Non-equilibrium and stochastic thermodynamics
Simulating heat flow through a quantum spin between hot and cold baths
Open access · cc by · source: Europe PMC
A trick that replaces a warm environment with an equivalent cold one lets a single wave-function simulation reproduce finite-temperature quantum heat flow, including strong-coupling effects.
Study at a glance
- Design
- Computational / modelling — Matrix-product-state (1TDVP) wave-function simulations of the Ohmic spin-boson model using the T-TEDOPA mapping of thermal baths onto zero-temperature proxy chains.
- N
- No sample; simulations span a grid of coupling strengths and bath temperatures for single-bath and two-bath models.
- Population
- Model quantum two-level system coupled to bosonic harmonic-oscillator baths
- Outcome
- Spin relaxation and steady-state polarisation, bath mode occupations, entanglement entropy and heat currents between baths
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Key findings
The final spin polarisation depended on coupling strength, not just temperature, because strong coupling shrinks the effective energy gap (polaron effect); analytical predictions matched once the coupling was rescaled by a constant factor of 0.66. With two baths, the gap renormalisation was non-additive: two equal baths do not simply multiply their individual effects. A net heat current flowed from hot to cold bath in steady state, roughly linear (Fourier-like) for small temperature differences and saturating for large ones.
Methodology
The authors simulated a quantum two-level system (a spin) strongly coupled to one or two baths of harmonic oscillators at set temperatures. They used the T-TEDOPA method, which maps a thermal bath onto an extended zero-temperature bath with positive and negative frequencies, and then onto a chain that can be evolved as a matrix product state. They compared spin relaxation, steady states and heat currents against analytical rate equations with polaron renormalisation of the energy gap.
Limitations
This is a model calculation with an idealised Ohmic spectral density and hard cut-off, not an experiment on a real device. The number of bath excitations and the entanglement in the simulation grow without bound over time, so long-time steady-state results need care and computing costs rise. The negative-frequency modes are non-physical bookkeeping, so their dynamics describe the simulation rather than the real environment. Agreement with theory relied on an empirically chosen rescaling of the coupling.
How this study connects
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