We present a theoretical and experimental investigation of the effects of a magnetic field on quasi-twodimensional excitons. We calculate the internal structures and dispersion relations of spatially direct and indirect excitons in single and coupled quantum wells in a magnetic field perpendicular to the well plane. We find a sharp transition from a hydrogenlike exciton to a magnetoexciton with increasing the center-of-mass momentum at fixed weak field. At that transition the mean electron-hole separation increases sharply and becomes ϰ P/B Ќ , where P is the magnetoexciton center-of-mass momentum and B Ќ is the magnetic field perpendicular to the quantum well plane. The transition resembles a first-order phase transition. The magneticfield-exciton momentum phase diagram describing the transition is constructed. We measure the magnetoexciton dispersion relations and effective masses in GaAs/Al 0.33 Ga 0.67 As coupled quantum wells using tilted magnetic fields. The calculated dispersion relations and effective masses are in agreement with the experimental data. We discuss the impact of magnetic field and sample geometry on the condition for observing exciton condensation.
Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order's omnipresence has long been recognized by the scientific community, as evidenced by a myriad of related concepts, theoretical and phenomenological frameworks, and experimental phenomena such as turbulence, $1/f$ noise, dynamical complexity, chaos and the butterfly effect, the Richter scale for earthquakes and the scale-free statistics of other sudden processes, self-organization and pattern formation, self-organized criticality, etc. Although several successful approaches to various realizations of DLRO have been established, the universal theoretical understanding of this phenomenon remained elusive. The possibility of constructing a unified theory of DLRO has emerged recently within the approximation-free supersymmetric theory of stochastics (STS). There, DLRO is the spontaneous breakdown of the topological or de Rahm supersymmetry that all stochastic differential equations (SDEs) possess. This theory may be interesting to researchers with very different backgrounds because the ubiquitous DLRO is a truly interdisciplinary entity. The STS is also an interdisciplinary construction. This theory is based on dynamical systems theory, cohomological field theories, the theory of pseudo-Hermitian operators, and the conventional theory of SDEs. Reviewing the literature on all these mathematical disciplines can be time consuming. As such, a concise and self-contained introduction to the STS, the goal of this paper, may be useful.Comment: 98 pages; 13 figures; revtex 4-
It is well known that dynamical systems may be employed as computing machines. However, not all dynamical systems offer particular advantages compared to the standard paradigm of computation, in regard to efficiency and scalability. Recently, it was suggested that a new type of machines, named digital -hence scalable-memcomputing machines (DMMs), that employ non-linear dynamical systems with memory, can solve complex Boolean problems efficiently. This result was derived using functional analysis without, however, providing a clear understanding of which physical features make DMMs such an efficient computational tool. Here, we show, using recently proposed topological field theory of dynamical systems, that the solution search by DMMs is a composite instanton. This process effectively breaks the topological supersymmetry common to all dynamical systems, including DMMs. The emergent long-range order -a collective dynamical behaviorallows logic gates of the machines to correlate arbitrarily far away from each other, despite their non-quantum character. We exemplify these results with the solution of prime factorization, but the conclusions generalize to DMMs applied to any other Boolean problem.Unconventional computing paradigms that employ topological features have considerable advantages over standard ones. The prototypical example is topological quantum computation [1,2] that exploits, in an essential way, the topological character of the ground states of some strongly-correlated quantum electron systems, such as p-wave superconductors and fractional quantum Hall systems, to realize computation unencumbered by decoherence and noise. [3] Recently, a new computing paradigm has been advanced, named memcomputing [4][5][6] that employs non-linear (nonquantum) dynamical systems to compute in and with memory. Implemented in digital (hence scalable) form, memcomputing machines (DMMs) are a collection of logic gates networked
A new series of liquid-crystalline Schiff base lanthanide compounds of the general formula (L′′H) 2 L′′MX 2 was prepared (L′′H ) H 2n+1 C n OC 6 H 3 (OH)CHNC m H 2m+1 ; n ) 7, 12; m ) 14, 18; M ) La, Tb, Dy, Er, Nd, Ho, Eu, Pr, and Gd; X ) NO 3 or Cl). The thermal behavior of these complexes was examined by polarizing microscopy, differential scanning calorimetry, and X-ray diffraction experiments. The ligands L′′H are nonmesomorphic, but all lanthanide complexes show smectic A mesophases. Further, temperature-dependent magnetic susceptibility measurements were carried out in order to obtain information about the magnetic anisotropy of the lanthanide compounds. The Tb(III) and Dy(III) derivatives could be oriented by a magnetic field. These liquid-crystalline lanthanide complexes display magnetic anisotropies which are two orders of magnitude greater than those of known liquid crystals.
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