Pith. sign in

REVIEW 4 major objections 5 minor 58 references

Suppression of superfluidity by dissipation -- An application to failed superconductor

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Dissipation alone can destroy superfluidity in a dilute boson fluid, leaving a metallic state at zero temperature — a mechanism for the 'failed superconductor'.

desk verdict A plausible dilute-boson route to dissipation-driven loss of superfluidity, but the zero-temperature transition leans heavily on an unproven Gaussian ansatz. read the letter →

arxiv 1908.06590 v2 pith:LRMXBQ3M submitted 2019-08-19 cond-mat.mes-hall cond-mat.str-elcond-mat.supr-con

Kou Misaki , Naoto Nagaosa This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.str-elcond-mat.supr-con
keywords bosemetaldissipationsuperfluiditysuperfluiddensitydilutebosonsOhmicheatbathquantumMonteCarlofailedsuperconductor
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that Ohmic dissipation — the coupling of bosons to a gapless heat bath — can by itself destroy superfluidity in a dilute boson system, leaving a metallic state with zero superfluid density even at zero temperature. If true, this supplies a concrete mechanism for the 'bose metal' or 'failed superconductor' state observed in two-dimensional superconductors, where Cooper pairs behave as charge-2e bosons and vortices with normal cores act as dissipative particles. The authors support the claim with Feynman's picture of superfluidity as macroscopic exchange of world lines, a quantum Monte Carlo simulation showing the superfluid fraction decreasing monotonically with dissipation, and a one-loop field-theoretic calculation in which the superfluid density vanishes at a critical dissipation strength.

What carries the argument

The load-bearing object is the off-diagonal single-particle density matrix y(|r−r′|) ∝ exp[−(r−r′)²⟨p²⟩/(2ℏ²)], whose Gaussian width is set by the momentum variance. In an Ohmic bath, ⟨p²⟩ computed from quantum Brownian motion (Caldeira–Leggett theory) saturates to a finite value as β→∞, so the exchange action stays finite while the entropy of exchange configurations stays constant; the competition then drives the transition temperature to zero at a critical dissipation strength. The paper also uses the winding-number Monte Carlo estimator of the superfluid density and the transverse current–current response at one-loop level in a Bogoliubov approximation as independent checks.

What would settle it

Measure or simulate the superfluid fraction of a dilute boson fluid with Ohmic dissipation at temperatures far below the boson exchange scale and extrapolate to T=0: the paper predicts ρs reaches exactly zero at a finite critical dissipation strength. A direct check of the criterion would compare the zero-temperature momentum variance to the interparticle spacing and verify that d²⟨p²⟩/ℏ² ≈ 1 at the same critical coupling.

Watch

Extended reading notes

Core claim

At zero temperature a translation-invariant boson fluid is normally a perfect superfluid, with superfluid density equal to the total density because Galilean invariance fixes the phase action. The paper's central claim is that a time-nonlocal dissipative term breaks that invariance in a way that suppresses superfluidity: in the Feynman picture the off-diagonal single-particle density matrix keeps a finite width (the momentum variance ⟨p²⟩ saturates) as T→0, so the action for macroscopic exchange processes no longer vanishes and bosons cannot condense into collective motion. The authors show numerically that the superfluid fraction ρs/ρ falls monotonically with dissipation strength, and analytically in a second model that ρs reaches zero at a finite critical dissipation while the condensate density ρ0 remains nonzero at that point.

Load-bearing premise

The extended Feynman argument assumes that in an interacting boson fluid the off-diagonal single-particle density matrix remains Gaussian and that interactions only renormalize the particle mass; if that fails, the zero-temperature transition is not rigorously established, and the numerical simulation alone only demonstrates suppression at finite temperature.

