Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1110.3678 · Physical Review B

Dynamics and universality in noise-driven dissipative systems

Emanuele G. Dalla Torre, Eugene Demler, Thierry Giamarchi, Ehud Altman

Published May 10, 2012• 87 citations
arXivHTMLPDF

Abstract

We investigate the dynamical properties of low-dimensional systems, driven by external noise sources. Specifically we consider a resistively shunted Josephson junction and a one-dimensional quantum liquid in a commensurate lattice potential, subject to $1/f$ noise. In absence of nonlinear coupling, we have shown previously that these systems establish a nonequilibrium critical steady state [Dalla Torre, Demler, Giamarchi, and Altman, Nat. Phys. 6, 806 (2010)]. Here, we use this state as the basis for a controlled renormalization group analysis using the Keldysh path integral formulation to treat the nonlinearities: the Josephson coupling and the commensurate lattice. The analysis to first order in the coupling constant indicates transitions between superconducting and localized regimes that are smoothly connected to the respective equilibrium transitions. However, at second order, the back action of the mode coupling on the critical state leads to renormalization of dissipation and emergence of an effective temperature. In the Josephson junction, the temperature is parametrically small allowing to observe a universal crossover between the superconducting and insulating regimes. The I-V characteristics of the junction displays algebraic behavior controlled by the underlying critical state over a wide range. In the noisy one-dimensional liquid, the generated dissipation and effective temperature are not small as in the junction. We find a crossover between a quasilocalized regime dominated by dissipation and another dominated by temperature. However, since in the thermal regime the thermalization rate is parametrically small, signatures of the nonequilibrium critical state may be seen in transient dynamics.

DOI
10.1103/physrevb.85.184302

Related papers

Noisy quantum phase transitions: an intuitive approach

Emanuele G Dalla Torre, Eugene Demler, Thierry Giamarchi +1 more

Equilibrium thermal noise is known to destroy any quantum phase transition. What are the effects of non-equilibrium noise? In two recent papers we have considered the specific case of a resistively-shunted Josephson junction driven by $1/f$ charge noise. At equilibrium, this system undergoes a sharp quantum phase transition at a critical value of the shunt resistance. By applying a real-time renormalization group (RG) approach, we found that the noise has three main effects: It shifts the phase transition, renormalizes the resistance, and generates an effective temperature. In this paper we explain how to understand these effects using simpler arguments, based on Kirchhoff laws and time-dependent perturbation theory. We also show how these effects modify physical observables and especially the current-voltage characteristic of the junction. In the appendix we describe two possible realizations of the model with ultracold atoms confined to one dimension.

arXiv:1205.3496•Physica Scripta•Nov 1, 2012•2 citations

Conductance of a dissipative quantum dot: Nonequilibrium crossover near a non-Fermi-liquid quantum critical point

Gu Zhang, E. Novais, Harold U. Baranger

We find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single barrier described by the boundary sine-Gordon model. The nonlinear conductance is then obtained from thermodynamic Bethe ansatz results in the literature, which were developed to treat tunneling in a Luttinger liquid. The current-voltage characteristics are thus found for any value of the resistance of the leads. For the special case of lead resistance equal to the quantum resistance, we find mappings onto, first, the two-channel Kondo model and, second, an effectively noninteracting model from which the nonlinear conductance is found analytically. A key feature of the general crossover function is that the nonequilibrium crossover driven by applied bias is different from the crossover driven by temperature---we find that the nonequilibrium crossover is substantially sharper. Finally, we compare to experimental results for both the bias and temperature crossovers: the agreement is excellent.

arXiv:2108.00064•Physical review. B./Physical review. B•Oct 25, 2021•3 citations

Nonequilibrium functional renormalization for driven-dissipative Bose-Einstein condensation

