Weak Interaction Approximation Research Articles

Two-atom van der Waals forces with one atom excited: The identical-atom limit

We compute the conservative van-der-Waals forces between two atoms, one of which is initially excited, in the limit of identical atoms. Starting with the perturbative calculation of the interaction between two dissimilar atoms, we show that a time-dependent approach in the weak-interaction approximation is essential in considering the identical atoms limit in the perturbative regime. In this limit we find that, at leading order, the van-der-Waals forces are fully-resonant and grow linearly in time, being different upon each atom. The resultant net force upon the two-atom system is related to the directionality of spontaneous emission, which results from the violation of parity symmetry. In contrast to the usual stationary van-der-Waals forces, the time-dependent conservative forces cannot be written as the gradients of the expectation values of the interaction potentials, but as the expectation values of the gradients of the interaction potentials only.

Surface and transport properties of liquid Ag–Sn alloys and a case study of Ag–Sn eutectic solder

This review represents the state of the art in the thermophysical properties of liquid Ag–Sn alloys highlighting the surface and wetting properties of Ag–Sn eutectic solder. It includes an atomistic approach developed within the framework of statistical mechanical theory in conjunction with a Quasi Lattice Theory that, through a rigorous mathematical formalism, provides exact relationships between the properties in terms of classical thermodynamics. The model predicted property values are substantiated by available experimental data. Based on the phase diagram evidence about the existence of e-Ag3Sn intermetallic compound, the surface (surface tension and surface composition), transport (viscosity and diffusivity) properties and microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) have been studied using the Compound Formation Model in a weak interaction approximation and Quasi Chemical Approximation for regular solutions. A case study of Ag–Sn eutectic alloy is presented. Taking into account its importance for design and development of lead free solder alternatives, the literature data on the wettability and the phases formed at the interface between Ag–Sn eutectic alloy and different substrates (Cu, Ni, Au, Pd) have also been analysed.

Four-momentum and angular four-momentum of the electromagnetic field of a system of relativistic charged particles in a weak interaction approximation

Four-momentum and angular four-momentum of the electromagnetic field of a system of relativistic charged particles in a weak interaction approximation

Resonant electronic excitation energy transfer by exchange mechanism in the quantum dot system

A microscopic theory of nonradiative resonance energy transfer between spherical A3B5 semiconductor quantum dots by the exchange mechanism is suggested. The interdot Coulomb interaction is taken into consideration. It is assumed that the quantum dot-donor and the quantum dot-acceptor are made from the same A3B5 compound and are embedded in the matrix of another material that produces potential barriers for electrons and holes. The dependences of the energy transfer rate on the quantum-dot system parameters are found in the frame of the Kane model that provides the most adequate description of the real spectra of A3B5 semiconductors. The analytical treatment is carried out with using the density matrix method, which enabled us to perform an energy transfer analysis both in the weak-interaction approximation and in the strong-interaction approximation. The numerical calculations showed the saturation of the energy transfer rate at the distances between the donor and the acceptor approaching the contact one. The contributions of the exchange and direct Coulomb intractions can be of the same order at the small distances and can have the same value in the saturation range.

Nonequilibrium-induced enhancement of dynamical quantum coherence and entanglement of spin arrays

The random magnetic field produced by nuclear spins has long been viewed as the dominating source of decoherence in the quantum-dot based spins. Here we obtain in both exact and analytical manner the dynamics of spin qubits coupled to nuclear spin environments via the hyperfine interaction, going beyond the weak system-bath interaction and Markovian approximation. We predict that the detailed-balance breaking produced by chemical potential gradient in nuclear baths leads to the rapid oscillations of populations, quantum coherence and entanglement, which are absent in the conventional case (i.e., Overhauser noise). This is attributed to the nonequilibrium feature of the system as shown in the relation between the oscillation period and the chemical potential imbalance. Our results reveal the essentiality of nonequilibriumness with detailed-balance breaking for enhancing the dynamical coherence and entanglement of spin qubits. Moreover, our exact solution explicitly demonstrates that the non-Markovian bath comprised by nuclear spins can preserve the collective quantum state, due to the recovery of coherence. Finally, we propose an experiment using ultracold trapped ions to observe these nonequilibrium and memory effects.

