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Related Concept Videos

Phase Transitions02:31

Phase Transitions

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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

Phase Diagrams

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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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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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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.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
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Phase Diagram01:19

Phase Diagram

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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

Spectrophotometry: Introduction

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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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Phase Transitions: Vaporization and Condensation02:39

Phase Transitions: Vaporization and Condensation

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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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Topology and Spectrum in Measurement-Induced Phase Transitions.

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

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

Physical Review Letters
|July 31, 2025
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Summary
This summary is machine-generated.

We introduce a Lyapunov analysis framework to understand entanglement phases in monitored quantum systems. This method identifies topological properties and distinguishes different entanglement phases, extending bulk-edge correspondence to quantum dynamics.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Topological Phases of Matter

Background:

  • Monitored quantum systems exhibit diverse entanglement phases due to competing measurements and unitary dynamics.
  • Characterizing these phases, especially topological ones, remains a challenge in quantum information science.
  • Understanding the interplay between entanglement, topology, and measurement is crucial for quantum technologies.

Purpose of the Study:

  • To propose a general framework using Lyapunov analysis for characterizing topological properties in monitored quantum systems.
  • To apply this framework to (1+1)-dimensional monitored circuits involving Majorana fermions.
  • To develop a method for distinguishing different entanglement phases and understanding critical phenomena.

Main Methods:

  • Lyapunov analysis of the system's spectrum and many-body topological invariants.
  • Analysis of (1+1)-dimensional monitored circuits with Majorana fermions.
  • Exploitation of fermion parity and twisted boundary measurements to construct a topological invariant.

Main Results:

  • Lyapunov analysis successfully identifies topological and trivial area-law entangled phases.
  • Edge-localized zero modes are detected in the topological phase, absent in the trivial phase.
  • A bulk gapless spectrum characterizes the critical phase, and a topological invariant distinguishes area-law phases.

Conclusions:

  • The proposed Lyapunov framework provides a robust method for characterizing topological properties in monitored quantum systems.
  • This approach successfully distinguishes between different entanglement phases, including critical ones.
  • The framework offers a general route to extend the bulk-edge correspondence to monitored quantum dynamics.