Electronically driven structure changes of Si captured by femtosecond electron diffraction

The excitation of a high density of carriers in semiconductors can induce an order-to-disorder phase transition due to changes in the potential-energy landscape of the lattice. We report the first direct resolution of the structural details of this phenomenon in freestanding films of polycrystalline and (001)-oriented crystalline Si, using 200-fs electron pulses. At excitation levels greater than approximately 6% of the valence electron density, the crystalline structure of the lattice is lost in <500 fs, a time scale indicative of an electronically driven phase transition. We find that the relaxation process along the modified potential is not inertial but rather involves multiple scattering towards the disordered state.     

Membrane gas diffusion measurements with MRI

Gas transport across polymeric membranes is fundamental to many filtering and separation technologies. To elucidate transport mechanisms, and understand the behaviors of membrane materials, accurate measurement of transport properties is required. We report a new magnetic resonance imaging (MRI) methodology to measure membrane gas phase diffusion coefficients. The MRI challenges of low spin density and short gas phase relaxation times, especially for hydrogen gas, have been successfully overcome with a modified one-dimensional, single-point ramped imaging with T(1) enhancement, measurement. We have measured the diffusion coefficients of both hydrogen gas and sulfur-hexafluoride in a model polymeric membrane of potential interest as a gas separator in metal hydride batteries. The experimental apparatus is a modified one-dimensional diaphragm cell which permits measurement of the diffusion coefficient in experimental times of less than 1 min. The H(2) gas diffusion coefficient in the membrane was 0.54 +/- 0.01 mm(2)/s, while that of sulfur-hexafluoride was 0.14 +/- 0.01 mm(2)/s, at ambient conditions.     

Magnetoresistance effect obtained from the band structure of a crystalline solid

This paper demonstrates that the Lorentz equation combined with the equation for electron drift in an external magnetic field gives a definite value for the relaxation time of the electron motion in a crystalline solid in the aforementioned field. The main result is that the product of the relaxation time and the strength of the magnetic field remain constant and are dependent only on the structure of the energy band of the solid. Free electrons, or nearly free electrons, result in the diagonal components of the tensor for magnetoresistance tending to zero for all electron states. For the electrons in a crystal lattice, the relaxation time considered along the cross-section line in the reciprocal space of a plane normal to the magnetic field and the surface of constant energy become highly anisotropic quantities.     

Two-dimensional analysis of natural frequencies and mode shapes of a wide beam: Application to the determination of mechanical characteristics of viscoelastic materials

The theory of plane elastodynamics is used to provide a simple method for calculating the natural frequencies and the normal mode shapes of a wide rectangular beam. The boundary conditions at both ends are prescribed in a mean-value sense. It is shown that the elementary (vibrating string) beam theory turns out to be an approximation of the theoretical model; the results obtained agree with those given by the Love theory. The method enables one to predict all frequency branches in terms of the width-to-length ratio, by comparatively simple calculations, in contrast to the situation when sufficiently elaborate one-dimensional theories are used. A second application is the determination of the complex Young's modulus and Poisson's ratio for viscoelastic materials.     

Momentum transfer in crystal lattices with vibrating atoms

A momentum transfer equation previously used to describe non-elastic deformation in crystalline solids represented by point masses at fixed lattice positions is extended to take into account the existence of intrinsic (e.g. thermal) small amplitude vibrations of the masses about their mean positions in a lattice. Use of the time-dependent Schroedinger equation to describe momentum transfer and deformation is also discussed in terms of this vibrating point-mass lattice model. The result is that a modified and identical differential equation for momentum transfer is obtained from each approach; some solutions to this equation are presented. The previous particle momentum wave frequency dependence on wave vector and resulting applications to non-elastic deformation are unchanged, but these particle momentum waves can now be considered as modulating the usual high-frequency waves associated with the elastic modes of a crystalline solid.     

原子链与弦中波包演化的比较分析

分析了一维单原子链中与连续弦中的波包的演化过程.弦中的波包以恒定速度移动,且保持形状不变;而原子链中的波包在演化过程中形状不断地发生变化.通过比较分析一维单原子链与弦振动的色散关系,讨论了波包演化的不同以及离散的原子链到连续弦的过渡.     