Uncondensed atoms in the regime of velocity-selective coherent population trapping

We consider the model of a Bose condensate in the regime of velocity-selective coherent population trapping. As a result of interaction between particles, some fraction of atoms is outside the condensate, remaining in the coherent trapping state. These atoms are involved in brief events of intense interaction with external resonant electromagnetic fields. Intense induced and spontaneous transitions are accompanied by the exchange of momenta between atoms and radiation, which is manifested as migration of atoms in the velocity space. The rate of such migration is calculated. A nonlinear kinetic equation for the many-particle statistical operator for uncondensed atoms is derived under the assumption that correlations of atoms with different momenta are insignificant. The structure of its steady-state solution leads to certain conclusions about the above-mentioned migration pattern taking the Bose statistics into consideration. With allowance for statistical effects, we derive nonlinear integral equations for frequencies controlling the migration. The results of numerical solution of these equations are represented in the weak interatomic interaction approximation.

Bulk and surface properties of liquid Al–Cr and Cr–Ni alloys

The energetics of mixing and structural arrangement in liquid Al–Cr and Cr–Ni alloys hasbeen analysed through the study of surface properties (surface tension and surfacesegregation), dynamic properties (chemical diffusion) and microscopic functions (concentrationfluctuations in the long-wavelength limit and chemical short-range order parameter) in theframework of statistical mechanical theory in conjunction with quasi-lattice theory. TheAl–Cr phase diagram exhibits the existence of different intermetallic compounds in thesolid state, while that of Cr–Ni is a simple eutectic-type phase diagram at hightemperatures and includes the low-temperature peritectoid reaction in the range near aCrNi2 composition. Accordingly, the mixing behaviour in Al–Cr and Cr–Ni alloy melts was studiedusing the complex formation model in the weak interaction approximation and by postulatingAl8Cr5 andCrNi2 chemical complexes, respectively, as energetically favoured.

Bulk and surface properties of liquid Sb–Sn alloys

The mixing behaviour of liquid Sb–Sn alloys has been described in terms of energetics and structure through the study of their thermodynamic, surface, transport and structural properties by using the Complex Formation Model (CFM) in the weak interaction approximation and by postulating SbSn chemical complexes as energetically favoured. The new Sb–Sn surface tension experimental data, obtained by the pinned drop method at temperatures ranging from 513 to 1023 K , have been analysed in the framework of the CFM and compared with the calculated values as well as with the corresponding literature data. The structural characteristics of Sb–Sn melts are described by the two microscopic functions, i.e. the concentration fluctuations in the long-wavelength limit and the Warren–Cowley short-range order parameter.

Quasiparticle theory of superfluid Bose systems with single-particle and pair condensates

A semi-phenomenological theory of superfluid Bose systems based on a quasiparticle description is examined. This theory makes it possible to study, from a unified standpoint, single-particle and pair condensates with repulsive, as well as attractive, forces. The resulting equations for the order parameters corresponding to these condensates are analyzed in the weak interaction approximation.

Thermodynamics and surface properties of liquid Bi–In alloys

The mixing behaviour of liquid Bi–In alloys has been described in terms of energetics and structure through the study of their thermodynamic, surface and structural properties by using the Complex Formation Model (CFM) in the weak interaction approximation and by postulating BiIn-chemical complexes as energetically favoured. The new Bi, In and Bi–In surface tension experimental data set, obtained by the large drop method in the temperature range 553–873 K, has been analysed in the framework of the CFM and compared with the calculated values as well as with corresponding literature data. The structural characteristics of Bi–In melts are described by the two microscopic functions, i.e. the concentration fluctuations in the long-wavelength limit and the Warren–Cowley short-range order parameter.

