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arXiv:2608.29830

Ballistic-to-Localized Dynamics as Signature of Quantum Phase Transition in Josephson Junction

Francesco Giuseppe Capone, ANTONIO DE CANDIA, G. Di Bello, V. Cataudella, Rosario Fazio, Naoto Nagaosa, C. A. Perroni, G. De Filippis

Published Aug 30, 2026• 0 citations
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Abstract

Using state-of-the-art numerical techniques, we investigate how quantum phase fluctuations and quasiparticle tunneling shape the behavior of a small-capacitance Josephson junction across Ohmic, sub-Ohmic, and super-Ohmic dissipation regimes. We show that increasing the Ohmic dissipation strength drives a Berezinskii-Kosterlitz-Thouless quantum phase transition at thermodynamic equilibrium. Deviations from Ohmic behavior profoundly alter this scenario: the super-Ohmic regime exhibits no phase transition, whereas the sub-Ohmic regime displays a continuous second-order transition, consistent with the universality classes of the spin-boson model. Within the Ohmic regime, real-frequency linear-response calculations reveal that the phase particle does not undergo the commonly assumed diffusive-to-localized crossover. Instead, finite resistance progressively suppresses the singular zero-frequency response, producing a ballistic-to-localized change in the dynamics. At finite frequencies, coupling to the environment generates a long-lived excitation in the charge response, which evolves into a resonance as the subgap and shunt resistances are reduced.

DOI
10.48550/arxiv.2608.29830

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Using state-of-the-art numerical techniques, we investigate how quantum phase fluctuations and quasiparticle tunneling shape the behavior of a small-capacitance Josephson junction across Ohmic, sub-Ohmic, and super-Ohmic dissipation regimes. We show that increasing the Ohmic dissipation strength drives a Berezinskii-Kosterlitz-Thouless quantum phase transition at thermodynamic equilibrium. Deviations from Ohmic behavior profoundly alter this scenario: the super-Ohmic regime exhibits no phase transition, whereas the sub-Ohmic regime displays a continuous second-order transition, consistent with the universality classes of the spin-boson model. Within the Ohmic regime, real-frequency linear-response calculations reveal that the phase particle does not undergo the commonly assumed diffusive-to-localized crossover. Instead, finite resistance progressively suppresses the singular zero-frequency response, producing a ballistic-to-localized change in the dynamics. At finite frequencies, coupling to the environment generates a long-lived excitation in the charge response, which evolves into a resonance as the subgap and shunt resistances are reduced.
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