Additional External Field Research Articles

Chaotic walking and fractal scattering of atoms in a tilted optical lattice

We consider analytically and numerically chaotic walking of cold atoms in a tilted optical lattice created by two counter-propagating running waves with an additional external field in the semiclassical and Hamiltonian approximations. The effect consists in random-like changing the direction of atomic motion in a rigid lattice under the influence of a constant force due to a specific behavior of the atomic dipole-moment component that changes abruptly in a random-like manner while atoms cross standing-wave nodes. Chaotic walking generates a fractal-like scattering of atoms that manifests itself in a self-similar structure of the scattering function in the atom–field detuning in the position and momentum spaces. We show that the probability distribution function of the scattering time decays in a non-exponential way with a power-law tail.

Superlinear convergence of the rational Arnoldi method for the approximation of matrix functions

A superlinear convergence bound for rational Arnoldi approximations to functions of matrices is derived. This bound generalizes the well-known superlinear convergence bound for the conjugate gradient method to more general functions with finite singularities and to rational Krylov spaces. A constrained equilibrium problem from potential theory is used to characterize a max-min quotient of a nodal rational function underlying the rational Arnoldi approximation, where an additional external field is required for taking into account the poles of the rational Krylov space. The resulting convergence bound is illustrated at several numerical examples, in particular, the convergence of the extended Krylov method for the matrix square root.

Particle localization in a double-well potential by pseudo-supersymmetric fields

We study properties of a particle moving in a double-well potential in the two-level approximation placed in an additional external time-dependent field. Using previously established property (J. Phys. A 41, 244023 (2008)) that any two-level system possesses a pseudo-supersymmetry we introduce the notion of pseudo-supersymmetric field. It is shown that these fields, even if their time dependence is not periodical, may produce the effect of localization of the particle in one of the wells of the double-well potential.

Phase transitions of two-dimensional dipolar fluids in external fields

In this work, we study condensation phase transitions of two-dimensional Stockmayer fluids under additional external fields using Monte-Carlo (MC) simulations in the grand-canonical ensemble. We employ two recently developed methods to determine phase transitions in fluids, namely Wang-Landau (WL) MC simulations and successive-umbrella (SU) sampling. Considering first systems in zero field (and dipolar coupling strengths μ(2)∕εσ(3) ≤ 6), we demonstrate that the two techniques yield essentially consistent results but display pronounced differences in terms of efficiency. Indeed, comparing the computation times for these systems on a qualitative level, the SU sampling turns out to be significantly faster. In the presence of homogeneous external fields, however, the SU method becomes plagued by pronounced sampling difficulties, yielding the calculation of coexistence lines essentially impossible. Employing the WL scheme, on the other hand, we find phase coexistence even for strongly field-aligned systems. The corresponding critical temperatures are significantly shifted relative to the zero-field case.

Effect of electromagnetic Stirring on the Element Distribution in Laser Beam Welding of Aluminium with Filler Wire

Additional external electromagnetic fields are used in laser beam welding of aluminium with silicon containing filler wire to manipulate the flow of the liquid metal due to induced volume forces and hence to modify the element distribution. Aiming for a better understanding of the fluid-dynamic processes inside the meld pool, a CFD model has been implemented to simulate the melt flow. In this paper, simulation results on the resulting element distribution of filler wire material under a coaxial magnetic field with different frequencies is compared to experimental results for the same parameters. It is shown that in both cases the concentration of alloying elements of the filler material has a spatial periodicity. From the CFD model it can be concluded that the change of the distribution of the filler material results from a modulation of the melt flow due to the periodic induced electromagnetic volume forces.

From first principles of QED to an application: hyperfine structure of P states of muonic hydrogenThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010.

The purpose of this article is twofold. First, we attempt to give a brief overview of the different application areas of quantum electrodynamics (QED). These include fundamental physics (prediction of atomic energy levels), where the atom may be exposed to additional external fields (hyperfine splitting and g factor). We also mention QED processes in highly intense laser fields and more applied areas like Casimir and Casimir–Polder interactions. Both the unifying aspects as well as the differences in the the theoretical treatment required by these application areas (such as the treatment of infinities) are highlighted. Second, we discuss an application of the formalism in the fundamentally interesting area of the prediction of energy levels, namely, the hyperfine structure of P states of muonic hydrogen.

Self-assembled colloidal structures for photonics

Colloidal self-assembly has been investigated as a promising and practical approach for the fabrication of photonic nanostructures, including colloidal crystals, composite and inverse opals, and photonic glasses. Depending on the interactions between the colloidal particles, colloidal structures can be affected dramatically and modulated by applying an additional external field. Furthermore, in contrast to other approaches, self-assembled nanostructures with large areas or designed shapes can be prepared at low cost. As a result, the use of such colloidal systems has been investigated in many practical photonic applications. In this review article, we describe the colloidal self-assembly of periodic and non-periodic photonic nanostructures in brief and then summarize recent achievements in the field of colloidal photonic nanostructures and their applications, which include displays, optical devices, photochemistry and biological sensors.