A numerical study on nonresonant interactions of gravity waves in a compressible atmosphere

Applying a second‐order numerical scheme, nonresonant interactions of gravity waves in a compressible atmosphere are investigated. The numerical results show that the nonresonant interaction of the gravity waves does occur, and an apparent energy exchange among the interacting waves can be observed, which indicates that the gravity waves with different spatial and temporal scales can extensively interact. In the nonresonant interaction, the wave energy generally tends to transfer from the primary wave with the highest frequency to the secondary and excited waves, which is different from that in the resonant interaction. Under the same initial energy of the secondary wave, the final energy of the excited wave is almost proportional to the initial energy of the primary wave. When the initial energies of the primary waves are identical, the final energy of the excited wave increases slowly with the increasing initial energy of the secondary wave. Similar to that in the resonant interaction, in the nonresonant interaction, wave vector and frequency of the excited wave show temporal variability. The wave vectors of the interacting triad do not satisfy the matching conditions which should be obeyed in the weak interaction theory. We also investigate the effects of the background wind field and viscous dissipation on the nonresonant interaction. The positive and negative background winds show tendencies to strengthen and weaken the wave energy transfer, respectively. This also differs from the weak interaction theory, in which only a Doppler shift can be caused. The primary effect of the viscosity is to dissipate the energy of the interacting waves. The viscosity can hardly prevent the nonresonant excitation, suggesting that the restriction of amplitude threshold on the interaction in the presence of viscosity predicted by the weak interaction approximation seems to be rather loose. As in the resonant interaction, the principal energy exchange is finished before the waves depart from each other, which indicates that the interacting characteristic time does exist in the nonresonant interaction. The characteristic time and evolutions of wavelength and intrinsic frequency for the excited wave are insensitive to the small initial wave amplitudes and Gaussian packet widths of the interacting waves, horizontal background wind field, and viscosity. However, the characteristic time is relevant to the wavelengths of the interacting waves.

Stark structure of the energy spectrum of the Am3+ ion in LaCl3

We have analyzed the structure of the energy spectrum of the Am3+ ion in LaCl3 in the weak and intermediate configuration interaction approximation. We have established that in the intermediate configuration interaction approximation, the mean-square deviation of the calculated values of the Stark level energies from the experimental values is 53% smaller than in the weak configuration interaction approximation. We have determined the even and odd crystal field parameters and the covalency parameters. We conclude that based on analysis of the Stark structure of the energy spectrum, we can make quantitative estimates of the intensity characteristics.

Research on superfluidity and superconductivity on the basis of the Fermi liquid concept

This review develops the Fermi liquid approach to the theory of superfluidity (superconductivity) based on the extension of combinatorial expression for the entropy for the case when the state of the Fermi liquid is described not only by a normal distribution function but by an abnormal distribution function and the state of the Bose liquids is described by these and by overcondensate amplitude as well. The energy of superfluid Fermi and Bose liquids is specified in the form of a functional of these functions. The Fermi liquid approach is equivalent to BCS theory in the weak interaction approximation. The interaction of Fermi liquid with electromagnetic field is included in a gauge-invariant way. The theory of triplet pairing is developed as well as the theory of singlet pairing. On the base of unified variation principle leading to the theory of superfluidity (superconductivity) Londons' equations and Ginsburg-Landau's equation are obtained. Applications of the theory connected with construction of ideal two-component hydrodynamics equations are considered.

Perturbation theory in the exact linearized kinetic equation for a plasma.

An analysis is performed of the perturbation theory dealing with particle interactions in the exact linearized collision integral (CI) for a plasma in an electric field. It is shown that for a fully ionized plasma the usual results of kinetic theory correspond to a high-frequency expansion of the CI, whereas the static limit of the exact CI in a weak-interaction approximation is in disagreement with the usual kinetic theory.

