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Quantum State-to-State Rates for Multistate Processes from Coherences.

Reshmi Dani1, Nancy Makri1,2,3

  • 1Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States.

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This study reveals that imaginary coherences dictate population dynamics in multistate systems. Even in incoherent limits, these coherences determine state-to-state rates and equilibrium populations.

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Area of Science:

  • Quantum mechanics
  • Chemical kinetics
  • Statistical mechanics

Background:

  • Understanding population dynamics in complex systems is crucial for predicting chemical reactions and quantum processes.
  • Traditional methods often struggle with multistate systems coupled to general environments.

Purpose of the Study:

  • To establish a novel method for calculating population dynamics in multistate systems.
  • To generalize existing reactive flux methods to encompass multistate processes.
  • To demonstrate the fundamental role of coherences in governing population evolution and equilibrium.

Main Methods:

  • Analysis of time derivatives of populations in terms of imaginary components of coherences (off-diagonal elements of the reduced density matrix).
  • Derivation of state-to-state rates from early plateau values of imaginary coherences for rate dynamics.
  • Utilizing short-time simulation results and kinetic equations for population evolution.

Main Results:

  • Time derivatives of populations are directly linked to imaginary coherences.
  • All state-to-state rates can be extracted from the imaginary components of coherences.
  • Short-time values of imaginary coherences fully determine equilibrium populations via detailed balance.

Conclusions:

  • Population evolution in multistate systems is fundamentally governed by coherences, even in the incoherent limit.
  • The presented method offers a generalized approach to reactive flux methods for complex systems.
  • This work provides a new perspective on the relationship between coherences, rates, and equilibrium populations.