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arxiv: 2605.19643 · v1 · pith:7SR3SH64new · submitted 2026-05-19 · ❄️ cond-mat.quant-gas · cond-mat.stat-mech· cond-mat.supr-con

Quantum effective action for dissipative semiclassical dynamics

Cesare Vianello , Andrea Bardin , Luca Salasnich This is my paper

Pith reviewed 2026-05-20 02:00 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.stat-mechcond-mat.supr-con
keywords quantum effective actiondissipative dynamicssemiclassical LangevinSchwinger-Keldysh formalismzero-point energyJosephson junctionbosonic junctionEhrenfest theorem
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The pith

Quantum corrections to dissipative semiclassical Langevin dynamics arise from zero-point energy of fluctuations at the classical underdamped frequency.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives quantum corrections to the semiclassical dynamics of dissipative systems by using the quantum effective action in the Schwinger-Keldysh formalism. It connects these corrections to the Ehrenfest theorem and shows that in the low-temperature and weak-damping regime they are fixed by the zero-point energy evaluated at the classical underdamped frequency, mirroring the structure found in conservative systems. The results are applied to a resistively and capacitively shunted Josephson junction and to an elongated bosonic junction, where the corrections can reach the percent level for realistic parameters. A sympathetic reader would care because the work supplies a systematic route to include quantum effects in the equations that govern macroscopic dissipative motion without solving the full quantum problem.

Core claim

Using the quantum effective action in the Schwinger-Keldysh formalism, the authors derive quantum corrections to the semiclassical Langevin dynamics of a dissipative system governed by a macroscopic degree of freedom. They establish the connection with the Ehrenfest theorem and demonstrate that, in the low-temperature and weak-damping regime, these quantum corrections are determined by the zero-point energy of fluctuations evaluated at the classical underdamped frequency, closely paralleling the conservative case. The general results are then applied to the resistively and capacitively shunted superconducting Josephson junction and to an elongated bosonic junction.

What carries the argument

The quantum effective action in the Schwinger-Keldysh formalism, which supplies the corrections to the semiclassical Langevin equation through its link to the Ehrenfest theorem when evaluated at the classical underdamped frequency.

If this is right

  • The semiclassical Langevin equation for the Josephson junction acquires an explicit quantum correction term proportional to the zero-point energy at the underdamped frequency.
  • The same correction applies to the dynamics of an elongated bosonic junction and can reach the percent level for realistic trap parameters and temperatures.
  • The structure of the correction remains formally identical to the conservative case once the classical underdamped frequency is inserted.
  • Higher-order quantum effects are suppressed in the stated low-temperature and weak-damping window.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same zero-point-energy prescription may extend to other weakly damped macroscopic oscillators whose classical frequency can be measured independently.
  • Numerical simulations of the corrected Langevin equation could be used to predict the size of quantum shifts in existing Josephson-junction experiments.
  • The approach suggests a route to incorporate quantum corrections into models of dissipative phase transitions without invoking full open-system quantum field theory.

Load-bearing premise

The derivation assumes that the quantum effective action yields identifiable corrections to dissipative dynamics via the Ehrenfest theorem connection, which can be evaluated specifically at the classical underdamped frequency in the low-temperature and weak-damping regime.

What would settle it

A direct measurement of the effective potential or frequency shift in a resistively shunted Josephson junction at millikelvin temperatures and weak damping, compared against the zero-point energy calculated at the measured classical underdamped frequency.

Figures

Figures reproduced from arXiv: 2605.19643 by Andrea Bardin, Cesare Vianello, Luca Salasnich.

Figure 1
Figure 1. Figure 1: FIG. 1. Quantum corrections to the dynamics of the bosonic [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
read the original abstract

Using the quantum effective action in the Schwinger-Keldysh formalism, we derive quantum corrections to the semiclassical Langevin dynamics of a dissipative system governed by a macroscopic degree of freedom. We discuss the connection with the Ehrenfest theorem and show that, in the low-temperature and weak-damping regime, quantum corrections are determined by the zero-point energy of fluctuations evaluated at the classical underdamped frequency, closely paralleling the conservative case. We apply these general results to the resistively and capacitively shunted superconducting Josephson junction and to an elongated bosonic junction, where quantum corrections can reach the percent level under realistic conditions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper derives quantum corrections to semiclassical Langevin dynamics for dissipative systems using the quantum effective action in the Schwinger-Keldysh formalism. It establishes a connection to the Ehrenfest theorem and argues that, in the low-temperature and weak-damping regime, these corrections are set by the zero-point energy of fluctuations evaluated at the classical underdamped frequency, paralleling the conservative case. The results are applied to a resistively and capacitively shunted Josephson junction and an elongated bosonic junction, where corrections can reach the percent level.

