STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Cell-dynamical simulation of magnetic hysteresis in the two-dimensional Ising system

We present results from numerical simulations using a ‘‘cell-dynamical system’’ to obtain solutions to the time-dependent Ginzburg-Landau equation for a scalar, two-dimensional (2D), (Φ2)2 model in the presence of a sinusoidal external magnetic field. Our results confirm a recent scaling law proposed by Rao, Krishnamurthy, and Pandit [Phys. Rev. B 42, 856 (1990)], and are also in excellent agreement with recent Monte Carlo simulations of hysteretic behavior of 2D Ising spins by Lo and Pelcovits [Phys. Rev. A 42, 7471 (1990)].

Signatures of an anomalous Nernst effect in a mesoscopic two-dimensional electron system

We investigate the Nernst effect in a mesoscopic two-dimensional electron system (2DES) at low magnetic fields, before the onset of Landau level quantization. The overall magnitude of the Nernst signal agrees well with semiclassical predictions. We observe reproducible mesoscopic fluctuations in the signal that diminish significantly with an increase in temperature. We also show that the Nernst effect exhibits an anomalous component that is correlated with an oscillatory Hall effect. This behavior may be able to distinguish between different spin-correlated states in the 2DES.

Unconventional metallicity and giant thermopower in a strongly interacting two-dimensional electron system

We present thermal and electrical transport measurements of low-density (10(14) m(-2)), mesoscopic two-dimensional electron systems (2DESs) in GaAs/AlGaAs heterostructures at sub-Kelvin temperatures. We find that even in the supposedly strongly localized regime, where the electrical resistivity of the system is two orders of magnitude greater than the quantum of resistance h/e(2), the thermopower decreases linearly with temperature indicating metallicity. Remarkably, the magnitude of the thermopower exceeds the predicted value in noninteracting metallic 2DESs at similar carrier densities by over two orders of magnitude. Our results indicate a new quantum state and possibly a novel class of itinerant quasiparticles in dilute 2DESs at low temperatures where the Coulomb interaction plays a pivotal role.

Evidence of novel quasiparticles in a strongly interacting two-dimensional electron system: giant thermopower and metallic behaviour

We report thermopower (S) and electrical resistivity (rho (2DES) ) measurements in low-density (10(14) m(-2)), mesoscopic two-dimensional electron systems (2DESs) in GaAs/AlGaAs heterostructures at sub-Kelvin temperatures. We observe at temperatures a parts per thousand(2)0.7 K a linearly growing S as a function of temperature indicating metal-like behaviour. Interestingly this metallicity is not Drude-like, showing several unusual characteristics: (i) the magnitude of S exceeds the Mott prediction valid for non-interacting metallic 2DESs at similar carrier densities by over two orders of magnitude; and (ii) rho (2DES) in this regime is two orders of magnitude greater than the quantum of resistance h/e (2) and shows very little temperature-dependence. We provide evidence suggesting that these observations arise due to the formation of novel quasiparticles in the 2DES that are not electron-like. Finally, rho (2DES) and S show an intriguing decoupling in their density-dependence, the latter showing striking oscillations and even sign changes that are completely absent in the resistivity.

Spin dynamics of electrons in the first excited subband of a high-mobility low-density two-dimensional electron system

We report on time-resolved Kerr rotation measurements of spin coherence of electrons in the first excited subband of a high-mobility low-density two-dimensional electron system in a GaAs/Al0.35Ga0.65As heterostructure. While the transverse spin lifetime (T-2(*)) of electrons decreases monotonically with increasing magnetic field, it has a nonmonotonic dependence on the temperature and reaches a peak value of 596 ps at 36 K, indicating the effect of intersubband electron-electron scattering on the electron-spin relaxation.

Electronic states of a two-dimensional electron system in a lateral superlattice and a perpendicular magnetic field

The electronic state of a two-dimensional electron system (2DES) in the presence of a perpendicular uniform magnetic field and a lateral superlattice (LS) is investigated theoretically. A comparative study is made between a LS induced by a spatial electrostatic potential modulation (referred to as a PMLS) and that induced by a spatial magnetic-field modulation (referred ro asa MMLS). By utilizing a finite-temperature self-consistent Hartree-Fock approximation scheme; the dependence of the electronic state on different system parameters (e.g., the modulation period, the modulation strength, the effective electron-electron interaction strength, the averaged electron density, and the system temperature) is studied in detail. The inclusion of exchange effect is found to bring qualitative changes to the electronic state of a PMLS, leading generally to a nonuniform spin splitting, and consequently the behavior of the electronic state becomes similar to that of a MMLS. The Landau-level coupling is taken into account, and is found to introduce some interesting features not observed before. It is also found that, even in the regime of intermediate modulation strength, the density dependence of the spin splitting of energy levels, either for a PMLS or a MMLS, can be qualitatively understood within the picture of a 2DES in a perpendicular magnetic field with the modulation viewed as a perturbation. [S0163-1829(97)02248-0].

