Emergent Viscous Hydrodynamics From a Single Quantum Particle
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arXiv
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| Format: | Preprint |
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2025
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| author | Zhou, Zhi-Li Hippert, Mauricio Mullins, Nicki Noronha, Jorge |
| author_facet | Zhou, Zhi-Li Hippert, Mauricio Mullins, Nicki Noronha, Jorge |
| contents | We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single non-relativistic quantum particle linearly coupled to a thermal bath of noninteracting harmonic oscillators at temperature $T$, a la Caldeira and Leggett. Taking advantage of decoherence in the position representation, we expand the reduced density matrix in powers of the off-diagonal spatial components, so that high-order terms are suppressed at late times. Truncating the resulting power series at second order leads to a set of dissipative transient hydrodynamic equations similar to the non-relativistic limit of equations widely used in simulations of the quark-gluon plasma formed in ultrarelativistic heavy-ion collisions. Transport coefficients are directly determined by the damping constant $γ$, which quantifies the influence of the environment. The asymptotic limit of our hydrodynamic equations reduces to the celebrated Navier-Stokes equations for a compressible fluid in the presence of a drag force. Our results shed new light on the onset of hydrodynamic behavior in open quantum systems where a system with few degrees of freedom is coupled to a large thermal environment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06618 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Emergent Viscous Hydrodynamics From a Single Quantum Particle Zhou, Zhi-Li Hippert, Mauricio Mullins, Nicki Noronha, Jorge Statistical Mechanics High Energy Physics - Theory Nuclear Theory Quantum Physics We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single non-relativistic quantum particle linearly coupled to a thermal bath of noninteracting harmonic oscillators at temperature $T$, a la Caldeira and Leggett. Taking advantage of decoherence in the position representation, we expand the reduced density matrix in powers of the off-diagonal spatial components, so that high-order terms are suppressed at late times. Truncating the resulting power series at second order leads to a set of dissipative transient hydrodynamic equations similar to the non-relativistic limit of equations widely used in simulations of the quark-gluon plasma formed in ultrarelativistic heavy-ion collisions. Transport coefficients are directly determined by the damping constant $γ$, which quantifies the influence of the environment. The asymptotic limit of our hydrodynamic equations reduces to the celebrated Navier-Stokes equations for a compressible fluid in the presence of a drag force. Our results shed new light on the onset of hydrodynamic behavior in open quantum systems where a system with few degrees of freedom is coupled to a large thermal environment. |
| title | Emergent Viscous Hydrodynamics From a Single Quantum Particle |
| topic | Statistical Mechanics High Energy Physics - Theory Nuclear Theory Quantum Physics |
| url | https://arxiv.org/abs/2506.06618 |