Editorial extensions

If this is right

  • Dilute bosons coupled to an Ohmic bath remain metallic at zero temperature, providing a microscopic route to the bose metal.
  • In two-dimensional superconductors in a magnetic field, dissipative vortex cores lose their superfluidity; since vortex density grows with field, this gives a giant positive magnetoresistance.
  • Dissipation also modifies the zero-field vortex-loop proliferation transition, leading to a phase distinct from the ordinary superfluid.
  • A retarded, time-nonlocal interaction that breaks Galilean invariance is sufficient to destroy superfluidity even without disorder or a lattice.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same mechanism should apply to other gapless baths or retarded interactions that freeze the off-diagonal density matrix; the criterion d²⟨p²⟩/ℏ² ~ 1 offers a quantitative test in any bosonic simulator.
  • The one-loop result that condensate density remains finite when superfluid density vanishes is likely an artifact of the approximation; the Josephson relation suggests both should vanish together, which is testable with improved numerics.
  • Engineered dissipation in cold-atom or superconducting-circuit platforms could continuously tune a superfluid into a metal, making the predicted zero-temperature metallic phase observable.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The manuscript argues that Ohmic dissipation, modeled by a nonlocal imaginary-time action, suppresses superfluidity in a dilute boson system and can drive it into a metallic state with vanishing superfluid density at zero temperature. The argument is developed in three parts: first, an extension of Feynman's polygon picture in which the off-diagonal single-particle density matrix of a dissipative quantum Brownian particle is inserted into the exchange-action estimate, yielding a criterion for a zero-temperature dissipative transition; second, path-integral Monte Carlo simulations of a first-quantized boson fluid with Aziz interactions at T = 2 K in three dimensions (N = 64) and T = 0.5 K in two dimensions (N = 25), showing a monotonic decrease of the superfluid fraction and condensate fraction with dissipation strength; and third, a zero-temperature one-loop Bogoliubov calculation in a second-quantized model with a frequency-dependent dissipative term, showing that the superfluid density vanishes at a critical dissipation strength. The results are connected to the 'failed superconductor' scenario in which vortices are subjected to dissipation from normal cores.

Significance. If the zero-temperature claim is correct, this would be an important contribution to the bose-metal problem, proposing a mechanism distinct from disorder and relevant to experiments on two-dimensional superconductors. The paper has real strengths: it presents an explicit first-quantized action, a direct quantum Monte Carlo simulation with a standard worm algorithm, a separate field-theoretic calculation with explicit formulas, and the authors are candid about the assumptions and limitations. The finite-temperature trend is robust and physically plausible. However, the central zero-temperature claim is currently supported only by combining a single-particle quantum Brownian motion result with an unproven Gaussian and mass-renormalization assumption, a heuristic order-one threshold, and finite-temperature numerics without zero-temperature extrapolation. The one-loop field theory is internally inconsistent at the point where the superfluid density vanishes because the condensate density remains finite, in conflict with the Josephson relation unless additional assumptions are made. The significance of the paper is therefore conditional on resolving these gaps.

