The Aharonov-Bohm effect for a knotted magnetic solenoid

We show that the linking of a semiclassical path of a charged particle with a knotted magnetic solenoid results in the Aharonov-Bohm effect. The phase shift in the wave function is proportional to the flux intersecting a certain connected and orientable surface bounded by the knot (a Seifert surface of the knot).     

Semiclassical Asymptotics of the Aharonov‐Bohm Interference Process

We systematically derive the semiclassical limit of a charged particle's motion in the presence of an infinitely long and infinitesimally thin solenoid carrying magnetic flux. Our limit establishes the connection of the particle's quantum mechanical canonical angular momentum to the latter's classical counterpart. A picture of Aharonov‐Bohm interference of two half‐waves acquiring Dirac's magnetic phase when passing on either side of the solenoid naturally emerges from the quantum propagator. The resulting interference pattern is fully determined by the ratio of the angular part of Hamilton's principal function to Planck's constant, and the wave interference smoothes out discontinuities in the semiclassical propagator which is recovered in the limit when the above ratio diverges. We discuss the relation of our results to the whirling‐wave representation of the exact propagator, and to previous approaches on the system's asymptotics.     

Gauge-invariant charged,monopole and dyon fields in gauge theories

We propose explicit recipes to construct the Euclidean Green functions of gauge-invariant charged, monopole and dyon fields in four-dimensional gauge theories whose phase diagram contains phases with deconfined electric and/or magnetic charges. In theories with only either abelian electric or magnetic charges, our construction is an Euclidean version of Dirac's original proposal, the magnetic dual of his proposal, respectively. Rigorous mathematical control is achieved for a class of abelian lattice theories. In theories where electric and magnetic charges coexist, our construction of Green functions of electrically or magnetically charged fields involves taking an average over Mandelstam strings or the dual magnetic flux tubes, in accordance with Dirac's flux quantization condition. We apply our construction to 't Hooft-Polyakov monopoles and Julia-Zee dyons. Connections between our construction and the semiclassical approach are discussed.     

Momentum-transfer scattering cross section and the Aharonov-Bohm effect on a toroidal solenoid

The quantum-mechanical Aharonov-Bohm effect in the diffraction of charged particles by a toroidal solenoid containing a magnetic field is investigated. The total and differential elastic scattering cross sections depend on the magnetic flux inside the solenoid, even in the presence of a “black” ring-shaped screen which prevents charged particles from entering the region where the magnetic field is localized. Relations describing the momentum-transfer cross section for the elastic scattering of charged particles by a toroidal solenoid are obtained in the eikonal approximation and in a unitary model of scattering with a sharp jump in the partial amplitudes. The momentum-transfer scattering cross section is proportional to the average transfer of the longitudinal momentum of the scattered particle and can be expressed in terms of a force operator. It is shown that in the absence of a screen the momentum-transfer scattering cross section of toroidal solenoid is indeed determined only by the part of the incident beam that intersects the inner region of the toroidal solenoid, where the magnetic field intensity and, therefore, the Lorentz force are nonzero. At the same time, the momentum-transfer cross section for the scattering of charged particles by a toroidal solenoid covered by a “black” ring-shaped screen does not depend on the magnetic flux inside the solenoid and is identical to the momentum-transfer cross section for diffraction by the same screen. The contribution from scattering by an opening in the screen, which depends on the magnetic flux, is completely compensated by the contribution of the interference of the scattering amplitudes of the opening and the “black” screen.     

Magnetization of disordered ballistic quantum billards

We study the magnetic response of mesoscopic quantum dots in the ballistic regime where the mean free path l_e is larger that the size L of the sample, yet smaller than L(K_FL)^d?1. In this regime, disorder plays an important role. Employing a semiclassical picture we calculate the contribution of long tranjectories which are strongly affected by static disorder and which differ sharply from those of clean systems. In the case of a magnetic field, they give rise to a large linear paramagnetic susceptibility (which is disorder independent), whose magnitude is in agreement with recent experimental results. In the case of a Aharonov-Bohm flux, the susceptibility is disorder dependent and is proportional to the mean free path as in the diffusive regime. We also discuss the corresponding non-linear susceptibilities.     

2D laser collimation of a cold Cs beam induced by a transverse <Emphasis Type="Italic">B</Emphasis> field

We describe transverse collimation of a continuous cold cesium beam (longitudinal temperature 75 μK) induced by a two-dimensional, blue-detuned near-resonant optical lattice. The mechanism described for a lin-‖-lin configuration is made possible by the application of a transverse magnetic field B_⊥. The phenomenon described differs from gray molasses, for which any small magnetic field degrades cooling, as well as from magnetically induced laser cooling in red-detuned optical molasses, where there are no dark states. The lowest transverse temperature is experimentally found to vary as B _⊥ ² . The collimated flux density shows a dip as a function of B_⊥, the width of which is proportional to the cube root of the laser intensity, general features predicted by our semiclassical model. This technique provides a sensitive tool for canceling transverse magnetic fields in situ at the milligauss level.     

