Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Green's Function Approach to Josephson Dot Dynamics and Application to Quantum Mpemba Effects

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read A Green's-function derivation shows quantum Mpemba effects in phase-quenched Josephson dots.

desk verdict Solid GF-based rate derivation for Andreev levels, but the quantum Mpemba predictions rest on an unjustified sudden-quench initialization that ignores the rotation of the Andreev spinors. read the letter →

arxiv 2501.11609 v2 pith:MF6HNEK7 submitted 2025-01-20 cond-mat.mes-hall cond-mat.stat-mech

Kateryna Zatsarynna , Andrea Nava , Reinhold Egger , Alex Zazunov This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.stat-mech
keywords Green'sfunctionJosephsonjunctionAndreevboundstatesquantumMpembaeffectLindbladmasterequationspin-orbitcouplingZeemanfieldphasequench
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

This paper develops a Green's-function method for computing quasiparticle transition rates in multi-level quantum dots coupled to superconducting leads and a bosonic environment, avoiding explicit Bogoliubov–de Gennes eigenstate calculations. It applies the method to a Josephson dot whose average phase difference is suddenly quenched, and argues that the resulting open-system relaxation can exhibit quantum Mpemba effects, where a copy prepared farther from the final phase difference reaches the steady state faster. For a short single-channel junction, the paper finds parameter windows for both type-I and type-II quantum Mpemba effects; for an intermediate-length junction with spin-orbit coupling and a Zeeman field, it predicts that type-II effects dominate. The predictions matter because they identify a concrete, tunable superconducting platform where Mpemba accelerations could be observed through microwave spectroscopy of Andreev-level populations.

What carries the argument

The central object is the retarded boundary Green's function of the BCS leads, $g^R(\omega) = -\pi\nu_F (\omega\tau_0 + \Delta\tau_x)/\zeta(\omega)$, which is used to integrate out the leads and obtain a time-nonlocal effective Schrödinger equation for the $4\ell$-component dot wavefunction. Transition rates follow from first-order perturbation theory in the phase fluctuation, yielding $\Gamma_{\lambda\to n} = 2\pi |I_{n\lambda}|^2 J(\omega) n_B(\omega)$ at $\omega = E_n - E_\lambda$, with current matrix elements $I_{n\lambda} = \eta_n^\dagger[\tau_z I(E_\lambda) - I(E_n)\tau_z]\eta_\lambda$. Rates to the continuum are obtained by resolving the spectral function into eigenstates $\xi_n(\omega)$, and the resulting expressions are consistent with earlier Bogoliubov–de Gennes calculations while avoiding explicit wavefunction matching in the leads. This machinery converts the nonequilibrium dynamics of Andreev levels into a Pauli master equation whose rates depend only on matrices in dot-level space.

What would settle it

Measure the relaxation time $\tau$ as a function of pre-quench phase $\phi_0^{(i)}$ for fixed post-quench phase $\phi_0^{(eq)}$ in a short, high-transparency junction with $T\approx 0.99$ and $T_{qp}>T_b$; the central claim predicts non-monotonic $\tau$ with local minima ('Mpemba arcs') and both QME types, so a flat, monotonic landscape in this regime would falsify it. Observing a QME at $T_{qp}=T_b$, where the paper predicts none, would also falsify it.

Watch

Extended reading notes

Core claim

The paper's central claim is that the low-energy Andreev sector of a Josephson dot obeys a Markovian Lindblad equation whose rates can be obtained from the poles and spectral eigenvectors of the retarded Green's function of the dot-lead system, and that these rates produce quantum Mpemba effects after a rapid phase quench. In the short-junction limit with high transparency, the steady-state Andreev populations become non-monotonic functions of the phase bias once the quasiparticle temperature exceeds the bath temperature, and this non-monotonicity is what lets a 'far' pre-quench phase relax faster than a 'close' one. The paper distinguishes type-I QME, where the far copy is closer to equilibrium for all times, from type-II QME, where the far copy crosses the close copy at a finite time, and shows both can be realized. In longer junctions with spin-orbit and Zeeman terms, the broken phase-reflection symmetry removes the mirror symmetry of the relaxation-time map, making type-II QME the dominant outcome. The authors identify 'Mpemba arcs' in the pre- versus post-quench phase plane, curves where stationary populations coincide, as necessary and sufficient for the effect.

Load-bearing premise

The continuum of BCS quasiparticles stays in a thermal Fermi distribution at an effective temperature $T_{qp}$, chosen independently of the bosonic bath and with $T_{qp}\ge T_b$; without that assumption the predicted Mpemba windows do not emerge.

