Two alternative approaches to electro-optical detection of terahertz pulses

The electro-optical detection of terahertz radiation is analyzed theoretically. While a conventional detection scheme of this type is based on the measurement of the phase shift of an optical pulse arising from its interaction with the terahertz field in a nonlinear medium, it is shown that both the phase and amplitude of the optical pulse vary because of this interaction. The amplitude modulation carries information on the dynamics of the amplitude and phase of the terahertz field and can be used to measure these parameters. With this energy-sensitive detection scheme, avoiding all restrictions on the symmetry type of the nonlinear medium is much simpler than with the phase scheme. Variants of the electro-optical detection technique using periodically poled crystals with the lithium-niobate symmetry and crystals with the zincblende structure are considered. It is shown that spectral sensitivities of the methods based on measurements of the phase and amplitude modulations are related as the frequencies of the laser and terahertz fields.     

Elastic interaction between defects in thin and 2D films

Elastic interactions between defects is investigated at the surface of thin layers, a question on which we have given a brief account [P. Peyla et al. Phys. Rev. Lett. 82, 787 (1999)]. Two isotropic defects do not interact in an unlimited medium, regardless of the spatial dimension, a result which can be shown on the basis of the Gauss theorem in electrostatics. Within isotropic elasticity theory, defects interact only (i) if they are, for example, at a surface (or at least if they feel a boundary), or if their action on the material is anisotropic (e.g. they create a non central force distribution, though the material elasticity is isotropic). It is known that two identical isotropic defects on the surface of a semi-infinite material repel each other. The repulsion law behaves as 1/r ³(r = defects separation). We first revisit the Lau-Kohn theory and extend it to anisotropic defects. Anisotropy is found to lead to attraction. We show that in thin films defects may either attract or repel each other depending on the local geometric force distribution caused by the defect. It is shown that the force distribution (or more precisely the forces configuration symmetry) fixes the exponent in the power law 1/r ⁿ (e.g. for a four-fold symmetry n = 4). We discuss the implication of this behaviour in various situations. We treat the interactions in terms of the symmetries associated with the defect. We argue that if the defects are isotropic, then their effective interaction in an unlimited 2D (or a thin film) medium arises from the induced interaction, which behaves as 1/r ⁴ for any defect symmetry. We shall also comment on the contribution to the interaction which arises from flexion of thin films. Received 7 October 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: chaouqi.misbah@ujf-grenoble.fr     

Molecular-dynamics study of the effect of simple defects on B2 lattice stability

The molecular-dynamics method is used in conjunction with the Parinelli-Rahman Lagrangian to investigate the influence of simple defects on the stability of the B2 lattice of the model alloy TiNi. Common defect types associated with deviation from stoichiometry and atomic disorder are considered. Under conditions of small elastic moduli, the displacement fields around the defects have a long-range nature, leading to a cooperative interaction of the defects and a lowering of the energy of the system when the defects are ordered. Depending on the symmetry of the displacement fields that are formed, the defects may either stabilize the B2 structure or tend to make it unstable and facilitate a martensite transformation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 3–8, January, 1992.     

The sphericalp-spin interaction spin glass model: the statics

The static properties of the sphericalp-spin interaction spin glass model are calculated using the replica method. It is shown that within the Parisi scheme the most general solution is the one-step replica symmetry breaking. The transition from the replica symmetric solution to the replica replica symmetry broken one is either continuous or discontinuous inq ₁–q₀ depending on the strength of the external magnetic field. The model can be solved explicitly for anyp at any temperature and magnetic field. Below the transition we find an infinite number of metastable states.     

SU(2) symmetry in a Hubbard model with spin-orbit coupling

We study the underlying symmetry in a spin-orbit coupled tight-binding model with Hubbard interaction. It is shown that, in the absence of the on-site interaction, the system possesses the SU(2) symmetry arising from the time reversal symmetry. The influence of the on-site interaction on the symmetry depends on the topology of the networks: The SU(2) symmetry is shown to be the spin rotation symmetry of a simply-connected lattice even in the presence of the Hubbard interaction. On the contrary, the on-site interaction breaks the SU(2) symmetry of a multi-connected lattice. This fact indicates that a discrete spin-orbit coupled system has exclusive features from its counterpart in a continuous system. The obtained rigorous result is illustrated by a simple ring system.     

Nonlocal symmetry and consistent Riccati expansion integrability of the (1+1)-dimensional integrable nonlinear dispersive-wave system

Under investigation in this paper is nonlocal symmetry, consistent Riccati expansion (CRE) integrability of the (1+1)-dimensional integrable nonlinear dispersive-wave system, which can be used to describes a bidirectional soliton for wave propagation. We construct the Bäcklund transformation and consider the truncated Painlevé expansion of the system. It’s Schwarzian form is derived, whose nonlocal symmetry is localized to provide the corresponding nonlocal group. Furthermore, we verify that the system is solvable via the CRE. Based on the CRE, we further present its soliton-cnoidal wave interaction solution in terms of Jacobi elliptic functions and the third type of incomplete elliptic integral.     

