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When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...
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Free expansion of a gas is an adiabatic process. However, there are few differences between free expansion and adiabatic expansion. During free expansion, no work is done, and there is no change in internal energy. But, for an adiabatic expansion, work is done, and there is a change in internal energy. During an adiabatic process, the relation between the pressure and volume is obtained from the condition for the adiabatic process, that is,
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Time Scale for Adiabaticity Breakdown in Driven Many-Body Systems and Orthogonality Catastrophe.

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The adiabatic theorem in quantum mechanics requires slow Hamiltonian changes for ground state preservation. This study simplifies adiabaticity conditions for many-body systems, avoiding spectral analysis.

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Area of Science:

  • Quantum Mechanics
  • Many-Body Physics
  • Quantum Dynamics

Background:

  • The adiabatic theorem is crucial in quantum mechanics, ensuring systems remain in their ground state if Hamiltonians change slowly.
  • Current understanding of "slowly enough" is limited to systems with small Hilbert spaces.
  • Applications span quantum field theory to molecular dynamics.

Purpose of the Study:

  • To provide a practicable quantitative understanding of adiabaticity conditions for a broader class of systems.
  • To simplify the derivation of adiabaticity criteria in complex many-body systems.

Main Methods:

  • Analysis of many-body systems exhibiting an orthogonality catastrophe.
  • Derivation of adiabaticity conditions from scaling properties of the ground state.
  • Avoiding direct computation of the excitation spectrum.

Main Results:

  • A simplified method to determine adiabaticity conditions for systems with large Hilbert spaces.
  • Adiabaticity criteria derived from ground-state scaling properties, not excitation spectra.
  • Bridging the gap in quantitative understanding of the adiabatic theorem's applicability.

Conclusions:

  • The developed method simplifies the complex problem of adiabatic time evolution in large Hilbert spaces.
  • This work offers a more accessible approach to understanding adiabaticity in many-body systems.
  • The findings enhance the practical application of the adiabatic theorem in diverse physical systems.