Related Experiment Video
Updated: Aug 6, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Rigorous Bound on Hydrodynamic Diffusion for Chaotic Open Spin Chains
Dimitrios Ampelogiannis1, Benjamin Doyon1
1Department of Mathematics, King's College London, Strand, London, WC2R 2LS UK.
Journal of Statistical Physics
|July 23, 2026
Summary
Researchers established a lower bound for spin diffusion in chaotic quantum spin chains using Lindbladian evolution. This breakthrough demonstrates that spin transport depends on quantum jumps, offering new insights into many-body quantum systems.
Area of Science:
- Quantum physics
- Condensed matter theory
- Mathematical physics
Background:
- Diffusion is a fundamental phenomenon in many-body interacting, chaotic systems.
- Rigorously proving diffusive behavior of correlation functions, like spin, is a major challenge in mathematical physics.
Purpose of the Study:
- To establish a rigorous lower bound for spin diffusion in open quantum spin systems.
- To investigate the role of quantum jumps and irreversibility in spin transport.
Main Methods:
- Utilizing Lindbladian evolution for open quantum systems.
- Applying the Green-Kubo formula and projection techniques.
- Establishing correlation decay bounds for chaotic, translation-invariant systems.
Main Results:
- A strictly positive lower bound on spin diffusion was derived for a quantum spin-1/2 chain.
- The bound is positive if and only if local quantum jumps transport spin.
- A contribution to spin diffusion strength from irreversibility was identified and shown to vanish in reversible cases.
Conclusions:
- The study provides the first rigorous lower bound on spin diffusion in chaotic open quantum spin chains.
- The findings highlight the crucial role of quantum jumps and irreversibility in spin transport.
- The methods are extendable to various quantum systems, including quantum circuits.
Related Concept Videos
01:17Radical Chain-Growth Polymerization: Chain Branching
The skeletal structure of polymers synthesized via radical polymerization is always branched. For example, the polymerization of ethylene by radical polymerization results in a low-density grade of polyethylene with a heavily branched skeletal structure. Here, the radical site abstracts hydrogen from the growing chain, and the radical site shifts from the end (a primary carbon center) to anywhere within the growing chain (a secondary carbon center). Consequently, the part of the chain from the...
01:09Radical Chain-Growth Polymerization: Mechanism
The radical chain-growth polymerization mechanism consists of three steps: initiation, propagation, and termination of polymerization. The polymerization initiates when a free radical generated from the radical initiator adds to the unsaturated bond in the monomer. The unpaired electron of the free radical and one π electron in the unsaturated bond creates a σ bond between the free radical and the monomer. As a result, the other π electron in the unsaturated bond converts this species into the...
01:08Spin–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...
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...
01:10Entropy Change in Reversible Processes
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
02:05Entropy and Solvation
The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ ≥ 15); an...
01:17Spin–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,...