⚛️ quantum physics

Hawking Radiation in non-Hermitian Microscopic Analogues

This paper proposes a microscopic fermionic open quantum system coupled to Markovian reservoirs that emulates black-hole physics through an effective non-Hermitian geometry, demonstrating how steady-state currents and frequency-resolved correlations reveal analogue Hawking radiation signatures and fermionic partner amplitudes.

Original authors: Diego F. Munoz-Arboleda, Cristiane Morais Smith, Marcus Stålhammar

Published 2026-09-09

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CC BY 4.0

Original authors: Diego F. Munoz-Arboleda, Cristiane Morais Smith, Marcus Stålhammar

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

Gravity is often described as the curvature of space and time, a concept so vast it usually belongs to the realm of black holes and distant stars. Yet, the fundamental rules governing how particles behave near these cosmic traps are not unique to gravity; they are kinematic effects that can appear wherever waves or particles encounter a sudden change in their environment. This insight has led physicists to build "analogues" of black holes in the laboratory, using fluids, light, or sound to mimic the extreme conditions of space. In these experiments, a horizon is created not by mass, but by a flow that moves faster than the waves trying to escape it, trapping them just as a black hole traps light. The most famous prediction of such horizons is Hawking radiation, a faint glow of particles that should emerge from the edge of the trap, created in pairs where one escapes and the other falls in. For decades, scientists have searched for this radiation in the lab, but detecting it is difficult because the signal is weak and easily confused with ordinary noise. Furthermore, while many experiments have looked for this effect in systems made of bosons, like atoms that clump together, the behavior of fermions—particles like electrons that strictly avoid sharing the same state—presents a different and largely unexplored challenge.

A team of researchers at Utrecht University and Uppsala University has now constructed a microscopic model to study this phenomenon using fermions in an open quantum system. They designed a theoretical chain of atoms where particles can hop from one site to the next, but with a crucial twist: the system is coupled to an environment that constantly absorbs and injects particles, a process known as dissipation. This interaction creates a non-Hermitian environment, a term physicists use to describe systems where energy is not perfectly conserved within the system itself because it leaks out or flows in. By carefully tuning how these particles interact with their surroundings, the researchers engineered a landscape where the effective flow of particles changes speed across the chain. This setup creates two distinct boundaries, or horizons, within the chain. At these boundaries, the flow of particles transitions from a slow regime to a fast one, mimicking the event horizon of a black hole on one side and a white hole—a theoretical object that expels everything—on the other.

The researchers first analyzed the mathematical structure of this system to see if the horizons would survive the inevitable noise and fluctuations of a real, open environment. They found that the system's behavior is governed by a spectrum of complex frequencies, which they call rapidities. In this spectrum, the black hole and white hole regions appear as distinct sectors separated by special points where the system's behavior changes abruptly. These points form cone-shaped structures in the mathematical space of the system, confirming that the horizon geometry is not just a short-lived illusion but a robust feature that persists even as the system settles into a steady state. When they calculated the density of particles and the flow of current across the chain, they observed sharp transitions exactly at the locations of these horizons. The particles piled up and the current changed direction in a way that clearly marked the presence of the analogue event horizons, proving that the geometric structure of the black hole model survives the long-term dynamics of the open system.

To move beyond simply observing the horizons and actually detect the Hawking radiation, the team had to address a specific challenge with fermions. Unlike bosons, which can crowd together to form a coherent signal, fermions are forbidden from occupying the same state, which constrains how they can correlate with one another. To simulate the pair production required for Hawking radiation, the researchers introduced a controlled mechanism that allowed particles to be created in pairs, linking a particle moving outward with a partner moving inward. They then tracked how these pairs scattered as they passed through the horizon. The results showed a clear signature of Hawking radiation: the outgoing particle and its partner were strongly correlated across the horizon, forming a distinct pattern in the data that resembled the "Hawking moustache" previously seen in bosonic systems. This correlation was not present in control simulations where the horizon was removed or where the flow did not cross the critical speed, confirming that the signal was indeed generated by the horizon itself and not by the background noise or the pairing mechanism alone.

Crucially, the researchers verified that these correlations obeyed the strict physical laws governing fermions. They checked that the strength of the connection between the particle and its partner did not exceed the limits imposed by the Pauli exclusion principle, which dictates that fermions cannot be too strongly correlated. The data satisfied this condition, showing that the system remained in a physically valid state throughout the process. This work demonstrates that the microscopic dynamics of an open quantum system can give rise to an effective geometry that mimics a black hole, and that this geometry can generate the specific, horizon-dependent correlations predicted for Hawking radiation. By successfully modeling this process with fermions, the study provides a new platform for exploring the intersection of quantum mechanics, open-system dynamics, and analogue gravity, offering a way to test these fundamental concepts in a controlled, table-top setting without the need for actual black holes.