Editorial extensions

If this is right

  • For a short, high-transparency junction, both type-I and type-II quantum Mpemba effects can be produced by a rapid phase quench, with relaxation times set by the slowest eigenvalue of the Pauli master equation.
  • The existence of at least one 'Mpemba arc' in the pre- versus post-quench phase plane is necessary and sufficient for a quantum Mpemba effect in this system.
  • For an intermediate-length junction with spin-orbit coupling and a Zeeman field, the type-II effect dominates, because the broken $\phi_0\to 2\pi-\phi_0$ symmetry makes Mpemba arcs invisible in the initial distance but visible in relaxation time.
  • The effect is robust to the shape of the environment spectral density: similar QME regimes appear for both Lorentzian microwave-resonator and Ohmic environments.
  • The steady-state current-phase relation develops pronounced minima near the phase values where Andreev population components have extrema, providing an experimentally accessible indicator of the $T_{qp}>T_b$ regime.

Reading between the lines

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

  • Editorial inference: the same Green's-function rate formulas apply to a dot with Coulomb interactions, and the paper states the formalism allows this but does not pursue it; an interacting Josephson dot is therefore a natural next place to search for QMEs.
  • Editorial inference: because the relaxation-time map loses mirror symmetry when spin-orbit and Zeeman terms break $\phi_0\to 2\pi-\phi_0$, comparing quenches on the two sides of the phase interval would give a sharp test of the predicted type-II dominance.
  • Editorial inference: the 'avoided QME' crossings visible in the authors' time traces suggest that experiments using only crossing times as a QME diagnostic could misclassify an avoided QME; a population-resolved measurement of the full distance function would be needed to confirm the type.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript develops a Green's-function-based equation-of-motion approach for multi-level quantum dots coupled to superconducting leads and a bosonic environment, and uses it to derive Markovian transition rates for Andreev bound states interacting with phase fluctuations. It then applies the resulting Lindblad/Pauli dynamics to study quantum Mpemba effects after a sudden phase quench, claiming both type-I and type-II QMEs in short junctions and type-II-dominated QMEs in intermediate-length spin-orbit-coupled junctions. The central technical results are the rate formulas Eqs. (2.56), (2.77), and (2.79), and the central predictions are encoded in the phase-quench protocol of Sec. IIIA2 and the numerical maps of Figs. 5, 6, and 8.

Significance. If the results hold, the paper provides a useful simplification: transition rates that previously required explicit BdG wavefunction matching are obtained from dot-level matrices, and the explicit comparison with Refs. [9,10] lends credibility to the GF route. The application to QMEs is concrete and experimentally falsifiable in principle, since the trace distance in Eq. (3.22) is tied to microwave-spectroscopy measurements of ABS populations, and the paper is unusually explicit about its assumptions (Tqp, spectral-density forms, parameter choices). The numerical results are supported by a data-availability statement. However, the credibility of the QME predictions hinges on two load-bearing steps that are not fully justified: the mapping of pre-quench to post-quench populations under the phase quench, and the truncation of principal-value contributions in the ABS-continuum rate derivation.