On the Convergence of Rational Ritz Values

Ruhe's rational Krylov method is a popular tool for approximating eigenvalues of a given matrix, though its convergence behavior is far from being fully understood. Under fairly general assumptions we characterize in an asymptotic sense which eigenvalues of a Hermitian matrix are approximated by rational Ritz values and how fast this approximation takes place. Our main tool is a constrained extremal problem from logarithmic potential theory, where an additional external field is required for taking into account the poles of the underlying rational Krylov space. Several examples illustrate our analytic results.

Finite frequency response of small magnetic structures under an external static field

We apply the Holstein-Primakoff and Bogoliubov transformations to compute the spin-wave states of small magnetic structures including the effect of the dipolar interaction. We found that as the film gets thicker, states with a significant q = 0 component, are hybridized with states with higher Fourier components. In the presence of a static magnetic field opposite to the magnetization direction, surface states that are responsible for magnetization reversal are coupled to the extended states. The response function is increased by an order of magnitude. This suggests an intriguing scenario for assisted switching of the magnetization with an additional external ac field.

Travelling Waves with a Singularity in Magnetic Nanowires

We model the evolution of the magnetization in an infinite cylinder by harmonic map heat flow with an additional external field. Using variational methods, we prove the existence of corotationally symmetric travelling wave solutions with a moving vortex. We moreover show that for weak and strong fields the travelling waves connect the original state anti-parallel to the external magnetic field with the totally reversed state in direction of the external field. Our results match numeric simulations. For thicker wires several groups have found a reversal mode where a domain wall with a corotational symmetry and a vortex is propagating through the wire.

Coherent control of the spin current through a quantum dot

Within the weak-coupling regime the spin current through a quantum dot system is calculated using a quantum master equation approach which includes a sum over Matsubara terms. To be able to efficiently calculate, also at low temperatures, the time evolution of the reduced density matrix a high-temperature approximation was derived which proves to be rather accurate in comparison to the exact results. In the present model it is assumed that the energy levels of the dot are split by a constant magnetic field. An additional external (laser) field is used to control the currents of the two spin polarizations. This is either done using the phenomenon of coherent destruction of tunneling or optimal control theory. Scenarios are studied in which the spin current is reversed while the charge current is kept constant.

Photoassociation of cold heteronuclear dimers in static electric fields

The formation of heteronuclear molecules in their electronic ground states from a mixture of two ultracold atomic species via a one-photon stimulated emission process is investigated. The presence of an additional external homogeneous and static electric field is shown to severely influence the induced emission process. Using the LiCs molecule as a prototype, we study the corresponding cross section and its dependence on the continuum energy, final rovibrational state, and static electric field strength. The possibility of controlling the single-photon association process via an additional static electric field is demonstrated.

Controlling electrohydrodynamic pumping in microchannels through defined temperature fields

An electrohydrodynamic micropump driven by a high-frequency traveling electric wave (1–10MHz) at low voltage (4–10V) is presented. The pumping rate is dependent on the profile (inhomogeneities) of the dielectric properties of the medium. Defined temperature fields serve as a versatile mean for the control of these profiles. We produce temperature fields in two ways: by the electric wave itself and by external Peltier elements. We investigated experimentally the influence of two-dimensional and three-dimensional electrode arrays on the pumping behavior and compared it to theoretical predictions of temperature field calculations using finite element analysis. The two results are in good agreement. Furthermore, we demonstrate the effect of an additional external temperature field that results in an advanced performance of the pump.

Modeling of Adsorption and Nucleation in Infinite Cylindrical Pores by Two-Dimensional Density Functional Theory

In this paper, we present an analysis of argon adsorption in cylindrical pores having amorphous silica structure by means of a nonlocal density functional theory (NLDFT). In the modeling, we account for the radial and longitudinal density distributions, which allow us to consider the interface between the liquidlike and vaporlike fluids separated by a hemispherical meniscus in the canonical ensemble. The Helmholtz free energy of the meniscus was determined as a function of pore diameter. The canonical NLDFT simulations show the details of density rearrangement at the vaporlike and liquidlike spinodal points. The limits of stability of the smallest bridge and the smallest bubble were also determined with the canonical NLDFT. The energy of nucleation as a function of the bulk pressure and the pore diameter was determined with the grand canonical NLDFT using an additional external potential field. It was shown that the experimentally observed reversibility of argon adsorption isotherms at its boiling point up to the pore diameter of 4 nm is possible if the potential barrier of 22kT is overcome due to density fluctuations.

The role of defects in light induced domain inversion in lithium niobate

Using the tightly focussed laser beam within a confocal luminescence microscope we were able to induce electric space charge fields through photoionization of trace defects in lithium niobate. These fields are sufficient to selectively induce domain inversion when a additional external field is applied that is below the regular coercive field. Once a domain is nucleated it grows laterally in a direction that can be dictated by the laser. We studied the presence and the range of the space charge fields utilizing the electro-optical effect and the Stark shifts observed in emission spectra of Er 3 + ions.