major comments (4)
  1. [Extended Feynman's argument, Eq. (3)] The analytical zero-temperature criterion uses Eq. (3), which is the free-particle quantum Brownian motion result, and assumes that interactions only renormalize the mass and preserve the Gaussian form of the off-diagonal density matrix. The authors state this explicitly, writing that 'we assume that this form remains valid even in the presence of the interaction between particles' and that 'the effect of the interaction can be renormalized to the effective mass of the particle,' but no independent test is provided. This assumption is load-bearing because the exchange-action estimate for superfluidity requires the off-diagonal density matrix of the interacting dissipative system; if the distribution deviates from Gaussian or the mass renormalization is scale- or density-dependent, the predicted strong suppression could be quantitatively wrong or qualitatively inapplicable. A direct check would be to extract the off-diagonal density matrix or its second moment from the interacting QMC data and compare it with the single-particle expression Eq. (S2).
  2. [Extended Feynman's argument, critical criterion after Eq. (3)] The zero-temperature critical coupling is fixed by the heuristic condition d^2 <p^2>_{T=0}/hbar^2 ~ 1, where the constant is left unspecified as order one. Since the phase boundary in Fig. 1 is additionally calibrated by setting the dissipationless transition temperature to T = 2 K rather than by a microscopic criterion, the quantitative location of the predicted zero-temperature transition is schematic. This is acceptable for a conjecture, but it is not a derivation of the critical dissipation strength, and the statement that dissipation 'can lose the superfluidity' at zero temperature is not quantitatively established by this argument.
  3. [Result of the numerical calculation, Figs. 2 and S3] The Monte Carlo results show a monotonic decrease of the superfluid fraction with dissipation strength at one finite temperature in each dimensionality (T = 2 K in three dimensions and T = 0.5 K in two dimensions), each with a single system size and no error bars. No temperature sweep or finite-size scaling is presented, so the data demonstrate a finite-temperature suppression but do not establish a zero-temperature transition to a phase with rho_s = 0. The text later states that 'the transition to the phase with rho_s = 0 in this model remains intact,' but the numerical support for this statement is missing; an extrapolation in temperature and system size would be needed.
  4. [Second Model, Fig. 5 and the Josephson relation] The one-loop field-theoretic calculation shows that rho_s vanishes while rho_0 remains finite at the critical dissipation, and the authors concede that 'assuming the smooth behavior of the single particle Green function at the critical point, the Josephson relation requires that both rho_0 and rho_s becomes zero.' This is an acknowledged internal inconsistency in the only zero-temperature calculation of the second model. Consequently, the one-loop result cannot serve as an internally consistent proof of a zero-temperature normal phase; resolving whether rho_0 actually vanishes at the critical point, or whether the one-loop approximation breaks down, is required before the second model can be regarded as independent confirmation of the central claim.
minor comments (5)
  1. [Eq. (2) and following text] The replacement of the finite-temperature dissipative kernel by the zero-temperature kernel with periodic image lines is only sketched; a derivation or a more explicit reference to the polaron analogy in footnotes [33,57,58] would clarify the validity of this step at finite beta.
  2. [Fig. 3 and text near it] The fitting function for the off-diagonal density matrix omits the coupling term, and the authors note that this leads to an overestimation of n0; the magnitude of this overestimation is not quantified, which weakens the quantitative meaning of the condensate fraction shown in Fig. 3.
  3. [Result of the numerical calculation] The Monte Carlo section reports no statistical error bars in Figs. 2, 3, S1, and S3; adding error bars and reporting the binning analysis would make the monotonic trends more convincing.
  4. [Eqs. (5) and (6)] The quantities epsilon_k and omega_k used in the Green functions are not explicitly defined in the main text; the authors should state that epsilon_k = k^2/2m and give the explicit Bogoliubov dispersion used.
  5. [Eq. (4)] The word 'discritized' should be 'discretized'; there are also several typographical inconsistencies with mathematical symbols in the displayed action in the introduction.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: dissipation strength enters as an input and superfluidity is evaluated by independent estimators (winding-number QMC and one-loop current response); the paper's approximations are stated assumptions, not fitted targets.

full rationale

The paper's central claim is that Ohmic dissipation can drive dilute bosons into a metallic state. The derivation chain is not circular. In the first model, the dissipative action (Eq. 1) contains η as an external parameter; the off-diagonal density matrix result (Eq. 3) is the standard quantum-Brownian-motion expression from Weiss and Caldeira-Leggett, and it is used in Feynman's polygon criterion to infer a phase boundary. The Gaussian form and mass renormalization are explicitly assumed, not derived from the target conclusion, and the QMC cross-check computes ρs from the independent winding-number estimator rather than from the assumed Gaussian form. In the second model, ρs is computed from the transverse current-current response (Eq. 5) with η as a control parameter, ρ0 determined from Eq. (6), and cutoffs stated; no parameter is fitted to enforce ρs = 0. The Josephson-relation caveat (Fig. 5 discussion) is an acknowledged consistency limitation of the one-loop calculation, not a circular use of the conclusion. The only self-citation ([27], a textbook used for the Ohmic-bath action) is not load-bearing, since the same input is standard and independently cited via Caldeira-Leggett and Weiss. The finite-temperature QMC limitation and the Gaussian-assumption uncertainty are correctness concerns, not circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard dissipative-boson modeling, Feynman's exchange picture, a strong mass-renormalization assumption, and one-loop Bogoliubov theory. No new particles or forces are introduced. The free parameters are the hand-wavy transition threshold and regularization cutoffs, all of which can influence the quantitative critical dissipation.