major comments (3)
  1. [Sec. IIIA2, after Eq. (3.15)] The quench protocol initializes the post-quench Pauli master equation with the pre-quench stationary populations P^{(c,f)}_{r,stat}. This equates occupations in the old and new Andreev bases, but the ABS eigenspinors η_ν(ϕ0) in Eq. (2.34) depend on ϕ0, so a sudden change from ϕ0^(i) to ϕ0^(eq) rotates the quasiparticle basis. A density matrix that was diagonal in the old basis acquires coherences in the new basis, and the new occupations are not equal to the old ones: they are given by a projection involving overlaps such as |⟨η_n(ϕ_eq)|η_ν(ϕ_i)⟩|² in the occupation sector. This overlap is never computed or estimated. For the high-transparency case T=0.99 used in Figs. 5 and 6, the short-junction dispersion (3.4) spans from Δ down to about 0.1Δ, so the spinor rotation with ϕ0 is substantial and the approximation P(t=0)=P_{r,stat}(ϕ_i) is not obviously negligible. Since the Mpemba arcs and the type-I/type-II classification in Figs. 5, 6, and 8 are defined by relaxation times obtained from these initial conditions, the central QME claim is affected. Please compute the projection of the pre-quench stationary state onto the post-quench ABS basis, or provide a controlled argument for why the overlap correction can be dropped.
  2. [Sec. IIC3, Eq. (2.74)] The replacement G^R_{nk}(E) = -iπ δ_{nk} ρ_n(E) discards the principal-value integrals in Eq. (2.69) under the assumption that ρ_m(z) is smooth. Smoothness alone does not make a principal-value integral vanish: the integrand also contains the overlap factors ξ†_n(E)ξ_m(z), and the principal value generally gives a nonzero off-shell contribution whose magnitude depends on the model parameters. This step enters directly into the continuum rates Γ^out_λ and Γ^in_λ in Eqs. (2.77) and (2.79), and hence into every QME prediction in Sec. III. The agreement with the BdG-based rates of Refs. [9,10] is reassuring, but the derivation given here does not establish the truncation. The authors should either prove the cancellation for this model, or quantify the omitted principal-value terms by evaluating Eq. (2.69) numerically for the multi-level examples of Sec. IIIB.
  3. [Sec. IIB2 and Sec. IIIA1] The continuum of BCS quasiparticles is modeled by a global thermal Fermi function at an effective quasiparticle temperature Tqp, and the QME regimes shown in Figs. 3 and 4 appear only for Tqp > Tb (compare panels (a) with (b,c)). The parameter Tqp is introduced with a qualitative physical discussion (local cooling of the dot region, phonon-induced lead equilibration), but it is not derived from a microscopic calculation or tied to an experimentally controllable quantity. As a result, the central prediction is conditional on an unquantified free parameter. The authors should specify how Tqp is set in a concrete experimental protocol, or map the QME region in the (Tqp,Tb) plane and state how robust the type-I/type-II classification is to plausible Tqp variations.
minor comments (5)
  1. [Eqs. (2.51), (2.65), and (2.71)] The notation Q_T is overloaded: Eq. (2.65) states Q_T(E) = T Q_T(E) with Q_T defined in Eq. (2.51), but Eq. (2.71) is only correct for the redefined object. Please use a separate symbol, e.g., R_T(E) = T Q_T(E), and make the factor of T explicit in Eq. (2.65).
  2. [Figs. 3 and 4] The population curves are distinguished only by dashed/dot-dashed/dotted styles; in printed or grayscale versions these may be difficult to tell apart, especially where the curves cross. Adding markers or labels inside the panels would improve readability.
  3. [Sec. IIIA2, Eq. (3.22)] The sentence immediately after Eq. (3.22) notes that DM(P(t)) differs from DM(Pr(t)) because the second component of Pr is counted twice. It would be helpful to write the explicit relation to avoid confusion about the factor 1/2 in the definition.
  4. [Sec. IIIA3] The statement that the existence of at least one Mpemba arc is a necessary and sufficient condition for the QME is stronger than what is shown; the numerical evidence establishes sufficiency-type behavior for the studied parameters, but a proof or a more cautious wording would be appropriate.
  5. [Appendix, Eq. (A6)] The truncation of the infinite Hamiltonian matrix to eigenstates below an energy cutoff comparable to Δ is mentioned, but the convergence of the hybridization matrices (2.25) with respect to this cutoff is not discussed. A brief convergence test for the L=1.7ξ0 case would strengthen the numerical results in Sec. IIIB.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: transition rates are derived in-paper from the Green's-function equations, and the quantum Mpemba label is applied via an adopted protocol rather than used to fit the rates.

full rationale

The paper's central derivation chain is self-contained: Eqs. (2.56), (2.77), and (2.79) follow from the EOM and perturbative Green's-function calculation in Secs. IIB-IIC, and the QME application in Sec. III solves the resulting Pauli master equation. The comparisons with BdG results in Refs. [9,10] are consistency checks, not inputs: the rates are derived before the comparison is invoked, and the agreement is not used to determine any parameter. The only prominent self-reference is the QME protocol of Ref. [38] by two of the present authors, adopted in Sec. IIIA2; however, the protocol is a definitional framework (trace-distance monitoring and the type-I/type-II distinction), not a fitted or imported result that forces the prediction. The effective quasiparticle temperature Tqp is an explicitly stated modeling assumption, not a parameter fitted to the predicted Mpemba arcs; the prediction is conditional on Tqp >= Tb, and the paper states this. A limitation worth noting is the sudden-quench initialization with pre-quench populations after the phase change (text after Eq. (3.15)); a rigorous treatment would require projecting the old ABS density matrix onto the new ABS basis. This is a physical approximation that could affect the quantitative predictions, but it is not a circular reduction of the output to the input. Overall, no load-bearing circular step is present; score 2 reflects only the minor self-citation of the QME protocol.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on several modeling choices rather than on newly invented physical entities. The most important are the ad hoc quasiparticle temperature Tqp, the weak-fluctuation expansion, the level-counting continuity assumption, and the Markovian master equation. The paper introduces no new particle, force, or conserved quantity. The QR-like 'Mpemba arcs' are features of the numerical dynamics, not new entities.

