SLIPS: Multidisciplinary Insights

• SLIPS are engineered materials with lubricant-infused porous surfaces that minimize contact-angle hysteresis and enable controlled droplet mobility.
• In superconductors and ultracold atomic circuits, phase slips are discrete 2π changes that facilitate coherent tunneling, state switching, and dissipation control.
• Beyond fluid dynamics, the term 'slips' extends to archaeological bamboo fragments, polymer slip-springs, and robotic slip detection, reflecting a theme of discontinuous motion.

“SLIPS” is not a single technical object but a polysemous term spanning several research traditions. In surface science it denotes slippery liquid-infused porous surfaces and related slippery liquid-infused membranes, where a lubricant stabilized by capillarity presents a low-hysteresis liquid interface to an external phase (Muschi et al., 2018, Bazyar et al., 2018). In superconductivity, cold atoms, and nonlinear dynamics, “slips” more often denotes phase slips: discrete $2\pi$ changes of an order-parameter phase or winding number that mediate dissipation, state switching, or coherent tunneling between metastable sectors (Petkovic et al., 2016, Pérez-Obiol et al., 2021). In archaeology, “slips” refers to ancient bamboo slips, the narrow bamboo strips used as a writing medium and now studied with physics-driven machine learning for fragment rejoining (Zhu et al., 13 May 2025). The term also appears in adjacent contexts such as slip-spring polymer models, frictional slip in elastic strips, and online slip detection in legged robots (Schneider et al., 2022, Sano et al., 2016, Liu et al., 23 Jun 2026).

1. Slippery liquid-infused porous surfaces and membranes

In the surface-science sense, SLIPS are porous nanostructures impregnated with a low-surface-tension lubricant. The lubricant masks the rough solid and replaces a water-solid contact line by a liquid-liquid interface, thereby strongly reducing contact-angle hysteresis and enabling droplet mobility and rebound (Muschi et al., 2018). A representative architecture consists of a glass substrate coated with a nanoporous silica film produced by a sol-gel route using PMMA nanoparticles as a porogen, followed by fluorosilanization and infusion with Krytox 100 fluorinated oil; in the cited study the final porous silica thickness was about $2.1\ \mu\mathrm{m}$, with estimated volume porosity about $60\%$ and AFM surface porosity about $38\%$ (Muschi et al., 2018).

The wetting signature of functional SLIPS is not an exceptionally high apparent contact angle but a collapse of hysteresis. Before infusion, the fluorosilanized porous substrate had advancing and receding contact angles $\theta_a=140^\circ$ and $\theta_r=95^\circ$, giving $\Delta\theta=45^\circ$. After infusion with Krytox 100, these became $\theta_a=119^\circ$, $\theta_r=115^\circ$, and $\Delta\theta\approx 4^\circ$, and this low hysteresis persisted for all oil thicknesses studied up to 2500 rpm (Muschi et al., 2018). This distinguishes SLIPS from merely hydrophobic controls: the cited fluorinated-glass control had a similar static contact angle around $2.1\ \mu\mathrm{m}$0 but much larger hysteresis, $2.1\ \mu\mathrm{m}$1, and did not support rebound (Muschi et al., 2018).

Lubricant thickness has a threshold-like rather than continuously strong dynamical role. In the functional range, changing oil thickness had little effect on static contact angle, maximum spreading, or rebound/contact dynamics. However, if the lubricant layer became too thin, dewetting spots proliferated and slippery behavior degraded. In the cited experiments, all infused samples except the 5000 rpm case remained slippery; the 5000 rpm sample had a sliding angle of $2.1\ \mu\mathrm{m}$2 and was classified as non-slippery (Muschi et al., 2018). Within the functional range, water-drop impact obeyed the scaling $2.1\ \mu\mathrm{m}$3, with contact time about $2.1\ \mu\mathrm{m}$4, rebound time about $2.1\ \mu\mathrm{m}$5 below the splash threshold, and splashing beginning around $2.1\ \mu\mathrm{m}$6 (Muschi et al., 2018). The paper interprets the weak thickness dependence through a dissipation ratio

$2.1\ \mu\mathrm{m}$7

which is small for the reported viscosities and thicknesses, so dissipation in the lubricant layer is negligible compared with dissipation inside the water drop (Muschi et al., 2018).

