic effects of order v²/c². The role of these effects is discussed along with the effects of a high-frequency field. The cases of weak and strong electric fields are distinguished [2] in the drift theory of the motion of charged particles in weakly inhomogeneous magnetic and electric fields. In the case of a weak electric field, the electric-drift velocity is v_E v, where v is the characteristic velocity of the particle. For a strong electric field,v _Ev.The drift theory has now been reasonably well developed for the case of weak electric fields in the classical and relativistic cases, for the absence of high-frequency fields and for the presence of these [1–3], Extension of the theory to strong electric fields involves considerable mathematical difficulties, and this has been done only in the classical approximation with and without hf fields [2–4], Here we consider the drift theory of charged-particle motion for the case of a strong electric field in the weakly relativistic approximation, incorporating terms of order v²/c², where c is the velocity of light. Also hf fields may be present.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 7–9, September, 1981.     

A generalization of the fluctuation-dissipation theorem for the case of excess noise

Electrical fluctuations proportional to the square of the external field are investigated in the case of quasiequilibrium conditions. The binary correlation fluctuation proportional to the square of the external field is expressed in terms of the zero-field quaternary correlation function for both quantum and classical cases. This result can be considered as a generalization of the fluctuation-dissipation theorem. As applied to the electrical $\text{1}\text{f}$ noise the novel method investigation both in theory and in experiment is presented. The frequency dependence of zero-field quaternary potential correlation function is suggested to be investigated instead of binary correlation function proportional to the square of external field.     

Limitations of the strong field approximation in ionization of the hydrogen atom by ultrashort pulses

We present a theoretical study of the ionization of hydrogen atoms as a result of the interaction with an ultrashort external electric field. Doubly-differential momentum distributions and angular momentum distributions of ejected electrons calculated in the framework of the Coulomb-Volkov and strong field approximations, as well as classical calculations are compared with the exact solution of the time dependent Schr ödinger equation. We show that in the impulsive limit, the Coulomb-Volkov distorted wave theory reproduces the exact solution. The validity of the strong field approximation is probed both classically and quantum mechanically. We found that classical mechanics describes the proper quantum momentum distributions of the ejected electrons right after a sudden momentum transfer, however pronounced the differences at latter stages that arise during the subsequent electron-nucleus interaction. Although the classical calculations reproduce the quantum momentum distributions, it fails to describe properly the angular momentum distributions, even in the limit of strong fields. The origin of this failure can be attributed to the difference between quantum and classical initial spatial distributions.     

Influence of the inhomogeneous field at the tip on quantitative piezoresponse force microscopy

Ferroelectric domain imaging with piezoresponse force microscopy (PFM) relies on the converse piezoelectric effect: a voltage applied to the sample leads to electromechanical deformations. In the case of PFM one electrode is realized by a tip, therefore generating a strongly inhomogeneous electric field distribution inside the sample which reaches values up to 10⁸ V/m directly underneath the apex of the tip. Although often assumed, this high electric field does not lead to an enhancement of the electromechanical deformation of the sample. On the contrary, internal clamping of the material reduces the deformation as compared to the theoretically expected value which depends only on the voltage applied to the tip, thus being independent of the exact field distribution. PACS 77.80.Dj; 68.37.Ps; 77.84.-s     

Solitons in photovoltaic photorefractive media with an external electric field

We use the classical Lie-group method for studying the evolution equation in photovoltaic photorefractive media with an external electric field, reducing it to some similarity equations firstly, and then obtain some exact analytical solutions including the soliton solution, the period solution and the oscillatory solution. We also obtain the bright soliton, dark soliton, gray soliton from these similarity equations with the numerical method. Furthermore, we investigate what factors contribute to the beamwidth of these solitons with the numerical method and know the beamwidth of these solitons are associated with the external electric field, the photovoltaic field and the intensity ratio of the incident soliton.     

Covariant change of signature in classical relativity

This paper gives a covariant formalism enabling investigation of the possibility of change of signature in classical General Relativity, when the geometry is that of a Robertson-Walker universe. It is shown that such changes are compatible with the Einstein field equations, both in the case of a barotropic fluid and of a scalar field. A criterion is given for when such a change of signature should take place in the scalar field case. Some examples show the kind of resulting exact solutions of the field equations.     

Theoretical study of spin-singlet contributions to zero-field splitting of a 3d6 ion in a trigonal ligand field and applications to Fe2+ in FeSiF6 · 6H2O and FeCO3

The complete energy matrix (210 × 210) for d⁶(d⁴) configuration ions in a trigonal ligand field is constructed. The energy levels and zero-field splitting parameters in ferrous fluosilicate and ferrous carbonate are studied. The contributions of spin singlets to zero-field splitting parameters in a trigonal ligand field are investigated for the first time. The calculation results indicate that the spin-singlet contribution to second-order zero-field splitting parameter D is negligible, but the contributions to fourth-order zero-field splitting parameter a ? F cannot be neglected. Moreover, it is found that the stronger the trigonal ligand field, the larger are the spin-singlet contributions to the zero-field splitting parameters.     

Spin-correlated crystal fields: A study of two-body and relativistic effects for Gd3+ in lanthanum ethylsulphate

Matrix elements of a spin-correlated crystal field (SCCF) operator have been evaluated using exact calculations for two-body double tensor operators and compared with earlier approximate calculations for Gd³⁺ in lanthanum ethylsulphate. In this latter case reductions to products of matrix elements of one-body operators were used. These approximations are shown to be accurate for the determination of zero-field splittings (ZFS) only to within 40%. Nonstandard rank combinations resulting from relativistic effects have also been incorporated which are shown to yield negligible contributions to the ZFS. The two-body form of the SCCF has been made relativistic as well in order to investigate the importance of new tensorial terms for the calculations of the ZFS. Again, their contribution has been shown to be very small.