Significance. If the central derivation is free of hidden frequency renormalizations from the bath, the work supplies a systematic route to quantum corrections in dissipative semiclassical dynamics without introducing new free parameters. The explicit applications to experimentally relevant systems (Josephson junction, bosonic junction) and the clean parallel to the conservative zero-point correction constitute the main strengths; the manuscript would benefit from explicit verification that the Ehrenfest link preserves the underdamped frequency to the order kept in the expansion.

major comments (1)
  1. [Derivation of quantum corrections via Ehrenfest theorem] The central claim that quantum corrections are determined by zero-point energy evaluated at the unmodified classical underdamped frequency (abstract and the section connecting the effective action to Langevin dynamics) rests on the assumption that dissipative bath terms induce no O(γ/ω0) shift in the relevant fluctuation frequency. An explicit expansion of the quadratic part of the influence functional or the effective action is needed to confirm that any renormalization appears only at higher order than the zero-point correction itself; otherwise the claimed parallelism with the conservative case fails at the same perturbative order.
minor comments (2)
  1. The abstract states the regime restrictions (low-T, weak-damping) but the manuscript would be clearer if these restrictions were restated with explicit inequalities (e.g., ħω0 ≫ kT, γ ≪ ω0) immediately before the main result.
  2. Notation for the underdamped frequency and the effective mass or damping coefficient should be introduced once and used consistently across the Josephson-junction and bosonic-junction applications.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We are pleased that the referee recognizes the potential of the approach and the relevance of the applications. We address the single major comment below.

read point-by-point responses

  1. Referee: The central claim that quantum corrections are determined by zero-point energy evaluated at the unmodified classical underdamped frequency (abstract and the section connecting the effective action to Langevin dynamics) rests on the assumption that dissipative bath terms induce no O(γ/ω0) shift in the relevant fluctuation frequency. An explicit expansion of the quadratic part of the influence functional or the effective action is needed to confirm that any renormalization appears only at higher order than the zero-point correction itself; otherwise the claimed parallelism with the conservative case fails at the same perturbative order.

    Authors: We agree that an explicit verification of the frequency renormalization is valuable for clarity. In the Schwinger-Keldysh effective action, the quadratic fluctuations are determined by the classical underdamped oscillator frequency plus the real part of the bath-induced self-energy. For the standard Ohmic bath, the real part of the self-energy is odd in frequency and vanishes at the relevant perturbative order in the weak-damping limit, so that any shift in the fluctuation frequency enters only at O((γ/ω0)^2). We will add a short appendix to the revised manuscript that carries out this explicit expansion of the quadratic influence functional, confirming that the underdamped frequency remains unmodified to the order at which the zero-point correction is computed. This addition will make the parallelism with the conservative case fully transparent. revision: yes

Circularity Check

0 steps flagged

Derivation from Schwinger-Keldysh effective action is self-contained with no reduction to inputs

full rationale

The paper starts from the quantum effective action in the Schwinger-Keldysh formalism, connects it to semiclassical Langevin dynamics through the Ehrenfest theorem, and then identifies the low-temperature weak-damping corrections as the zero-point energy evaluated at the classical underdamped frequency. This is presented as a derived result that parallels the conservative case rather than an input. No equations, self-citations, or statements in the provided text demonstrate that the underdamped frequency is defined in terms of the quantum correction (or vice versa), that a parameter is fitted and then renamed as a prediction, or that a uniqueness theorem or ansatz is smuggled in via prior work by the same authors. The central claim therefore retains independent content from the formalism and regime assumptions; the derivation chain does not collapse to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract does not introduce or list any free parameters, axioms, or invented entities; the work relies on the established Schwinger-Keldysh formalism and the Ehrenfest theorem.

