Spin correlation and discrete symmetry in spinor Bose-Einstein condensates

We study spin correlations in Bose-Einstein condensates of spin 1 bosons with scatterings dominated by a total spin equal 2 channel. We show that the low energy spin dynamics in the system can be mapped into an o(n) nonlinear sigma model. n = 3 at the zero magnetic field limit and n = 2 in the presence of weak magnetic fields. In an ordered phase, the ground state has a discrete Z2 symmetry and is degenerate under the group [U(1)xS(n-1)]/Z(2). We explore consequences of the discrete symmetry and propose some measurements to probe it.     

Spin-current-induced classical and quantum effects in the dynamics of a mesoscopic magnet

The dynamics of a high-spin quantum system with magnetic anisotropy of the easy plane type under the action of spin-polarized current permeating this system is considered. The spin-polarized current (with electron spins polarized along the hard magnetic axis of the system) induces the reorientation of the magnetic moment of the system from the easy plane to the hard magnetic axis. Analytical expressions describing characteristics of the reorientation process in the limiting cases of strong and weak dissipation are obtained. Under strong dissipation conditions, the reorientation is shown to have a threshold character with “soft” (continuous) displacement of the magnetic moment from the easy plane. Under weak dissipation, the reorientation occurs as a discrete process, that is, is accompanied by magnetic moment jumps and hysteresis as the spin current increases and decreases. At a fairly low temperature and weak damping, quantum effects arise in the system. The spin current induces excitations quasi-anionic in character, Bloch oscillations of magnetic moment precession, and tunneling between different precession quantum modes. These quantum effects, in particular, manifest themselves in the system under consideration by magnetic moment jumps and magnetic susceptibility peaks.     

Mathematical Modeling of the Magnetization of a Two-Dimensional System of Magnetic Moments

Using a system that reaches its minimum energy of interaction at equilibrium, the magnetization of a discrete two-dimensional system of interacting magnetic dipoles by an external magnetic field is modeled mathematically. Magnetization curves for rectangular two-dimensional clusters of dipoles and the region of the magnetic domain are calculated.     

Two-dimensional electron-hole liquid in the strong magnetic field

The Matsubara diagram technique is used to study the formation and thermodynamic properties of an electron-hole liquid (EHL) in the two-dimensional system in the transverse strong magnetic field. The system has discrete energy spectra, i.e. a motion of particles becomes “zero-dimensional”. Therefore, the exchange interaction alone is sufficient to form EHL, the correlation correction being negligible.     

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.     

A different algebraic method for the fifth-order combined geometric-chromatic aberrations of practical magnetic electron lenses

In this paper, differential algebraic (DA) method is applied to fifth-order combined geometric-chromatic aberrations of practical magnetic electron lenses. The magnetic fields of magnetic electron lenses, which are computed by FEM or FDM method, are in the form of discrete arrays. Thus the developed new DA method is applicable to engineering design and programs were written for computing the fifth-order combined geometric-chromatic aberrations of practical magnetic electron lenses. An example is given. The combined geometric-chromatic aberrations up to fifth order are calculated. It is proved that the numerical results for the magnetic fields in the form of discrete arrays have good accuracy compared with the results computed by using the magnetic fields expressed in analytical form. The accuracy is limited only by the accuracy of the numerical computation of the fields and the arithmetic errors. Finally, a practical magnetic electron lens is analyzed and discussed as an example.     

Induced spin interactions in the early universe from discrete time quantum theory

By considering a system of spinning particles in an external magnetic field we demonstrate that the system develops non-local spin interactions due to discrete time quantum effects. Such interactions can lead to a domain like structure in the early universe possibly serving as generic seeds to large scale structure.     

Spontaneous transformations of the magnetic structure of a film nanocontact

The magnetization distributions in a symmetric magnetic film nanocontact for oppositely magnetized ferromagnetic electrodes are analyzed based on numerically solving the Landau-Lifshitz and magnetostatic equations as a function of magnetic and geometrical factors. It is found that a symmetric magnetic configuration is unstable when the head-to-head domain wall dividing the regions with opposite orientations of magnetization is located at the center of the nanocontact. The instability arises when the uniaxial magnetic anisotropy constant reaches a certain critical value K _c below which it spontaneously leaves the center of the nanocontact. The transition from the symmetric state (wall at the center) to an asymmetric one can be continuous (second order) or discrete (first order), depending on the geometrical and physical parameters of the nanocontact (length to width ratio, anisotropy constant, and saturation magnetization). The phase diagram is constructed in terms of the variable’s nanocontact length vs. anisotropy constant. This diagram divides the symmetric and asymmetric magnetic configurations of the system. The occurrence of a tricritical point in the phase diagram is its characteristic feature.     

