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Related Concept Videos

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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Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

1.1K
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.
1.1K
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

1.1K
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
1.1K
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.2K
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...
1.2K
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

1.2K
In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
1.2K
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

1.2K
Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
1.2K

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Updated: Apr 22, 2026

Site Directed Spin Labeling and EPR Spectroscopic Studies of Pentameric Ligand-Gated Ion Channels
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Effective ergodicity in single-spin-flip dynamics.

Mehmet Süzen1

  • 1Applied Mathematical Physiology Lab, Bonn University, Sigmund-Freud-Strasse 25, 53127 Bonn, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2014
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Summary
This summary is machine-generated.

The Thirumalai-Mountain (TM) metric quantifies convergence to ergodicity in spin-flip dynamics. Caution is advised when using the TM metric with Ising models exhibiting strong correlations.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics

Background:

  • Ergodicity is crucial for understanding the long-time behavior of dynamical systems.
  • The Thirumalai-Mountain (TM) metric provides a quantitative measure for assessing convergence to effective ergodicity.

Purpose of the Study:

  • To apply the Thirumalai-Mountain (TM) metric to Metropolis and Glauber single-spin-flip dynamics.
  • To monitor the time evolution of effective ergodic convergence for Ising magnetization.
  • To identify diffusion regimes of ergodic convergence under varying system parameters.

Main Methods:

  • Utilized the exact solution for a one-dimensional Ising model to compute finite lattice ensemble averages.
  • Employed Monte Carlo simulations to compute time averages.
  • Applied the TM metric to analyze spin-flip dynamics.

Main Results:

  • Identified diffusion regimes of effective ergodic convergence for magnetization.
  • Observed the influence of lattice size, temperature, and external field on convergence.
  • Demonstrated that strong correlations can affect the reliability of the TM metric.

Conclusions:

  • The TM metric is a valuable tool for analyzing ergodic convergence in spin dynamics.
  • System parameters significantly influence the rate and nature of ergodic convergence.
  • Care must be exercised when applying the TM metric in systems with strong correlations.