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Adiabatic Processes for an Ideal Gas01:18

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Atomization, converting samples into gas-phase atoms and ions, is essential for atomic spectroscopy. The flame temperature required for atomization affects the efficiency of the atomic spectroscopic methods by increasing the atomization efficiency and the relative population of the excited and ground states.
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Updated: Jul 1, 2025

Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures
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Adiabatic Evolution of Low-Temperature Many-Body Systems.

Rafael L Greenblatt1, Markus Lange2, Giovanna Marcelli3

  • 1Mathematics Department, University of Rome "Tor Vergata", viale della Ricerca Scientifica 1, 00133 Rome, Italy.

Communications in Mathematical Physics
|March 11, 2024
PubMed
Summary

This study analyzes fermionic lattice models under perturbations, deriving a convergent expansion for thermal equilibrium state evolution. This rigorously establishes linear response theory and state closeness to instantaneous Gibbs states at low temperatures.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Statistical Mechanics

Background:

  • Understanding the dynamics of quantum systems out of equilibrium is crucial.
  • Fermionic lattice models are fundamental to condensed matter physics.
  • Perturbations can drive systems away from their equilibrium states.

Purpose of the Study:

  • To derive a convergent expansion for the evolution of thermal equilibrium states in fermionic lattice models under weak, time-dependent perturbations.
  • To rigorously establish the validity of linear response theory for these systems.
  • To prove the closeness of the time-evolved state to the instantaneous Gibbs state.

Main Methods:

  • Derivation of a convergent expansion in the perturbation strength.
  • Application of a rigorous Wick rotation to relate real-time dynamics to Euclidean correlation functions.
  • Utilizing fermionic cluster expansion for precise decay estimates.

Main Results:

  • A convergent expansion for the average evolution of local observables was derived for small temperatures.
  • Convergence is uniform in system size and, under a spectral gap assumption, in temperature.
  • The time-evolved state is shown to be close to the instantaneous Gibbs state.
  • The validity of linear response theory is established.

Conclusions:

  • The developed expansion provides a rigorous framework for studying non-equilibrium dynamics in fermionic lattice models.
  • The results confirm theoretical predictions about system behavior under perturbations.
  • This work advances the understanding of thermalization and response in quantum many-body systems.