High-temperature transition of uranium dioxide to the super-ion state

A microscopic model of the high-temperature (T≈2670 K) phase transition of uranium dioxide to the super-ion state is developed. It is shown that accounting for the interaction of the point defect subsystem with the electron subsystem in the mean-field approximation (where this interaction leads to significant additional screening of the charge of some of the defects) and then calculating the configurational entropy of the point defects with allowance for the actual symmetry of the UO₂ crystalline lattice affords satisfactory agreement with the available experimental data on the degree of disorder of the anion sublattice and the behavior of the specific heat of uranium dioxide in the given temperature range. Zh. éksp. Teor. Fiz. 111, 585–599 (February 1997)     

Tri-bimaximal mixing from twisted Friedberg–Lee symmetry

We investigate the Friedberg–Lee (FL) symmetry and its promotion to include the μ–τ symmetry, and call this the twisted FL symmetry. Based on the twisted FL symmetry, two possible schemes are presented toward the realistic neutrino mass spectrum and the tri-bimaximal mixing. In the first scheme, we suggest the semi-uniform translation of the FL symmetry. The second one is based on the S ₃ permutation family symmetry. The breaking terms, which are twisted FL symmetric, are introduced. Some viable models in each scheme are also presented.     

Empirical construction of interatomic potentials for studies of grain boundaries and other crystal defects: Pure metals and binary alloys

It is first argued that pair potentials are physically meaningful if they are regarded as describing interaction between atoms embedded in an environment of similar density as that for which their derivation was made. These potentials are capable of describing structural aspects of lattice defects but not the cohesive properties. Guidelines for determination of the shape of potentials and an empirical scheme for their construction in pure metals is then outlined. It is shown that this method when applied to simple metals leads to potentials similar to those obtained on the basis of a pseudopotential theory and extension of this scheme to other metals is discussed. An empirical scheme of construction of potentials for binary alloys is then briefly described. It is shown that concentration dependences of elastic constants and lattice stability evaluated using these potentials agree with experimental data and thus these potentials are suitable for studies of defects in binary alloys.     

Dynamics and control of oscillations in a complex crystalline lattice

A highly nonlinear system of acoustic and optical oscillations in a complex crystalline lattice consisting of two sublattices is analyzed. The system is obtained as a generalization of the linear Carman–Born–Kun Huang theory. Large displacements of atoms up to structure stability loss and restructuring are admitted. It is shown that the system has nontrivial solutions describing movements of fronts, emergence of periodic structures and defects. Strong interaction of acoustic and optical modes of oscillation for media without center of symmetry is demonstrated. A possibility of energy-excitation of the optical mode by means of controlling torque applied to the ends of the lattice is examined. Control algorithm based on speed-gradient method is proposed and analyzed numerically. Simulation results demonstrate that application of control may eliminate or reduce influence of initial conditions. An easily realizable nonfeedback version of control algorithm is proposed possessing similar properties.     

Preferred shapes and modes of internal motion in a system of three identical fermions

The states havingL=0, even parity,S=1/2 or 3/2 of a model system of three identical fermions have beeninvestigated. The pairwise interaction adopted has a repulsive core and an attractive tail. Information on the preferred shapes and on internal motions have been extracted from the wave functions. A comparison is made among the states having symmetric, mixed-symmetric and antisymmetric spatial permutation symmetry. It is found that the symmetry plays an essential role in determining the microscopic structures.     

Frozen Rigging Model of the Energy Dominated Universe

Composite rigging systems, involving membranes that meet on strings that meet on monopoles, arise naturally by the Kibble mechanism as topological defects in field theories involving spontaneous symmetry breaking. Such systems will tend to freeze out into static lattice type configurations with energy contribution ultimately be provided by the membranes. It has been suggested by Bucher and Spergel that on scales large compared with the relevant (interstellar separation) distance characterizing the relevant mesh length, such a system may behave as a rigidity-stabilized solid, having an approximately isotropic stress energy tensor with negative pressure, as given by a polytropic index γ = w+1 = 1/3. It has recently been shown that such a system can be rigid enough to be stable if the number of membranes meeting at a junction is even (though not if it is odd). Using as examples an approximaely O(3) symmetric scalar field model that can provide an “8-color” (body-centered) cubic lattice, and an approximate U(1)× U(1) model offering a disordered “5-color” lattice, it is argued that such a mechanism can account naturally for the observed dark energy dominance of the universe, without ad hoc assumptions, other than that the relevant symmetry breaking phase transition should have occurred somewhere about the Kev energy range.     

Comparison of the third-order dispersion terms of interaction between chiral molecules

Using a quantum electrodynamic approach, the coupling between chiral molecules derived from the exchange of three virtual photons of the electric dipole type is investigated. The resulting interaction potential, which involves the first nonlinear polarizability of the molecules, is compared with a previously derived interaction potential involving the optical activity of the molecules; the latter is accounted for by the exchange of two virtual photons, one being electric dipolar and the other being electric quadrupolar or magnetic dipolar. The symmetry properties of the new term is considered and its quasi-static limit is derived. It appears that the two interaction terms, which both are third-order dispersion processes, might have the same order of magnitude; thus none can a priori be neglected and both might equally contribute to the possibility of a helical ordering.     

