A Dirac particle in a running electric field

The wave function of the Dirac particles in the longitudinal electric field running with the velocity of light is investigated, and the condition of particle capture by this field is presented. The Dirac particles with mass m₀ and charge e that were previously stationary are captured by a repulsive field of strength E if the longitudinal field extension exceeds l = m₀c²/eE. The captured Dirac particles concentrate, like classical particles, at the distance l from the forefront of the running field, but unlike classical particles, the nth part of the Dirac particles is not captured by the field, where n = exp(−l/2λ₀) and λ₀ is the Compton wavelength of the particle. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 25–33, October, 2006.     

Time-Dependent Gaussian Solution for the Kostin Equation Around Classical Trajectories

The structure of time-dependent Gaussian solutions for the Kostin equation in dissipative quantum mechanics is analyzed. Expanding the generic external potential near the center of mass of the wave packet, one conclude that: the center of mass follows the dynamics of a classical particle under the external potential and a damping proportional to the velocity; the width of the wave packet satisfy a non-conservative Pinney equation. An appropriate perturbation theory is developed for the free particle case, solving the long standing problem of finding analytic expressions for square integrable solutions of the free Kostin equation. The associated Wigner function is also studied.     

Horizontal rolls in convective flow above a partially heated surface

Considering the nonlinearity arising from the interaction between electrons and lattice vibrations, an effective electronic model with a self-interaction cubic term is employed to study the interplay between electron-electron and electron-phonon interactions. Based on numerical solutions of the time-dependent nonlinear Schroedinger equation for an initially localized two-electron singlet state, we show that the magnitude of the electron-phonon coupling χ necessary to promote the self-trapping of the electronic wave packet decreases as a function of the electron-electron interaction U. We show that such dependence is directly linked to the narrowing of the band of bounded two-electron states as U increases. We obtain the transition line in the χ × U parameter space separating the phases of self-trapped and delocalized electronic wave packets. The present results indicates that nonlinear contributions plays a relevant role in the electronic wave packet dynamics, particularly in the regime of strongly correlated electrons.     

Inertial and gravitational mass in quantum mechanics

We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the spatial modulation of the corresponding energy wave function is determined by the third root of the product of the two masses. Moreover, the discrete energy spectrum of a particle constrained in its motion by a linear gravitational potential and an infinitely steep wall depends on the inertial as well as the gravitational mass with different fractional powers. This feature might open a new avenue in quantum tests of the universality of free fall.     

Quantum instability for a wave packet kicked periodically by a quadratic potential

The quantal behaviour of wave packet periodically kicked by a quadratic potential has been investigated using Floquet theory. The wave function of the particle afterN kicks has been determined. This wave function has been utilized to obtain the packet width, energy and loss of memory as a function of the number of kicks. It has also been shown that the free particle wave packet quasienergy spectrum makes a transition from discrete to absolutely continuous atɛ T=2. The behaviour forɛT>2 is quantum mechanically irregular.     

Second-order corrections to neutrino two-flavor oscillation parameters in the wave packet approach

We report about an analytic study involving the intermediate wave packet formalism for quantifying the physically relevant information which appears in the neutrino two-flavor conversion formula and helping us to obtain more precise limits and ranges for neutrino flavor oscillation. By following the sequence of analytic approximations where we assume a strictly peaked momentum distribution and consider the second-order corrections in a power series expansion of the energy, we point out a residual time-dependent phase which, coupled with the spreading/slippage effects, can subtly modify the neutrino-oscillation parameters and limits. Such second-order effects are usually ignored in the relativistic wave packet treatment, but they present an evident dependence on the propagation regime so that some small modifications to the oscillation pattern, even in the ultra-relativistic limit, can be quantified. These modifications are implemented in the confrontation with the neutrino-oscillation parameter range (mass-squared difference Δm² and the mixing angle θ) where we assume the same wave packet parameters previously noticed in the literature in a kind of toy model for some reactor experiments. Generically speaking, our analysis parallels the recent experimental purposes which are concerned with higher precision parameter measurements. To summarize, we show that the effectiveness of a more accurate determination of Δm² and θ depends on the wave packet width a and on the averaged propagating energy flux Ē which still correspond to open variables for some classes of experiments. PACS 02.30.Mv; 03.65.Pm; 14.60.Pq     

Hole-electron mechanism of F-H pair generation in RbCl crystals with impurity electron traps

