Limit Of Small Field Research Articles

On the conductivity of lateral-surface superlattices in magnetic fields

The authors present results for the band conductivity and the density of states of electrons in realistic two-dimensional periodic potentials and magnetic fields. They show the effects of the number of flux quanta per unit cell in producing Hofstader's-butterfly-like splittings in the limit of small field, but outside the simple tight-binding limit, and for high fields where the dominant effect is the local splitting of Landau levels to form weakly coupled edge states round the minima and maxima of the potential. The broadening and splitting of these states to form Hofstader's butterfly then occurs on a much finer energy scale.

Lower critical dimension of the XY spin glass.

We develop an argument for the absence of spin-glass ordering in short-range vector spin systems with random symmetric exchange interactions in spatial dimension d≤4. The present argument supplements our previous theory; we consider the possibility of divergence in some correlation functions in the limit of small external field. It is also shown that the comment of Schwartz and Young on our previous theory is inappropriate

Spatiotemporal instabilities of lasers in models reduced via center manifold techniques.

Several models of partial differential equations describing the dynamics of lasers with transverse effects are introduced by using the center manifold theorem for the elimination of irrelevant variables. By taking advantage of the different time scales associated with the relaxations of the variables, we first eliminate the polarization and later the population inversion. We show that in contrast with the plane-wave models, the use of center manifold techniques is necessary to properly describe the spatiotemporal behaviors of lasers. In particular, we characterize unsuspected Hopf bifurcations for the model obtained from the adiabatic elimination of the polarization and discuss the presence of diffusive terms induced by the interaction of radiation and matter after the elimination of the population inversion. A complex Ginzburg-Landau equation is also obtained in the small-field limit.

Nonlinear effects in the dielectric response of ferroelectric liquid crystals

Abstract The unwinding of the helicoidal structure of ferroelectric liquid crystals by a static electric field is studied theoretically in the constant amplitude approximation. The field dependence of the pitch, of the induced polarization and of the static dielectric susceptibility is evaluated. Close to Tc nonlinear effects in the susceptibility become important and the dielectric susceptibility, which is defined as the susceptibility in the limit of small fields is hard to evaluate experimentally, simply because it is hard to perform experiments at sufficiently small fields. By our calculation we present a way to get around this problem and we show how to determine the Goldstone mode dielectric susceptibility also if comparatively large fields are used in an experiment.

Nonparabolicity effects in a quantum well: Sublevel shift, parallel mass, and Landau levels.

The influence of nonparabolicity on the subband structure in a quantum well is analyzed. Starting from an accurate expression for the bulk conduction-band structure expanded up to fourth order in k, we determine both the shift of the confinement energies and the energy dispersion parallel to the layers E${(\mathrm{k}}_{?}$). The resulting eigenvalue equations are of the same form as in the parabolic case, but somewhat more complicated. The anisotropy of the bulk conduction band is included, and it is found to have a larger effect in quantum wells than in the bulk. The results can be expressed in terms of the perpendicular mass, which is relevant for the determination of confinement energies, and the parallel mass, which gives the curvature of E${(\mathrm{k}}_{?}$) at the bottom of a subband. We derive approximate expressions for these masses in the form of explicit functions of the confinement energy, which is experimentally accessible. The enhancement of the parallel mass relative to the bulk mass is found to be 2--3 times stronger than that of the perpendicular mass. It is shown that the boundary conditions need to be modified in the nonparabolic case. The nonintuitive result is that the confinement energy for the ground state usually is increased relative to a similar calculation in the parabolic approximation. We include the effect of a perpendicular magnetic field and derive an analytic expression for the Landau levels. The cyclotron mass is found to increase with magnetic field and approach the parallel mass in the limit of small magnetic fields. The parallel mass is also relevant for transport parallel to the layers, density of states, and exciton properties. The agreement with experiment is encouraging. Previous theoretical approaches are critically reviewed and the differences and similarities with this work are pointed out.

Laser excitation of Stark-induced resonances.

We study laser excitation of a hydrogen atom in the presence of a static electric field in the energy region slightly above the zero-field photoionization threshold. With the help of a multiple-scattering expansion, we derive an analytic expression for the time evolution of the initial-state probability, which is nonperturbative with respect to the laser field and which is asymptotically valid in the limit of small electric fields. This allows us to study how the characteristics of the classical periodic orbit, which qualitatively has been associated with the Stark-induced resonances above the zero-field photoionization threshold, manifest themselves in the dynamics of the laser-excitation process.