free parameters (3)
  • Threshold constant in T=0 transition criterion = 1 (dimensionless)
    The condition d^2 <p^2>_{T=0}/\hbar^2 ~ 1 uses a right-hand side of order unity chosen by hand, not derived from a first-principles criterion. This sets the critical dissipation strength in the first model.
  • Bath UV cutoff tau_c in Monte Carlo = 0.2 (3D), 0.05 (2D)
    The discretized dissipative kernel is truncated at (1-tau_c) N_tau to regularize the divergence. The superfluid fraction could depend on this numerical cutoff.
  • Energy and frequency cutoffs in field theory = epsilon_c = 900 rho g, omega_c = 1000 rho g
    These cutoffs are chosen so that the entire spectrum couples to the bath. The critical dissipation value likely depends on these choices, and they are not derived from microscopic parameters.
assumptions (4)
  • domain assumption Feynman's exchange-picture characterization of superfluidity: superfluidity is associated with macroscopic exchange processes and winding-number fluctuations.
    The paper bases its analytical argument on this picture, citing Feynman's 1953 papers. It is a standard but non-rigorous framework for interacting bosons.
  • domain assumption The Caldeira-Leggett model with Ohmic spectral density describes the coupling to the environment.
    The dissipative term in Eq. (1) is taken as the model for dissipation. This is a standard phenomenological choice.
  • ad hoc to paper The off-diagonal density matrix remains Gaussian in the presence of interactions, with interactions only renormalizing the mass.
    Stated in 'Extended Feynman's argument': 'we assume that this form remains valid even in the presence of the interaction between particles' and 'the effect of the interaction can be renormalized to the effective mass.' This is a strong simplifying assumption without proof.
  • domain assumption Bogoliubov approximation in the field-theoretic model: only quadratic fluctuations around the condensate are retained.
    The second model substitutes psi = sqrt(rho0) + phi and keeps terms up to quadratic order. Standard when depletion is small, but may fail near the critical dissipation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Suppression of superfluidity by dissipation -- An application to failed superconductor." pith.science (2026). https://pith.science/paper/LRMXBQ3M

@misc{pith2026190806590,
  author       = {Pith},
  title        = {Pith review of: Suppression of superfluidity by dissipation -- An application to failed superconductor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LRMXBQ3M}},
  note         = {Machine review of arXiv:1908.06590}
}
read the original abstract

The ground states of bosons have been classified into superfluid, Mott insulator, and bose glass. Recent experiments in two-dimensional superconductors strongly suggest the existence of the fourth quantum state of Cooper pairs, i.e., bose metal or quantum metal, where the resistivity remains constant at lowest temperature. However, its theoretical understanding remains unsettled. In this paper, we show theoretically that the bosons in the dilute limit subject to dissipation can lose the superfluidity and remain metallic, utilizing the Feynman's picture of superfluidity in the first quantized formulation. This result is relevant to the quantum vortices under an external magnetic field in two-dimensional superconductors with the finite resistivity of the normal core as the source of dissipation.

Figures

Figures reproduced from arXiv: 1908.06590 by the authors.

Figure 2
Figure 2. The superfluid fraction ρs/ρ and the kinetic en￾ergy EK as a function of ˜η = ηd2 , where d = 3.570 ˚A is the interparticle distance. The blue circle represents the kinetic energy, while the green triangle represents the superfluid frac￾tion [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. The condensate fraction at zero momentum, ˜n [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. ρs/ρ and ρ0/ρ obtained from Eqs. (5) and (6). The parameters are c/(ρg) = 900, ωc/(ρg) = 1000, mg = 1. as η Θ(ω 2 c −ω 2 ), where Θ(x) is the step function. We also introduced the cutoff for the energy k at c, and choose c < ωc, so that the whole energy spectrum of the system is coupled to the heat bath. To calculate ρs, we regard η as a control parameter, calculate ρ0 as a function of η and then calculate ρs(η,… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

58 extracted references · 54 canonical work pages

  1. [1]

    Kapitulnik, S

    A. Kapitulnik, S. A. Kivelson, and B. Spivak, Reviews of Modern Physics 91, 011002 (2019)

    work page 2019

  2. [2]

    Dalidovich and P

    D. Dalidovich and P. Phillips, Physical Review Letters84, 737 (2000)

    work page 2000

  3. [3]

    L. Zhu, Y. Chen, and C. M. Varma, Physical Review B 91, 205129 (2015)

    work page 2015

  4. [4]