Production of F, Cl ₃ ⁻ , Ag⁰, and Tl⁰ centers in RbCl:Ag and RbCl:Tl crystals by photons having energies ranging from 5 to 10 eV has been studied at 295 and 180 K. It is shown that creation of near-impurity excitations is accompanied by formation of F centers localized in the vicinity of Ag⁺ and Tl⁺ ions. F centers are produced in direct optical generation of self-trapped excitons. In addition to the well-known mechanism of F-H pair production in nonradiative recombination of electrons with self-trapped holes, a hole-electron process has been revealed for the first time to operate in RbCl:Ag having deep electron traps. By this mechanism, F-H pairs appear in the following sequence of stages: thermally stimulated unfreezing of hopping diffusion of self-trapped holes (V _K centers), tunneling electron transfer from Ag⁰ to the approaching V _K centers, and subsequent nonradiative decay of triplet self-trapped excitons near Ag⁺ ions. Fiz. Tverd. Tela (St. Petersburg) 40, 1238–1245 (July 1998)     

On the problem of constraints in minimally coupled relativistic wave equations for particles of unique mass

We study the problem of a possible change in the number of constraints in linear relativistic wave equations (-iβ _μ ∂ ^μ +m)ψ=0 for particles of unique mass, on introduction of minimal coupling to an external electromagnetic field. Complementing our earlier work in which we obtained conditions for non-loss of constraints in equations characterised by the minimalβ-algebraβ ₀ ⁵ =β ₀ ³ we derive here the conditions for such theories not to generate more constraints than in the free case. The results are illustrated by considering specific equations and a fallacy in certain conclusions of Kobayashi and Shamaly on this problem is pointed out.     

Crossover from Quantum to Boltzmann Statistics for Free Particles in a Single Harmonic Trap

With invoking analytical formulae in number theory and numerical calculations, we calculate the number of microstates in microcanonical ensemble for free particles in a single harmonic trap which in whole space defines a thermodynamic system but not a spatially homogeneous one. Once the number of excitation quanta m is larger than the square of the particle number N ² as m⪰O(N ²) when N≫1, the number of microcanonical microstates for an ideal, harmonically trapped Bose or Fermi gas gradually converge to the Boltzmann microcanonical microstates for the classical particles with a proper consideration of the indistinguishability.     

Constraints on the axion-electron coupling constant for solar axions appearing owing to bremsstrahlung and the compton process

The axio-electric effect in silicon atoms is sought for solar axions appearing owing to bremsstrahlung and the Compton process. Axions are detected using a Si(Li) detector placed in a low-background setup. As a result, a model-independent constraint on the axion-electron coupling constant |g _Ae | ≤ 2.2 × 10⁻¹⁰ has been obtained, which leads to the bounds m _A ≤ 7.9 eV and m _A ≤ 1.4 eV (at 90% C.L.) for the mass of the axion in the DFSZ and KSVZ models, respectively.     

Quantum mechanics of relativistic spinless particles

A relativistic one-particle, quantum theory for spin-zero particles is constructed uponL ²(x, ct), resulting in a positive definite spacetime probability density. A generalized Schrödinger equation having a Hermitian HamiltonianH onL ²(x, ct) for an arbitrary four-vector potential is derived. In this formalism the rest mass is an observable and a scalar particle is described by a wave packet that is a superposition of mass states. The requirements of macroscopic causality are shown to be satisfied by the most probable trajectory of a free tardyon and a nontrivial framework for charged and neutral particles is provided. The Klein paradox is resolved and a link to the free particle field operators of quantum field theory is established. A charged particle interacting with a static magnetic field is discussed as an example of the formalism.     

Model basis states for photons and "empty waves"

From the perspective of physical realism (PR), a photon is a localized entity that carries energy and momentum, and which is surrounded by a wave packet (anempty wave) that is devoid of observable energy or momentum. In creating quantized PR basis states for a photon wave packet, three requirements must be met:(1) The basis states must each carry the frequency of the wave;(2) They must closely resemble the photon, so that e.g. they scatter in the same manner from an optical mirror;(3) They must have infinitesimal energy, linear momentum, and angular momentum. An essentially zero-energy "empty wave" quantum-a "zeron"-is defined which meets these requirements. It is created as an asymmetric single-particle (or single-antiparticle) excitation of the vacuum state, with the "particle" (or "antiparticle") and its associated "hole" (or "antihole") forming a rotational bound state. The photon is reproduced as a symmetric particle-antiparticle excitation of the vacuum state, with the "particle" and "antiparticle" also forming a rotational bound state. The relativistic transformation problem is discussed. A key point in this development is the deduction of the correct equation of motion for a "hole" state in an external electrostatic field.     