Excitation spectra of ferromagnets with crystal fields

We have investigated the ferromagnetic phase transition and excitation spectrum of systems, such as the rare earths, where the crystalline fields are significant in determining the magnetic properties. Using the full level scheme appropriate to a system ofJ-4 ions in a crystal field of cubic symmetry and assuming a Heisenberg interaction, we have calculated the full temperature- andq-dependence of the dynamic susceptibility within the RPA, both in the paramagnetic and ordered regimes. Variations in behavior, both with changes in crystal field parameter and with changes in magnetic interaction strength are discussed, and emphasis is placed on the limiting case which corresponds to current experiments in the light rare earths.     

Quantum fluctuations in a two-dimensional antiferromagnet with four-spin interaction of cubic symmetry

The excitation spectrum of a non-Heisenberg 2D antiferromagnet with the four-spin interaction of cubic symmetry has been calculated in the first order of 1/2S. It has been shown that, for weak anisotropy, the Néel state is destroyed by quantum fluctuations. The phase diagrams showing the stability regions of the Néel phase in the space of spin-anisotropy parameters have been plotted.     

Free energy fluctuations in Ising spin glasses

The sample-to-sample fluctuations of the free energy in finite-dimensional Ising spin glasses are calculated, using the replica method, from higher order terms in the replica number n. It is shown that the Parisi symmetry breaking scheme does not give the correct answers for these higher order terms. A modified symmetry breaking scheme with the same stability is shown to resolve the problem.     

Formation of E4-Centers (E c – 0.76 eV) in Gallium Arsenide

The paper deals with the effects of the bombarding-electron energy on the velocity of E4 center (E _c – 0.76 eV) formation and the temperature dependences of the efficiency of the latter in a neutral volume and the space-charge region of n–type gallium arsenide. The specimens were Schottky diodes manufactured by depositing titanium onto epitaxial layers of n-GaAs with n = (2–4)·10¹⁵ cm³. The defect concentration was obtained by the DLTS spectroscopy method. It is shown that the number of E4 centers in the total amount of irradiation-induced defects sharply increases with increasing the bombarding-electron energy from 1.3 to 2.2 MeV. It is found out that the velocity of introducing E4 centers into the space-charge region does not depend on irradiation temperature and is by far higher than that in a neutral volume. In the latter, however, this velocity is non-linearly increasing with the irradiation temperature. It is assumed that an E4 center is a complex consisting of two unit defects generated in the adjacent sites of the Ga and As sublattices through a single collision. It is noted that its final configuration is formed as a result of interaction of these defects, which depends on the dynamics of transformation of their primary charge states.     

Stability of the critical behavior of weakly disordered systems with respect to the introduction of an interaction potential breaking replica symmetry

The critical behavior of weakly disordered systems with a p-component order parameter is described using field-theoretic methods. A renormalization-group analysis of the effective model replica Hamiltonian with an interaction potential breaking replica symmetry is performed directly for three-dimensional systems in the two-loop approximation. For the case of a one-step replica symmetry breaking, fixed points of renormalization group equations are found using the Padé-Borel summation technique. It is established that the critical behavior of weakly disordered systems is stable with respect to replica symmetry breaking and that the former scenario of the influence of structural defects on the critical behavior of these systems is realized.     

Model of periodic superstructure formation induced by mobile defects on a semiconductor surface

A model for forming a periodic superstructure on a semiconductor surface with mobile defects is proposed. It is shown that a self-organized system of such defects could lead to considerable modulation of incommensurate phase parameters in near-surface layers under the conditions of defect interaction with an incommensurate displacement wave. This type of defect system could induce a substantial energy decrease for the incommensurate phase and its additional stabilization on the one hand, and an increase in modulation amplitude that might be accompanied by a soliton-like nonsinusoidal incommensurate displacement wave on the other. The model allows us to explain the experimental results regarding the periodic superstructure discovered by G.V. Benemanskaya et al. on the surface of a GaN semiconductor. In particular, the model enables us to explain the nature of such superstructures based on the self-organization of mobile neutral triad-type defects, composed of negatively charged (3−) vacancies of the host lattice centers of Ga³⁺ and surface impurity ions of Cs⁺ and Ba²⁺, under conditions of triad interaction with an incommensurate displacement wave.     

Multistability of the optical response in a system of quasi-two-dimensional exciton polaritons

The nonlinear dynamic properties of a system of polaritons in a planar semiconductor microcavity under conditions of external coherent photoexcitation have been investigated. It has been shown that the interaction between polaritons with identical projections of the total angular momentum (J _z ) can give rise to multistability of the response of the excited polariton state. As a result, nonequilibrium transitions between different stability branches become possible due to fluctuations or arbitrarily smooth variations of the excitation parameters and occur with abrupt changes in the intensity and optical polarization of the field in the microcavity. It has been demonstrated that a relatively weak attraction between polaritons with opposite total angular momenta J _z leads to a possibility of spontaneously breaking the symmetry of circularly polarized field components in the microcavity under strictly linear (symmetric) polarization conditions of external excitation.