The membrane analogue is the slippery liquid-infused membrane. In that setting, the central question is not only mobility but retention of the infusion liquid during immiscible displacement. Liquid-liquid displacement porometry, pore-flow modeling, and microfluidic porous-medium imaging show that water opens pores according to capillary entry pressure, forms preferential flow pathways, and leaves behind substantial infused liquid as trapped wetting structures and thin liquid linings (Bazyar et al., 2018). The threshold pressure is expressed by

$2.1\ \mu\mathrm{m}$8

and in the PVDF/Krytox-water system the observed initial critical pressure, about $2.1\ \mu\mathrm{m}$9 Pa, agreed closely with the Young-Laplace estimate $60\%$0 Pa based on the measured largest pore radius $60\%$1 (Bazyar et al., 2018).

The membrane data indicate incomplete clearing of the infused liquid. Relative to a pre-wetted membrane, the active-pore fraction increased over five cycles from 0.09 to 0.57, while permeability rose from $60\%$2 to $60\%$3 Darcy; the pre-wetted membrane was $60\%$4 Darcy (Bazyar et al., 2018). The residual morphology, imaged in a microfluidic porous-medium analogue, consisted of pools, bridges, and thin films around pillar structures, consistent with capillary fingering and invasion percolation with trapping. The reported steady fractal dimension $60\%$5 and residual invading-phase saturation below unity reinforce the interpretation that SLIM transport preserves liquid-lined pores rather than simply stripping the infused phase from the substrate (Bazyar et al., 2018).

2. Phase slips in superconductors

In superconductivity, a phase slip is a topological event in which the phase winding of the complex order parameter changes by an integer multiple of $60\%$6. If

$60\%$7

then a continuous change in winding requires $60\%$8 to momentarily vanish at some point, allowing the phase to unwind (Petkovic et al., 2016). In one-dimensional or quasi-one-dimensional systems, such events govern the decay of supercurrent, produce finite resistance below the mean-field transition temperature, and mediate switching between metastable current-carrying states (Petkovic et al., 2016, Kimmel et al., 2017).

One well-characterized regime is the deterministic phase slip in mesoscopic superconducting rings. In isolated, flux-biased aluminum rings measured by cantilever torque magnetometry, the persistent-current branches were described quantitatively by one-dimensional Ginzburg-Landau theory over the range $60\%$9, and the switching points tracked the finite-circumference stability boundary

$38\%$0

rather than merely the long-ring estimate (Petkovic et al., 2016). In that experiment, phase slips were deterministic in the sense that switching occurred when the metastable state lost stability because the barrier to a neighboring winding-number state vanished. The observed transitions satisfied $38\%$1 throughout the measured range down to $38\%$2 mK, consistent with strongly damped dynamics (Petkovic et al., 2016).

A different near-$38\%$3 problem is the thermal phase slip in two-dimensional superconducting films. For an infinite current-carrying film near $38\%$4, the cited 2025 analysis reduces the Ginzburg-Landau saddle-point problem to the elliptic Boussinesq equation

$38\%$5

and obtains an exact vortex-free instanton with anisotropic sizes

$38\%$6

The corresponding activation barrier scales as

$38\%$7

in contrast to the one-dimensional Langer-Ambegaokar scaling $38\%$8 (Skvortsov et al., 22 Jun 2025). For wide strips with $38\%$9, the optimal fluctuation is a half-instanton near the boundary with activation energy $\theta_a=140^\circ$0 (Skvortsov et al., 22 Jun 2025).