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Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    E. M. Lifshitz and L. P. Pitaevskii,Statistical Physics. Part 2: Theory of the Condensed State (Course of Theo- retical Physics, Vol. 9)(Butterworth-Heinemann, 1980)

    work page 1980

  2. [2]

    B. V. Svistunov, E. S. Babaev, and N. V. Prokof’ev,Su- perfluid States of Matter(CRC Press, 2015)

    work page 2015

  3. [3]

    B. D. Josephson, Possible new effects in superconductive tunneling, Phys. Lett.1, 251 (1962)

    work page 1962

  4. [4]

    P. W. Anderson and J. M. Rowell, Probable observation of the Josephson superconducting tunneling effect, Phys. Rev. Lett.10, 230 (1963)

    work page 1963

  5. [5]

    Barone and G

    A. Barone and G. Patern` o,Physics and Applications of the Josephson Effect(John Wiley & Sons, 1982)

    work page 1982

  6. [6]

    Smerzi, S

    A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates, Phys. Rev. Lett. 79, 4950 (1997)

    work page 1997

  7. [7]

    Albiez, R

    M. Albiez, R. Gati, J. F¨ olling, S. Hunsmann, M. Cris- tiani, and M. K. Oberthaler, Direct observation of tunnel- ing and nonlinear self-trapping in a single bosonic Joseph- son junction, Phys. Rev. Lett.95, 010402 (2005)

    work page 2005

  8. [8]

    Larkin and A

    A. Larkin and A. Varlamov,Theory of Fluctuations in Superconductors(Oxford University Press, 2005)

    work page 2005

  9. [9]

    Furutani and L

    K. Furutani and L. Salasnich, Quantum and thermal fluc- tuations in the dynamics of a resistively and capacitively shunted Josephson junction, Phys. Rev. B104, 014519 (2021)

    work page 2021

  10. [10]

    Pigneur, T

    M. Pigneur, T. Berrada, M. Bonneau, T. Schumm, E. Demler, and J. Schmiedmayer, Relaxation to a phase- locked equilibrium state in a one-dimensional bosonic Josephson junction, Phys. Rev. Lett.120, 173601 (2018)

    work page 2018

  11. [11]

    J. Polo, V. Ahufinger, F. W. J. Hekking, and A. Min- guzzi, Damping of Josephson oscillations in strongly cor- related one-dimensional atomic gases, Phys. Rev. Lett. 121, 090404 (2018)

    work page 2018

  12. [12]

    Binanti, K

    F. Binanti, K. Furutani, and L. Salasnich, Dissipation and fluctuations in elongated bosonic Josephson junc- tions, Phys. Rev. A103, 063309 (2021)

    work page 2021

  13. [13]

    R. H. Koch, D. J. Van Harlingen, and J. Clarke, Quantum-noise theory for the resistively shunted Joseph- son junction, Phys. Rev. Lett.45, 2132 (1980)

    work page 1980

  14. [14]

    R. H. Koch, D. J. Van Harlingen, and J. Clarke, Obser- vation of zero-point fluctuations in a resistively shunted Josephson tunnel junction, Phys. Rev. Lett.47, 1216 (1981)

    work page 1981

  15. [15]

    R. H. Koch, D. J. Van Harlingen, and J. Clarke, Measure- ments of quantum noise in resistively shunted Josephson junctions, Phys. Rev. B26, 74 (1982)

    work page 1982

  16. [16]

    J. M. Martinis, M. H. Devoret, and J. Clarke, Energy- level quantization in the zero-voltage state of a current- biased Josephson junction, Phys. Rev. Lett.55, 1543 (1985)

    work page 1985

  17. [17]

    M. H. Devoret, J. M. Martinis, and J. Clarke, Mea- surements of macroscopic quantum tunneling out of the zero-voltage state of a current-biased Josephson junction, Phys. Rev. Lett.55, 1908 (1985)

    work page 1908

  18. [18]

    Clarke, A

    J. Clarke, A. N. Cleland, M. H. Devoret, D. Esteve, and J. M. Martinis, Quantum mechanics of a macroscopic variable: The phase difference of a Josephson junction, Science239, 992 (1988)

    work page 1988

  19. [19]

    Vianello, M

    C. Vianello, M. Ferraretto, and L. Salasnich, Finite- temperature entanglement and coherence in asymmetric bosonic Josephson junctions, Phys. Rev. A111, 063310 (2025)

    work page 2025

  20. [20]

    Vianello, S

    C. Vianello, S. Salvatore, and L. Salasnich, Quantum ac- tion of the Josephson dynamics, Int. J. Theor. Phys.64, 315 (2025)

    work page 2025

  21. [21]

    Furutani, J

    K. Furutani, J. Tempere, and L. Salasnich, Quantum ef- fective action for the bosonic Josephson junction, Phys. Rev. B105, 134510 (2022)

    work page 2022

  22. [22]

    Salasnich, Effective action approach to quantum and thermal effects: From one particle to Bose-Einstein con- densates, Atoms13, 95 (2025)

