Path-integral formulation of conformal anomalies

We present a path-integral formulation of conformal anomalies and point out an intimate interplay of the local Poincaré anomaly and the dilatational anomaly. A key observation in our approach is that the algorithm of the path-integral formulation has natural foundation within the zeta-function regularization scheme. This observation shows us how to treat nonlinear systems as well as higher-order anomalies and suggests a way to understand the Adler-Bardeen theorem for chiral anomalies within the path-integral approach.     

An alternative formulation for the analysis and interpretation of the Dirac hydrogen atom

The second-order radial differential equations for the relativistic Dirac hydrogen atom are derived from the Dirac equation treated as a system of partial differential equations. The quantum operators which arise in the development are defined and interpreted as they appear. The splitting in the energy levels is computed by applying the theory of singularities for second-order differential equations to the Klein-Gordon and Dirac relativistic equations. In the Dirac radial equation additional terms appear containing a constant, which is shown to be the radius of the electron. It is concluded that the minute perturbation of the radial eigenfunction in the vicinity of the proton brought about by the extension of the elementary particles, which appears naturally out of the Dirac equations, results in the prediction of the observed splitting of the hydrogen atom energy levels by the Dirac theory. The extension of the particles arises even though the Dirac hydrogen atom is originally formulated for point charges.     

The improved quantization rule and the Langer modification

An improved quantization rule is used to obtain a generalized formulation of Langer modification. The relations between the improved quantization rule and the Langer modification are studied. Two typical quantum systems, hydrogen atom and harmonic oscillator, are studied to show the relations between them.     

Path-integral formulation of two-dimensional gauge theories with massless fermions

We study (1 + 1) dimensional gauge theories [with SU(N) and diagonal SU(N) color symmetry] using the functional integral method. We construct an effective lagrangian by performing a change in the fermionic variables, and then investigate relevant phenomena such as the intrinsic Higgs mechanism and color screening.     

二维氢原子的相对论修正

求解了二维氢原子的狄拉克方程,得到了精确的相对论能级与波函数,并详细讨论了非相对论极限.     

Path-integral formulation of chiral invariant fermion models in two dimensions

We study the Thirring and chiral-invariant Gross-Neveu (CGN) models using the functional integral method. By introducing an auxiliary vector field we disclose a relation with two-dimensional gauge theories coupled to fermions and then extend a technique based on a chiral change in the functional variables to study purely fermionic models.We obtain the exact Klaiber solution for the massless Thirring model (for spin $\text{1}\text{2}$) in a very simple way and we then extend our technique to investigate the CGN model. We show the factorization of a free fermionic part at the level of Green functions on very general grounds. We then impose certain restrictions on the behavior of the fields — which render our treatment exact only in the zero winding number sector, but allow the computation of the U(1) part of the CGN Green functions exactly, showing, in particular, its complete decoupling from the color part and the almost long-range order behaviour in the infrared region.In our approach, the non-triviality of the jacobian arising from the chiral transformation — directly related to the topological density and the axial anomaly — appears to be crucial for the functional integral treatment of these models.     

氢原子的总电流及其经典对应

定态下氢原子平均电流密度只有一个沿纬线的分量非零,本文在这一结果的基础上计算了氢原子的总电流,发现它与经典力学中行星运动的开普勒定律之间有明确的对应关系．     

Development of lattice inversion modified embedded atom method and its applications

The modified embedded atom method (MEAM) has been widely used in describing the physical properties of elemental crystals, alloys and compounds with multiple lattice structures. We report here the development of a reliable procedure to reduce the complexity of the MEAM formalism by removing the many-body screening function. In the proposed formulation, the interatomic pair potential is obtained by applying Chen-Möbius lattice inversion up to fifth nearest neighbors, so that the cohesive energy curve can be reproduced faithfully. The newly developed model (Lattice Inversion MEAM, LI-MEAM), which can be viewed as a direct extension of the embedded atom method (EAM), no longer requires the computation of many-body screen functions and has fewer adjustable parameters than MEAM. As an illustration, we optimized the potential parameters of body centered cubic iron (bcc-Fe). The values of the calculated physical properties agree well with experimental results. We further investigated the size-dependent melting behavior of bcc-Fe nanoparticles (NPs) with particle size ranging from 725-atom (∼25 Å) to 22899-atom (∼80 Å) using replica exchange molecular dynamics (REMD) simulations. Our simulations show advantages of LI-MEAM in modeling of the melting process and quantitatively reveals that the liquid skin melting (LSM) process of bcc-Fe NPs.     