Time-dependent Ginzburg-Landau theory also yields a dynamical onset picture in superconducting weak links. For a one-dimensional weak link with locally suppressed superconductivity, the cited work finds that stable and unstable stationary superconducting solutions merge at a critical current and the periodic phase-slip state emerges via an infinite-period bifurcation. Near onset, the period diverges as

$\theta_a=140^\circ$1

and the weak-link critical current is exponentially suppressed with inclusion width and strength,

$\theta_a=140^\circ$2

This framework explains why the phase-slip center localizes at the inclusion and why a weakly nonlinear reduction is possible in a weak link but not in a homogeneous wire (Kimmel et al., 2017).

Three-dimensional nanostructures support yet another regime. In a tubular Nb diabolo structure with a narrow central constriction, time-dependent Ginzburg-Landau simulations show periodic phase slips localized at the waist under dc transport current, yielding GHz voltage oscillations. With an added ac modulation $\theta_a=140^\circ$3, the emitted spectrum contains mixed frequencies

$\theta_a=140^\circ$4

with comb spacing $\theta_a=140^\circ$5 and a center frequency controlled by the phase-slip repetition rate $\theta_a=140^\circ$6 (Deenen et al., 14 Mar 2025). The work distinguishes a vortex-free quasi-1D slip regime from a higher-current regime in which vortex–antivortex nucleation and annihilation occurs directly in the constriction, altering the comb structure (Deenen et al., 14 Mar 2025).

Electrostatic tuning of phase-slip dynamics has also been demonstrated statistically. In all-metallic titanium Dayem-bridge Josephson nanotransistors, switching-current probability distributions reveal the standard low-temperature sequence of QPS, TAPS, and MPS under temperature tuning, with crossovers near $\theta_a=140^\circ$7 mK and $\theta_a=140^\circ$8 mK, but gate-voltage tuning produces a qualitatively different broadening pattern (Puglia et al., 2019). The gate-induced regime, termed electrically activated phase slips (EAPS), begins near $\theta_a=140^\circ$9 V, reaches widths of about $\theta_r=95^\circ$0 nA, and cannot be fit by a conventional thermal Kurkijärvi-Fulton-Dunkleberger model without unphysical parameters (Puglia et al., 2019). The work argues that this excludes simple overheating as the mechanism and instead implies a nonthermal modification of phase-slip dynamics by the electrostatic field (Puglia et al., 2019).

3. Coherent quantum phase slips and their statistics

A specialized superconducting literature concerns coherent quantum phase slips (CQPS), where slips act as tunneling amplitudes between fluxoid or winding sectors rather than as dissipative decay events. In a long Josephson-junction array acting as a “slippery wire,” the total phase-slip amplitude is a coherent sum over junctions,

$\theta_r=95^\circ$1

and the Aharonov-Casher phase $\theta_r=95^\circ$2 makes the resulting amplitude sensitive to offset charges on the array islands (Manucharyan et al., 2010). In the fluxonium realization studied there, the broadening of qubit transitions was traced to this charge-sensitive interference, with the CQPS-induced linewidth

$\theta_r=95^\circ$3

and a particularly strong effect near half-integer flux (Manucharyan et al., 2010).

A subsequent fluxonium study systematized this mechanism by fabricating several qubits with similar $\theta_r=95^\circ$4 but different array-junction impedances $\theta_r=95^\circ$5, thereby changing the single-junction phase-slip energy

$\theta_r=95^\circ$6

by orders of magnitude (Randeria et al., 2024). The CQPS amplitude in the array is again a coherent sum,

$\theta_r=95^\circ$7

which induces a qubit-frequency correction $\theta_r=95^\circ$8 and a Ramsey dephasing rate

$\theta_r=95^\circ$9

Across six devices, the measured $\Delta\theta=45^\circ$0 at $\Delta\theta=45^\circ$1 ranged from $\Delta\theta=45^\circ$2 to $\Delta\theta=45^\circ$3, in agreement with the CQPS scaling model (Randeria et al., 2024).