Wave‐wave interactions in a compressible atmosphere: 1. A general formulation including rotation and wind shear

We present here a formulation of the resonant and nonresonant interactions among gravity waves, acoustic waves, and vortical modes in the atmosphere under the weak interaction approximation. This work generalizes previous studies by including the effects of rotation and wind shear. Rotation influences both wave and vortical mode structures, while wind shear is shown to influence the relative frequencies of gravity waves and vortical modes and thus may alter the conditions for gravity wave‐vortical mode interactions occurring in its absence. The theory is applied in the absence of rotation and is shown to permit interactions that depend in a complex manner on the gravity wave and vortical mode characteristics and relative orientation and on the mean wind shear. In a companion paper we apply this formalism in a study of the influences of variable stratification and inhomogeneity on resonant and nonresonant interactions.

The Fokker-Planck coefficients of cosmic ray transport in random electromagnetic fields

The authors derive the three Fokker-Planck coefficients Dmu mu , Dmu p, Dpp of cosmic ray particle transport in a uniform magnetic field with superposed small-amplitude electromagnetic plasma waves in the weak interaction approximation by calculating first-order corrections to the particle's orbit. The calculations are done in the full electromagnetic case avoiding the magnetostatic approximation and any restriction on the waves' propagation direction and the waves' dispersion relation. Special attention is given to low-frequency magnetohydrodynamic waves because of their importance in space physics and astrophysics, and the Fokker-Planck coefficients Dmu mu and Dmu p are simplified by expanding the general expressions to zeroth and first order in omega j/kc<<1, respectively. Then the concept of slab and isotropic turbulence is critically re-examined leading to the introduction of the cone model in which waves can propagate with an angle psi < chi with respect to the background magnetic field. The Fokker-Planck coefficients Dmu mu and Dmu p for this cone model can be further simplified and results depend critically on the value of delta = mod tan chi mod . For transverse Alfven waves, results are given for small cone opening values delta <<1.

Self-consistent effective-medium parameters for oceanic internal waves

In this paper we apply a formalism introduced in a previous paper to write down a self-consistent set of equations for the functions that describe the near-equilibrium time behaviour of random oceanic internal waves. These equations are based on the direct-interaction approximation. The self-consistent equations are solved numerically (using the Garrett-Munk spectrum as input) and the results are compared to parameters obtained in the weak-interaction approximation (WIA). The formalism points out that an extra parameter that is implicitly vanishingly small in the WIA has a significant effect on decay rates when computed self-consistently. We end by mentioning possible future self-consistent calculations that would improve upon our own.

Thermodynamic Properties of Compound Forming Molten Alloys in a Weak Interaction Approximation

Abstract It is shown that the expressions derived in a previous paper for the free energy of mixing and other thermodynamic quantities for compound forming molten alloys simplify considerably if the various interaction parameters are assumed to be small. The procedure is similar to that which for a regular solution reduces the well-known quasi-chemical expressions to the “zeroth approximation” or conformal solution expressions. Numerical application is made to AgAl.

Quantization of solitons

We hope that we have succeeded in convincing the reader that this one-dimensional nonlinear model of field theory has a number of attractive properties. Let us list some of them. 1. The Lagrangian of the theory contains only one field, but a complete spectrum of particles is manifested. In the weak interaction approximation the solitons are heavy particles and they interact strongly. 2. The solitons have a quantum number which has a topological nature, and this can be interpreted as a charge. Solitons with the same charge repel each other, while solitons with different charge attract oacl other. 3. In the weak interaction approximation a prescription exists for calculating in perturbation theory. The quantum corrections are small for small coupling constants, and the quasiclassical treatment determines the entire nonanalytic contribution to the physical quantities.

Kinetic equations for plasmas subjected to a strong time-dependent extenal field. Part 2. The weak-interaction approximation

The general theory developed in part 1 is illustrated for a plasma described by the weak-coupling (Landau) approximation. The kinetic equation, valid for arbitrarily strong external fields, is written out explicitly.