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arXiv:2607.23127

Quantum fluctuation-driven transport crossover between two liquid states in distinguishable helium-4

Mika Tanabe, Momoko Tsujimoto, Kenichi Kinugawa

cond-mat.stat-mechcond-mat.dis-nncond-mat.mtrl-scicond-mat.quant-gasquant-phSubmitted Jul 25, 2026• Announced Jul 28, 2026• Revised Oct 27, 2026 (v2)
v1 · Jul 25, 2026v2 · Oct 27, 2026
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Abstract

We show the emergence of a quantum fluctuation-driven transport crossover between two liquid states in distinguishable helium-4 obeying Boltzmann statistics, in the absence of atomic exchange. Using path integral centroid molecular dynamics simulations over 0.1-3.3 K and 1-60 bar, we investigate the transport properties of two distinct liquid states: the low quantum dispersion liquid (LQDL) and the high quantum dispersion liquid (HQDL). While LQDL exhibits conventional liquid behavior consistent with the Stokes-Einstein (SE) relation, HQDL emerges at lower temperatures and displays anomalous gas-like transport characterized by superdiffusion and ultralow viscosity, accompanied by a breakdown of the SE relation. This counterintuitive emergence of gas-like dynamics upon cooling reflects the dominant role of nuclear quantum fluctuations, in contrast to thermal fluctuations at higher temperatures. Across the LQDL-HQDL boundary, we identify a transport crossover marked by a qualitative change in the velocity autocorrelation function (VAF), a transition in the Prandtl number, and the emergence of transport minima in shear and kinematic viscosities, thermal conductivity, and thermal diffusivity. These minima reflect a crossover from liquid-like to gas-like transport upon cooling in the low-temperature subcritical region, in addition to the universal transport minima observed in the supercritical regime. The transition from oscillatory to monotonic VAF defines a second Frenkel line, distinct from the conventional Frenkel line observed in the supercritical region. LQDL is a heat-transport-dominated dissipative fluid, whereas HQDL is a momentum-dominated inertial fluid. These results demonstrate that nuclear quantum fluctuations alone induce gas-like liquid behavior and provide a unified picture of transport phenomena in distinguishable helium-4 without superfluidity.

Journal reference
J. Chem. Phys. 165, 164507 (2026)
DOI
10.1063/5.0354210
Comments
main text (28 pages containing 15 figures) and supplementary material (30 pages)

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We show the emergence of a quantum fluctuation-driven transport crossover between two liquid states in distinguishable helium-4 obeying Boltzmann statistics, in the absence of atomic exchange. Using path integral centroid molecular dynamics simulations over 0.1-3.3 K and 1-60 bar, we investigate the transport properties of two distinct liquid states: the low quantum dispersion liquid (LQDL) and the high quantum dispersion liquid (HQDL). While LQDL exhibits conventional liquid behavior consistent with the Stokes-Einstein (SE) relation, HQDL emerges at lower temperatures and displays anomalous gas-like transport characterized by superdiffusion and ultralow viscosity, accompanied by a breakdown of the SE relation. This counterintuitive emergence of gas-like dynamics upon cooling reflects the dominant role of nuclear quantum fluctuations, in contrast to thermal fluctuations at higher temperatures. Across the LQDL-HQDL boundary, we identify a transport crossover marked by a qualitative change in the velocity autocorrelation function (VAF), a transition in the Prandtl number, and the emergence of transport minima in shear and kinematic viscosities, thermal conductivity, and thermal diffusivity. These minima reflect a crossover from liquid-like to gas-like transport upon cooling in the low-temperature subcritical region, in addition to the universal transport minima observed in the supercritical regime. The transition from oscillatory to monotonic VAF defines a second Frenkel line, distinct from the conventional Frenkel line observed in the supercritical region. LQDL is a heat-transport-dominated dissipative fluid, whereas HQDL is a momentum-dominated inertial fluid. These results demonstrate that nuclear quantum fluctuations alone induce gas-like liquid behavior and provide a unified picture of transport phenomena in distinguishable helium-4 without superfluidity.
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Decoherent quantum equations of motion are derived that yield the trajectory of an open quantum system. The viscosity of superfluid Lennard-Jones helium-4 is obtained with a quantum stochastic molecular dynamics algorithm. The momentum state occupancy entropy is counted with a continuous representation of boson number and averages are obtained with umbrella sampling. Instantaneous snapshots of the Bose-Einstein condensed system show multiple highly occupied momentum states. The viscosity is obtained from the Onsager-Green-Kubo relation with the time correlation function modified in the quantum case. On the saturation curve, at higher temperatures the viscosities of the classical and quantum liquids are equal. With decreasing temperature the viscosity of the classical liquid increases whereas that of the quantum liquid decreases. Below the λλλ-transition the viscosity lies significantly below the classical value, being small but positive due to the mixture of condensed and uncondensed bosons. The computed trajectories give a physical explanation of the molecular mechanism for superfluidity.
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