Quantum zigzag transition in ion chains

A string of trapped ions at zero temperature exhibits a structural phase transition to a zigzag structure, tuned by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short wavelength vibrational modes. We argue that this is a quantum phase transition, which can be experimentally realized and probed. Indeed, by means of a mapping to the Ising model in a transverse field, we estimate the quantum critical point in terms of the system parameters, and find a finite, measurable deviation from the critical point predicted by the classical theory. A measurement procedure is suggested which can probe the effects of quantum fluctuations at criticality. These results can be extended to describe the transverse instability of ultracold polar molecules in a one-dimensional optical lattice.     

Numerical method based on the lattice Boltzmann model for the Fisher equation

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.     

Static and dynamic double-exchange effects in doped manganites

It is shown that antiferromagnetic ordering in doped manganites with strong double-exchange interaction is transformed into ferromagnetic canted ordering with residual antiferromagnetic behavior in the basal plane as a result of hopping of mobile electron. The canting angle between the core magnetiztions is controlled by the competition of the Heisenberg antiferromagnetic exchange and double exchange. The temperatures of the paramagnet-antiferromagnet and paramagnet-canted ferromagnetic phase transitions are calculated. The results on the dependence of the magnetization in the canted phase and critical temperatures on the doping degree are in qualitative agreement with experiment. The form of uniform oscillations of core magnetiztions in the canted ferromagnetic phase of a doped manganite sample with hopping conduction is analyzed with and without allowance for relaxation of mobile electrons to the lattice. We propose a mechanism for the ferromagnetic resonance broadening and its resonance frequency shift in a ferromagnetic conducting sample (hopping conduction) of doped manganite due to double exchange. The resonance frequency shift and the ferromagnetic resonance damping constant (linewidth) are calculated in this model. In contrast to other relaxation mechanisms, the model is based on the fact that mobile electrons rapidly relax to the lattice (over a time on the order of the precession period).     

The conformal factor and DiffS1/S1

Two-dimensional gravity coupled with an open string is considered to geometrically construct a string field theory following Bowick and Rajeev. The phase space of this system can be thought of as an extended loop space, and is in fact a Kähler manifold. Each loop carries a conformal factor. Bowick and Rajeev's proposal is modified so that the ghost fields stand on the same footing as the x^μ-fields. The closed string field is modified to be the Kähler potential of the extended loop space. The canonical line bundle is not needed for the equation of motion for a closed string field. A covariant (free) open string field theory is constructed as a by-product in this approach.     

Finite diffraction models for electron bandstructures

Truncations of the infinite determinant resulting from the plane wave expansion method for an electron in a periodic potential are analysed to determine how well they can reproduce the low-lying eigenvalues or energy bands. The availability of rigorous expansions for the solutions of the Mathieu equation, essentially the Schrödinger equation for an electron in a one-dimensional cosine potential, suggests that problem for definitive comparisons. Since the only models which can reproduce the fundamental quadratic behaviour of bands at the zone centre have symmetric (odd) sets of reciprocal lattice vectors, the lowest order candidate has an odd determinant of size 3 × 3 through the reciprocal lattice vectors which define the 1st. Brillouin zone of the one-dimensional lattice. As zone centred determinants are not symmetric about zone boundaries they will not give a vanishing group velocity at that point and the effects of truncation will be at their worst. The 3 × 3 or cubic model factorises at the zone centre and a detailed analysis in closed form is straightforward. Agreement with the rigorous results is better than 1% everywhere. The next largest model, with a 5 × 5 determinant, gives errors which are several orders of magnitude smaller throughout the 1st. Brillouin zone. In addition it is found that even the 3 × 3 model gives much better results for the lowest eigenvalue than does second order perturbation theory. Numerical comparisons are also made for the group velocity and (inverse) effective mass using a Hellman-Feynmann approach to calculate the derivatives. Extensions to complex periodic potentials and higher dimensions are briefly discussed.     

Higher-order surface solitons in one-dimensional Bessel optical lattices

We demonstrate the existence of higher-order solitons occurring at an interface separating two one-dimensional (1D) Bessel optical lattices with different orders or modulation depths in a defocusing medium. We show that, in contrast to homogeneous waveguides where higher-order solitons are always unstable, the Bessel lattices with an interface support branches of higher-order structures bifurcating from the corresponding linear modes. The profiles of solitons depend remarkably on the lattice parameters and the stability can be enhanced by increasing the lattice depth and selecting higher-order lattices. We also reveal that the interface model with defocusing saturable Kerr nonlinearity can support stable multi-peaked solitons. The uncovered phenomena may open a new way for soliton control and manipulation.     

