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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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Phase Diagrams02:39

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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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Spectrophotometry: Introduction01:16

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Spectrophotometry is the quantitative measurement of the absorption, reflection, diffraction, or transmission of electromagnetic radiation through a material as a function of the intensity and wavelength of the radiation. A spectrophotometer is a device used to measure the change in the radiation intensity caused by its interaction with the material.
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The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase...
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测量诱导的相变中的拓学和频谱.

Hisanori Oshima1,2, Ken Mochizuki1,2, Ryusuke Hamazaki2,3

  • 1University of Tokyo, Department of Applied Physics, Tokyo 113-8656, Japan.

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概括

我们介绍了一个Lyapunov分析框架,以了解监控量子系统中的纠阶段. 这种方法识别了拓性质,并区分了不同的纠阶段,将批量边缘对应扩展到量子力学.

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科学领域:

  • 量子信息科学 量子信息科学
  • 凝聚物质物理学 凝聚物质物理学
  • 关于物质的拓阶段

背景情况:

  • 监控的量子系统由于竞争的测量和单元动力学,表现出不同的纠阶段.
  • 描述这些阶段,特别是拓阶段,在量子信息科学中仍然是一个挑战.
  • 了解纠,拓和测量之间的相互作用对于量子技术至关重要.

研究的目的:

  • 提出使用利亚普诺夫分析来描述监控量子系统中的拓性质的一般框架.
  • 将这个框架应用于 (1+1) 维监控电路,其中涉及Majorana子.
  • 开发一种方法来区分不同的纠阶段和理解关键现象.

主要方法:

  • 对系统的光谱和多体拓不变的利亚普诺夫分析.
  • 用马约拉纳费米子对 (1+1) 维的监控电路进行分析.
  • 利用费米子平价和扭曲边界测量来构建一个拓不变量.

主要成果:

  • 利亚普诺夫分析成功地确定了拓学和微不足道的面积规律纠的阶段.
  • 边缘定位的零模式在拓阶段被检测出来,在微不足道阶段没有.
  • 大量无间隙光谱特征关键阶段,而拓不变量区分面积定律阶段.

结论:

  • 拟议的Lyapunov框架提供了一个强大的方法来表征监控量子系统中的拓性质.
  • 这种方法成功地区分了不同的纠阶段,包括关键阶段.
  • 该框架提供了一条通往扩大大批量边缘对应到监测量子动态的一般路线.