The same superconducting duality also yields a full counting-statistics description of QPS in nanowires. In the low-frequency limit, the cumulants of the voltage operator obey Poisson statistics,

$\Delta\theta=45^\circ$4

with $\Delta\theta=45^\circ$5 the flux quantum (Semenov et al., 2019). The zero-frequency noise takes the Schottky-like form

$\Delta\theta=45^\circ$6

which reduces to $\Delta\theta=45^\circ$7 for $\Delta\theta=45^\circ$8 (Semenov et al., 2019). At finite frequency, however, the statistics ceases to be Poissonian. In short wires, all finite-frequency cumulants can still be written explicitly in terms of the current-voltage characteristic, but they depend on shifted arguments such as $\Delta\theta=45^\circ$9 and on the environment response, so the tunneling events are no longer statistically independent on those time scales (Semenov et al., 2019).

A particularly striking prediction appears in long wires at $\theta_a=119^\circ$0: the QPS-induced voltage-noise spectrum vanishes above the threshold

$\theta_a=119^\circ$1

The paper attributes this to the fact that a single QPS event under current bias releases energy $\theta_a=119^\circ$2, which is converted into plasmons propagating in opposite directions, so only half that energy can reach a given detector end (Semenov et al., 2019). This establishes a direct connection between QPS shot noise and the kinematics of plasmon emission.

4. Phase slips in ultracold atomic circuits

Ultracold gases realize phase slips in a language of circulation, winding number, and atomtronic current states. In a toroidal $\theta_a=119^\circ$3Na Bose-Einstein condensate with a rotating optical weak link, the condensate order parameter

$\theta_a=119^\circ$4

supports quantized circulation

$\theta_a=119^\circ$5

The rotating weak link acts as a controllable analog of magnetic-flux bias in a SQUID. At moderate rotation, well-defined phase slips drive transitions $\theta_a=119^\circ$6 between persistent-current states; above $\theta_a=119^\circ$7, the response crosses over to vortex entry into the annulus (Wright et al., 2012). The cited experiment used a ring radius $\theta_a=119^\circ$8, a radial Thomas-Fermi half-width $\theta_a=119^\circ$9, and barrier heights around $\theta_r=115^\circ$0 and $\theta_r=115^\circ$1, and observed deterministic phase slips whose threshold decreased with increasing barrier height because the weak-link critical current was reduced (Wright et al., 2012).

One-dimensional bosonic lattices exhibit a different phenomenology, where phase slips are inferred from dissipation rather than directly imaged as current-state switching. In 1D Bose gases moving in an optical lattice, the damping rate $\theta_r=115^\circ$2 of center-of-mass oscillations is related to the phase-slip nucleation rate by

$\theta_r=115^\circ$3

The reported data show a crossover from a velocity-independent, temperature-sensitive regime to a velocity-dependent, nearly temperature-independent regime. The crossover velocity $\theta_r=115^\circ$4 scaled linearly with $\theta_r=115^\circ$5, with fitted relation

$\theta_r=115^\circ$6

consistent with the expected crossover between thermally activated and quantum phase slips (Abbate et al., 2017).

The most explicitly coherent cold-atom realization in the supplied corpus is a pair of weakly coupled bosonic ring lattices. There, QPS are defined as discrete changes in ring winding and are realized as coherent transfer of one unit of circulation between two rings whose particle populations remain nearly fixed (Pérez-Obiol et al., 2021). The system is governed by a two-ring Bose-Hubbard Hamiltonian with synthetic fluxes $\theta_r=115^\circ$7 and a weak inter-ring link,

$\theta_r=115^\circ$8

and after a flux quench the dynamics reduces to a two-state oscillation

$\theta_r=115^\circ$9

In the noninteracting limit, the phase-slip gap is

$\Delta\theta\approx 4^\circ$0

whereas for strong interactions and even $\Delta\theta\approx 4^\circ$1, $\Delta\theta\approx 4^\circ$2 and $\Delta\theta\approx 4^\circ$3 (Pérez-Obiol et al., 2021). The work emphasizes that these oscillations are driven by entangled superpositions of current states and cannot be captured by mean-field theory, and it proposes time-of-flight momentum distributions as a direct experimental signature (Pérez-Obiol et al., 2021).

