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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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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,...
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Nonequilibrium phase transition in a periodically driven XY spin chain.

Tomaž Prosen1, Enej Ilievski

  • 1Department of Physics, FMF, University of Ljubljana, Slovenia.

Physical Review Letters
|September 10, 2011
PubMed
Summary

We developed a new method to study Floquet states in open quantum systems. This approach reveals complex phase diagrams with reentrant phases in spin chains, offering insights into quantum correlations.

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Area of Science:

  • Quantum Many-Body Physics
  • Open Quantum Systems
  • Condensed Matter Theory

Background:

  • Understanding Floquet states in open quantum systems is crucial for quantum technologies.
  • Markovian quasifree fermionic systems present unique challenges due to their complexity.
  • Periodic driving and dissipation significantly alter system dynamics.

Purpose of the Study:

  • To present a general formulation for Floquet states in open Markovian quasifree fermionic systems.
  • To analyze the dynamics and phase diagram of a periodically kicked XY spin-½ chain coupled to reservoirs.
  • To connect the phase diagram structure to the properties of Floquet quasiparticle dispersion relations.

Main Methods:

  • Formulation of Floquet states using a discrete Lyapunov equation.
  • Analysis of a spin-½ XY chain coupled to two Lindblad reservoirs.
  • Investigation of spin-spin correlations and phase transitions.
  • Characterization of phase diagram structure via stationary points of quasiparticle dispersion.

Main Results:

  • A general formulation for Floquet states in the studied systems is established.
  • A complex phase diagram for the kicked XY spin-½ chain is presented.
  • Reentrant phases exhibiting long-range and decaying spin-spin correlations are identified.
  • The phase diagram structure is successfully reproduced using Floquet quasiparticle dispersion analysis.

Conclusions:

  • The discrete Lyapunov equation provides an effective tool for studying Floquet states in open quantum systems.
  • The XY spin-½ chain exhibits rich phase behavior, including reentrant phases, under periodic driving and dissipation.
  • Floquet quasiparticle dispersion relations offer a powerful method for understanding the complex phase diagrams of such systems.