Lukas M. Sieberer, Sebastian D. Huber, Ehud Altman +1 more

We present a comprehensive analysis of critical behavior in the driven-dissipative Bose condensation transition in three spatial dimensions. The starting point is a microscopic description of the system in terms of a many-body quantum master equation, where coherent and driven-dissipative dynamics occur on an equal footing. An equivalent Keldysh real-time functional integral reformulation opens up the problem to a practical evaluation using the tools of quantum field theory. In particular, we develop a functional renormalization group approach to quantitatively explore the universality class of this stationary nonequilibrium system. Key results comprise the emergence of an asymptotic thermalization of the distribution function, while manifest nonequilibrium properties are witnessed in the response properties in terms of a new, independent critical exponent. Thus, the driven-dissipative microscopic nature is seen to bear observable consequences on the largest length scales. The absence of two symmetries present in closed equilibrium systems---underlying particle number conservation and detailed balance, respectively---is identified as the root of this new nonequilibrium critical behavior. Our results are relevant for broad ranges of open quantum systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases.

arXiv:1309.7027•Physical Review B•Apr 29, 2014•129 citations

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

Francesco Giuseppe Capone, ANTONIO DE CANDIA, G. Di Bello +5 more

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.

arXiv:2608.29830•Aug 30, 2026•0 citations

Quantum phase transition with dissipative frustration

Dominik Maile, Sabine Andergassen, Wolfgang Belzig +1 more

We study the quantum phase transition of the one-dimensional phase model in the presence of dissipative frustration, provided by an interaction of the system with the environment through two noncommuting operators. Such a model can be realized in Josephson junction chains with shunt resistances and resistances between the chain and the ground. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a nonmonotonic behavior as a function of the dissipative coupling strength. This result is a consequence of the frustration between (i) one dissipative coupling that quenches the quantum phase fluctuations favoring the ordered phase and (ii) one that quenches the quantum momentum (charge) fluctuations leading to a vanishing phase coherence. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that quantum frustration increases the range in which the phase transition is second order. The nonmonotonic behavior is reflected also in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as an entanglement measure that encodes the internal quantum correlations in the chain.

arXiv:1711.11346•Physical review. B./Physical review. B•Apr 23, 2018•23 citations

Dissipation and noise in strongly driven Josephson junctions

Vasilii Vadimov, Yoshiki Sunada, Mikko Möttönen

In circuit quantum electrodynamical systems, the quasiparticle-related losses in Josephson junctions are suppressed due to the gap in the superconducting density of states which is much higher than the typical energy of a microwave photon. In this work, we show that a strong drive even at a frequency lower than twice the superconductor gap parameter can activate dissipation in the junctions due to photon-assisted breaking of the Cooper pairs. Both the decay rate and noise strength associated with the losses are sensitive to the dc phase bias of the junction and can be tuned in a broad range by the amplitude and the frequency of the external driving field, making the suggested mechanism potentially attractive for designing tunable dissipative elements. We also predict pronounced memory effects in the driven Josephson junctions, which are appealing for both theoretical and experimental studies of non-Markovian physics in superconducting quantum circuits. We illustrate our theoretical findings by studying the spectral properties and the steady-state population of a low-impedance resonator coupled to the driven Josephson junction: we show the emergence of non-Lorentzian spectral lines and broad tunability of effective temperature of the steady state.

