🔬 condensed matter

Viscous hydrodynamics from correlated losses

This paper demonstrates that correlated two-body losses can induce elastic scattering via the quantum Zeno effect, enabling a nondegenerate gas to exhibit hydrodynamic flow with viscosity and thermal conductivity comparable to those of a unitary Fermi gas.

Original authors: Aleksandr N. Mikheev, Orjan Ameye, Oded Zilberberg, Jeff Maki

Published 2026-10-15

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Aleksandr N. Mikheev, Orjan Ameye, Oded Zilberberg, Jeff Maki

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quiet world of ultra-cold atoms, scientists study how collections of particles behave when they are chilled to temperatures near absolute zero. Usually, whether a gas flows like a fluid or moves like a stream of independent bullets depends on how often the particles bump into one another. If the particles rarely collide, they fly in straight lines, maintaining their speed and direction until they hit the edge of their container. This is the behavior of an ideal gas. However, if the particles collide frequently, they constantly exchange momentum and energy, forcing the group to settle into a local balance where heat and motion spread out smoothly. This is the behavior of a fluid, governed by properties like viscosity, which measures how thick or resistant the fluid is to flow. For decades, researchers have created these fluid-like states by tuning the forces between atoms, making them interact strongly so that collisions happen as often as quantum mechanics allows.

But what if the gas has no forces between its particles at all? What if it is a perfect, ideal gas where atoms should never touch? For a long time, the answer seemed obvious: without collisions, there can be no fluid flow. Yet, a new study from researchers at the University of Konstanz suggests that even in a gas with no internal interactions, a fluid can emerge if the system is losing particles in a specific way. The key lies not in what the particles do to each other, but in how they disappear. When atoms are lost from a trap, they usually vanish one by one, which does not change the motion of the survivors. But if atoms are lost only when they meet in pairs, the act of disappearing forces them to interact. This counterintuitive discovery shows that loss itself can engineer the collisions necessary to turn a gas into a flowing fluid.

The researchers focused on a gas of atoms that were not interacting with one another, meaning they had no natural tendency to scatter or bounce off each other. In a typical experiment, such a gas would simply drift apart or decay if particles were removed. However, the team considered a scenario where particles are removed only when two of them happen to be in the same place at the same time. This is known as two-body loss. It happens in real experiments when two atoms collide and stick together to form a molecule that flies out of the trap, or when they react chemically and leave the system. The researchers found that this requirement for a pair to be present creates a hidden mechanism. Because the loss process removes pairs, it effectively forces the remaining atoms to scatter off one another to avoid being lost.

This phenomenon relies on a fundamental rule of quantum physics called the optical theorem, which links the probability of a particle being absorbed to the probability of it scattering. In this case, the "absorption" is the loss of the pair from the trap. The theorem dictates that if a process can remove a pair, it must also cause some pairs to bounce off each other elastically, changing their direction without being lost. Usually, this elastic scattering is a tiny side effect compared to the loss. However, the researchers showed that when the loss is very strong, the situation flips. The strong loss acts like a continuous measurement, constantly checking if two atoms are close together. This "watching" keeps the atoms apart, preventing them from being lost, but it simultaneously maximizes the chance that they will bounce off each other. The result is a gas where collisions are driven entirely by the threat of loss, rather than by any inherent force between the atoms.

The team calculated how this gas would behave over time and found that it flows just like the most collisional fluids known in nature, such as the unitary Fermi gas, which is famous for having the lowest possible viscosity. In their model, the gas developed a viscosity and thermal conductivity that approached these extreme limits, even though the atoms had no intrinsic attraction or repulsion. As the gas slowly lost particles, it also heated up. The researchers discovered a precise pattern in this heating: the temperature and density changed over time following a universal rule, growing or shrinking with a specific exponent of three-eighths. This means that as the gas thinned out and got hotter, its ability to flow and conduct heat increased in a predictable way, dictated not by the strength of the loss, but by the fundamental limits of quantum mechanics.

This finding challenges the traditional view that fluid behavior requires strong, coherent interactions between particles. Instead, it demonstrates that engineered dissipation—the careful design of how a system loses energy or particles—can create the very collisions that make a fluid. The researchers emphasized that this effect is most prominent when the loss is strong enough to dominate the system's behavior, pushing the gas into a regime where it behaves as if it were at the "unitary limit," the point of maximum possible interaction allowed by quantum laws. They noted that this applies to both bosons and fermions, provided the gas is not so dense that quantum statistics take over.

The study suggests that scientists can use this mechanism to create and study fluid dynamics in systems where interactions are otherwise absent. By tuning the rate at which pairs of atoms are lost, researchers could potentially control the flow of quantum matter without needing to tune magnetic fields to create strong forces. This opens a new path for exploring transport in quantum materials, where loss is no longer seen as a nuisance that ruins experiments, but as a resource that can be used to build new states of matter. The work provides a clear theoretical framework for how to observe this effect in cold atom experiments, pointing toward specific conditions where the gas would transition from a ballistic, non-interacting state into a hydrodynamic fluid driven solely by the act of losing particles.

