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Heat capacity is the ratio of heat absorbed by the substance corresponding to its temperature change. It is also called thermal capacity and the SI unit of heat capacity is J/K. Whereas, specific heat capacity is defined as the amount of heat necessary to change the temperature of 1 kg of a substance by 1 K and is also called massic heat capacity. Its SI unit is J/kg⋅K.
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Multidimensional uniform semiclassical instanton thermal rate theory.

Eli Pollak1

  • 1Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel.

The Journal of Chemical Physics
|December 11, 2023
PubMed
Summary

We developed a new uniform semiclassical instanton rate theory for many-dimensional systems. This approach avoids the divergence issue found in previous theories at the crossover temperature.

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Area of Science:

  • Quantum mechanics
  • Chemical reaction dynamics
  • Statistical mechanics

Background:

  • Instanton-based rate theory is crucial for studying tunneling in complex systems.
  • A key limitation is its divergence at the crossover temperature.
  • Previous work established a uniform theory in one dimension.

Purpose of the Study:

  • To generalize uniform semiclassical instanton rate theory to many-dimensional systems.
  • To resolve the divergence issue at the crossover temperature.
  • To revise existing theories for dissipative systems.

Main Methods:

  • Utilizing Kemble's uniform semiclassical transmission probability.
  • Extending the one-dimensional uniform theory to multiple dimensions.
  • Applying the generalized theory to dissipative systems.

Main Results:

  • A novel, divergence-free uniform semiclassical instanton rate theory for many-dimensional systems.
  • The new theory requires the same input as traditional instanton theory.
  • A revised, non-divergent analytical expression for the rate in dissipative systems.

Conclusions:

  • The generalized uniform theory offers a robust alternative to traditional instanton rate theory.
  • This advancement resolves a critical limitation in studying multidimensional tunneling.
  • The revised theory provides more accurate rate calculations for dissipative processes.