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Related Experiment Video

Updated: Jun 12, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Non-Markovian quantum mechanics on comb.

Alexander Iomin¹

¹Solid State Institute, Technion, Haifa 32000, Israel and Max-Planck Institute for Physics of Complex Systems, 01187 Dresden, Germany.

Chaos (Woodbury, N.Y.)

|September 23, 2024

Summary

This summary is machine-generated.

Quantum particle dynamics on a 2D comb structure exhibit non-Markovian behavior. This study introduces fractional time Schrödinger equations to describe this complex quantum mechanics, yielding analytical Green function solutions.

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Area of Science:

Quantum mechanics
Condensed matter physics
Mathematical physics

Background:

The study investigates quantum dynamics on a unique two-dimensional comb structure.
Topologically constrained geometries in Hamiltonian systems can lead to complex behaviors like non-Markovian dynamics.

Purpose of the Study:

To analyze the quantum dynamics of a particle on a 2D comb structure.
To rigorously demonstrate the emergence of fractional time derivatives for non-Markovian quantum mechanics.
To derive analytical solutions for Green functions in both conservative and driven systems.

Main Methods:

Rigorous analytical consideration of a Hamiltonian system.
Application of fractional time Schrödinger equations.
Derivation of Green functions for quantum systems.

Main Results:

The quantum dynamics on the 2D comb structure are shown to be non-Markovian.
Fractional time derivatives naturally arise in the description of this non-Markovian quantum mechanics.
Analytical solutions for Green functions are obtained for both conservative and time-driven Hamiltonian systems.

Conclusions:

The complex geometry of the comb structure dictates non-Markovian quantum dynamics.
Fractional calculus provides a suitable framework for describing such quantum systems.
The obtained Green functions offer valuable tools for understanding particle behavior in these systems.