Technical Summary: Viscous Hydrodynamics from Correlated Losses

Problem Statement
The central question addressed is whether a three-dimensional ideal quantum gas, devoid of intrinsic coherent elastic interactions, can exhibit hydrodynamic flow solely due to two-body particle loss. In standard kinetic theory, hydrodynamic behavior arises from frequent collisions that redistribute momentum and energy, establishing local equilibrium. While single-particle loss depletes a gas without altering the ballistic motion of remaining particles, two-body loss (where particles are removed only upon meeting) introduces a correlation-dependent mechanism. Previous studies suggested that while two-body loss probes pair correlations and, via the quantum Zeno effect, suppresses overlap, it does not inherently generate the elastic scattering required for hydrodynamics. This work investigates whether the optical theorem, which links absorption to scattering, allows two-body loss to induce sufficient elastic collisions to drive a gas into a hydrodynamic regime.

Methodology
The authors employ a microscopic kinetic theory derived from the Keldysh action formalism for open quantum systems.

Model Formulation: They consider a homogeneous, non-degenerate three-dimensional Fermi gas subject to both single-particle ( $\gamma_1$ ) and two-body ( $\gamma_2$ ) loss, described by a Lindblad master equation. The two-body loss is modeled via a jump operator $\hat{L} = \hat{\psi}_\uparrow \hat{\psi}_\downarrow$ , which introduces an imaginary contact interaction $i\gamma_2$ .
Derivation of the Boltzmann Equation: Using the two-particle-irreducible (2PI) effective action formalism, the authors derive a semiclassical Boltzmann equation. This equation incorporates the full dynamics of the lossy system, including the generation of an effective elastic scattering channel.
Scattering Analysis: The two-body $T$ -matrix is calculated, revealing that the complex scattering length $a = a' - i a''$ (with $a'=0$ for the ideal gas case) leads to both an absorption cross-section ( $\sigma_{in}$ ) and an elastic cross-section ( $\sigma_{el}$ ). The optical theorem dictates that the imaginary part of the $T$ -matrix (loss) necessitates a real part (elastic scattering).
Hydrodynamic Expansion: The authors apply a Chapman-Enskog expansion to the derived Boltzmann equation. They expand the distribution function $f = f^{(0)} + \delta f$ , where $f^{(0)}$ represents a time-dependent local equilibrium (Maxwell-Boltzmann) and $\delta f$ describes deviations responsible for transport.
Transport Coefficients: By solving the linearized Boltzmann equation for the relaxation of shear stress and heat currents, they calculate the shear viscosity ( $\eta$ ) and thermal conductivity ( $\kappa$ ). They analyze these coefficients across different regimes of the dimensionless parameter $a''/\lambda_T$ , where $\lambda_T$ is the thermal de Broglie wavelength.

Key Contributions and Results

Loss-Induced Elasticity: The paper demonstrates that two-body loss alone induces elastic scattering. While weak loss ( $a'' \ll \lambda_T$ ) primarily removes particles, strong loss ( $a'' \gg \lambda_T$ ) triggers the quantum Zeno effect, which suppresses the loss rate but saturates the elastic scattering cross-section at the unitary limit ( $k\sigma_{el} = 4\pi/k$ ).
Emergent Hydrodynamics: In the strong loss regime, the gas relaxes its momentum and heat currents far faster than it decays in density. Consequently, the gas flows hydrodynamically despite the absence of any coherent interaction ( $a'=0$ ).
Transport Coefficients: The shear viscosity and thermal conductivity of this loss-driven fluid approach the universal values of the unitary Fermi gas. Specifically, the relaxation times $\tau_\eta$ and $\tau_\kappa$ converge to the unitary limit $\tau_u = 15\pi/(16\sqrt{2})$ scaled by the fugacity and temperature.
Universal Scaling: As the gas decays, the preferential loss of slow particles heats the remaining gas. This leads to a universal scaling behavior for density and temperature: $n(t) \propto t^{-3/4}$ and $T(t) \propto t^{1/4}$ . Consequently, the shear viscosity and thermal conductivity grow in time with a universal exponent of $3/8$ ( $\eta, \kappa \propto t^{3/8}$ ), a signature fixed by the unitary limit rather than the specific loss strength.
Prandtl Number: The Prandtl number ( $Pr = c_p \eta / \kappa$ ) is found to be $2/3$ in the strong loss (unitary) limit, matching the value for a unitary Fermi gas. In the weak loss limit, it rises to $\approx 1.21$ .

Significance and Claims
The authors claim that this work establishes a counterintuitive mechanism where dissipation (loss) acts as a resource to engineer collisions and transport in quantum matter. By invoking the optical theorem, they show that correlated loss can transform an ideal gas into a near-unitary fluid without the need for tunable coherent interactions.

The significance lies in the demonstration that:

Dissipation as a Driver: Engineered dissipation can create the very collisions necessary for hydrodynamic flow, challenging the view of loss merely as a nuisance that limits experiments.
Universality: The resulting fluid exhibits transport properties (viscosity, thermal conductivity, Prandtl number) identical to those of the unitary Fermi gas, a state typically requiring strong coherent interactions.
Experimental Feasibility: The paper suggests that these effects are observable in ultracold atomic gases, particularly near Feshbach resonances where the scattering length can be tuned to have a large imaginary component (e.g., via photoassociation or decaying closed channels) while the real part is suppressed.

The results are presented as holding for non-degenerate gases of both bosons and fermions, with the kinetic theory derived from first principles using the Keldysh formalism. The work complements concurrent research on density decay by specifically addressing the induced hydrodynamic transport generated by loss-induced collisions.

Technical Summary: Viscous Hydrodynamics from Correlated Losses

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