5. Other technical uses of “slip” and “slips”

Outside SLIPS surfaces and phase slips, the term remains technically important in several disciplines. In synchronized noisy oscillator networks, a rare slip is a fluctuation-driven event in which the phase difference between two nodes exceeds $\Delta\theta\approx 4^\circ$4. In the small-noise limit, the most probable trajectory goes from a stable phase-locked state to a saddle phase-locked state and then departs deterministically along the unstable manifold (Hindes et al., 2018). For tree networks near a saddle-node bifurcation $\Delta\theta\approx 4^\circ$5, the action obeys

$\Delta\theta\approx 4^\circ$6

with $\Delta\theta\approx 4^\circ$7 determined by topology and frequency imbalance across the critical cut (Hindes et al., 2018).

In soft-matter hydrodynamics, “slip” usually refers to a boundary condition rather than a topological event. For dewetting polymer microdroplets, the Navier slip law

$\Delta\theta\approx 4^\circ$8

regularizes the contact-line singularity and becomes a leading control parameter when the slip length is comparable to droplet size (McGraw et al., 2015). In that regime, the early-time dewetting law is

$\Delta\theta\approx 4^\circ$9

and the transient droplet morphology changes qualitatively with $2.1\ \mu\mathrm{m}$00, with pronounced ridges at smaller $2.1\ \mu\mathrm{m}$01 and more global, elongational flow at larger $2.1\ \mu\mathrm{m}$02 (McGraw et al., 2015).

In polymer rheology, slip-springs are auxiliary elastic connectors used to encode entanglements in highly coarse-grained chain models. For systems with explicit liquid-vapor interfaces, the cited SLSP framework combines FENE slip-springs with MDPD interactions and an explicit compensating potential

$2.1\ \mu\mathrm{m}$03

so that the slip-springs alter dynamics without distorting equilibrium interface structure (Schneider et al., 2022). In droplet spreading simulations, the wetting dynamics depended strongly on the slip-spring fugacity $2.1\ \mu\mathrm{m}$04, with strongly entangled droplets showing delayed core relaxation and transient rebound (Schneider et al., 2022).

In mechanics, “slip” can denote frictional motion at a contact. For an elastic strip compressed vertically onto a frictional rigid substrate, the morphology is classified into pinned, partially slipped, and completely slipped states. The small-strain depinning threshold is

$2.1\ \mu\mathrm{m}$05

while the maximum strain for the pinned point-contact state is estimated as

$2.1\ \mu\mathrm{m}$06

(Sano et al., 2016). This is a purely mechanical slip instability, distinct from both hydrodynamic slip and phase slip.

Robotics uses the term operationally. In the cited quadruped study, slip means tangential displacement of the foot during stance on low-friction terrain. A custom multimodal foot sensor with an IMU and eight piezoresistive elements feeds an LSTM-based ground-reaction-force estimator and an LSTM autoencoder for one-class slip detection. On a Unitree Go1, the system reached $2.1\ \mu\mathrm{m}$07 overall slip-detection accuracy and detected early-stage slips down to $2.1\ \mu\mathrm{m}$08 on average for the 30 smallest correctly classified slip stances, versus $2.1\ \mu\mathrm{m}$09 for a kinematic baseline (Liu et al., 23 Jun 2026). This usage is again distinct from SLIPS surfaces and phase slips.

6. Bamboo slips and the archaeological meaning of “slips”

In archaeology and manuscript studies, slips refers to the bamboo strips used as a major writing medium before widespread paper in East Asia. The cited 2025 work addresses the reconstruction of fragmented ancient bamboo slips rather than fluidic or superconducting SLIPS (Zhu et al., 13 May 2025). Because excavated documents may yield thousands of irregular pieces whose fracture surfaces are degraded by burial, rejoining becomes a combinatorial retrieval problem rather than a simple curve-matching task (Zhu et al., 13 May 2025).