An etched porous interface for on-line capillary electrophoresis-based two-dimensional separation system

The construction and evaluation of an on-column etched fused-silica porous junction for on-line coupling of capillary isoelectric focusing (CIEF) with capillary zone electrophoresis (CZE) are described. Where two separation columns were integrated on a single piece of fused-silica capillary through the etched similar to4 to 5-mm length porous junction along the capillary. The junction is easily prepared by etching a short section of the capillary wall with HF after removing the polyimide coating. The etched section becomes a porous glass membrane that allows only small ions related to the background electrolyte to pass through when high voltage is applied across the separation capillary. The primary advantages of this novel porous junction interface over previous designs (in which the interface is usually formed by fracturing the capillary followed by connecting the two capillaries with a section of microdialysis hollow fiber membrane) are no dead volume, simplicity, and ruggedness, which is particularly well suited for an on-line coupling capillary electrophoresis-based multiple dimensional separation system. The performance of the 2D CIEF-CZE system constructed by such an etched porous junction was evaluated by the analyses of protein mixtures.

Coherent electron dynamics in a two-dimensional random system with mobility edges

We study numerically the dynamics of a one-electron wavepacket in a two-dimensional random lattice with long-range correlated diagonal disorder in the presence of a uniform electric field. The time-dependent Schrodinger equation is used for this purpose. We find that the wavepacket displays Bloch-like oscillations associated with the appearance of a phase of delocalized states in the strong correlation regime. The amplitude of oscillations directly reflects the bandwidth of the phase and allows us to measure it. The oscillations reveal two main frequencies whose values are determined by the structure of the underlying potential in the vicinity of the wavepacket maximum.

Magnetoresistance in a High Mobility Two-Dimensional Electron System as a Function of Sample Geometry

In a high mobility two-dimensional electron gas (2DEG) realized in a GaAs/Al0.3Ga0.7As quantum well we observe changes in the Shubnikov-de Haas oscillations (SdHO) and in the Hall resistance for different sample geometries. We observe for each sample geometry a strong negative magnetoresistance around zero magnetic field which consists of a peak around zero magnetic field and of a huge magnetoresistance at larger fields. The peak around zero magnetic field is left unchanged for different geometries.

Two-dimensional moist stratified turbulence and the emergence of vertically sheared horizontal flows

Moist stratified turbulence is studied in a two-dimensional Boussinesq system influenced by condensation and evaporation. The problem is set in a periodic domain and employs simple evaporation and condensation schemes, wherein both the processes push parcels towards saturation. Numerical simulations demonstrate the emergence of a moist turbulent state consisting of ordered structures with a clear power-law type spectral scaling from initially spatially uncorrelated conditions. An asymptotic analysis in the limit of rapid condensation and strong stratification shows that, for initial conditions with enough water substance to saturate the domain, the equations support a straightforward state of moist balance characterized by a hydrostatic, saturated, vertically sheared horizontal flow (VSHF). For such initial conditions, by means of long time numerical simulations, the emergence of moist balance is verified. Specifically, starting from uncorrelated data, subsequent to the development of a moist turbulent state, the system experiences a rather abrupt transition to a regime which is close to saturation and dominated by a strong VSHF. On the other hand, initial conditions which do not have enough water substance to saturate the domain, do not attain moist balance. Rather, the system is observed to remain in a turbulent state and oscillates about moist balance. Even though balance is not achieved with these general initial conditions, the time scale of oscillation about moist balance is much larger than the imposed time scale of condensation and evaporation, thus indicating a distinct dominant slow component in the moist stratified two-dimensional turbulent system. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3694805]

Spin precession induced by an effective magnetic field in a two-dimensional electron gas

We theoretically study the spatial behaviors of the spin precession in a two-dimensional electron system with spin-orbit interaction. Through analysis of interaction between the spin and the effective magnetic field in the system, we obtain the general conditions to generate a persistent spin helix and predict a persistent spin helix pattern in [001]-grown quantum wells. Particularly, we demonstrate that the phase of spin can be locked to propagate in a quantum well with SU(2) symmetry.

Symmetry of one-dimensional dynamical systems in terms of transfer matrix parameters

The concept of symmetry for passive, one-dimensional dynamical systems is well understood in terms of the impedance matrix, or alternatively, the mobility matrix. In the past two decades, however, it has been established that the transfer matrix method is ideally suited for the analysis and synthesis of such systems. In this paper an investigatiob is described of what symmetry means in terms of the transfer matrix parameters of an passive element or a set of elements. One-dimensional flexural systems with 4 × 4 transfer matrices as well as acoustical and mechanical systems characterized by 2 × 2 transfer matrices are considered. It is shown that the transfer matrix of a symmetrical system, defined with respect to symmetrically oriented state variables, is involutory, and that a physically symmetrical system may not necessarily be functionally or dynamically symmetrical.