free parameters (4)
  • Tqp = 0.5 in main QME plots; 0.14-0.5 scanned
    Effective temperature of BCS continuum quasiparticles, not derived from the microscopic Hamiltonian; QME appears only for Tqp > Tb.
  • epsilon_c = 1e-4
    Accuracy cutoff that defines the relaxation time in Eq. (3.25); the authors state the result is robust under variations of this value.
  • environment spectral density parameters = Lorentzian: Omega_e=0.01, eta=0.1, kappa=0.1; Ohmic: alpha_d=0.1, omega_c=1, with Delta=1
    Chosen to produce QME-visible regimes; the authors claim robustness for order-of-magnitude changes in Omega_e and eta.
  • junction transparency parameters = T=0.99 (epsilon=0.46, Gamma=6.5), T=0.85 (epsilon=2.74), T=0.3 (epsilon=9.8); L=0.6 xi0 short, L=1.7 xi0 intermediate…
    Set by hand; the existence and position of Mpemba arcs depend strongly on transparency and on SOI/Zeeman parameters.
assumptions (6)
  • domain assumption Phase fluctuations are small, so first-order expansion in phi_tilde is valid.
    Invoked in Eq. (2.23) to linearize the tunneling couplings; all transition rates are computed only to first order in the bath coupling.
  • domain assumption Continuum quasiparticles are in thermal quasi-equilibrium at temperature Tqp, are not entangled with ABSs, and Tqp >= Tb.
    Sec. IIB2; this is essential for the Lindblad rates and for the QME to appear in the numerical results.
  • ad hoc to paper The number of subgap Andreev solutions stays 2ell by continuity of root flow in Gamma-Delta parameter space.
    Sec. IIB1; this level-counting assumption is not proven but is needed to identify 2ell ABSs for arbitrary Gamma/Delta.
  • domain assumption Phonon-induced relaxation is negligible compared to phase-fluctuation relaxation.
    Sec. IIB2, inequality (2.38); used to drop electron-phonon terms from the effective EOM.
  • ad hoc to paper Principal-value parts in the ABS-continuum Green's function expansion are negligible because spectral functions are smooth.
    Eqs. (2.69)-(2.74); this simplification yields the Fermi-golden-rule rates with diagonal continuum couplings.
  • domain assumption The reduced dynamics of ABS populations is Markovian and obeys a Lindblad/Pauli master equation with decoupled coherences.
    Sec. IID and Sec. IIIA; required for the trace-distance QME criterion and the population-vector analysis.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Green's Function Approach to Josephson Dot Dynamics and Application to Quantum Mpemba Effects." pith.science (2026). https://pith.science/paper/MF6HNEK7

@misc{pith2026250111609,
  author       = {Pith},
  title        = {Pith review of: Green's Function Approach to Josephson Dot Dynamics and Application to Quantum Mpemba Effects},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MF6HNEK7}},
  note         = {Machine review of arXiv:2501.11609}
}
read the original abstract

We develop a Green's function approach for the nonequilibrium dynamics of multi-level quantum dots coupled to multiple fermionic reservoirs in the presence of a bosonic environment. Our theory is simpler than the Keldysh approach and goes beyond scattering state constructions. In concrete terms, we study Josephson junctions containing a quantum dot and coupled to an electromagnetic environment. In the dot region, spin-orbit interactions, a Zeeman field, and in principle also Coulomb interactions can be included. We then study quantum Mpemba effects, assuming that the average phase difference across the Josephson junction is subject to a rapid quench. For a short singlechannel junction, we show that both types of quantum Mpemba effects allowed in open quantum systems are possible. We also study an intermediate-length junction, where spin-orbit interactions and a Zeeman field are included. Again quantum Mpemba effects are predicted.

Figures

Figures reproduced from arXiv: 2501.11609 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic setup: The average phase difference [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Schematic illustration of the six transition rates [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Steady-state populations [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Steady-state populations [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. QME in Josephson dots of short length, [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The four positive ABS energies vs [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Time dependence of the distance function [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 8
Figure 8. Figure 8: FIG. 8. QME in a Josephson dot of intermediate length, [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The quantum Mpemba effects

    cond-mat.stat-mech 2025-02 accept novelty 2.0 of 10

    A review of the quantum Mpemba effect covering open and isolated quantum systems, key theories, experiments, and open questions.