arXiv:2504.06877•SciPost Physics Core•Oct 6, 2025•1 citation
We investigate the dynamical properties of low-dimensional systems, driven by external noise sources. Specifically we consider a resistively shunted Josephson junction and a one-dimensional quantum liquid in a commensurate lattice potential, subject to 1/f1/f1/f noise. In absence of nonlinear coupling, we have shown previously that these systems establish a nonequilibrium critical steady state [Dalla Torre, Demler, Giamarchi, and Altman, Nat. Phys. 6, 806 (2010)]. Here, we use this state as the basis for a controlled renormalization group analysis using the Keldysh path integral formulation to treat the nonlinearities: the Josephson coupling and the commensurate lattice. The analysis to first order in the coupling constant indicates transitions between superconducting and localized regimes that are smoothly connected to the respective equilibrium transitions. However, at second order, the back action of the mode coupling on the critical state leads to renormalization of dissipation and emergence of an effective temperature. In the Josephson junction, the temperature is parametrically small allowing to observe a universal crossover between the superconducting and insulating regimes. The I-V characteristics of the junction displays algebraic behavior controlled by the underlying critical state over a wide range. In the noisy one-dimensional liquid, the generated dissipation and effective temperature are not small as in the junction. We find a crossover between a quasilocalized regime dominated by dissipation and another dominated by temperature. However, since in the thermal regime the thermalization rate is parametrically small, signatures of the nonequilibrium critical state may be seen in transient dynamics.
Equilibrium thermal noise is known to destroy any quantum phase transition. What are the effects of non-equilibrium noise? In two recent papers we have considered the specific case of a resistively-shunted Josephson junction driven by 1/f1/f1/f charge noise. At equilibrium, this system undergoes a sharp quantum phase transition at a critical value of the shunt resistance. By applying a real-time renormalization group (RG) approach, we found that the noise has three main effects: It shifts the phase transition, renormalizes the resistance, and generates an effective temperature. In this paper we explain how to understand these effects using simpler arguments, based on Kirchhoff laws and time-dependent perturbation theory. We also show how these effects modify physical observables and especially the current-voltage characteristic of the junction. In the appendix we describe two possible realizations of the model with ultracold atoms confined to one dimension.
We find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single barrier described by the boundary sine-Gordon model. The nonlinear conductance is then obtained from thermodynamic Bethe ansatz results in the literature, which were developed to treat tunneling in a Luttinger liquid. The current-voltage characteristics are thus found for any value of the resistance of the leads. For the special case of lead resistance equal to the quantum resistance, we find mappings onto, first, the two-channel Kondo model and, second, an effectively noninteracting model from which the nonlinear conductance is found analytically. A key feature of the general crossover function is that the nonequilibrium crossover driven by applied bias is different from the crossover driven by temperature---we find that the nonequilibrium crossover is substantially sharper. Finally, we compare to experimental results for both the bias and temperature crossovers: the agreement is excellent.
We present a comprehensive analysis of critical behavior in the driven-dissipative Bose condensation transition in three spatial dimensions. The starting point is a microscopic description of the system in terms of a many-body quantum master equation, where coherent and driven-dissipative dynamics occur on an equal footing. An equivalent Keldysh real-time functional integral reformulation opens up the problem to a practical evaluation using the tools of quantum field theory. In particular, we develop a functional renormalization group approach to quantitatively explore the universality class of this stationary nonequilibrium system. Key results comprise the emergence of an asymptotic thermalization of the distribution function, while manifest nonequilibrium properties are witnessed in the response properties in terms of a new, independent critical exponent. Thus, the driven-dissipative microscopic nature is seen to bear observable consequences on the largest length scales. The absence of two symmetries present in closed equilibrium systems---underlying particle number conservation and detailed balance, respectively---is identified as the root of this new nonequilibrium critical behavior. Our results are relevant for broad ranges of open quantum systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases.
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.
We study the quantum phase transition of the one-dimensional phase model in the presence of dissipative frustration, provided by an interaction of the system with the environment through two noncommuting operators. Such a model can be realized in Josephson junction chains with shunt resistances and resistances between the chain and the ground. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a nonmonotonic behavior as a function of the dissipative coupling strength. This result is a consequence of the frustration between (i) one dissipative coupling that quenches the quantum phase fluctuations favoring the ordered phase and (ii) one that quenches the quantum momentum (charge) fluctuations leading to a vanishing phase coherence. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that quantum frustration increases the range in which the phase transition is second order. The nonmonotonic behavior is reflected also in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as an entanglement measure that encodes the internal quantum correlations in the chain.
In circuit quantum electrodynamical systems, the quasiparticle-related losses in Josephson junctions are suppressed due to the gap in the superconducting density of states which is much higher than the typical energy of a microwave photon. In this work, we show that a strong drive even at a frequency lower than twice the superconductor gap parameter can activate dissipation in the junctions due to photon-assisted breaking of the Cooper pairs. Both the decay rate and noise strength associated with the losses are sensitive to the dc phase bias of the junction and can be tuned in a broad range by the amplitude and the frequency of the external driving field, making the suggested mechanism potentially attractive for designing tunable dissipative elements. We also predict pronounced memory effects in the driven Josephson junctions, which are appealing for both theoretical and experimental studies of non-Markovian physics in superconducting quantum circuits. We illustrate our theoretical findings by studying the spectral properties and the steady-state population of a low-impedance resonator coupled to the driven Josephson junction: we show the emergence of non-Lorentzian spectral lines and broad tunability of effective temperature of the steady state.