Heat Crawls through New Material at Exceptionally Slow, Logarithmic Rates

Researchers have discovered unexpectedly slow heat propagation within a chain of Josephson junctions, challenging conventional understanding of thermal conductivity in such systems. Angelo Russomanno from the Dipartimento di Fisica “E. Pancini”, Universit`a di Napoli Federico II, alongside colleagues, demonstrate that heat travels logarithmically slowly along the chain, rather than through typical diffusion. This finding, detailed through Langevin dynamics modelling, reveals a thermalisation length and energy increase with time in a manner reminiscent of Anderson localisation, even within a perfectly clean, classical Hamiltonian system. The observed behaviour suggests potential resilience to ergodic effects, offering new insights into non-ergodic behaviour in charge-quantised regimes and potentially impacting the design of novel thermal management technologies.

Logarithmic Thermalisation in Josephson Junction Chains Mimics Many-Body Localisation

Researchers have uncovered a surprisingly slow propagation of heat within a chain of Josephson junctions, revealing behaviour typically associated with complex quantum systems. The work details how heat transfer occurs logarithmically slowly through the system, a departure from the expected diffusive behaviour.

This unusual thermal transport is evidenced by a thermalization length and energy increase that both grow logarithmically with time. The discovery, made using a classical model of a clean Josephson-junction chain coupled to a thermal bath, mirrors phenomena observed in disordered quantum materials and many-body localized systems.

This study employed Langevin dynamics to model the behaviour of the Josephson-junction chain, specifically focusing on scenarios where the Josephson energy is significantly smaller than the charging energy. Numerical simulations revealed that the thermalization length, a measure of how far heat has spread, increases logarithmically in time.

Simultaneously, the total energy within the system also exhibits a logarithmic increase, beginning after an initial period of thermal pre-equilibration. This logarithmic behaviour indicates a fundamentally different mechanism of heat propagation than conventional diffusion, suggesting a robust resistance to the effects of disorder.

The observed phenomenon is particularly noteworthy as it appears in a clean, classical system, challenging the expectation that such slow heat transport is exclusive to quantum systems exhibiting disorder or strong interactions. Researchers found this logarithmic propagation front is consistent with extremely slow thermalization times previously observed in similar models.

The team’s analysis provides a new perspective on the glassy behaviour of these Josephson-junction chains, offering insights into the potential for non-ergodic behaviour even in seemingly simple systems. Furthermore, the research establishes a connection between the logarithmic increase in thermalization length and the logarithmic increase in energy, suggesting a unifying analytical model may be possible.

The circuit scheme utilised involves a chain of superconducting islands connected by Josephson junctions, with one end coupled to a thermal bath via a resistance. By applying Kirchhoff’s laws and employing the Verlet algorithm with noise, the researchers were able to accurately simulate the system’s dynamics and observe this unique heat propagation behaviour, representing the first observation of this phenomenon in a classical, clean system.

Langevin dynamics simulation of thermalization length in Josephson junction chains

Researchers investigated heat propagation within Josephson junction chains by modelling a system comprising a chain of junctions coupled to a thermal bath via a resistance. Langevin dynamics were employed within the classical regime, specifically focusing on scenarios where the Josephson energy is significantly smaller than the charging energy.

This allowed for the determination of a thermalization length, which was found to increase logarithmically with time, indicating a remarkably slow heat propagation process. The study revealed that energy increases logarithmically over time, diverging from typical diffusive behaviour. This logarithmic behaviour, reminiscent of Anderson or Mott localization, was also observed within a clean, classical glassy Hamiltonian.

The methodology involved defining and tracking the temporal evolution of the thermalization length to characterise the propagation of thermal energy through the junction chain. By analysing the logarithmic increase in both the thermalization length and energy, researchers demonstrated a non-diffusive heat transport mechanism.

Furthermore, the work proposes that this phenomenon could confer robustness against ergodic inclusions, potentially impacting the non-ergodic behaviour observed in charge-quantized regimes. The precision of the classical simulations, combined with the careful analysis of the logarithmic time dependence, enabled the identification of this unusual heat transport and its potential implications for understanding complex systems exhibiting localization phenomena. This detailed analysis provides insight into the dynamics of energy flow in these engineered systems.

Logarithmic heat propagation and emergent thermalization length in Josephson junction chains

Researchers observed a logarithmic propagation of heat through a Josephson-junction chain, revealing an atypical thermal response. The study detailed that heat does not propagate diffusively, but rather exhibits a logarithmic increase in time, as evidenced by a defined thermalization length. This behaviour, reminiscent of Anderson localization, was observed within a clean, classical glassy Hamiltonian system.

The thermalization length increased logarithmically with time, analogous to findings in many-body localization systems. Numerical simulations, employing a Langevin-equation approach, demonstrated this slow heat propagation in a classical regime where Josephson energy is significantly smaller than charging energy.

The energy within the system also increased logarithmically in time, beginning after an extended prethermal plateau. Analysis of the system, comprising L superconducting islands each with capacitance C and charging energy EC = (2e)2/C, alongside Josephson energy EJ, revealed this unusual dynamic. The Langevin dynamics were modelled using equations governing charge qj and superconducting phase θj on each island, coupled to a thermal bath via a resistance R at the first site.

Simulations utilised the Verlet algorithm with a time step of ∆t = 10−4, averaging over Nr = 990 realizations to ensure convergence. A thermalization length, h(t), was defined as the ratio of the sum of squared charges to the total number of sites, providing a measure of how far the thermal equilibrium had propagated.

Plots of h(t) versus time for EJ = 10−2EC and L = 20, at varying rescaled temperatures τ, clearly showed a logarithmic increase, with faster propagation occurring at lower temperatures. This logarithmic behaviour was also reflected in the energy, which increased proportionally to h(t) under the approximation that each site reaching thermal equilibrium contributes kBT/2 to the total energy.

Logarithmic Thermal Transport and Extended Nonergodicity in a Clean Josephson Junction Chain

Researchers have demonstrated that heat propagates logarithmically slowly through a clean Josephson-junction chain coupled to a thermal bath, a behaviour previously observed only in disordered quantum systems. This unconventional propagation, characterised by a thermalization length and energy that increase logarithmically with time, arises within a classical glassy Hamiltonian despite the absence of localized integrals of motion typically found in quantum localized systems.

The finding is significant because it reveals a novel mechanism for slow heat propagation in a classically clean system, suggesting potential robustness to the effects of ergodic inclusions for nonergodic behaviour. Specifically, the observed logarithmic propagation front implies that the Thouless time, representing the slowest thermalization time, scales exponentially with the system size, exceeding the Heisenberg time and indicating a strong resistance to ergodicity-breaking perturbations.

The authors acknowledge that their analysis is limited to the classical regime and a specific parameter range where Josephson energy is much smaller than charging energy. Future research could extend this work to investigate the quantized Josephson-junction chain, potentially revealing a connection between slow energy increase and entanglement entropy growth, which would facilitate analysis using matrix-product state methods. Establishing logarithmic heat propagation in the quantum case would further strengthen the implications for the robustness of nonergodicity when the system is coupled to an ergodic inclusion, offering insights into the behaviour of complex quantum systems.