Reference graph

Works this paper leans on

71 extracted references · 50 canonical work pages · cited by 1 Pith paper

  1. [1]

    root flow

    No fluctuations In the absence of phase fluctuations,˜ϕ = 0, the above equations simplify to [i∂t − h(i∂t)] γ(t) = 0, h (ω) = ϵτz + Λ(ω), (2.31) where h(i∂t) plays the role of an effective single-particle Hamiltonian. However, this operator is nonlocal in time since it can be expanded into an infinite series in∂t. In particular, we observe from Eqs. (2.20...

    work page

  2. [2]

    quasiparticle temperature

    Phase fluctuation effects We now return to the full EOM (2.26) in the presence of phase fluctuations ˜ϕ. Since Eq. (2.26) is linear in the field operator γ(t), it is convenient to switch to a first-quantized framework for the fermionic part. In first quantization, ABS and continuum quasiparticles are representedbya 4ℓ-componentwavefunction Ψ(t), which obe...

    work page

  3. [3]

    Taking∆ → ∞, see Eq

    Atomic limit Before tackling the full expression (2.41), it is instructive to first study the atomic limit, where substantial simplifications are possible. Taking∆ → ∞, see Eq. (2.32), we find GR(ω) = 2ℓX ν=1 " ηνη† ν ω − Eν + iδ+ + η¯νη† ¯ν ω + Eν + iδ+ # , (2.42) where we used the completeness of the ABSorthonormal basis. In this limit, the perturbation...

    work page

  4. [4]

    (2.41), where we may write Ψ(1) λ (t) = X n∈{ν,¯ν} an(t)ηne−iEnt + ˜Ψ(t), η ¯ν = τxη∗ ν, (2.49) with ν ∈ {1,

    Transition rates between Andreev states Wereturntothescatteringproblem(2.39)with Ψ(1) λ (t) in Eq. (2.41), where we may write Ψ(1) λ (t) = X n∈{ν,¯ν} an(t)ηne−iEnt + ˜Ψ(t), η ¯ν = τxη∗ ν, (2.49) with ν ∈ {1, . . . ,2ℓ}. We recall that ˜Ψ(t) represents above-gap continuum states and that, in general,η† nηn′ ̸= 0 for n ̸= n′. For very long timest = T, an(t)...

    work page

  5. [5]

    However, they cannot be described by eigenstates ofh(ω) ̸= h†(ω) for |ω| > ∆

    Transition rates between ABSs and continuum states Next, to compute transition rates connecting ABSs to the continuum sector, we first recall that after integratingoutthesuperconductingleads, thecontinuum quasiparticles are encoded in GR/A(ω). However, they cannot be described by eigenstates ofh(ω) ̸= h†(ω) for |ω| > ∆. To calculate the transition rates, ...

    work page

  6. [6]

    coherences

    describing the dynamics of the ABS sector within the above approximations, see also Ref. [10]. In second- quantized notation and carefully taking into account double-counting effects, the reduced density matrixρA(t) describing the state dynamics in the ABS sector obeys the Lindblad equation ∂tρA = −i X λ Eλ[a† λaλ, ρA] + X λ,λ′ Γλ′→λ L h a† λaλ′ i ρA + + ...

    work page

  7. [7]

    We go beyond this restriction in Sec

    Case Γ ≫ ∆ We first describe an analytical approach for identifying the QME for a single-level dot with large hybridization to the superconducting leads, Γ ≫ ∆. We go beyond this restriction in Sec. IIIA3 by performing numerical calculations. For Γ ≫ ∆, the quantum dot model in Sec. IIA implies the well-known ABS dispersion relation [1, 54, 55] E1(ϕ0) ≃ ∆...

    work page

  8. [8]

    far” vs “close

    QME protocol Following Ref. [38], see also Sec. I, the protocol for detecting the QME consists of comparing two copies of the system prepared at time t < 0 in the pre-quench stationary states P(c) r,stat and P(f ) r,stat corresponding to the phase differences ϕ(c) 0 and ϕ(f ) 0 , respectively, with all other model parameters kept identical. At time t = 0,...

    work page

Show all 71 references
  1. [9]

    Mpemba arcs

    Arbitrary Γ/∆ If the condition Γ ≫ ∆ is not satisfied, instead of Eq. (3.4), one needs to employ the numerically exact ABS dispersion obtained by solving Eq. (2.34). Similarly, one then has to numerically evaluate the transition rates in Eq. (3.3) from the corresponding genera...

    2004

  2. [10]

    Y. V. Nazarov and Y. M. Blanter,Quantum transport: Introduction to Nanoscience (Cambridge University Press, Cambridge, 2009)

    2009

  3. [11]

    Breuer and F

    H.-P. Breuer and F. Petruccione,The Theory of Open Quantum Systems (Oxford University Press, Oxford,

  4. [12]

    Giuliano and I

    D. Giuliano and I. Affleck, The Josephson current through a long quantum wire, Journal of Statistical Mechanics: Theory and Experiment 2013, P02034 (2013)

    2013

  5. [13]

    Giuliano and I

    D. Giuliano and I. Affleck, dc Josephson current in a long multichannel quantum wire, Phys. Rev. B 90, 045133 (2014)

    2014

  6. [14]

    Zazunov, A

    A. Zazunov, A. Brunetti, A. L. Yeyati, and R. Egger, Quasiparticle trapping, Andreev level population dynamics, and charge imbalance in superconducting weak links, Phys. Rev. B90, 104508 (2014)

