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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
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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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Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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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 Transitions01:21

Phase Transitions

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A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Related Experiment Video

Updated: Apr 17, 2026

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Quantum phase transitions exposed by rotating the spins.

Xin Li1, Yu Shi2

  • 1Department of Physics & State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China and Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 14, 2015
PubMed
Summary
This summary is machine-generated.

Quantum phase transitions are revealed by geometric phases or survival probability in nonadiabatic processes. The XY spin chain demonstrates how these phenomena indicate transitions even without adiabatic changes.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • The study of quantum phase transitions (QPTs) is crucial for understanding critical phenomena in quantum systems.
  • Nonadiabatic variations in Hamiltonians present challenges for traditional QPT detection methods.

Purpose of the Study:

  • To explore novel methods for detecting QPTs under nonadiabatic conditions.
  • To investigate the role of geometric phases and survival probability in revealing QPTs.

Main Methods:

  • Utilizing the exactly solvable XY spin chain as a model system.
  • Analyzing nonadiabatic variations of the Hamiltonian along isospectral trajectories.
  • Examining the accumulated geometric (Aharonov-Anandan) phase.
  • Calculating the survival probability of quantum states.

Main Results:

  • Nonadiabatic geometric phases can effectively signal QPTs when a system cycles through states.
  • Survival probability indicates QPTs and exhibits revival phenomena when starting from an instantaneous ground state under nonadiabatic evolution.
  • The XY spin chain serves as a concrete example illustrating these findings.

Conclusions:

  • Geometric phases and survival probability offer robust indicators for QPTs in nonadiabatic regimes.
  • These findings provide new perspectives on detecting and understanding quantum phase transitions.