Stochastic resonance in low-disperse magnets: Mechanism of subbarrier magnetization reversal

The phenomenon of stochastic resonance is studied theoretically in a system of single-domain particles with an “easy-axis”-type magnetic anisotropy at temperatures close to absolute zero, for which the tunneling of the magnetic moment vector between stable states dominates. Calculations are made on the basis of the master equation in the model of discrete orientations in the quasi-adiabatic approximation. The dynamic magnetic susceptibility components of the system under the action of a weak rf field are calculated. The critical temperature at which a transition from the above-the-barrier mechanism of magnetization reversal to the subbarrier mechanism occurs is estimated.     

Spectra of soft ring graphs

We discuss a ring-shaped soft quantum wire modelled by δ interaction supported by the ring with a generally nonconstant coupling strength. We derive the condition which determines the discrete spectrum of such systems, and analyse the dependence of the eigenvalues and eigenfunctions on the coupling and ring geometry. In particular, we illustrate that a random component in the coupling leads to a localization. The discrete spectrum is also investigated in the situation when the ring is placed into a homogeneous magnetic field or threaded by an Aharonov–Bohm flux and the system exhibits persistent currents.

(Some figures in this article are in colour only in the electronic version)     

Imparting magnetic dipole heterogeneity to internalized iron oxide nanoparticles for microorganism swarm control

Tetrahymena pyriformis is a single cell eukaryote that can be modified to respond to magnetic fields, a response called magnetotaxis. Naturally, this microorganism cannot respond to magnetic fields, but after modification using iron oxide nanoparticles, cells are magnetized and exhibit a constant magnetic dipole strength. In experiments, a rotating field is applied to cells using a two-dimensional approximate Helmholtz coil system. Using rotating magnetic fields, we characterize discrete cells’ swarm swimming which is affected by several factors. The behavior of the cells under these fields is explained in detail. After the field is removed, relatively straight swimming is observed. We also generate increased heterogeneity within a population of cells to improve controllability of a swarm, which is explored in a cell model. By exploiting this straight swimming behavior, we propose a method to control discrete cells utilizing a single global magnetic input. Successful implementation of this swarm control method would enable teams of microrobots to perform a variety of in vitro microscale tasks impossible for single microrobots, such as pushing objects or simultaneous micromanipulation of discrete entities.     

Spectra of soft ring graphs

We discuss a ring-shaped soft quantum wire modelled by δ interaction supported by the ring with a generally nonconstant coupling strength. We derive the condition which determines the discrete spectrum of such systems, and analyse the dependence of the eigenvalues and eigenfunctions on the coupling and ring geometry. In particular, we illustrate that a random component in the coupling leads to a localization. The discrete spectrum is also investigated in the situation when the ring is placed into a homogeneous magnetic field or threaded by an Aharonov-Bohm flux and the system exhibits persistent currents.

(Some figures in this article are in colour only in the electronic version)     

Different algebraic method for computing the high-order aberrations of practical combined focusing-deflection systems

Differential algebraic (DA) method is an effective technique in computer numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. Some complicated nonlinear dynamics problem including high-order aberrations of electron optical systems can be solved effectively by mapping properties of DA quantities. However, the existing study applying DA method to the practical system is limited to simple electron lenses. In this paper, the application of DA method is extended to practical combined focusing-deflection systems, and the aberrations up to fifth order are calculated. The electric and magnetic fields of the electron lenses and deflectors, which are computed by finite element method (FEM) or finite difference method (FDM), are in the form of discrete arrays. Local analytical expressions for electric and magnetic field quantities are constructed from these arrays for arbitrary place where electron is traced in DA computation. Thus the developed DA method is applicable for engineering design and computing problem. Based on the study of the expressions and the structure of the aberration coefficients for the fifth-order aberrations of the combined focusing-deflection system and the local analytic expression of the practical electromagnetic field, correlative computer software was developed, whose interface is convenient to calculate the high-order aberrations of the practical systems. The new DA method and software are tested with a uniform magnetic field deflection having an analytic solution. And the results show that the accuracy is sufficiently high, only limited by machine precision. Finally, as an example, a practical combined magnetic focusing and magnetic deflection system is analyzed and discussed.     

Discrete breathers in nonlinear magnetic metamaterials

Magnetic metamaterials composed of split-ring resonators or U-type elements may exhibit discreteness effects in THz and optical frequencies due to weak coupling. We consider a model one-dimensional metamaterial formed by a discrete array of nonlinear split-ring resonators where each ring interacts with its nearest neighbors. On-site nonlinearity and weak coupling among the individual array elements result in the appearance of discrete breather excitations or intrinsic localized modes, both in the energy-conserved and the dissipative system. We analyze discrete single and multibreather excitations, as well as a special breather configuration forming a magnetization domain wall and investigate their mobility and the magnetic properties their presence induces in the system.     