    2014

  7. [15]

    Campagnano, P

    G. Campagnano, P. Lucignano, D. Giuliano, and A. Tagliacozzo, Spin-orbit coupling and anomalous Josephson effect in nanowires, Journal of Physics: Condensed Matter27, 205301 (2015)

    2015

  8. [16]

    Park and A

    S. Park and A. L. Yeyati, Andreev spin qubits in multichannel Rashba nanowires, Phys. Rev. B96, 125416 (2017)

    2017

  9. [17]

    Minutillo, D

    M. Minutillo, D. Giuliano, P. Lucignano, A. Tagliacozzo, and G. Campagnano, Anomalous Josephson effect in S/SO/F/S heterostructures, Phys. Rev. B 98, 144510 (2018)

    2018

  10. [18]

    Ackermann, A

    N. Ackermann, A. Zazunov, S. Park, R. Egger, and A. L. Yeyati, Dynamical parity selection in superconducting weak links, Phys. Rev. B107, 214515 (2023)

    2023

  11. [19]

    Zatsarynna, A

    K. Zatsarynna, A. Nava, A. Zazunov, and R. Egger, Many-body quantum dynamics of spin-orbit coupled Andreev states in a Zeeman field, Phys. Rev. B 109, 214505 (2024)

    2024

  12. [20]

    Fauvel, J

    Y. Fauvel, J. S. Meyer, and M. Houzet, Opportunities for the direct manipulation of a phase-driven Andreev spin qubit, Phys. Rev. B109, 184515 (2024)

    2024

  13. [21]

    Lidal and J

    J. Lidal and J. Danon, Andreev bound states and supercurrent in disordered spin-orbit-coupled nanowire superconductor-normal-superconductor junctions, Phys. Rev. B111, 064516 (2025)

    2025

  14. [22]

    Weiss, Quantum Dissipative Systems , 4th ed

    U. Weiss, Quantum Dissipative Systems , 4th ed. (World Scientific, Singapore, 2012) https://www.worldscientific.com/doi/pdf/10.1142/8334

    2012 doi

  15. [23]

    M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys.82, 3045 (2010)

    2010

  16. [24]

    E. B. Mpemba and D. G. Osborne, Cool?, Physics Education 4, 172 (1969)

    1969

  17. [25]

    Jeng, The Mpemba effect: When can hot water freeze faster than cold?, American Journal of Physics74, 514 (2006)

    M. Jeng, The Mpemba effect: When can hot water freeze faster than cold?, American Journal of Physics74, 514 (2006)

    2006

  18. [26]

    Lu and O

    Z. Lu and O. Raz, Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse, Proceedings of the National Academy of Sciences114, 5083 (2017)

    2017

  19. [27]

    Lasanta, F

    A. Lasanta, F. Vega Reyes, A. Prados, and A. Santos, When the Hotter Cools More Quickly: Mpemba Effect in Granular Fluids, Phys. Rev. Lett.119, 148001 (2017)

    2017

  20. [28]

    Baity-Jesi, E

    M. Baity-Jesi, E. Calore, A. Cruz, L. A. Fernandez, J. M. Gil-Narvión, A. Gordillo-Guerrero, D. Iñiguez, A. Lasanta, A. Maiorano, E. Marinari, V. Martin- Mayor, J. Moreno-Gordo, A. Muñoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, F. Ricci-Tersenghi, J. J. Ruiz-Lorenzo, S....

    2019

  21. [29]

    Torrente, M

    A. Torrente, M. A. López-Castaño, A. Lasanta, F. V. Reyes, A. Prados, and A. Santos, Large Mpemba-like effect in a gas of inelastic rough hard spheres, Phys. Rev. E 99, 060901 (2019)

    2019

  22. [30]

    Santos and A

    A. Santos and A. Prados, Mpemba effect in molecular gases under nonlinear drag, Physics of Fluids32, 072010 (2020)

    2020

  23. [31]

    Megías, A

    A. Megías, A. Santos, and A. Prados, Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag, Phys. Rev. E105, 054140 (2022)

    2022

  24. [32]

    Chétrite, A

    R. Chétrite, A. Kumar, and J. Bechhoefer, The Metastable Mpemba Effect Corresponds to a Non- monotonic Temperature Dependence of Extractable Work, Frontiers in Physics9, 654271 (2021)

    2021

  25. [33]

    M. R. Walker and M. Vucelja, Mpemba effect in terms of mean first passage time (2023), arXiv:2212.07496 [cond- mat.stat-mech]

    2023 arXiv

  26. [34]

