Gross properties of heavy-ion transfer reactions: (I). Formulation

A simple approximation to the semiclassieal theory of heavy-ion transfer reactions is presented. For one-nucleon transfer reactions it reduces to the matching condition model given by Brink. Inelastic scattering and multinucleon transfer reactions can also be treated for either case in which heavy ions follow a straight-line trajectory or temporarily form a dinuclear system. For multistep processes a binary-step approximation is introduced, in which some effects of the time differences between consecutive transfer events are taken into account. Finally the possibility of treating the multinucleon transfer reaction as a Markov process is suggested.     

Semiclassical description of reactions at energies near the Coulomb barrier

The modified semiclassical approximation of Coulomb matrix elements is extended to include effects of distorting nuclear potentials in the scattering wave functions. The applicability and efficiency of the proposed semiclassical method are discussed. The advantages of this approximation are shown for a typical heavy-ion transfer reaction.     

On the reaction mechanism of two-nucleon transfer between heavy ions

The competition between simultaneous and successive transfer of two nucleons between heavy ions is studied in the semiclassical approximation. It is shown that second order effects often dominate the reaction.     

Semiclassical analysis of the spin polarization of 12B in the 100Mo(14N, 12B)102Ru reaction

Polarization of ¹²B in the ¹⁰⁰Mo(¹⁴N, ¹²B)¹⁰²Ru reaction at 90 MeV incident energy is studied on the basis of the semiclassical theory of transfer reactions proposed by Brink. Gross behaviors of both the polarization and the cross section as functions of product kinetic energy can be predicted successfully by the theory. But disagreement in the numerical values of the polarization is found for low-energy ¹²B.     

Geodesic deviation and particle creation in curved spacetimes

A quantum mechanical picture, relating accelerated geodesic deviation to creation of massive particles via quantum tunneling in curved background spacetimes, is presented. The effect is analogous to pair production by an electric field and leads naturally to production of massive particles in de Sitter and superluminal FRW spacetimes. The probability of particle production in de Sitter space per unit volume and time is computed in a leading semiclassical approximation and shown to coincide with the previously obtained expression.     

Geometric quantization and quantum field theory in curved space-time

The Kostant-Souriau geometric quantization theory is applied to the problem of constructing a generally covariant quantum field theory. The occupation number formalism for a scalar field is introduced as a semiclassical approximation which is valid in low curvature regions of space-time and which depends on making a particular choice of polarization in the classical phase space of a single massive particle. The application of the formalism to particle creation problems is outlined.     

Semiclassical theory of molecular collisions: Real and complex-valued classical trajectories for collinear atom Morse oscillator collisions

Real and complex-valued classical trajectories have been calculated for the collinear collision of an atom with a Morse oscillator. They are used in three semiclassical approximations for the transition probability: a Bessel uniform approximation, an Airy uniform approximation and a primitive semiclassical approximation. Comparison with exact quantum results shows that the Bessel uniform approximation is accurate even for near elastic collisions where the Airy and primitive approximations break down. The Airy and Bessel approximations agree quite closely for inelastic collisions however. The primitive semiclassical approximation is less accurate than either the Airy or Bessel approximation.     

Semiclassical approximation of the Dirac equation with supersymmetry

The general scheme of the successive construction of semiclassical approximation for the classical Dirac equation in a background Yang-Mills field, where the usual Dirac operator is replaced by that with supersymmetry, is suggested. The first two terms of the semiclassical expansion in Planck’s constant are derived in an explicit form. It is shown that supersymmetry of the initial Dirac operator leads to appearance of new additional terms in the classical equation of motion for spin of a particle and ipso facto requires appropriate modification for the Lagrangian of the spinning particle. The result obtained is used for the construction of one-to-one mapping between two Lagrangians of a classical color-charged spinning particle, one of which possesses local supersymmetry, and another doesn’t. It is demonstrated that for recovery of the one-to-oneness the additional terms obtained above in the semiclassical approximation of the Dirac operator with supersymmetry should be added to the Lagrangian without supersymmetry.     

Hadronic density of states from string theory

We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Güven limit of the Maldacena-Nù?ez embedding of the N=1 super Yang-Mills (SYM) into string theory. It is established that the theory exhibits a Hagedorn density of states. We propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of a Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM theory, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge.     