Modeling of nanoscale transport phenomena: Application to information technology

We develop the fundamentals in rule-based mathematics and physics dealing with nanoscale transport processes and apply our formulations to the design of nano/information technology systems. We showcase the versatility of lattice Boltzmann method (LBM) as a tool to simulate apparently different physical systems and present the underlying similarity in the discrete rules required in different systems which helps in providing the insight into one system by using an analogous system. We use a unified framework to simulate nanoscale air bearing and heat transfer. LBM not only enhances the computational capability of a nanoscale confined gaseous system by calculating both velocity and pressure fields simultaneously but also simulates nanoscale energy transport in both magnetic and electronic material accurately.     

The Interchangeable Module Stellarator

The Interchangeable Module Stellarator (IMS) is a new toroidal stellarator-type device under design and construction at the University of Wisconsin Torsatron/Stellarator Laboratory. A new design strategy for constructing stellarator magnetic fields from discrete modular coils has been developed, utilizing orthogonal toroidal coordinates. Application of this method has resulted in a modular coil system (IMS), whose magnetic structure closely approximates that of the Proto-Cleo Q = 3 7-field period device (i. e., rotational transform, shear, flux volume, etc.).     

Hall quantum Hamiltonians and electric 2D-curvature

For the Dirac 2D-operator in a constant magnetic field with perturbing electric potential, we derive Hamiltonians describing the quantum quasiparticles (Larmor vortices) at Landau levels. The discrete spectrum of this Hall-effect quantum Hamiltonian can be computed to all orders of the semiclassical approximation by a deformed Planck-type quantization condition on the 2D-plane; the standard magnetic (symplectic) form on the plane is corrected by an ??electric curvature?? determined via derivatives of the electric field. The electric curvature does not depend on the magnitude of the electric field and vanishes for homogeneous fields (i.e., for the canonical Hall effect). This curvature can be treated as an effective magnetic charge of the inhomogeneous Hall 2D-nanosystem.     

Stochastic Resonance in Finely Dispersed Magnets: Influence of a Constant Magnetic Field Applied along the Direction of Easy Magnetization

The dynamic susceptibility of an uniaxial single-domain iron particle is calculated under conditions of stochastic resonance as a function of the strength of an additional constant magnetic field applied along the direction of easy magnetization. Calculations are performed for the model of discrete orientations using the governing equation for the Kramers above-the-barrier transition rates of the magnetic moment vector of the particle. It is demonstrated that the presence of this constant field that breaks the symmetry of the bistable potential results in a decrease in the magnitude of the system response to an external periodic perturbation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 26–31, July, 2005.     

Avalanche dynamics of magnetic flux in a two-dimensional discrete superconductor

The critical state of a two-dimensional discrete superconductor in an external magnetic field is studied. This state is found to be self-organized in the generalized sense, i.e., is a set of metastable states that transform to each other by means of avalanches. An avalanche is characterized by the penetration of a magnetic flux to the system. The sizes of the occurring avalanches, i.e., changes in the magnetic flux, exhibit the power-law distribution. It is also shown that the size of the avalanche occurring in the critical state and the external magnetic field causing its change are statistically independent quantities.     

A novel formulation for the numerical computation of magnetization modes in complex micromagnetic systems

The small oscillation modes in complex micromagnetic systems around an equilibrium are numerically evaluated in the frequency domain by using a novel formulation, which naturally preserves the main physical properties of the problem. The Landau–Lifshitz–Gilbert (LLG) equation, which describes magnetization dynamics, is linearized around a stable equilibrium configuration and the stability of micromagnetic equilibria is discussed. Special attention is paid to take into account the property of conservation of magnetization magnitude in the continuum as well as discrete model. The linear equation is recast in the frequency domain as a generalized eigenvalue problem for suitable self-adjoint operators connected to the micromagnetic effective field. This allows one to determine the normal oscillation modes and natural frequencies circumventing the difficulties arising in time-domain analysis. The generalized eigenvalue problem may be conveniently discretized by finite difference or finite element methods depending on the geometry of the magnetic system. The spectral properties of the eigenvalue problem are derived in the lossless limit. Perturbation analysis is developed in order to compute the changes in the natural frequencies and oscillation modes arising from the dissipative effects. It is shown that the discrete approximation of the eigenvalue problem obtained either by finite difference or finite element methods has a structure which preserves relevant properties of the continuum formulation. Finally, the generalized eigenvalue problem is solved for a rectangular magnetic thin-film by using the finite differences and for a linear chain of magnetic nanospheres by using the finite elements. The natural frequencies and the spatial distribution of the natural modes are numerically computed.