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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

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.
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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. This...
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

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 energy to a nearby...
The de Broglie Wavelength02:32

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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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Related Experiment Video

Updated: May 27, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Quantum Smoluchowski equation for a spin bath.

Sudarson Sekhar Sinha1, Arnab Ghosh, Deb Shankar Ray

  • 1Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 9, 2011
PubMed
Summary
This summary is machine-generated.

We explore quantum Brownian motion in a spin bath, finding that while quantization boosts particle escape rates, higher temperatures reduce this effect. Coherence plays a key role in this quantum system.

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Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions
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Last Updated: May 27, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions
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Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter physics

Background:

  • Brownian motion describes particle movement influenced by random collisions.
  • Quantum effects become significant in small systems or at low temperatures.
  • Spin baths involve interactions with magnetic properties of atoms.

Purpose of the Study:

  • To develop a quantum mechanical model for overdamped Brownian motion.
  • To investigate particle escape rates from metastable states in a spin bath.
  • To analyze the influence of temperature and quantization on system dynamics.

Main Methods:

  • Derivation of the quantum Smoluchowski equation.
  • Calculation of the escape rate from a metastable state.
  • Analysis of temperature-dependent behavior and coherence effects.

Main Results:

  • A finite decay rate at 0 Kelvin was determined.
  • Quantization was found to enhance the decay rate.
  • Higher temperatures led to thermal saturation, reducing system-bath coupling.

Conclusions:

  • Quantum effects and temperature significantly alter Brownian motion in spin baths.
  • Understanding these dynamics is crucial for quantum system control.
  • Coherence is an important factor influencing system-bath interactions.