    L. Salasnich, Effective action approach to quantum and thermal effects: From one particle to Bose-Einstein con- densates, Atoms13, 95 (2025)

    work page 2025

  23. [23]

    Goldstone, A

    J. Goldstone, A. Salam, and S. Weinberg, Broken sym- metries, Phys. Rev.127, 965 (1962). 12

    work page 1962

  24. [24]

    Jona-Lasinio, Relativistic field theories with symmetry-breaking solutions, Nuovo Cim.34, 1790 (1964)

    G. Jona-Lasinio, Relativistic field theories with symmetry-breaking solutions, Nuovo Cim.34, 1790 (1964)

    work page 1964

  25. [25]

    Coleman and E

    S. Coleman and E. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking, Phys. Rev. D 7, 1888 (1973)

    work page 1973

  26. [26]

    Coleman, R

    S. Coleman, R. Jackiw, and H. D. Politzer, Spontaneous symmetry breaking in the O(N) model for largeN, Phys. Rev. D10, 2491 (1974)

    work page 1974

  27. [27]

    D. S. Petrov, Quantum mechanical stabilization of a col- lapsing Bose-Bose mixture, Phys. Rev. Lett.115, 155302 (2015)

    work page 2015

  28. [28]

    R. N. Bisset, R. M. Wilson, D. Baillie, and P. B. Blakie, Ground-state phase diagram of a dipolar condensate with quantum fluctuations, Phys. Rev. A94, 033619 (2016)

    work page 2016

  29. [29]

    Salasnich, Self-consistent derivation of the modified Gross-Pitaevskii equation with Lee-Huang-Yang correc- tion, Appl

    L. Salasnich, Self-consistent derivation of the modified Gross-Pitaevskii equation with Lee-Huang-Yang correc- tion, Appl. Sci.8, 1998 (2018)

    work page 1998

  30. [30]

    Aybar and M

    E. Aybar and M. O. Oktel, Temperature-dependent den- sity profiles of dipolar droplets, Phys. Rev. A99, 013620 (2019)

    work page 2019

  31. [31]

    Guebli and A

    N. Guebli and A. Boudjemˆ aa, Quantum self-bound droplets in Bose-Bose mixtures: Effects of higher-order quantum and thermal fluctuations, Phys. Rev. A104, 023310 (2021)

    work page 2021

  32. [32]

    Bardin, F

    A. Bardin, F. Lorenzi, and L. Salasnich, Quantum fluc- tuations in atomic Josephson junctions: the role of di- mensionality, New J. Phys.26, 013021 (2024)

    work page 2024

  33. [33]

    Schwinger, Brownian motion of a quantum oscillator, J

    J. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys.2, 407 (1961)

    work page 1961

  34. [34]

    L. V. Keldysh, Diagram technique for nonequilibrium processes, Sov. Phys. JEPT20, 1018 (1965)

    work page 1965

  35. [35]

    Metiu and G

    H. Metiu and G. Sch¨ on, Description of quantum noise by a Langevin equation, Phys. Rev. Lett.53, 13 (1984)

    work page 1984

  36. [36]

    Kubo, The fluctuation-dissipation theorem, Rep

    R. Kubo, The fluctuation-dissipation theorem, Rep. Prog. Phys.29, 255 (1966)

    work page 1966

  37. [37]

    P. S. Bauer, Dissipative dynamical systems, Proc. Natl. Acad. Sci. U.S.A.17, 311 (1931)

    work page 1931

  38. [38]

    Bateman, On dissipative systems and related varia- tional principles, Phys

    H. Bateman, On dissipative systems and related varia- tional principles, Phys. Rev.38, 815 (1931)

    work page 1931

  39. [39]

    Caldirola, Forze non conservative nella meccanica quantistica, Nuovo Cim.18, 393 (1941)

    P. Caldirola, Forze non conservative nella meccanica quantistica, Nuovo Cim.18, 393 (1941)

    work page 1941

  40. [40]

    Kanai, On the quantization of the dissipative systems, Prog

    E. Kanai, On the quantization of the dissipative systems, Prog. Theor. Phys.3, 440 (1948)

    work page 1948

  41. [41]

    Riewe, Nonconservative Lagrangian and Hamiltonian mechanics, Phys

    F. Riewe, Nonconservative Lagrangian and Hamiltonian mechanics, Phys. Rev. E53, 1890 (1996)

    work page 1996

  42. [42]

    Riewe, Mechanics with fractional derivatives, Phys

    F. Riewe, Mechanics with fractional derivatives, Phys. Rev. E55, 3581 (1997)

    work page 1997

  43. [43]