    Murciano, F

    S. Murciano, F. Ares, I. Klich, and P. Calabrese, Entanglement asymmetry and quantum Mpemba effect in the XY spin chain, Journal of Statistical Mechanics: Theory and Experiment2024, 013103 (2024)

    2024

  27. [35]

    Rylands, K

    C. Rylands, K. Klobas, F. Ares, P. Calabrese, S. Murciano, and B. Bertini, Microscopic Origin of the Quantum Mpemba Effect in Integrable Systems, Phys. Rev. Lett.133, 010401 (2024)

    2024

  28. [36]

    Aharony Shapira, Y

    S. Aharony Shapira, Y. Shapira, J. Markov, G. Teza, N. Akerman, O. Raz, and R. Ozeri, Inverse Mpemba Effect Demonstrated on a Single Trapped Ion Qubit, 21 Phys. Rev. Lett.133, 010403 (2024)

    2024

  29. [37]

    L. K. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Calabrese, C. F. Roos, and M. K. Joshi, Observing the Quantum Mpemba Effect in Quantum Simulations, Phys. Rev. Lett.133, 010402 (2024)

    2024

  30. [38]

    A. K. Chatterjee, S. Takada, and H. Hayakawa, Quantum Mpemba Effect in a Quantum Dot with Reservoirs, Phys. Rev. Lett.131, 080402 (2023)

    2023

  31. [39]

    A. K. Chatterjee, S. Takada, and H. Hayakawa, Multiple quantum Mpemba effect: Exceptional points and oscillations, Phys. Rev. A110, 022213 (2024)

    2024

  32. [40]

    Wang and J

    X. Wang and J. Wang, Mpemba effects in nonequilibrium openquantumsystems,Phys.Rev.Res. 6,033330(2024)

    2024

  33. [41]

    D. J. Strachan, A. Purkayastha, and S. R. Clark, Non-Markovian Quantum Mpemba effect (2024), arXiv:2402.05756 [quant-ph]

    2024

  34. [42]

    Liu, H.-K

    S. Liu, H.-K. Zhang, S. Yin, and S.-X. Zhang, Symmetry Restoration and Quantum Mpemba Effect in Symmetric Random Circuits, Phys. Rev. Lett.133, 140405 (2024)

    2024

  35. [43]

    Turkeshi, P

    X. Turkeshi, P. Calabrese, and A. D. Luca, Quantum Mpemba Effect in Random Circuits (2024), arXiv:2405.14514 [quant-ph]

    2024 arXiv

  36. [44]

    Kochsiek, F

    S. Kochsiek, F. Carollo, and I. Lesanovsky, Accelerating the approach of dissipative quantum spin systems towards stationarity through global spin rotations, Phys. Rev. A106, 012207 (2022)

    2022

  37. [45]

    Klich, O

    I. Klich, O. Raz, O. Hirschberg, and M. Vucelja, Mpemba Index and Anomalous Relaxation, Phys. Rev. X 9, 021060 (2019)

    2019

  38. [46]

    F. Ares, V. Vitale, and S. Murciano, The quantum Mpemba effect in free-fermionic mixed states (2024), arXiv:2405.08913 [cond-mat.stat-mech]

    2024 arXiv

  39. [47]

    Nava and R

    A. Nava and R. Egger, Mpemba Effects in Open NonequilibriumQuantumSystems,Phys.Rev.Lett. 133, 136302 (2024)

    2024

  40. [48]

    X. Wang, J. Su, and J. Wang, Mpemba Meets Quantum Chaos: Anomalous Relaxation and Mpemba Crossings in Dissipative Sachdev-Ye-Kitaev Models (2024), arXiv:2410.06669 [quant-ph]

    2024

  41. [49]

    J. W. Dong, H. F. Mu, M. Qin, and H. T. Cui, Quantum Mpemba effect of Localization in the dissipative Mosaic model (2024), arXiv:2411.03734 [quant-ph]

    2024 arXiv

  42. [50]

    D. Qian, H. Wang, and J. Wang, Intrinsic Quantum Mpemba Effect in Markovian Systems and Quantum Circuits (2024), arXiv:2411.18417 [quant-ph]

    2024

  43. [51]

    F. Ares, P. Calabrese, and S. Murciano, The quantum Mpemba effects (2025), arXiv:2502.08087 [cond-mat.stat-mech]

    2025 arXiv

  44. [52]

    G. Teza, J. Bechhoefer, A. Lasanta, O. Raz, and M. Vucelja, Speedups in nonequilibrium thermal relaxation: Mpemba and related effects (2025), arXiv:2502.01758 [cond-mat.stat-mech]

    2025

  45. [53]

    Ibáñez, C

    M. Ibáñez, C. Dieball, A. Lasanta, A. Godec, and R. A. Rica, Heating and cooling are fundamentally asymmetric and evolve along distinct pathways, Nature Physics20, 135 (2024)