High-energy frenkel cation exciton and specific features of its self-trapping in the CdI<Subscript>2</Subscript>-PbI<Subscript>2</Subscript> crystal system

It has been shown using atomic-force microscopy that the PbI₂ impurity is embedded in the CdI₂ crystal lattice in the form of nanocrystalline inclusions. The model of a high-energy cation exciton related to the ³ P ₂ state of a free Pb²⁺ ion has been considered for the impurity absorption (excitation) band at 3.23 eV. The resonance narrow photoluminescence bands with the split absorption band at 3.12 and 3.20 eV have been compared with the emission of a free Frenkel exciton. It has been demonstrated that, in the temperature range 25–45 K, there arises a self-trapped exciton state, and the main role in its formation is played by the bending vibrations of the CdI₂ crystal lattice. The potential barrier separating the self-trapped state from the free exciton is 23 meV. The photoluminescence band at 2.4 eV is assigned to the emission of the self-trapped high-energy cation exciton of PbI₂ in the CdI₂ crystal lattice.     

Convexity relation for energy in quantum mechanics

The dependence of the ground-state energy E of a quantum-mechanical system on the parameter λ appearing linearly in the Hamiltonian is studied. A variation of the scale makes it possible to supplement the convexity-concavity relation for energy as a function of this parameter with a refined relation between the energies of systems that go over to one another upon a change in the particle charges or masses. This relation follows from the fundamentals of quantum mechanics and is valid for exact energies of the systems being considered. Its application does not require calculating wave functions and makes it possible to determine the boundaries of the ground-state energy level and the boundaries of the region of obvious stability of various systems. The results of applying the theory to m ₁⁺ m ₂⁺ m ₃⁻ and m ₁⁺ m ₂⁺ m ₄⁻ three- and four-particle mesic atoms and molecules featuring particles of various mass are presented.     

Fluid-dynamical representations of the Dirac equation

A relative kinetic mass operator is defined bym =c ⁻²·(E −eΦ), and it is shown that bt using it in a symmetric form one can correlate the (charge) velocity operatorα in the Dirac theory exactly with the general quantum mechanical momentum —ih∇. Then the net force, defined as the rate of change of the relative momentum with time, is exactly equal to the Lorentz force. The contribution due to the time variation of mass equals the negative of space variation of the scalar potential, the Newtonian force, whereas the time variation of the charge current absorbs the entire vector potential dependence. The analogous Euler equations can be written either in terms of the charge current or in terms of the mass current. For a many particle system one needs the usual net single particle parameters and the consideration of both the direct and exchange contributions of the two particle interaction. These Euler equations yield two different conditions of the stationary state. It is shown that the charge-current condition is necessary but not sufficient, whereas the mass-current condition retains the appropriate scalar potential dependence. These two conditions are compared for the spherically symmetric case. The charge density, charge current and relative mass current are tabulated for atomic spinors. Differences between the quantum and classical forces for the H ₂ ⁺ molecular ion exhibit the inadequacy of ordinary atomic spinor basis in forming molecular spinors.     

Mean square number fluctuation for a fermion source and its dependence on neutrino mass for the universal cosmic neutrino background

Using the general formulation for obtaining chemical potentialμ of an ideal Fermi gas of particles at temperature T, with particle rest mass m₀ and average density 〈N〉/V, the dependence of the mean square number fluctuation 〈ΔN ²〉/V on the particle mass m₀ has been calculated explicitly. The numerical calculations are exact in all cases whether rest mass energym ₀c² is very large (non-relativistic case), very small (ultra-relativistic case) or of the same order as the thermal energy k_BT. Application of our results to the detection of the universal very low energy cosmic neutrino background (CNB), from any of the three species of neutrinos, shows that it is possible to estimate the neutrino mass of these species if from approximate experimental measurements of their momentum distribution one can extract, someday, not only the density 〈N _v〉/V but also the mean square fluctuation 〈Δ _v ² 〉/V. If at the present epoch, the universe is expanding much faster than thermalization rate for CNB, it is shown that our analysis leads to a scaled neutrino massm _v instead of the actual massm _0v .