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Related Concept Videos

¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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 slanted or...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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,...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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 have a...
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
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...
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...

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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Long-range order in nonequilibrium interacting quantum spin chains.

Tomaz Prosen1, Marko Znidaric

  • 1Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia.

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

Nonequilibrium boundary conditions can induce long-range order in quantum chains. Density matrix renormalization group simulations reveal phase transitions and emergent order, even when integrability is broken.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Nonequilibrium steady states are crucial for understanding open quantum systems.
  • Locally interacting quantum chains provide a tractable framework for studying complex quantum phenomena.
  • Understanding the emergence of order in driven quantum systems is a fundamental challenge.

Purpose of the Study:

  • To investigate whether nonequilibrium boundary conditions can induce long-range order in quantum chains.
  • To explore the behavior of quantum spin chains driven far from equilibrium.
  • To identify phase transitions and the conditions for emergent long-range order.

Main Methods:

  • Large-scale density matrix renormalization group (DMRG) simulations.
  • Modeling quantum spin-1/2 chains with unequal Lindblad reservoirs at the boundaries.
  • Analyzing spin-spin correlations to detect long-range order.

Main Results:

  • Nonequilibrium boundary conditions generically trigger long-range order in quantum chains.
  • A phase transition from decaying to long-range correlations was observed in an integrable Heisenberg XXZ chain by tuning the anisotropy parameter.
  • Long-range order also emerged in non-integrable models.

Conclusions:

  • Nonequilibrium boundary conditions are a powerful mechanism for generating long-range order in quantum systems.
  • The emergence of order is robust and can occur even in non-integrable models.
  • These findings have implications for designing and controlling quantum states in open systems.