Classical Description of Two-Cluster Transfer Reactions in a Coulomb Field

The theory of two-cluster transfer reactions is reconsidered on the basis of a simple semiclassical approximation. The obtained expression for the differential cross section is in a closed form so as to be easily calculated. A theoretical study with calculations for the angular distribution for different incoming and outgoing energies, and also for different angular momentum transfer is introduced. Comparing our theoretical calculations with experimental data, satisfactory agreement is obtained especially in the backward direction.     

Formation of plasmon pulses in the cooperative decay of excitons of quantum dots near a metal surface

The formation of pulses of surface electromagnetic waves at a metal–dielectric boundary is considered in the process of cooperative decay of excitons of quantum dots distributed near a metal surface in a dielectric layer. It is shown that the efficiency of exciton energy transfer to excited plasmons can, in principle, be increased by selecting the dielectric material with specified values of the complex permittivity. It is found that in the mean field approximation, the semiclassical model of formation of plasmon pulses in the system under study is reduced to the pendulum equation with the additional term of nonlinear losses.     

Energy scaling for model hamiltonians in molecule-surface scattering

It is shown that scattering by model potentials for gas-surface interactions scales exactly with energy. The semiclassical sudden approximation preserves this property. Some applications are discussed in the framework of the sudden approximation.     

Application of a uniform semiclassical theory to the multiple Coulomb excitation of heavy ions

Transition probabilities of classically allowed multiple Coulomb excitation of deformed heavy nuclei induced by heavy ions are calculated within a uniform semiclassical approximation. It is found that a Bessel uniform approximation is necessary and that caustics have to be treated carefully.     

The semiclassical functional equation

A semiclassical analog of the functional equation for the Riemann zeta function is considered. In the case of the zeta function itself, this equation forms the basis for a finite approximation to the Dirichlet series, known as the approximate functional equation. In the same way, the semiclassical functional equation can be shown to give rise to a finite approximation to the semiclassical representation of the quantum spectral determinant as a sum over classical pseudo-orbits. This finite approximation has been called the Riemann-Siegel look-alike formula. The formal nature of the derivation of this result is discussed and the fact that it appears to imply a remarkable relationship between long and short pseudo-orbits is shown.     

Pairing collective modes in superfluid nuclei: a semiclassical approach

Collective pairing excitations in superfluid nuclei are studied by using the semiclassical time-dependent Hartree-Fock-Bogoliubov equations of motion in a linear approximation. It is found that the strength function associated with the semiclassical anomalous density response function has a resonance structure with a sharp peak around double energy gap that displays the monopole pairing collective mode.     

Cosmological perturbations and quantum fields in curved space

We identify the quantum theory of cosmological perturbations with the quantum field theory in curved spacetime with emphasis on its field concept. We materialize this idea by using a coherent state as a quantum analogue of a nontrivial classical field configuration. We present analytic results in a de Sitter universe for the massless and massive minimal free scalar fields. Some new features on the spectrum of perturbations are obtained for the massive case. We also show how such quantum field theories can be derived from quantum gravity using the semiclassical approximation. A physical degree of freedom is picked up from three scalar perturbations in the quantum gravity scalar system and its Schrödinger equation is derived. Peculiar features of quantum fields at imaginary time and its possible implications on boundary conditions for the wave function of the universe are also discussed.     

开放量子台球体系散射的赝路径半经典近似

本文讨论正方形量子台球的输运性质,考虑电子以费米能量穿过台球区域,在台球出口和入口处对入射和出射波函数采用基尔霍夫散射.采用微扰论的Dyson方程得到半经典格林函数,并把赝路径半经典近似作微扰展开得到体系的传输矩阵元.比较了传输矩阵元的傅立叶变换谱的峰位置与腔内自由电子经典轨道长度,发现在精度允许范围内它们符合的很好.     

Semiclassical correlation functions of Wilson loops and local vertex operators

We analyze correlation functions of Wilson loop observables and local vertex operators within the strong-coupling regime of the AdS/CFT correspondence. When the local operator corresponds to a light string state with finite conserved charges the correlation function can be evaluated in the semiclassical approximation of large string tension, where the contribution from the light vertex can be neglected. We consider the cases where the Wilson loops are described by two concentric surfaces and the local vertices are the superconformal chiral primary scalar or a singlet massive scalar operator.