Bifurcation phenomena of photodetached electron flux in parallel external fields

A semiclassical method based on the closed-orbit theory is applied to analysing the dynamics of photodetached electron of H$^- $ in the parallel electric and magnetic fields. By simply varying the magnetic field we reveal spatial bifurcations of electron orbits at a fixed emission energy, which is referred to as the fold caustic in classical motion. The quantum manifestations of these singularities display a series of intermittent divergences in electronic flux distributions. We introduce semiclassical uniform approximation to repair the electron wavefunctions locally in a mixed phase space and obtain reasonable results. The approximation provides a better treatment of the problem.     

Photo-Detachment of a Noncollinear Triatomic Anion

Photo-detachment of a noncollinear triatomic anion is investigated by considering each atom of the molecular anion as a coherent source of detached-electron waves, originating in all possible directions. The waves traveling along three different trajectories result in a quantum interference that displays on a screen placed at a very large distance from the system. To explain this quantum interference, an analytical formula of detached-electron flux is derived using a collinear three-center model recently published. The detached-electron flux versus laser photon energy expression displays molecular geometry-dependent oscillatory structures on an observation plane. This oscillatory behavior in the result can be explained using the semiclassical closed-orbit theory. The outgoing electron waves produced from one coherent center are propagated in the vicinity of the sources at other two coherent centers which cause these oscillations. It is also observed that in a particular case, the noncollinear triatomic system reduces to the collinear three-center system.     

Fano and Kondo resonance in electronic current through nanodevices

Electronic transport through a quantum dot strongly coupled to electrodes is studied within a model with two conduction channels. It is shown that multiple scattering and interference of transmitted waves through both channels lead to Fano resonance associated with Kondo resonance. Interference effects are also pronouncedly seen in transport through the Aharonov-Bohm ring with the Kondo dot, where the current characteristics continuously evolve with the magnetic flux.     

Effects of inhomogeneous magnetic fields on the electron transport through a quantum-wire system

The electron transport through a quantum-wire system in the presence of inhomogeneous magnetic fields is investigated theoretically. The system consists of two parallel quantum wires coupled by two ballistic windows, while the magnetic fields applied are uniform and equal in the two wires but vanishing in the two coupling windows and everywhere between the wires. Various transmissions of the system are calculated. It is found that the inhomogeneous magnetic fields induce irregular transmission oscillations in the low and moderate magnetic-field regions, and regular ones in the high field region. These transmission oscillations are due to interference between the electron waves traveling through different coupling windows and can be interpreted in terms of a semiclassical model. The Hall resistance of the system is also calculated and is found to show similar regular oscillations at high magnetic fields.     

Quantum transport in coupled resonators enclosed synthetic magnetic flux

Quantum transport properties are instrumental to understanding quantum coherent transport processes. Potential applications of quantum transport are widespread, in areas ranging from quantum information science to quantum engineering, and not restricted to quantum state transfer, control and manipulation. Here, we study light transport in a ring array of coupled resonators enclosed synthetic magnetic flux. The ring configuration, with an arbitrary number of resonators embedded, forms a two-arm Aharonov–Bohm interferometer. The influence of magnetic flux on light transport is investigated. Tuning the magnetic flux can lead to resonant transmission, while half-integer magnetic flux quantum leads to completely destructive interference and transmission zeros in an interferometer with two equal arms.     

Viscous fingering and the shape of an electronic droplet in the quantum Hall regime

We show that the semiclassical dynamics of an electronic droplet, confined in a plane in a quantizing inhomogeneous magnetic field in the regime where the electrostatic interaction is negligible, is similar to viscous (Saffman-Taylor) fingering on the interface between two fluids with different viscosities confined in a Hele-Shaw cell. Both phenomena are described by the same equations with scales differing by a factor of up to 10(-9). We also report the quasiclassical wave function of the droplet in an inhomogeneous magnetic field.     

Parametric decay of a magnetic island structure

It is shown that a spatially periodic magnetic island structure can decay into a tearing mode and long-wavelength magnetohydrodynamic fluctuations. The tearing mode has a linger wavelength than that of the island structure, and the growth rate is proportional to $\text{?}{}^{\mathrm{<mtext>3</mtext><mtext>4</mtext>}}$, where ε is the ratio of the reconnection magnetic flux to the shear field flux in the original structure.     

