Solution to Double Counting of Zero-Point Energy: Partitioned Quantum Thermal Baths for Mixed Quantum–Classical Dynamics
Abstract
Mixed quantum–classical simulations in which a tunnelling coordinate is propagated as a wavefunction and its environment as classical trajectories under a quantum thermal bath (QTB), count the zero-point energy twice: the wavefunction carries it intrinsically and the QTB noise supplies it again. This work removes this double counting by partitioning the thermostat spectrum, assigning its zero-point part to the wavefunction and driving the bath with the thermal part only. In the harmonic Caldeira–Leggett limit the partitioned scheme reproduces the exact variance to 0.3–1.1%, with a residual given in closed form, whereas the unpartitioned hybrid (wavefunction coupled to a standard QTB) is off by a factor of two. In a dissipative double well the partition removes the zero-point heating and holds the quantum energy at 100 K; the heating that remains at 300 K is traced to the mean-field back-reaction.
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BibTeX
@misc{dhiman2026solution,
title = {{Solution to Double Counting of Zero-Point Energy: Partitioned Quantum Thermal Baths for Mixed Quantum–Classical Dynamics}},
author = {Mukul Dhiman},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05789904v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Solution to Double Counting of Zero-Point Energy: Partitioned Quantum Thermal Baths for Mixed Quantum–Classical Dynamics
AU - Mukul Dhiman
PY - 2026
DA - 2026/10/09
PB - HAL
UR - https://hal.science/hal-05789904v1
AB - Mixed quantum–classical simulations in which a tunnelling coordinate is propagated as a wavefunction and its environment as classical trajectories under a quantum thermal bath (QTB), count the zero-point energy twice: the wavefunction carries it intrinsically and the QTB noise supplies it again. This work removes this double counting by partitioning the thermostat spectrum, assigning its zero-point part to the wavefunction and driving the bath with the thermal part only. In the harmonic Caldeira–Leggett limit the partitioned scheme reproduces the exact variance to 0.3–1.1%, with a residual given in closed form, whereas the unpartitioned hybrid (wavefunction coupled to a standard QTB) is off by a factor of two. In a dissipative double well the partition removes the zero-point heating and holds the quantum energy at 100 K; the heating that remains at 300 K is traced to the mean-field back-reaction.
ER -