    Kamenev,Field Theory of Non-Equilibrium Systems (Cambridge University Press, 2011)

    A. Kamenev,Field Theory of Non-Equilibrium Systems (Cambridge University Press, 2011)

    work page 2011

  44. [44]

    Uguccioni,Quantum Transport in Mesoscopic Sys- tems: a Non-Equilibrium Field Theory Approach, Ph.D

    M. Uguccioni,Quantum Transport in Mesoscopic Sys- tems: a Non-Equilibrium Field Theory Approach, Ph.D. thesis, Universit` a di Padova (2025)

    work page 2025

  45. [45]

    H. B. Callen and T. A. Welton, Irreversibility and gen- eralized noise, Phys. Rev.83, 34 (1951)

    work page 1951

  46. [46]

    P. C. Martin, E. D. Siggia, and H. A. Rose, Statistical dy- namics of classical systems, Phys. Rev. A8, 423 (1973)

    work page 1973

  47. [47]

    Janssen, On a Lagrangean for classical field dynam- ics and renormalization group calculations of dynamical critical properties, Z

    H.-K. Janssen, On a Lagrangean for classical field dynam- ics and renormalization group calculations of dynamical critical properties, Z. Phys. B23, 377 (1976)

    work page 1976

  48. [48]

    De Dominicis, Techniques de renormalisation de la th´ eorie des champs et dynamique des ph´ enom` enes cri- tiques, J

    C. De Dominicis, Techniques de renormalisation de la th´ eorie des champs et dynamique des ph´ enom` enes cri- tiques, J. Phys. Colloques37, 247 (1976)

    work page 1976

  49. [49]

    Furutani and L

    K. Furutani and L. Salasnich, Fokker-Planck equations for a trapped particle in a quantum-thermal Ohmic bath: general theory and applications to Josephson junctions, AAPPS Bull.33, 19 (2023)

    work page 2023

  50. [50]

    C. P. Burgess,Introduction to Effective Field Theory (Cambridge University Press, 2021)

    work page 2021

  51. [51]

    Kleinert,Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets (World Scientific, 2009)

    H. Kleinert,Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets (World Scientific, 2009)

    work page 2009

  52. [52]

    Jackiw, Functional evaluation of the effective poten- tial, Phys

    R. Jackiw, Functional evaluation of the effective poten- tial, Phys. Rev. D9, 1686 (1974)

    work page 1974

  53. [53]

    Iliopoulos, C

    J. Iliopoulos, C. Itzykson, and A. Martin, Functional methods and perturbation theory, Rev. Mod. Phys.47, 165 (1975)

    work page 1975

  54. [54]

    Enrico Fermi

    F. Cametti, G. Jona-Lasinio, C. Presilla, and F. Toninelli, Comparison between quantum and classical dynamics in the effective action formalism, in Proc. Int. School of Physics “Enrico Fermi”, Course CXLIII, G. Casati, I. Guarnieri, and U. Smilansky (Eds.), pp. 431-448(IOS Press, Amsterdam, 2000)

    work page 2000

  55. [55]

    G. W. Ford and M. Kac, On the quantum Langevin equa- tion, J. Stat. Phys.46, 803 (1987)

    work page 1987

  56. [56]

    Weiss,Quantum Dissipative Systems, 5th ed

    U. Weiss,Quantum Dissipative Systems, 5th ed. (World Scientific, 2021)

    work page 2021

  57. [57]

    C. M. Fraser, Calculation of higher derivative terms in the one-loop effective Lagrangian, Z. Phys. C28, 101 (1985)

    work page 1985

  58. [58]

    A. O. Caldeira and A. J. Leggett, Influence of dissipa- tion on quantum tunneling in macroscopic systems, Phys. Rev. Lett.46, 211 (1981)

    work page 1981

  59. [59]

    A. O. Caldeira and A. J. Leggett, Quantum tunnelling in a dissipative system, Ann. Phys.149, 374 (1983)

    work page 1983

  60. [60]

    R. P. Feynman and A. R. Hibbs,Quantum Mechanics and Path Integrals(Dover Publications, 2010)

    work page 2010

  61. [61]

    E. T. Whittaker,A Treatise on the Analytical Dynam- ics of Particles and Rigid Bodies(Cambridge University Press, 2012)

    work page 2012

  62. [62]

    F. T. Brandt, J. Frenkel, and J. C. Taylor, Noise in re- sistively shunted Josephson junctions, Phys. Rev. B82, 014515 (2010)

    work page 2010