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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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The effective concentration of a species in a solution can be expressed precisely in terms of its activity. Activity considers the effect of electrolytes present in the vicinity of the species of interest and depends on the ionic strength of the solution. The activity of a species is expressed as the product of molar concentration and the activity coefficient of the species.
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Exact solution to quantum dynamical activity.

Tomohiro Nishiyama1, Yoshihiko Hasegawa2

  • 1Independent Researcher, Tokyo 206-0003, Japan.

Physical Review. E
|May 17, 2024
PubMed
Summary
This summary is machine-generated.

Calculating quantum dynamical activity, a key thermodynamic cost, is now feasible. We provide an exact solution using the continuous matrix product state method, enabling new insights into quantum speed limits.

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Area of Science:

  • Quantum Thermodynamics
  • Quantum Information Theory
  • Statistical Mechanics

Background:

  • Quantum dynamical activity is a crucial metric in quantum thermodynamics, appearing in fundamental trade-off relations like the quantum speed limit and the quantum thermodynamic uncertainty relation.
  • Calculating quantum dynamical activity has been computationally challenging, limiting its practical application and theoretical exploration.
  • Understanding these thermodynamic costs is essential for advancing quantum technologies and comprehending quantum systems' dynamics.

Purpose of the Study:

  • To present an exact analytical solution for calculating quantum dynamical activity.
  • To establish an upper bound for quantum dynamical activity based on system properties.
  • To validate the theoretical findings through numerical simulations.

Main Methods:

  • The study employs the continuous matrix product state (MPS) method, a powerful numerical technique for simulating quantum many-body systems.
  • The exact solution for quantum dynamical activity is derived using the developed continuous MPS framework.
  • An upper bound for dynamical activity is determined by analyzing the standard deviation of the system Hamiltonian and jump operators.

Main Results:

  • An exact solution for quantum dynamical activity has been successfully derived using the continuous matrix product state method.
  • The derived solution allows for the determination of an upper bound for dynamical activity, related to the standard deviation of system Hamiltonian and jump operators.
  • Numerical simulations confirm the accuracy of both the exact solution and the derived upper bound.

Conclusions:

  • The development of an exact solution for quantum dynamical activity overcomes previous computational hurdles.
  • The established upper bound provides a practical tool for estimating and bounding dynamical activity in quantum systems.
  • This work facilitates a deeper understanding of thermodynamic costs in quantum dynamics and their implications for quantum information processing.