Magnetization profile near a wall in the planar Ising ferromagnet.

The local magnetization in a semi-infinite planar Ising ferromagnet with an edge field ${H}_{1}$ is examined as a function of distance from the edge. The asymptotic form of this magnetization profile for distances large compared to the bulk correlation length has a nontrivial dependence on the edge field. The exact scaling function for this dependence in the limit of small edge field can be derived from a simple droplet argument.

Nonperturbative analysis of the two-level atom: Applications to multiphoton excitation.

Excitation of an atomic system subjected to a slowly varying external electromagnetic field is studied using a two-level model. Time evolution of the system is found using an approach which is nonperturbative in the field strength. There is no constraint to small values of the applied field, that is, the field (in appropriate energy units) need not be small compared to the difference in energies of the two levels. Rather, we use the fact that the situation of interest to us is where the frequency of the exciting field is small compared to the frequency associated with the level difference. Transition probabilities and resonance conditions are found which circumscribe both the large- and small-field limits. In the weak-field limit the previous results of high-order perturbation theory are readily recovered. For a monochromatic field the characteristic features of resonance excitation at high harmonic number of the applied field are (a) extremely narrow resonance widths and (b) shifts in resonance positions which are strong functions of field intensity. Because of this sensitivity, we are able to demonstrate that when slow temporal evolution of the field amplitude is taken into account (e.g., due to finite pulse duration) the appropriate mean excitation rate is that due to the uncorrelated contribution of many resonances. The results of this analysis are used to estimate excitation rates in a specific atomic system, ${\mathrm{Cd}}^{12+}$, which are then compared to multiphoton-ionization rates. Our calculations suggest that the ionization rate exceeds the excitation rate by several orders of magnitude.

Theory of antiferromagnets with random anisotropy and exchange

The influence of small random fluctuations of the antiferromagnetic exchange, the easy-axis direction and the strength of the coherent z axis anisotropy on the magnetic ground-state properties of a classical three-dimensional antiferromagnet is discussed. A strong influence of easy-axis fluctuations on the M(H) curve for longitudinal magnetic fields is found. The critical spin-flop field is decreased both by exchange and by anisotropy fluctuations. For transverse magnetic fields the slope of the M(H) curve is influenced by exchange and easy-axis fluctuations in the opposing manner. A comparison of the results with experiments on MnxZn1-xF2 shows that the experimentally observed trends can be interpreted by the interplay of both antiferromagnetic-exchange and easy-axis fluctuations. Finally, the author investigated the stability of the magnetic long-range order. In agreement with Imry and Ma (1975) the easy-axis fluctuations cause an instability of the long-range order against formation of domains in the limit of small coherent anisotropy and small magnetic field.

Condensation of a charged relativistic Bose gas in the presence of a magnetic field

The relationship between the two different ordering procedures taking place in an ideal charged relativistic Bose gas in the presence of a uniform external magnetic field B is investigated in an arbitrary number of spatial dimensions d. In particular the analytical form of the charge-density condensate ${q}_{c}$ and the magnetization density \ensuremath{\rho} are calculated as a function of B and the inverse temperature \ensuremath{\beta} for relativistic bosons without spin. In the small-field limit (B\ensuremath{\rightarrow}0) this system exhibits the complete restoration of the symmetry of the ideal relativistic Bose gas for all d at any finite temperature.

On the Bosonization of the Many Electron Problem

The Garbaczewski bosonization procedure is applied to the many-electron problem. It leads to a non-local c-number path integral representation for the trace of the evolution operator which also depends on a mapping of the lattice points in the natural numbers. This mapping is needed for the implementation of the bosonization. We argue that the non-local interactions and the dependence on the mapping can be disregarded in the limit of small electron c-number field. We can then discuss the physics of the saddle point contribution. In the discussion the effects of the Pauli exclusion principle are introduced phenomenologically.

