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Adiabatic Processes for an Ideal Gas01:18

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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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Consider the adiabatic compression of an ideal gas in the cylinder of an automobile diesel engine. The gasoline vapor is injected into the cylinder of an automobile engine when the piston is in its expanded position. The temperature, pressure, and volume of the resulting gas-air mixture are 20 °C, 1.00 x 105 N/m2, and 240 cm3 , respectively. The mixture is then compressed adiabatically to a volume of 40 cm3. Note that, in the actual operation of an automobile engine, the compression is not...
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Hamiltonian transformability, fast adiabatic dynamics and hidden adiabaticity.

Lian-Ao Wu1,2, Dvira Segal3,4

  • 1Department of Theoretical Physics and History of Science, The Basque Country University (EHU/UPV), PO Box 644, 48080, Bilbao, Spain. lianaowu@gmail.com.

Scientific Reports
|February 26, 2021
PubMed
Summary
This summary is machine-generated.

We proved a unitary transformation exists to convert any two Hamiltonians in the same Hilbert space. This finding enables mimicking complex dynamics using simpler, controllable Hamiltonians, advancing quantum computation.

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Area of Science:

  • Quantum mechanics
  • Theoretical physics
  • Quantum information science

Background:

  • Hamiltonians describe quantum system evolution.
  • Transforming Hamiltonians is crucial for controlling quantum dynamics.
  • Current methods face limitations in flexibility and control.

Purpose of the Study:

  • To prove the existence of a unitary transformation between any two Hamiltonians in the same Hilbert space.
  • To establish a theoretical foundation for manipulating quantum dynamics.
  • To enable the implementation or mimicry of dynamics using controllable Hamiltonians.

Main Methods:

  • Mathematical proof of existence for a unitary transformation.
  • Theoretical framework for Hamiltonian transformation.
  • Illustrative examples demonstrating the transformation.

Main Results:

  • Existence of a unitary transformation between arbitrary Hamiltonians in a shared Hilbert space is proven.
  • The transformation provides a method to interconvert Hamiltonians.
  • The approach is demonstrated with concrete examples.

Conclusions:

  • The established unitary transformation offers a powerful tool for quantum control.
  • This work provides a foundation for implementing or mimicking quantum dynamics.
  • A key application is the advancement of adiabatic quantum computation through Hamiltonian engineering.