Approximate Analytical Solutions of Dirac Equation with Spin and Pseudo Spin Symmetries for the Diatomic Molecular Potentials Plus a Tensor Term with Any Angular Momentum

Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in the closed form and the spinor wave functions by using an algebraic method. We also perform numerical calculations for the Pöschl-Teller potential to show the effect of the tensor interaction. Our results are consistent with ones obtained before.     

Exact solution of a repulsive fermi model with enhanced superconducting correlations

We present the exact solution of a model of interacting fermions in any dimension with a pure repulsive interaction projecting out a given Cooper channel. The solution rests upon the infinite ranged character of the interaction in real space, leading to a functional integral that is dominated by a Gaussian term. The solution produces strong superconducting enhancements and quasi-long-ranged order in a channel that is not present in the Hamiltonian explicitly, but of the form given by arguments from order by projection.     

Triviality of a model of particles with point interactions in the thermodynamic limit

We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles effectively decreases the interaction strength. We show that the model becomes trivial in the thermodynamic limit, in the sense that the free energy density at any given particle density and temperature agrees with the corresponding expression for non-interacting particles.     

Spontaneous emission of an ensemble of 57Fe nuclei interacting with a coherent radiation field coupling the Zeeman sublevels of a nuclear excited 3/2 state

The concept “dressed nucleus” is introduced to describe the interaction of a nucleus (in a static magnetic field) with a coherent radiation field at resonance with the Zeeman sublevels. The idea is to consider the global system as a one quantum system in the Schrödinger representation. It is shown that it is possible to associate to each nuclear Zeeman substate an infinite number of equidistant energy levels, each of them having a four-fold degeneracy when any interaction with the coherent field is neglected. This periodic energy scheme, which is the same for any nuclear Zeeman substate, is a consequence of the resonance condition and of the specific form of the coherent state of the radiation field. When the interaction is included the energy degeneracy is lifted and each level splits into (2I+1)² equidistant levels, where I is the spin of the free nuclear state. The energy difference between two adjacent levels is proportional to the square root of the mean photon number in the coherent state. When the global system decays spontaneously to a possible ground state a \gamma-photon is produced. Taking into account the selection rules 24 different \gamma-energies are possible for a nuclear M1 3/2→1/2 transition.     

Interaction of a dielectric macroparticle with a point charge in plasma

The electrostatic interaction of a charged spherical dielectric macroparticle with a point charge in a plasma in the presence of an external uniform electric field is considered. The electrostatic force and the torque acting on the macroparticle have been determined, and the form of the interaction potential has been established for a nonuniform distribution of free charge on the macroparticle surface. A simple (for calculations) expression for the interaction potential that describes well the exact potential at all interparticle distances is proposed. The angular velocity of the spinning of dust particles caused by a nonuniform distribution of free charge over their surface has been estimated.     

Stable solutions for q(q) bound states with a regularized Breit potential

The Breit interaction contains singular terms which may lead to an instability in quark-antiquark bound state calculations. We regularize the Breit interaction by multiplying the singular terms in momentum space by the form factor μ2/(q2+μ2) such that the interaction is not singular at the origin and the intermediate-and long-range parts of the interaction remain unchanged. The singular terms in the Breit potential find their stable contributions in the calculations after being multiplied by the form factor with different powers. Such a regularized Breit potential with a linear and a relativistically corrected confining potential are applied to the study of qq bound states. The spectra for most familiar mesons are consistently obtained and agree well with the experimental data.     

The harmonic oscillator in a heat bath

We study the time evolution of a quantum-mechanical harmonic oscillator in interaction with an infinite heat bath, which is supposed to be initially in the canonical equilibrium at some temperature. We show that the oscillator relaxes from an arbitrary initial state to its canonical state at the same temperature, and that in the weak coupling limit the relaxation is Markovian, that is exponential. In contrast to earlier treatments of the problem [4, 5], the results are obtained without assuming any particular special form for the self-interaction of the heat bath. No use is made of coarse graining, finite memory assumptions or randomly varying Hamiltonians.     

Modulation instability in a medium with a nonlocal nonlinearity

The general conditions of appearance of the modulation instability of spatially homogeneous regimes in media with a nonlocal response of nonlinearity are determined. By using, as an example, the nonlocality in the form of the truncated Lennard-Jones potential, which is characteristic of interatomic interaction in Bose-Einstein condensates, the region of stability is found and the character of structures arising upon the loss of stability is discussed.     

