Quantum dissipation and the virial theorem
arXiv:2302.12008 · doi:10.1016/j.physa.2023.128999
Abstract
In this note, we study the celebrated virial theorem for dissipative systems, both classical and quantum. The classical formulation is discussed and an intriguing effect of the random force (noise) is made explicit in the context of the virial theorem. Subsequently, we derive a generalized virial theorem for a dissipative quantum oscillator, i.e. a quantum oscillator coupled with a quantum heat bath. Such a heat bath is modeled as an infinite collection of independent quantum oscillators with a certain distribution of initial conditions. In this situation, the non-Markovian nature of the quantum noise leads to novel bath-induced terms in the virial theorem. We also consider the case of an electrical circuit with thermal noise and analyze the role of non-Markovian noise in the context of the virial theorem.
arXiv commentv2: Revised version to appear in Physica A
References in corpus (10)
- Quantum analogue of energy equipartition theorem
- Quantum partition of energy for a free Brownian particle: Impact of dissipation
- Quantum Langevin equation of a charged oscillator in a magnetic field and coupled to a heat bath through momentum variables
- Quantum Counterpart of Classical Equipartition of Energy
- Quantum counterpart of energy equipartition theorem for a dissipative charged magneto-oscillator: Effect of dissipation, memory, and magnetic field
- A geometric approach to a generalized virial theorem
- Virial Theorem and Hypervirial Theorem in a spherical geometry
- Partition of kinetic energy and magnetic moment in dissipative diamagnetism
- Generalised energy equipartition in electrical circuits
- Generalized virial theorem for contact Hamiltonian systems
Cited by in corpus (4)
- Independent-oscillator model and the quantum Langevin equation for an oscillator: A review
- Stochastic thermodynamics and the Ericsson nano engine -- Efficiency from equilibrium results
- Weak-coupling limits of the quantum Langevin equation for an oscillator
- Detecting zero-point fluctuations with stochastic Brownian oscillators