Non-commutativity of space-time and the hydrogen atom spectrum

There has been disagreement in the literature on whether the hydrogen atom spectrum receives any tree-level correction due to non-commutativity. Here we shall clarify this issue and show that indeed a general argument on the structure of the proton as a non-elementary particle leads to the appearance of such corrections. As a showcase, we evaluate the corrections in a simple non-relativistic quark model with a result in full agreement with the previous one we had obtained by considering the electron moving in the external electric field of proton. Thus the previously obtained bound on the non-commutativity parameter, , using the Lamb shift data, remains valid.Received: 10 October 2003, Revised: 12 November 2003, Published online: 2 July 2004     

Atomic interferometer with amplitude gratings of light and its applications to atom based tests of the equivalence principle

We have developed a matter wave interferometer based on the diffraction of atoms from effective absorption gratings of light. In a setup with cold rubidium atoms in an atomic fountain the interferometer has been used to carry out tests of the equivalence principle on an atomic basis. The gravitational acceleration of the two isotopes 85Rb and 87Rb was compared, yielding a difference Deltag/g=(1.2+/-1.7)x10(-7). We also perform a differential free fall measurement of atoms in two different hyperfine states, and obtained a result of Deltag/g=(0.4+/-1.2)x10(-7).     

Parity nonconservation in the hydrogen atom

We investigate the possibility of observing parity nonconservation with a metastable hydrogen atom beam, by analyzing two effects which should permit detection of the 2S–2P admixture predicted by the Weinberg model.     

A dynamical formulation of one-dimensional scattering theory and its applications in optics

We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical equations. By decoupling and partially integrating these equations, we reduce the scattering problem to a second order linear differential equation with universal initial conditions that is equivalent to an initial-value time-independent Schrödinger equation. We give explicit formulas for the reflection and transmission amplitudes in terms of the solution of either of these equations and employ them to outline an inverse-scattering method for constructing finite-range potentials with desirable scattering properties at any prescribed wavelength. In particular, we construct optical potentials displaying threshold lasing, antilasing, and unidirectional invisibility.     

Path-integral approach to the two-dimensional magneto-conductivity problem

We express Green's function and conductivity of an electron impurity system in the presence of a magnetic field or arbitrary strength in terms of Feynman path integrals and obtain an approximate formula for both the propagator and conductivity as the lowest order contribution of a systematic cumulant expansion. This approach takes the coherent scattering of an electron by impurity clusters at least approximately into account, in contrast to the self-consistent Born approximation (GBA) and similar approximations which are based on a partial summation of diagrams.In part II of this paper we apply this approach to a two-dimensional system, e.g. the surface channel of a field effect transistor, where the GBA leads to inconsistencies which arise from the discrete nature of the unperturbed energy spectrum in a quantizing magnetic field.     

Group theory and orbital fluctuations of the hydrogen atom

We review some of the progress made in the past 27 years in understanding the group theoretic and path integral aspects of the hydrogen atom. The group theoretic development was triggered by A. O. Barut who suggested to me the search for a dynamical group larger than SO(4). In this way he became indirectly responsible also for important recent path integral developments.Supported in part by Deutsche Forschungsgemeinschaft under Grant K1 256.     

Perturbative approach to the hydrogen atom in a strong magnetic field

We consider states of the hydrogen atom with the principal quantum number n≤3 and zero magnetic quantum number in a constant homogeneous magnetic field ?. The perturbation theory series is summed using the Borel transformation and conformal mapping of the Borel variable. Convergence of the approximate energy eigenvalues and their agreement with the corresponding existing results are observed for external fields up to n³?/?₀～5, where ?₀ is the atomic magnetic field. The possibility of restoring the asymptotic behavior of energy levels using perturbation theory coefficients is also discussed.     

Coincidental spectral lines for the hydrogen atom

Asim Barut once,en passant, asked the question “For what transitions of the hydrogen atom do the spectral lines coincide”? It is a pleasure for us to give the answer in this paper.     

Perturbation of the excited states of the hydrogen atom and hydrogen-like ions by a neutral atom

Owing to the degeneracy of the energy levels, the wavefunction of the electron in the excited states of the hydrogen atom and hydrogen-like ions perturbed by a neutral atom B is significantly different from the wavefunction of the unperturbed state. The perturbed function has a wide high maximum in the region of atom B, which is explained by multiple collisions of the electron with atom B, because the classical trajectories in the Coulomb field are closed and the size of atom B is much smaller than the size of the excited-state orbit. The radiative lifetimes of the excited states are much larger than those of unperturbed states. The orbital angular momentum L of the excited electron is strongly changed in collisions with atom B owing to the quantum interference or mixing of the temporal phases of adiabatic wavefunctions. The cross sections for such a change in the orbital angular momentum are several orders of magnitude larger than the cross sections found in early investigations in the approximation of the single collision of the electron with atom B.