Quantum corrections to the semiclassical level density of the circular disk in homogeneous magnetic fields

In the semiclassical trace formula for the level density of a circular disk in homogeneous magnetic fields, quantum corrections to the Maslov phase have been shown to be important in strong fields. In this article further quantum corrections are considered, namely, grazing corrections which are relevant for whispering-gallery orbits, and a uniform approximation to the bifurcation points in strong fields is applied. Both corrections are shown to have a surprisingly small effect on the semiclassical level density. Implementing those corrections requires a technique different from the common Gaussian smoothing in the numerical evaluation of the trace formula. The appropriate generalization is presented. 1997 Elsevier Science B.V. All rights reserved.     

Kerr-Newman黑洞的熵修正

基于Majhi等人最近的工作,利用狄拉克方程,在半经典近似外讨论了Kerr-Newman黑洞的熵修正.在单位制G=c=kB=1下,由于普朗克常数与普朗克长度,普朗克质量和普朗克电荷的平方成正比,作用量的量子修正项与半经典项的比例常数被选为(Mrh-Q2/2)-1.结合视界方程的微分形式和黑洞热力学第一定律,本文得到了荷电稳态黑洞的修正熵并发现修正项同样包括Bekenstein-Hawking熵的对数项和倒数项.     

Higher-order semiclassical energy expansions for potentials with non-integer powers

In this paper, we present a semiclassical eigenenergy expansion for the potential |x|^α when α is a positive rational number of the form2n/m (n is a positive integer and m is an odd positive integer). Remarkably, this expansion is found to be identical to the WKB expansion obtained for the potentialx ^N(N-even), if2n/m is replaced byN. Taking the limitm → 2 of the above expansion, we obtain an explicit asymptotic energy expansion of symmetric odd power potentials |x|^2j+1 (j- positive integer). We then show how to develop approximate semiclassical expansions for potentials |x|^α when α is any positive real number.     

Semiclassical Limit for the Schrödinger Equation¶with a Short Scale Periodic Potential

We consider the dynamics generated by the Schr?dinger operator H=−?Δ+V(x)+W(ɛx), where V is a lattice periodic potential and W an external potential which varies slowly on the scale set by the lattice spacing. We prove that in the limit ɛ→ 0 the time dependent position operator and, more generally, semiclassical observables converge strongly to a limit which is determined by the semiclassical dynamics. Received: 7 February 2000 / Accepted: 7 July 2000     

Particle Creation in Anisotropically Expanding Universe

Using squeezed vacuum states formalism of quantum optics, a homogeneous and massive scalar field minimally coupled to gravity in Bianchi type-I model of the universe is examined in the frame work of semiclassical theory of gravity. Hence an approximate leading solution to the semiclassical Einstein equation is found. The next order solution for each scale factor in their respective direction show power law of expansion. It is further noted that evolution of scale factors are mutually correlated. The phenomena of nonclassical particle creation is also examined in the anisotropic background cosmology.     

Beyond the Semiclassical Description of Black Hole Evaporation

In the semiclassical treatment, i.e. in a classical black hole geometry, Hawking quanta emerge from trans-Planckian configurations because of scale invariance. There is indeed no scale to stop the blueshift effect encountered in the backward propagation toward the event horizon. On the contrary, when taking into account the gravitational interactions neglected in the semiclassical treatment, a new UV scale could be dynamically engendered and could stop the focusing. To show that this is the case, we use the large-N limit, where N is the number of matter fields. In this limit, the semiclassical treatment is the leading contribution. Nonlinear gravitational effects appear in the next orders and in the first of these, the effects are governed by the two-point correlation function of the energy–momentum tensor evaluated in the vacuum. In this case they can also be obtained by considering light propagation in a stochastic ensemble of metrics whose mean fluctuating properties are determined by this two-point function.     

Photodetachment of H- near an elastic surface in a magnetic field

This paper investigates the photodetachment of the negative hydrogen ion H near an elastic wall in a magnetic field.The magnetic field confines the perpendicular motion of the electron,which results in a real three-dimensional well for the detached electron.The analytical formulas for the cross section of the photodetachment in the threedimensional quantum well are derived based on both the quantum approach and closed-orbit theory.The magnetic field and the elastic surface lead to two completely different modulations to the cross section of the photodetachment.The oscillation amplitude depends on the strength of the magnetic field,the ion-wall distance and the photon polarization as well.Specially,for the circularly polarized photon-induced photodetachment,the cross sections display a suppressed(E E th) 1/2 threshold law with energy E in the vicinity above Landau energy E th,contrasting with the(E E th) 1/2 threshold law in the presence of only the magnetic field.The semiclassical calculation fits the quantum result quite well,although there are still small deviations.The difference is attributed to the failure of semiclassical mechanics.     

