# Quantum harmonic oscillators and thermalization

@inproceedings{Kim2021QuantumHO, title={Quantum harmonic oscillators and thermalization}, author={Hyeong-Chan Kim and Youngone Lee}, year={2021} }

We study a quantum harmonic oscillator undergoing thermalization. To describe the thermalization process, we generalize the Ermakov-Lewis-Riesenfeld (ELR) invariant method for the oscillator. After imposing appropriate conditions on the thermalization process, we introduce an ansatz equation that describes the time evolution effectively. We write down the first law for thermalization in the same form as that for ordinary thermodynamics. Here, the thermalization effect appears through a change…

## References

SHOWING 1-10 OF 31 REFERENCES

Equilibration and thermalization of the dissipative quantum harmonic oscillator in a nonthermal environment.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

A hierarchy of conditions for thermalization is found, together with the relation of the asymptotic temperature to the energy distribution in the initial bath state, based on the exact solution of the microscopic model obtained by means of operator equations of motion.

The harmonic oscillator in a heat bath

- Physics
- 1973

We study the time evolution of a quantum-mechanical harmonic oscillator in interaction with an infinite heat bath, which is supposed to be initially in the canonical equilibrium at some temperature.…

Decoherence and thermalization dynamics of a quantum oscillator

- Physics
- 2000

We introduce the quantitative measures characterizing the rates of decoherence and thermalization of quantum systems. We study the time evolution of these measures in the case of a quantum harmonic…

Thermalization in nature and on a quantum computer.

- Physics, MathematicsPhysical review letters
- 2012

A novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit is introduced and a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound is presented.

Nonequilibrium thermodynamics of a squeezed harmonic oscillator

- Physics
- 2008

We consider the thermodynamic properties of the squeezed vacuum state of a frequency--modulated quantum harmonic oscillator. We analytically relate the squeezing parameter to the irreversible work…

Independent oscillator model of a heat bath: Exact diagonalization of the Hamiltonian

- Physics
- 1988

The problem of a quantum oscillator coupled to an independent-oscillator model of a heat bath is discussed. The transformation to normal coordinates is explicitly constructed using the method of…

Decoherence and thermalization of a pure quantum state in quantum field theory.

- Physics, MedicinePhysical review letters
- 2010

It is demonstrated that, restricting one's attention to a subset of the infinite hierarchy of correlation functions, one observes an effective loss of purity or coherence and, on longer time scales, thermalization.

Geometric phase and nonadiabatic effects in an electronic harmonic oscillator.

- Physics, MedicinePhysical review letters
- 2012

This work uses a superconducting qubit as a nonlinear probe of the phase, which is otherwise unobservable due to the linearity of the oscillator, and shows that the geometric phase is proportional to the area enclosed in the quadrature plane.

Heisenberg-picture approach to the exact quantum motion of a time-dependent forced harmonic oscillator.

- Physics, MedicinePhysical review. A, Atomic, molecular, and optical physics
- 1996

In the Heisenberg picture, the generalized invariant and exact quantum motions are found for a time-dependent forced harmonic oscillator. We find the eigenstate and the coherent state of the…

Thermalization and its mechanism for generic isolated quantum systems

- Physics, MedicineNature
- 2008

It is demonstrated that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription, and it is shown that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch and Srednicki.