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The concept of the inertia tensor is employed to depict the mass distribution and rotational inertia of a solid or rigid object. This tensor is expressed through a three-by-three matrix. Each component within this matrix corresponds to varying moments of inertia about specific axes.
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Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other...
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Related Experiment Video

Updated: Jul 9, 2025

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

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Quantum correlation functions through tensor network path integral.

Amartya Bose1

  • 1Department of Chemical Sciences, Tata Institute of Fundamental Research, Mumbai 400005, India.

The Journal of Chemical Physics
|December 5, 2023
PubMed
Summary
This summary is machine-generated.

A new tensor network method efficiently calculates equilibrium correlation functions for open quantum systems. This approach enhances simulations of quantum dynamics, enabling studies of larger systems and longer timescales.

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Area of Science:

  • Quantum Mechanics
  • Computational Chemistry
  • Condensed Matter Physics

Background:

  • Tensor networks offer compressed representations for quantum wave functions and eigenstates.
  • Recent advances leverage tensor networks for efficient real-time non-equilibrium simulations using the Feynman-Vernon influence functional.

Purpose of the Study:

  • Develop a tensor network for non-perturbative calculation of equilibrium correlation functions in open quantum systems.
  • Utilize path integral methodology to incorporate solvent influence via an influence functional.
  • Design an optimal matrix product-like operator for a novel tensor network approach.

Main Methods:

  • A complex-time tensor network path integral approach is developed.
  • An optimal matrix product-like operator is designed to handle the unconventional structure of the influence functional.
  • The method is applied to the path amplitude matrix product state.

Main Results:

  • The developed tensor network provides an exceptionally efficient representation of the path integral.
  • Enables simulations for larger quantum systems interacting strongly with baths.
  • Allows for simulations at lower temperatures and extended timescales.

Conclusions:

  • The new tensor network method significantly advances the simulation capabilities for open quantum systems.
  • It facilitates accurate calculations of fundamental properties like reaction rates and response functions.
  • Demonstrates applicability through simulations of rate theory, spin correlation functions, and the Fenna-Matthews-Olson complex response.