Field-induced phase separation in one dimension

Phase separation is induced in the one-dimensional Ising chain (or lattice-gas model of a fluid) by means of an external field that changes sign in the middle of the chain. The magnetization profile (or density profile of the analogous fluid) is obtained analytically. It is found to decay exponentially rapidly to the bulk-phase magnetizations (or densities), the exponential decay parameter being the correlation length in the bulk phases in the presence of the field. This is in accord with earlier theoretical ideas. The interfacial tension is also obtained analytically. In an appropriately defined limit of large neighboring-site spin-spin interactions and small external field the interface becomes infinitely broad while the amplitude of the profile and the interfacial tension both vanish, in close imitation of the approach to a critical point in a real fluid. In this asymptotic limit the interfacial tension is related to the amplitude of the profile in the way that is predicted by earlier theories of interfaces near critical points, with critical-point exponents now those appropriate to one dimension. The exact interfacial profile and tension are used to test several approximations, including a corrected form of the “barometric law” and local (square-gradient) and nonlocal forms of the van der Waals theory.

Particle scattering in a plasma in the presence of a laser field

The authors present an approach for dealing with particle scattering by a large number of fluctuating plasma electrons when a laser field is present. Using first-order time-dependent perturbation theory to treat the particle-plasma interaction, and taking account of the fluctuations of the plasma potential, the scattering probability and the particle energy losses are derived and expressed in terms of the spectral density of the charge-density fluctuations of a plasma embedded in a laser field. The particle energy losses are considered in detail in the limit of small momentum transfers (classical limit) and weak fields, omega 0 approximately= omega p and omega 0>> omega p ( omega 0 and omega p being, respectively, the laser field and the plasma frequency). For omega 0 approximately= omega p the particle losses are larger than in the field-free case, while for omega 0>> omega p the losses may be smaller or larger, depending on the allowed amount of the particle energy transferred during the interaction. Within the present approach both close and distant collisions are accounted for, and also the field-free results are recovered when the laser field is zero, or when the scattered particle is an electron.

Effect of Kondo impurities on the Korringa relaxation time

Using Nozi\`eres Fermi-liquid theory, a simple result, valid for temperatures small compared to the Kondo temperature, is obtained which describes the effect of magnetic impurities on the nuclear-spin-relaxation time ${T}_{1}$ of a metal in the limit of small magnetic fields. When extended to the case of finite magnetic fields, using a semiphenomenological generalization of ground-state energy results of Ishii, the theory shows quite reasonable agreement with the available experimental data. Further experiments are suggested.

Low-temperature magnetoresistance of nearly magnetic transition metal-based alloys and actinides

The magnetoresistance of nearly magnetic transition metal-based alloys and actinides described by the one-band Wolff model is calculated within the localised spin fluctuation approximation. In the low-field, low-temperature limit the magnetoresistance is positive and proportional to H2/TK2(T<<H<<TK) with the coefficient of the H2 term being a parabolically decreasing function of temperature. At higher temperatures the magnetoresistance is negative and in the small-field limit it is proportional to H2/TK2(H<<TK<<T). In the intermediate temperature region the magnetoresistance is negative for small fields but changes sign as the strength of the magnetic field is increased.

Resistive Transition in a Superconducting Filament

The contribution of thermal fluctuations to the conductivity of a narrow superconducting filament is examined. A Fokker-Planck equation based on time-dependent Ginzburg-Landau theory is used to describe the system. A variational solution of this equation yields an upper bound for the resistivity as a function of temperature in the limit of small electric field. The result is accurate above ${T}_{c}$ and appears to be a better estimate of the resistivity at and just below ${T}_{c}$ than that given by previous calculations.

Magnetoconductivity of Hot Electrons

A theoretical analysis of galvanomagnetic phenomena in an intense electric field is given. The Boltzmann transport equation is solved for the case of acoustic-phonon and impurity scattering and the magnetoconductivity tensor is calculated. The dependence of the Hall and conductivity mobilities on electric and magnetic fields is determined both for spherical constant-energy surfaces and a band structure of the many-valley type. Expressions are derived for both the Hall and conductivity mobilities in the limit of small magnetic fields, where one considers quadratic variations of mobility in the magnetic fields, as well as the case of large magnetic fields. Negative magnetoresistance obtains for the case of spherical constant-energy surfaces and predominant acoustic-phonon scattering, whereas the sign of the mobility variation is shown to depend sensitively on the many-valley band structure and intervalley transition processes.