    L. Zhu, C. Hou, and C. M. Varma, Physical Review B 94, 235156 (2016)

    work page 2016

  5. [5]

    Hou and C

    C. Hou and C. M. Varma, Physical Review B 94, 201101(R) (2016)

    work page 2016

  6. [6]

    Chakravarty, G.-L

    S. Chakravarty, G.-L. Ingold, S. Kivelson, and A. Luther, Physical Review Letters 56, 2303 (1986)

    work page 1986

  7. [7]

    Chakravarty, G.-L

    S. Chakravarty, G.-L. Ingold, S. Kivelson, and G. Zi- manyi, Physical Review B 37, 3283 (1988)

    work page 1988

  8. [8]

    M. P. A. Fisher and G. Grinstein, Physical Review Letters 60, 208 (1988)

    work page 1988

Show all 58 references
  1. [9]

    M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Physical Review B 40, 546 (1989)

    1989

  2. [10]

    Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 2011)

    S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 2011)

    2011

  3. [11]

    Z. Cai, U. Schollw¨ ock, and L. Pollet, Physical Review Letters 113, 260403 (2014)

    2014

  4. [12]

    Greiter, F

    M. Greiter, F. Wilczek, and E. Witten, Mod.Phys.Lett. B3, 903 (1989)

    1989

  5. [13]

    Son and M

    D. Son and M. Wingate, Annals of Physics 321, 197 (2006)

    2006

  6. [14]

    I. J. R. Aitchison, P. Ao, D. J. Thouless, and X.-M. Zhu, Physical Review B 51, 6531 (1995)

    1995

  7. [15]

    I. J. R. Aitchison, G. Metikas, and D. J. Lee, Physical Review B 62, 6638 (2000)

    2000

  8. [16]

    V. N. Popov, Functional integrals and collective excita- tions, Cambridge monographs on mathematical physics (Cambridge Univ. Press, Cambridge, 1987)

    1987

  9. [17]

    H. T. C. Stoof, D. B. M. Dickerscheid, and K. Gubbels, Ultracold quantum fields (Springer, Berlin, 2009)

    2009

  10. [18]

    Imada, A

    M. Imada, A. Fujimori, and Y. Tokura, Reviews of Mod- ern Physics 70, 1039 (1998)

    1998

  11. [19]

    Huang and H.-F

    K. Huang and H.-F. Meng, Physical Review Letters 69, 644 (1992)

    1992

  12. [20]

    A. V. Lopatin and V. M. Vinokur, Physical Review Let- ters 88, 235503 (2002)

    2002

  13. [21]

    M. V. Feigelman, V. B. Geshkenbein, L. B. Ioffe, and A. I. Larkin, Physical Review B 48, 16641 (1993)

    1993

  14. [22]

    Weiss, Quantum Dissipative Systems , 4th ed

    U. Weiss, Quantum Dissipative Systems , 4th ed. (WORLD SCIENTIFIC, 2012)

    2012

  15. [23]

    R. P. Feynman, Physical Review 91, 1291 (1953)

    1953

  16. [24]

    R. P. Feynman, Physical Review 94, 262 (1954)

    1954

  17. [25]

    N. B. Kopnin, Theory of nonequilibrium superconductiv- ity, International series of monographs on physics No. 110 (Oxford Univ. Press, Oxford, 2009)

    2009

  18. [26]

    A. O. Caldeira and A. J. Leggett, Annals of Physics 149, 374 (1983)

    1983

  19. [27]

    Nagaosa, Quantum Field Theory in Condensed Matter Physics, Theoretical and Mathematical Physics (Springer- Verlag, Berlin Heidelberg, 1999)

    N. Nagaosa, Quantum Field Theory in Condensed Matter Physics, Theoretical and Mathematical Physics (Springer- Verlag, Berlin Heidelberg, 1999)

    1999

  20. [28]

    O. S. Duarte and A. O. Caldeira, Physical Review Letters 97, 250601 (2006)

    2006

  21. [29]

    R. P. Feynman, Physical Review 90, 1116 (1953)

    1953

  22. [30]

    E. L. Pollock and D. M. Ceperley, Physical Review B 36, 8343 (1987)

    1987

  23. [31]