Phonon-Assisted Photoluminescence in a Spherical Nanocrystal

Using the matrix density in the representation of path integrals for an electron, the multiphoton nonlinear absorption light coefficient in the second order of interaction energy with polar optical phonons is derived. This coefficient describes any electron interaction mechanism with phonons. From the interaction mechanism, the main role is played by dimensional resonance when the electron continuously absorbs energy from the field as a result of synchronizing its oscillation with the field. This dimensional resonance is possible when the frequency characterizing the laser field is a multiple of the phonon frequency. Whether a photon is absorbed or emitted, the initial level from where the transition occurs defines the temperature dependence. The absorption spectrum has the form of stripes whose intensity depends on the resonance character. The most pronounced absorption is at the triple resonance, where values of radiation and oscillatory and optical phonon frequencies are equal. __________ Published in Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 5, pp. 654–659, September–October, 2005.     

Interaction of a shear wave with a moving domain wall in an iron garnet crystal

The boundary-value problem of the interaction of a plane monochromatic shear wave with a moving Bloch wall in an iron garnet crystal is solved in the framework of the nonexchange magnetostatic approximation on the basis of the method of phase invariants for wave problems with moving boundaries. For a shear wave incident on the domain wall, the possibility of the reflectionless birefringence is demonstrated. Numerical results illustrating the resonance properties of the magnetic subsystem are presented. It is established that, at the upper bound of the reflectionless birefringence range, the interaction of the shear wave with the domain wall manifests itself as a degenerate resonance with the solution in the form of two combined antiphase, collinearly propagating shear waves of infinitely large amplitudes, which form a zero resulting field.     

Spin-polarized current through a lateral double quantum dot with spin–orbit interaction

We study the spin-polarized current through a vertical double quantum dot scheme. Both the Rashba spin–orbit (RSO) interaction inside one of the quantum dots and the strong intradot Coulomb interactions on the two dots are taken into account by using the second-quantized form of the Hamiltonian. Due to the existence of the RSO interaction, spin-up and spin-down electrons couple to the external leads with different strengths, and then a spin polarized current can be driven out of the middle lead by controlling a set of structure parameters and the external bias voltage. Moreover, by properly adjusting the dot levels and the external bias voltages, a pure spin current with no accompanying charge current can be generated in the weak coupling regime. We show that the difference between the intradot Coulomb interactions strongly influences the spin-polarized currents flowing through the middle lead and is undesirable in the generation of the net spin current. Based on the RSO interaction, the structure we propose can efficiently polarize the electron spin without the usage of any magnetic field or ferromagnetic material. This device can be used as a spin-battery and is realizable using the present available technologies.     

Nonpolynomial normal modes of the renormalization group in the presence of a constant vector potential background

We examine the renormalization group flow in the vicinity of the free-field fixed point for effective field theories in the presence of a constant, nondynamical vector potential background. The interaction with this vector potential represents the simplest possible form of Lorentz violation. We search for any normal modes of the flow involving nonpolynomial interactions. For scalar fields, the inclusion of the vector potential modifies the known modes only through a change in the field strength renormalization. For fermionic theories, where an infinite number of particle species are required in order for nonpolynomial interactions to be possible, we find no evidence for any analogous relevant modes. These results are consistent with the idea that the vector potential interaction, which may be eliminated from the action by a gauge transformation, should have no physical effects.     

A relativistic wave equation with a local kinetic operator and an energy-dependent effective interaction for the study of hadronic systems

We study a fully relativistic, two-body, quadratic wave equation for equal mass interacting particles. With this equation the difficulties related to the use of the square roots in the kinetic energy operators are avoided. An energy-dependent effective interaction, also containing quadratic potential operators, is introduced. For pedagogical reasons, it is previously shown that a similar procedure can be also applied to the well-known case of a one-particle Dirac equation. The relationships of our model with other relativistic approaches are briefly discussed. We show that it is possible to write our equation in a covariant form in any reference frame. A generalization is performed to the case of two particles with different mass. We consider some cases of potentials for which analytic solutions can be obtained. We also study a general numerical procedure for solving our equation taking into account the energy-dependent character of the effective interaction. Hadronic physics represents the most relevant field of application of the present model. For this reason we perform, as an example, specific calculations to study the charmonium spectrum. The results show that the adopted equation is able to reproduce with good accuracy the experimental data.     

