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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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The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
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Variational Ground-State Quantum Adiabatic Theorem.

Bojan Žunkovič1, Pietro Torta2,3, Giovanni Pecci4

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We introduce a quantum adiabatic theorem for variational methods. This theorem shows that variational dynamics can accurately follow the ground state, even with complex quantum states, simplifying quantum computations.

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Area of Science:

  • Quantum Computing
  • Quantum Dynamics
  • Theoretical Physics

Background:

  • The adiabatic theorem is crucial for quantum computation, ensuring systems evolve to their ground state.
  • Variational methods offer a powerful approach to approximate solutions in quantum mechanics.
  • Challenges arise in maintaining accuracy with complex quantum states and limited computational resources.

Purpose of the Study:

  • To present a variational quantum adiabatic theorem.
  • To demonstrate that projected adiabatic dynamics on variational manifolds can follow instantaneous ground states.
  • To explore the convergence of variational evolution to target ground states under specific conditions.

Main Methods:

  • Formulating a variational quantum adiabatic theorem.
  • Focusing on low-entanglement variational manifolds.
  • Considering target Hamiltonians with classical ground states.
  • Analyzing the convergence of variational dynamics.

Main Results:

  • The variational adiabatic theorem is established under stated assumptions.
  • Variational evolution converges to the target ground state, even with highly entangled intermediate states.
  • Theoretical predictions are validated through several illustrative examples.

Conclusions:

  • The proposed variational quantum adiabatic theorem provides a robust framework for quantum computation.
  • Low-entanglement variational manifolds are effective for approximating adiabatic ground states.
  • This approach offers a pathway to efficiently find ground states in complex quantum systems.