Use of a diabatic molecular expansion in studies on electron capture by He2+ ions in helium at keV energies

In this preliminary work, using a 3-state diabatic molecular expansion without any excited channels, we have studied within the semiclassical impact parameter approximation the single charge transfer process He²⁺+He(1s ²)→He⁺(1s)+He⁺(1s). Our results agree very well with experiment, which demonstrates the usefulness of this type of diabatic molecular basis in doubly charged ion-atom collision systems.     

On the semiclassical green's function in the energy-representation

We present a detailed discussion of the semiclassical approximation for the Green's function in the energy representation, G(qⁱ,q^j; E). In particular, we describe the way in which classical catastrophes influence the semiclassical approximation, and present a practical scheme to determine the phases with which the contributions due to the various classical trajectories enter the semiclassical result.     

Pair Interaction Potential of Particles for Two‐Component Plasma

In this work the semiclassical potential for plasma particles pair interactions, which takes into account the diffraction effects due to the uncertainty principle in two‐component plasma (the region of temperatures 10⁴K < T < 10⁸K and densities 10²¹cm^–3 < n ≤ 10²⁴cm^–3), was proposed. The values of this potential were numerically calculated and an interpolation formula was obtained (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantum Transport on KAM Tori

Although quantum tunneling between phase space tori occurs, it is suppressed in the semiclassical limit for the Schr?dinger equation of a particle in ℝ ^d under the influence of a smooth periodic potential. In particular this implies that the distribution of quantum group velocities near energy E converges to the distribution of the classical asymptotic velocities near E, up to a term of the order . Received: 14 December 1998 / Accepted: 19 February 1999     

Semiclassical approach to the three-body muon-transfer collisions

Muon-transfer rates in collisions of hydrogen-like atoms or with light nuclei t, ³He, ⁴He, ⁶Li or ⁷Li, are calculated in a semiclassical approximation to the Faddeev-Hahn equations. The two nuclei involved are treated classically, while the motion of the muon in their Coulomb field is considered from the quantum mechanical point of view. The experimentally observed strong dependence on the charge of the nuclei is reproduced. Received: 1st November 1997 / Revised: 26 March 1998 / Accepted: 18 August 1998     

Fermion tunnels of higher-dimensional anti-de Sitter Schwarzschild black hole and its corrected entropy

Applying the method beyond semiclassical approximation, fermion tunneling from higher-dimensional anti-de Sitter Schwarzschild black hole is researched. In our work, the “tortoise” coordinate transformation is introduced to simplify Dirac equation, so that the equation proves that only the (r−t) sector is important to our research. Because we only need to study the (r−t) sector, the Dirac equation is decomposed into several pairs of equations spontaneously, and we then prove the components of wave functions are proportional to each other in every pair of equations. Therefore, the suitable action forms of the wave functions are obtained, and finally the correctional Hawking temperature and entropy can be determined via the method beyond semiclassical approximation.     

Semiclassical approximation for the specific heat of non-crystalline solids at intermediate temperatures

The origin of the broad maximum in the specific heat (c _P) of glassy systems in the c _P/T ³ representation, in correspondence with the boson peak, has been described from a semiclassical perspective. A new model, based in the Debye approximation, taking into account the anharmonic vibrations of correlated atoms, is proposed. The theoretical predictions are shown to be in good agreement with the experimental data obtained in several glass samples in the temperature range 2–80 K.     

Quantum fluctuations around a non-instanton solution

We study the two-dimensional Euclidean CP ^n-1 model and illustrate some problems encountered with the semiclassical approximation in a particular case of a non-instanton solution. Further, we make some general remarks on the problem of quantum fluctuations around the complete solution manifold of the model.Research supported by the Swiss National Science Foundation.     

Associative ionization in slow collisions of atoms

An analysis of the modern theory of associative ionization (AI) is performed, and ways of its further development are discussed. The threshold behavior of the cross section of endothermic AI reactions is considered and it is shown that, in the quantum case, its dependence on the above-threshold energy E is strictly linear, i.e., significantly different from the E ^3/2 law ensuing from the semiclassical theory. This has a simple explanation, since the matrix elements of the scattering operator are finite at E = 0 due to the tunneling effect. The possibility of describing the dynamics of an elementary AI event within the framework of the diffusion approximation is substantiated, and the conditions of applicability of the theory of “quantum chaos” to treating the spectrum of highly excited Rydberg molecules are examined. The quantum properties of the exothermic processes of AI and Penning ionization in the case of the states of the interacting atoms being autoionizing are discussed in detail. A comparison with the semiclassical theory is presented.