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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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BIBO stability of continuous and discrete -time systems01:24

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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
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Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
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To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
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The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
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在无限潜力的离散时间晶体.

Yevgeny Bar Lev1, Achilleas Lazarides2

  • 1Department of Physics, <a href="https://ror.org/05tkyf982">Ben-Gurion University of the Negev</a>, Beer-Sheva 84105, Israel.

Physical review letters
|December 3, 2024
PubMed
概括
此摘要是机器生成的。

研究人员在一个无障碍系统中创建了一个离散时间晶体 (DTC),克服了以前对障碍的依赖. 这种强相对局部干扰是稳定的,推进了对非ergodic量子系统的研究.

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科学领域:

  • 凝聚物质物理学 凝聚物质物理学
  • 量子多体系统是一个量子多体系统.
  • 非平衡的统计力学.

背景情况:

  • 离散时间晶体 (DTC) 是物质的新型量子相,需要非adiabatic驱动和有限长时间状态.
  • 之前的DTC实现通常取决于灭混乱以实现非ergodicity.
  • 非能量性,驾驶和不存在障碍的相互作用之间的相互作用仍然是一个活跃的研究领域.

研究的目的:

  • 理论上构建和数值验证一个离散时间晶体 (DTC) 阶段在一个非失序的,不可整合的系统.
  • 在交互的周期驱动系统中确定实现DTC的一般条件.
  • 为了证明拟议的DTC阶段对抗局部干扰的稳定性.

主要方法:

  • 开发一个理论框架,用于DTCs在nonergodic系统.
  • 基于非失序,不可整合的伊辛格型相互作用的具体模型的建议.
  • 应用近似分析参数和直接的数值模拟.
  • 在局部周期性扰动下分析系统行为.

主要成果:

  • 在一个非失序,不可整合的Ising型系统中成功构建了一个DTC阶段.
  • 证明DTC至关重要的非ergodicity可以在没有混乱的情况下实现.
  • 数字证据证实了DTC阶段的存在及其稳定性.
  • 确定在驱动互动系统中实现DTC的关键条件.

结论:

  • 离散时间晶体可以实现在无障碍,不可整合的系统中,扩大它们的潜在应用.
  • 拟议的模型提供了一个可行的平台,用于研究无障碍的nonergodic现象.
  • 已证明的DTC阶段的稳定性表明其实际可行性和稳定性.