H-Theorem in an Isolated Quantum Harmonic Oscillator

We consider the H-theorem in an isolated quantum harmonic oscillator through the time-dependent Schrodinger equation. The effect of potential in producing entropy is investigated in detail, and we found that including a barrier potential into a harmonic trap would lead to the thermalization of the system, while a harmonic trap alone would not thermalize the system. During thermalization, Shannon entropy increases, which shows that a microscopic quantum system still obeys the macroscopic thermodynamics law. Meanwhile, initial coherent mechanical energy transforms to incoherent thermal energy during thermalization, which exhibiting the decoherence of an oscillating wave packet featured by a large decreasing of autocorrelation length. When reaching thermal equilibrium, the wave packet comes to a halt, with the density distributions both in position and momentum spaces well-fitted by a microcanonical ensemble of statistical mechanics.

Automated summary

This study investigates the H-theorem in an isolated quantum harmonic oscillator through the time-dependent Schrodinger equation. The effect of potential in producing entropy is examined in detail, revealing that the introduction of a barrier potential in a harmonic trap leads to the thermalization of the system. It is also observed that a coherent mechanical energy transforms into incoherent thermal energy during thermalization, accompanied by the decoherence of the oscillating wave packet.