Interferences in photo-detached electron spectra from a non-collinear tri-atomic anion

The electron flux oscillations in photo-detachment of a non-collinear tri-atomic anion have been studied by taking each atom of the system as a coherent source of detached-electron wave. These electron waves traversing along three different trajectories result in a quantum interference. An analytical expression of detached-electron flux is evaluated for various detached-electron energies and for different geometrical shapes of the system. The results show that the electron flux distributions exhibit molecular shape-induced oscillatory structures. These oscillations are explained using the semi- classical closed-orbit theory; the outgoing electron waves produced from one center are propagated in the vicinity of the sources at other centers. It is also observed that in a particular case our non-collinear tri-atomic system reduces to the collinear tri-atomic system recently published.     

级联型爆磁压缩发生器的等效电路计算

 动态级联型爆磁压缩发生器由多级构成,后一级俘获前一级的磁通进而将能量放大。用镜像电流法计算装置等效电感和电阻,用磁通俘获模型计算两级间磁通耦合,并假设损耗电阻正比于直流电阻。用该等效电路方法计算了一种两级动态级联型爆磁压缩发生器的静态和动态电路参数,并对其输出电流波形进行了模拟,同实际测量和实验结果进行了比较,同时对该装置通过脉冲变压器对脉冲形成线的充电过程进行了简单的模拟计算。结果表明,该计算方法对级联型爆磁压缩发生器的优化设计和应用研究具有较好的指导作用。另外两级磁通俘获模型对于间接馈电（线圈或永磁体）装置模拟计算也有一定的参考价值。     

Complex-Domain Semiclassical Theory: Application to Time-Dependent Barrier Tunneling Problems

Semiclassical theory based upon complexified classical mechanics is developed for periodically time-dependent scattering systems, which are minimal models of multi-dimensional systems. Semiclassical expression of the wave-matrix is derived, which is represented as the sum of the contributions from classical trajectories, where all the dynamical variables as well as the time are extended to the complex-domain. The semiclassical expression is examined by a periodically perturbed 1D barrier system and an excellent agreement with the fully quantum result is confirmed. In a stronger perturbation regime, the tunneling component of the wave-matrix exhibits a remarkable interference fringes, which is clarified by the semiclassical theory as an interference among multiple complex tunneling trajectories. It turns out that such a peculiar behavior is the manifestation of an intrinsic multi-dimensional effect closely related to a singular movement of singularities possessed by the complex classical trajectories.     

Light scattering,origin invariant multipole moments and molecular property tensors: the case of electric-field-gradient-induced birefringence

A comparison of semiclassical and quantum versions of molecular light scattering theory at finite temperatures is presented. A general formulation of the semiclassical radiation model is developed to the point where its relationship to the corresponding QED formalism can be established: the classical scattered electric field is proportional to the same R-matrix element as that obtained from QED for the photon scattering amplitude. The result is valid for non-resonant scattering at T = 0. The semiclassical theory conventionally also inherits aspects of a classical molecular model, principally origin-dependent molecular multipole moments. Origin independent multipoles, and corresponding response functions can be defined if the theory is cast in terms of centre-of-mass and translation invariant internal coordinates. Such a choice of coordinates brings molecular light scattering theory into line with the theory of the molecular Schrödinger equation. This is illustrated for the case of a diatomic molecule. A specific application of these results of current interest is electric-field-gradient induced birefringence (EFGB) for which there are four competing theories in the literature. In this paper we examine the treatment of finite temperature effects in two semiclassical accounts of EFGB in polar molecules and identify a likely source of the discrepancy between them revealed in a recent ab initio computational study.     

Röntgen quantum phase shift: a semiclassical local electrodynamical effect?

The R?ntgen quantum phase shift is exhibited by the interference of point particles endowed with an electric dipole moment due to their motion relative to a source of the magnetic field. Here we show, using arguments involving the classical concepts of force and its impulse, that the R?ntgen phase shift arises within a largely classical (semiclassical) theoretical framework. All the subtleties normally associated with the nonlocality of magnetic (Aharonov-Bohm-type) quantum phase phenomena are uncontroversially absent in the classical treatment.     

The Aharonov–Bohm Phase Shift and Boyer's Critical Considerations: New Experimental Result but Still an Open Subject?

The main experiments concerning the Aharonov–Bohm phase shifts, seen in an electron interference pattern, and their Boyer semiclassical explanations are reviewed. A new experiment is also presented which emphasizes the subtleties involved in the interpretations of the magnetic Aharonov–Bohm phase shift as a result of a non-dispersive or dispersive effect.