    2024

  46. [54]

    I. G.-A. Pemartín, E. Mompó, A. Lasanta, V. Martín- Mayor, and J. Salas, Shortcuts of Freely Relaxing Systems Using Equilibrium Physical Observables, Phys. Rev. Lett.132, 117102 (2024)

    2024

  47. [55]

    Nava and M

    A. Nava and M. Fabrizio, Lindblad dissipative dynamics in the presence of phase coexistence, Phys. Rev. B100, 125102 (2019)

    2019

  48. [56]

    N.VadakkayilandS.K.Das,Shouldahotterparamagnet transform quicker to a ferromagnet? Monte Carlo simulation results for Ising model, Phys. Chem. Chem. Phys. 23, 11186 (2021)

    2021

  49. [57]

    González-Adalid Pemartín, E

    I. González-Adalid Pemartín, E. Mompó, A. Lasanta, V. Martín-Mayor, and J. Salas, Slow growth of magnetic domainshelpsfastevolutionroutesforout-of-equilibrium dynamics, Phys. Rev. E104, 044114 (2021)

    2021

  50. [58]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information(Cambridge University Press, Cambridge, UK, 2000)

    2000

  51. [59]

    Wang and S

    X. Wang and S. G. Schirmer, Contractivity of the Hilbert-Schmidt distance under open-system dynamics, Phys. Rev. A79, 052326 (2009)

    2009

  52. [60]

    Martín-Rodero and A

    A. Martín-Rodero and A. L. Yeyati, Josephson and Andreev transport through quantum dots, Advances in Physics 60, 899 (2011)

    2011

  53. [61]

    S. B. Kaplan, C. C. Chi, D. N. Langenberg, J. J. Chang, S.Jafarey,andD. J.Scalapino,Quasiparticleand phonon lifetimes in superconductors, Phys. Rev. B 14, 4854 (1976)

    1976

  54. [62]

    Zazunov, V

    A. Zazunov, V. S. Shumeiko, G. Wendin, and E. N. Bratus’, Dynamics and phonon-induced decoherence of andreev level qubit, Phys. Rev. B71, 214505 (2005)

    2005

  55. [63]

    C. W. J. Beenakker and H. van Houten, Josephson current through a superconducting quantum point contact shorter than the coherence length, Phys. Rev. Lett. 66, 3056 (1991)

    1991

  56. [64]

    Furusaki and M

    A. Furusaki and M. Tsukada, Current-carrying states in Josephson junctions, Phys. Rev. B43, 10164 (1991)

    1991

  57. [65]

    J. Barr, G. Zicari, A. Ferraro, and M. Paternostro, Spectral density classification for environment spectroscopy, Machine Learning: Science and Technology 5, 015043 (2024)

    2024

  58. [66]

    R. A. Horn and C. R. Johnson, Matrix analysis (Cambridge University Press, Cambridge, UK, 2012)

    2012

  59. [67]

    Janvier, L

    C. Janvier, L. Tosi, L. Bretheau, Ç. Ö. Girit, M. Stern, P. Bertet, P. Joyez, D. Vion, D. Esteve, M. F. Goffman, H. Pothier, and C. Urbina, Coherent manipulation of Andreev states in superconducting atomic contacts, Science 349, 1199 (2015)

    2015

  60. [68]

    J. J. Wesdorp, L. Grünhaupt, A. Vaartjes, M. Pita-Vidal, A. Bargerbos, L. J. Splitthoff, P. Krogstrup, B. van Heck, and G. de Lange, Dynamical Polarization of the Fermion Parity in a Nanowire Josephson Junction, Phys. Rev. Lett. 131, 117001 (2023)

    2023

  61. [69]

    J. J. Wesdorp, F. J. Matute-Cañadas, A. Vaartjes, L. Grünhaupt, T. Laeven, S. Roelofs, L. J. Splitthoff, M. Pita-Vidal, A. Bargerbos, D. J. van Woerkom, P. Krogstrup, L. P. Kouwenhoven, C. K. Andersen, A. L. Yeyati, B. van Heck, and G. de Lange, Microwave spectroscopy of inter...

    2024

  62. [70]

    Carollo, A

    F. Carollo, A. Lasanta, and I. Lesanovsky, Exponentially AcceleratedApproachtoStationarityinMarkovianOpen Quantum Systems through the Mpemba Effect, Phys. Rev. Lett.127, 060401 (2021)

    2021

  63. [71]

    Zatsarynna, A

    K. Zatsarynna, A. Nava, R. Egger, and A. Zazunov, Green’s Function Approach to Josephson Dot Dynamics and Application to Quantum Mpemba Effects, 10.5281/zenodo.14937796 (2025)

    2025 doi

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.