    D. M. Ceperley, Reviews of Modern Physics 67, 279 (1995)

    1995

  24. [32]

    S. M. Apenko, Physical Review B 60, 3052 (1999)

    1999

  25. [33]

    We note that there is a similar problem in the treatment of the effective mass of polaron [57, 58]

  26. [34]

    Boninsegni, N

    M. Boninsegni, N. Prokof’ev, and B. Svistunov, Physical Review Letters 96, 070601 (2006)

    2006

  27. [35]

    Boninsegni, N

    M. Boninsegni, N. V. Prokof’ev, and B. V. Svistunov, Physical Review E 74, 036701 (2006)

    2006

  28. [36]

    Mezzacapo and M

    F. Mezzacapo and M. Boninsegni, Physical Review Let- ters 97, 045301 (2006)

    2006

  29. [37]

    Mezzacapo and M

    F. Mezzacapo and M. Boninsegni, Physical Review A 75, 033201 (2007)

    2007

  30. [38]

    R. A. Aziz, V. P. S. Nain, J. S. Carley, W. L. Taylor, and G. T. McConville, The Journal of Chemical Physics 70, 4330 (1979)

    1979

  31. [39]

    Ambegaokar and M

    V. Ambegaokar and M. Troyer, American Journal of Physics 78, 150 (2010)

    2010

  32. [40]

    S. A. Chin, Physics Letters A 226, 344 (1997)

    1997

  33. [41]

    Werner, M

    P. Werner, M. Troyer, and S. Sachdev, Journal of the Physical Society of Japan 74, 67 (2005)

    2005

  34. [42]

    Werner, K

    P. Werner, K. V¨ olker, M. Troyer, and S. Chakravarty, Physical Review Letters 94, 047201 (2005)

    2005

  35. [43]

    See supplemental material for the details of the off diag- onal density matrix and the numerical calculation in two dimension

  36. [44]

    H. R. Glyde, Reports on Progress in Physics 81, 014501 (2017)

    2017

  37. [45]

    Nozieres, Theory Of Quantum Liquids (CRC Press, 2018)

    P. Nozieres, Theory Of Quantum Liquids (CRC Press, 2018). 6

    2018

  38. [46]

    Griffin, Excitations in a Bose-condensed liquid (Cam- bridge University Press, Cambridge, 1993)

    A. Griffin, Excitations in a Bose-condensed liquid (Cam- bridge University Press, Cambridge, 1993)

    1993

  39. [47]

    Keeling, Physical Review Letters 107, 080402 (2011)

    J. Keeling, Physical Review Letters 107, 080402 (2011)

    2011

  40. [48]

    B. D. Josephson, Physics Letters 21, 608 (1966)

    1966

  41. [49]

    C. A. Mller, Physical Review A 91, 023602 (2015)

    2015

  42. [50]

    Caroli, P

    C. Caroli, P. G. De Gennes, and J. Matricon, Physics Letters 9, 307 (1964)

    1964

  43. [51]

    Stone, Physical Review B 53, 16573 (1996)

    M. Stone, Physical Review B 53, 16573 (1996)

    1996

  44. [52]

    Bardeen and M

    J. Bardeen and M. J. Stephen, Physical Review 140, A1197 (1965)

    1965

  45. [53]

    Saito, T

    Y. Saito, T. Nojima, and Y. Iwasa, Nature Communica- tions 9, 778 (2018)

    2018

  46. [54]

    L. L. Foldy, Physical Review 124, 649 (1961)

    1961

  47. [55]

    S. R. Hore and N. E. Frankel, Physical Review B 12, 2619 (1975)

    1975

  48. [56]

    J. C. Lee, Physical Review B 12, 2644 (1975)

    1975

  49. [57]

    R. P. Feynman, Physical Review 97, 660 (1955)

    1955

  50. [58]

    Suppression of superfluidity by dissipation — An application to failed superconductor

    D. C. Khandekar, K. V. Bhagwat, and S. V. Lawande, Physical Review B 37, 3085 (1988). 7 Supplemental material for “Suppression of superfluidity by dissipation — An application to failed superconductor” Off diagonal density matrix in three dimension Here, we will discuss the resu...

    1988

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.