Resonances in external fields without bound predecessors

For some potentials, such as the Hulth\'en and Yukawa potentials, the number of possible bound states depend on an internal potential parameter. Even if the parameters are chosen such that no bound state exists, resonances occur after coupling these systems to the continuum, e.g., by an additional external electric field. We will discuss those resonances which have no bound predecessor. The computations are based on complex coordinate rotations and finite elements.

Static magnetization induced by time-periodic fields with zero mean

We consider a single spin in a constant magnetic field or an anisotropy field. We show that additional external time-periodic fields with zero mean may generate nonzero time-averaged spin components which vanish for the time-averaged Hamiltonian. The reason is a lowering of the dynamical symmetry of the system. A harmonic signal with proper orientation is enough to display the effect. We analyze the problem both with and without dissipation. The results are of importance for controlling the system's state using high- or low-frequency fields and for using new resonance techniques which probe internal system parameters, to name a few.

New algebraic quantum many-body problems

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to root systems, in some cases with an additional external field. The quasi-exactly solvable models can be considered as deformations of the previous ones which share their algebraic character.

Linear giant magnetoresistance behavior of submicron scale Co/Cu multilayer strips with antiferromagnetic coupling

Linear magntoresistance (MR) response of Co/Cu multilayer strips with sub-μm width has been performed with a field sensitivity of sub-Oe. The orthogonal spin orientation for neighboring Co layers is initiated with an additional external field applied along the short axis of the strip. The thickness of the Cu layer was optimized to be 2.1 nm, at which the MR ratio of the as grown sample took a maximum value. The MR ratio of the as-grown film of [Co(2 nm)/Cu(2.1 nm)]3/Co(2 nm)/Cu(2 nm) was 12.4%. The multilayer was patterned into strips with the pattern width w down to 0.2 μm by means of electron beam lithography and Ar ion milling. The measured maximum MR ratio of the strips with w=0.4 and 0.2 μm were 9.3% and 8.2%, respectively. The observed parabolic MR profile shows good agreement with the micromagnetic simulation assuming the symmetric scissors motion of the magnetization in the multilayer. A linear MR response was observed in a giant MR strip with 0.4 μm width by applying alternating external fields, ranged from 0.1 to 10 Oe, under a transverse bias field of 300 Oe.

Quantum integrability and quantum chaos in the micromaser

The time-dependent quantum Hamiltonians $$\hat H\left( t \right) = \left\{ {\begin{array}{*{20}c} {\hat H,t_i< t< t_i + t_{int} } \\ {\omega _0 \hat N,t_i + t_{int}< t< t_i + 1,} \\ \end{array} } \right.$$ describe a maser with N two-level atoms coupled to a single mode of a quantized field inside the maser cavity: here, ti, i=1,2,…,Na, are discrete times, Na is large (∼105), $$\hat N$$ is the number operator in the Heisenberg-Weyl (HW) algebra, and ω0 is the cavity mode frequency. The N atoms form an (N+1)-dimensional representation of the su(2) Lie algebra, the single mode forming a representation of the HW algebra. We suppose that N atoms in the excited state enter the cavity at each ti and leave at ti+t int . With all damping and finite-temperature effects neglected, this model for N=1 describes the one-atom micromaser currently in operation with85Rb atoms making microwave transitions between two high Rydberg states. We show that $$\hat H$$ is completely integrable in the quantum sense for any N-1,2,… and derive a second-order nonlinear ordinary differential equation (ODE) that determines the evolution of the inversion operator SZ(t) in the su(2) Lie algebra. For N=1 and under the nonlinear condition $$\left[ {S^Z \left( t \right)} \right]^2 = \left( {1/} \right)4\hat I$$ , this ODE linearizes to the operator form of the harmonic oscillator equation, which we solve. For N=1, the motion in the extended Hilbert space H can be a limit-cycle motion combining the motion of the atom under this nonlinear condition with the tending of the photon number n to n0 determined by $$\sqrt {n_0 + 1} gt_{int} = r\pi $$ (where r is an integer and g is the atom-field coupling constant). The motion is steady for each value of ti; at each ti, the atom-field state is |e>|n0>, where |e> is the excited state of the two-level atom and $$\left. {\left. {\hat N} \right|n_0 } \right\rangle = \left. {\left. {n_0 } \right|n_0 } \right\rangle $$ . Using a suitable loop algebra, we derive a Lax pair formulation of the operator equations of motion during the times t int for any N. For N=2 and N=3, the nonlinear operator equations linearize under appropriate additional nonlinear conditions; we obtain operator solutions for N=2 and N=3. We then give the N=2 masing solution. Having investigated the semiclassical limits of the nonlinear operator equations of motion, we conclude that “quantum chaos’ cannot be created in an N-atom micromaser for any value of N. One difficulty is the proper form of the semiclassical limits for the N-atom operator problems. Because these c-number semiclassical forms have an unstable singular point, “quantum chaos” might be created by driving the real quantum system with an additional external microwave field coupled to the maser cavity.