Vectorial Pauli algebraic approach in polarization optics. II. Interaction of light with the canonical polarization devices

A theoretical approach to the interaction between polarized light and polarization devices, based on the vectorial and pure operatorial form of the Pauli algebra, is presented. In the first part of the paper we have established the vectorial Pauli-algebraic forms of the operators corresponding to various polarization devices and states of light polarization. In this second part we give the vectorial Pauli-algebraic treatment of the interaction between the canonical polarization devices and the various forms of light polarization. Unlike the standard (Jones and Mueller) approaches, this formalism does not appeal to any matrix representation of the involved operators. This approach establishes a bridge between the Hilbert space of the density operators of the polarization states and the Poincaré space of their geometric representations and gives a rigorous justification of the handling of the interactions between the polarization states and polarization systems on the Poincaré sphere and in the Poincaré ball. In such an approach, unlike the standard ones, the three relevant quantities that characterize the interaction - the gain, the Poincaré vector of the outgoing light and its degree of polarization - result straightforwardly, in block. A generalized form of Malus’ law, for any dichroic device and partially polarized light is also obtained this way.     

Clothed generators of the Poincaré group in a meson-nucleon system with nonlocal interaction

The nonlocal extension of trilinear Yukawa-type interaction in a meson-nucleon system is carried out in the momentum space by introducing cut-off functions (form factors) into each interaction vertex. The possibility of constructing a relativistic invariant field theory with nonlocal interaction in the clothed particle representation is shown within an algebraic approach. Original Russian Text ? V.Yu. Korda, P.A. Frolov, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 245–248.     

Interaction of a Plasma Beam with a Transverse Magnetic Barrier

The interaction of an energetic He plasma beam with a quasi step-like transverse magnetic barrier is reported. When the rate of flow of momentum in the incident beam is less than the pressure of the magnetic field, a collisionless electrostatic shock is observed to form in front of the barrier as a result of the drastic compression of the plasma. The initially cold plasma is substantially thermalized by the shock and the electron density is increased by a factor of four. In the opposite limit the plasma penetrates the barrier in a flute-like manner.     

具有非线性两模场和原子与场非线性耦合的Jaynes-Cummings模型的解

利用Lewis和Riesenfeld不变量方法求解了具有任意非线性场和依赖任意强度耦合的多光子双模场与二能级原子相互作用的JC模型,得到原子一光场的态矢、时间演化算符、原子布居和双模场的光子数算符的演化式.     

On the criterion for effectiveness of wave linear transformation in a smoothly inhomogeneous medium and of nonadiabatic transitions during atomic collisions

A universal criterion for effectiveness of linear transformation of waves with locally close characteristic exponents in smoothly inhomogeneous media is obtained. The same criterion is applicable for estimating the effectiveness of nonadiabatic transitions in slow atomic collisions. The formalism developed for an analysis of the linear interaction of waves is based of the WKB asymptotic form of the solution of a scalar nth order ordinary differential equation. The obtained criterion can be applied in any practical problem for drawing a conclusion about the effectiveness of the linear interaction of modes if only the characteristic equation of waves in a homogeneous medium and the coefficients of the initial differential equation are known. In this case, the solution of the problem is reduced to elementary arithmetic calculations.     

Chiral anomalies,low-energy theorems and the form factor of the VPP-interaction

It is shown that the account of form factors of the VPP interaction is very important for obtaining any low-energy theorems by a chiral effective lagrangian method. The connection of VPP form factors with chiral anomalies is analyzed.     

Proton radioactivity with a Yukawa effective interaction

The half-lives of proton radioactivity of proton emitters are investigated theoretically. Proton-nucleus interaction potentials are obtained by folding the densities of the daughter nuclei with a finite-range effective nucleon-nucleon interaction having Yukawa form. The Wood-Saxon density distributions for the nuclei used in calculating the nuclear as well as the Coulomb interaction potentials are predictions of the interaction. The quantum mechanical tunneling probability is calculated within the WKB framework. These calculations provide reasonable estimates for the observed proton radioactivity lifetimes. The effects of neutron-proton effective mass splitting in neutron-rich asymmetric matter as well as the nuclear matter incompressibility on the decay probability are investigated.