Technical Summary: Hawking Radiation in non-Hermitian Microscopic Analogues

Problem Statement
The paper addresses the challenge of realizing analogue black-hole physics and Hawking radiation within microscopic open quantum systems. While effective non-Hermitian models have successfully generated exceptional cones and analogue horizons, it remains unclear whether these geometric and spectral structures persist when quantum jumps and complete long-time dissipative dynamics are included. Furthermore, establishing genuine Hawking pair production in fermionic systems is complicated by constraints imposed by Pauli exclusion and fermionic covariance positivity, which distinguish physical fermionic states from non-classicality witnesses. The authors aim to construct a microscopic open fermionic system that emulates black-hole properties, verify the persistence of horizon signatures in the steady state, and formulate rigorous many-body witnesses for analogue Hawking radiation.

Methodology
The authors propose a microscopic open quantum system consisting of a fermionic tight-binding chain coupled to Markovian reservoirs. The methodology proceeds through three distinct theoretical stages:

Microscopic Lindblad Construction: The system is defined by a Hermitian tight-binding Hamiltonian ( $H_{TB}$ ) coupled to linear jump operators representing gain and loss processes. The dynamics are governed by the Lindblad master equation. By analyzing the conditional no-jump evolution, the authors derive an effective non-Hermitian Hamiltonian ( $H_{eff}^{nH}$ ) featuring gain/loss (GL) terms and non-reciprocal next-nearest-neighbor (NNN) hopping.
Exact Spectral Analysis: Using "third quantization," the authors double the Hilbert space to map the quadratic Lindbladian onto a damping matrix. They solve for the exact rapidity spectrum of the full Lindbladian, identifying two sectors corresponding to black-hole and white-hole analogues. They analyze the momentum-space correlation matrices to determine steady-state particle densities and currents.
Many-Body Scattering and Nambu Extension: To investigate Hawking pair production, the authors introduce a fermionic Gaussian Nambu extension. This involves coupling particle and hole sectors via an antisymmetric pairing matrix, breaking global $U(1)$ symmetry while preserving fermion parity. They formulate a frequency-resolved scattering problem, defining incoming and outgoing channels based on biorthogonal fluxes derived from the non-Hermitian Bloch Hamiltonian. The scattering matrix ( $S$ ) relates incoming vacuum states to outgoing Hawking and partner modes.

Key Contributions and Results

Emergent Geometry and Horizon Persistence: The study demonstrates that the full Lindblad spectrum separates into black-hole and white-hole sectors, characterized by tilted exceptional cones in the rapidity spectrum. These cones define an effective Painlevé-Gullstrand geometry. Crucially, the authors show that the horizon structure (located at interfaces where the non-reciprocal hopping profile $f(r)$ satisfies $|f(r)|=1$ ) persists in the nonequilibrium steady state. This is evidenced by sharp transitions in equal-momentum particle densities and steady-state currents at the interface locations, confirming that the analogue horizon is a stable feature of the long-time dissipative dynamics.
Biorthogonal Flux and Channel Classification: In the non-Hermitian regime, propagation directions are not defined by standard group velocities but by biorthogonal fluxes calculated from left and right eigenvectors. The authors use this flux to classify asymptotic Bloch modes, successfully identifying outgoing exterior (Hawking) and interior (partner) channels.
Hawking-Partner Correlations: By reconstructing real-space density-density correlations from the frequency-resolved scattering amplitudes, the authors identify "Hawking moustaches"—long-range anomalous correlations connecting cells on opposite sides of the horizon. These correlations follow an equal-travel-time trajectory determined by the biorthogonal velocities of the outgoing channels.
Control and Selectivity: The study employs three profiles: a horizon-crossing profile, a "no-crossing" control (where the profile remains below the critical value), and a uniform control. The anomalous correlations are strongly suppressed (by orders of magnitude) in the control profiles, demonstrating that the observed correlations are specifically organized by the horizon and not merely by the pairing term or spatial inhomogeneity.
Fermionic Consistency: The authors verify that the frequency-resolved Hawking-partner correlations satisfy the fermionic covariance-positivity constraint ( $\Theta_{HP}^F \leq 1$ ). This ensures that the calculated anomalous covariance is compatible with a physical fermionic state, distinguishing the result from a mere mathematical artifact.

Significance and Claims
The paper establishes a direct connection between microscopic open-system dynamics, emergent non-Hermitian geometry, and fermionic many-body probes of analogue Hawking radiation. The authors claim that their work provides a microscopic justification for the survival of analogue black-hole and white-hole sectors in the steady state of a dissipative system.

Regarding the nature of the radiation, the authors are modest in their claims. They state that the observed correlations and the satisfaction of the covariance-positivity criterion establish "horizon-selective fermionic Hawking-partner production" and the characteristic "Hawking-moustache" structure. However, they explicitly note that satisfying the covariance-positivity constraint is a requirement for physicality rather than a witness of non-classicality or entanglement. Consequently, the paper does not claim to have demonstrated genuine quantum entanglement between the Hawking and partner modes; rather, it provides a controlled phenomenological framework where the single-particle analogue geometry organizes pair correlations. The authors suggest that a future demonstration of genuine quantum character would require an independent fermionic entanglement criterion, such as logarithmic negativity, which is not evaluated in this work.

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