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# Introduction
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Quantum friction is an external potential added to the Hamiltonian that breaks time-reversal invariance so as to cool the system (decrease its total energy). It may be used to cool fermionic many-body systems with thousands of wavefunctions that must remain orthogonal. It is described in details in:
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* A. Bulgac, M. M. Forbes, K. J. Roche, G. Wlazłowski,
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_Quantum Friction: Cooling Quantum Systems with Unitary Time Evolution_,
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[arXiv:1305.6891](https://arxiv.org/abs/1305.6891)
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The quantum friction potential is given by:
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```math
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V_{\sigma}^{(qf)} = -\alpha \frac{\hbar\,\vec{\nabla}\cdot\vec{j}_\sigma}{\rho_0}
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```
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where $`\rho_0=\frac{k_F^3}{6\pi^2}`$ is reference density. By construction, this potential removes any irrotational currents. Thus it provides a convenient method of removing phonon excitations from the system.
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