Thermophoresis is the migration of a particle due to a thermal gradient. Here, we theoretically uncover a quantum version of thermophoresis, where both the bosonic nature of the thermal baths and quantum tunneling play significant roles. First, we find a thermophoretic force on a trapped quantum particle in a double-well potential. Then, we show that thermophoresis also takes place in an $N$-site model, for which we analytically derive a diffusion equation in the continuum limit ($N\to \infty$). We evidence additional quantum thermophoretic signatures in the transient particle-transport regime, which appear in the particle's average position and variance, as well as in the particle currents. Beyond establishing that single quantum particles can undergo thermally induced transport, our results suggest a route for quantum-state preparation with thermal gradients.

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• Brownian motion
• Irreversible processes
• Quantum thermodynamics
• Thermophoresis
• Quantum master equation