The proposed framework, WisePanda, is a physics-driven deep learning system trained not on manually labeled joins but on synthetic fracture pairs generated from a physical model of bamboo fracture and corrosion (Zhu et al., 13 May 2025). The paper emphasizes two empirical fracture classes, with transverse fractures accounting for about $2.1\ \mu\mathrm{m}$10 of cases, and uses a TripletNet-based ranking model operating on a 64-dimensional representation of fracture-edge curves (Zhu et al., 13 May 2025). The main bamboo benchmark, Bamboo236, contains 118 expert-verified pairs, while Bamboo1350 augments the same 118 true pairs with 1,114 interference fragments (Zhu et al., 13 May 2025).

On Bamboo1350, WisePanda achieves Top-50 accuracy $2.1\ \mu\mathrm{m}$11, compared with $2.1\ \mu\mathrm{m}$12 for SIS, $2.1\ \mu\mathrm{m}$13 for DTW, $2.1\ \mu\mathrm{m}$14 for FMM, and $2.1\ \mu\mathrm{m}$15 for random search (Zhu et al., 13 May 2025). In a human-in-the-loop test across five cases, WisePanda-assisted work reduced average matching time from $2.1\ \mu\mathrm{m}$16 s to $2.1\ \mu\mathrm{m}$17 s, about a 20-fold speedup (Zhu et al., 13 May 2025). This archaeological sense of “slips” is lexically unrelated to phase slips or slippery liquid-infused porous surfaces, but it is a major technical usage of the term in recent literature.

7. Conceptual distinctions and common structure

Across these literatures, “SLIPS” and “slips” organize around a small number of recurring ideas: interfacial mobility, threshold-driven switching, and stochastic or coherent rare events. The commonality is structural rather than ontological.

In surface science, SLIPS refers to a material architecture whose defining property is a capillary-stabilized lubricant layer that suppresses pinning and presents a low-hysteresis interface (Muschi et al., 2018, Bazyar et al., 2018). In superconductors and ultracold atoms, a phase slip is a topological event changing phase winding by $2.1\ \mu\mathrm{m}$18 and mediating switching, decay, or coherent tunneling between quantized current states (Petkovic et al., 2016, Pérez-Obiol et al., 2021). In nanowires and fluxonium arrays, those events may be stochastic and dissipative or coherent and spectroscopic, depending on whether the relevant observable is a voltage pulse, a linewidth, or a tunneling-induced level shift (Semenov et al., 2019, Manucharyan et al., 2010, Randeria et al., 2024). In mechanics and robotics, slip denotes relative tangential motion at a contact, controlled by frictional thresholds or anomaly-detection criteria rather than by order-parameter topology (Sano et al., 2016, Liu et al., 23 Jun 2026). In archaeology, slips are physical manuscript objects whose fractures can be modeled statistically and mechanically for reconstruction (Zhu et al., 13 May 2025).

A plausible implication is that the term is most stable when qualified. For arXiv-facing technical usage, SLIPS generally denotes slippery liquid-infused porous surfaces and related membranes (Muschi et al., 2018, Bazyar et al., 2018); phase slips denotes $2.1\ \mu\mathrm{m}$19 topological events in superconductors, superfluids, and oscillator networks (Petkovic et al., 2016, Kimmel et al., 2017, Hindes et al., 2018); bamboo slips denotes archaeological writing strips (Zhu et al., 13 May 2025); and slip-springs or slip detection belong to yet other vocabularies (Schneider et al., 2022, Liu et al., 23 Jun 2026). The contemporary literature therefore treats “SLIPS” less as a single concept than as a cluster of domain-specific technical terms unified mainly by the language of motion, discontinuity, and interface-mediated transition.