Theorie der Elektron-Phonon-Wechselwirkung in paramagnetischen Salzen

The electron-phonon hamiltonian of paramagnetic ions, derived from the assumption of a deformable potential of the surrounding ligands, is given as a function of the static crystalline field. With that it is possible to reduce the spin-lattice relaxation time to the coefficients of the expansion of the crystalline potential in terms of spherical harmonics, present in the treatment of energy splitting by the crystalline field. The anisotropy of the matrix elements of the electron-phonon hamiltonian relative to the propagation vector of lattice vibrations is discussed.     

Theory of periodic and solitary space charge waves in extrinsic semiconductors

We present a theory of the existence and stability of traveling periodic and solitary space charge wave solutions to a standard rate equation model of electrical conduction in extrinsic semiconductors which includes effects of field-dependent impurity impact ionization. A nondimensional set of equations is presented in which the small parameter β = (dielectric relaxation time) / (characteristic impurity time) 1 plays a crucial role for our singular perturbation analysis. For a narrow range of wave velocities a phase plane analysis gives a set of limit cycle orbits corresponding to periodic traveling waves. while for a unique value of wave velocity we find a homoclinic orbit corresponding to a moving solitary space charge wave of the type experimentally observed in p-type germanium. A linear stability analysis reveals all waves to be unstable under current bias on the infinite one-dimensional line. Finally, we conjecture that solitary waves may be stable in samples of finite length under voltage bias.     

The S-FFT calculation of Collins formula and its application in digital holography

We study analytically and numerically the properties of one-dimensional chain of cold ions placed in a periodic potential of optical lattice and global harmonic potential of a trap. In close similarity with the Frenkel-Kontorova model, a transition from sliding to pinned phase takes place with the increase of the optical lattice potential for the density of ions incommensurate with the lattice period. We show that at zero temperature the quantum fluctuations lead to a quantum phase transition and melting of pinned instanton glass phase at large values of dimensional Planck constant. After melting the ion chain can slide in an optical lattice. The obtained results are also relevant for a Wigner crystal placed in a periodic potential.     

Formation and thickness evolution of periodic twin domains in manganite films grown on SrTiO3(001) substrates

We present an extended synchrotron x-ray scattering study of the structure of thin manganite films grown on SrTiO3(001) substrates and reveal a new kind of misfit strain relaxation process which exploits twinning to adjust lattice mismatch. We show that this relaxation mechanism emerges in thin films as one-dimensional twinning waves which freeze out into a twin domain pattern as the manganite film continues to grow. A quantitative microscopic model which uses a matrix formalism is able to reproduce all x-ray features and provides a detailed insight into this novel relaxation mechanism. We further demonstrate how this twin angle pattern affects the transport properties in these functional films.     

A kinetic model for the premelting of a crystalline structure

An analytical kinetic approach to examine the premelting phenomenon is suggested by using a first passage time analysis. Premelting is considered to occur when the time of formation of a Frenkel type defect in the surface monolayer becomes sufficiently small. The mean time of defect formation on the surface lattice, i.e., the mean time necessary for a selected (surface-located) molecule to leave its lattice site and form a Frenkel defect, is calculated by using a first passage time analysis. The model is illustrated by numerical calculations for a crystalline structure composed of molecules interacting via the Lennard-Jones (LJ) potential. The lattice vectors in the plane parallel to the free surface of the crystal were assumed to be equal (to the lattice parameter) and the angle between them was varied. The model predictions of the Tammann temperature (of premelting) are very sensitive to the parameters of the LJ potential. In all the cases considered, the temperature dependence of the mean first passage time has two clearly distinct regimes: at low temperatures the dependence is sharp and at high temperatures it is weak.     

Level Statistics Crossover of Chiral Surface States in a Three-Dimensional Quantum Hall System

Recent experiments have demonstrated the realization of the three-dimensional quantum Hall effect in highly anisotropic crystalline materials, such as ZrTe|_5 and BaMnSb_2. Such a system supports chiral surface states in the presence of a strong magnetic field, which exhibit a one-dimensional metal-insulator crossover due to suppression of surface diffusion by disorder potential. We study the nontrivial surface states in a lattice model and find a wide crossover of the level-spacing distribution through a semi-Poisson distribution. We also discover a nonmonotonic evolution of the level statistics due to the disorder-induced mixture of surface and bulk states.