Anisotropic signatures in the spin-boson model

TL;DR

This paper investigates how anisotropic material symmetries affect the equilibrium properties of a classical spin coupled to an environment, revealing symmetry-dependent behaviors and potential for work extraction.

Contribution

It derives the mean force corrections for anisotropic materials at arbitrary coupling, linking symmetry to spin expectation values and energy inhomogeneities.

Findings

Spin expectation values depend on material symmetry and temperature.

Certain symmetries exhibit zero-temperature spin alignment transitions.

Energy inhomogeneities can be exploited for work extraction.

Abstract

Thermal equilibrium properties of nanoscale systems deviate from standard macroscopic predictions due to a non-negligible coupling to the environment. For anisotropic three-dimensional materials, we derive the mean force corrections to the equilibrium state of a classical spin vector. The result is valid at arbitrary coupling strength. Specifically, we consider cubic, orthorhombic, and monoclinic symmetries, and compare their spin expectation values as a function of temperature. We underpin the correctness of the mean force state by evidencing its match with the steady state of the simulated non-Markovian spin dynamics. The results show an explicit dependence on the symmetry of the confining material. In addition, some coupling symmetries show a spin alignment transition at zero temperature. Finally, we quantify the work extraction potential of the mean force-generated inhomogeneities in the energy shells. Such inhomogeneities constitute a classical equivalent to quantum coherences.