Papers

Cell migration is fundamental to development, tissue organization, immune response, and disease progression. Amoeboid motility is distinguished by rapid motion and strongly fluctuating cell shapes, reflecting the intrinsically nonlinear nature of active living matter far from equilibrium. Here we introduce a minimal active-shell model of an amoeboid cell that couples actin polymerization, cortical flows, and membrane deformation through nonlocal mechanical interactions. The model gives rise to a rich spectrum of emergent behaviors. A symmetric non-motile state can spontaneously break symmetry and transition toward persistent directed migration driven solely by polymerization-induced retrograde flow, even in the absence of shape deformation. Increasing activity further triggers a cascade of dynamical states, including circular trajectories, oscillatory zigzag motion, and irregular chaotic-like migration with fluctuating protrusions and multi-lobed morphologies. Although these migratory modes are observed experimentally in distinct cellular contexts, our results show that they can emerge from the same underlying physical mechanism, providing a unified framework for amoeboid dynamics. Notably, contractile stresses induced by molecular motors are not required to generate spontaneous motility, polarity, or complex migration patterns. Our findings highlight how collective active processes at the cellular scale can self-organize into complex dynamical states, revealing generic principles of nonlinear behavior in living systems.

We present a Renormalization Group (RG) framework based on a nonlocal effective action ansatz to analyze the strong coupling dynamics of the three-dimensional relativistic $\phi^{4}$ theory. By implementing a Hubbard-Stratonovich transformation, we decouple the quartic interaction into the primary field $\phi$ and an auxiliary field $\varphi \sim \phi^2$, allowing both exponents $\Delta_{\phi}$ and $\Delta_{\varphi}$ to act as independent, unconstrained variables rather than fixed scaling dimensions. Within this nonlocal propagator framework, both the field self-energies and vertex corrections are evaluated at the one-loop order. The resulting one-loop logarithmic derivatives determine the renormalization group flows of the couplings and the scaling exponents. For $d=3$ and $\epsilon\approx-0.198$, the self-consistent equations yield a representative fixed point at $\Delta_{\phi}\approx0.97714$, $\Delta_{\varphi}\approx-0.65260$, and $\Delta_{\phi^2}\approx1.04573$, corresponding to $\eta_{\phi}\approx0.04572$ and $\nu\approx0.51170$. Relative to the high-precision conformal-bootstrap benchmarks, the deviations are approximately $0.48\%$ for $\Delta_{\phi}$, $25.97\%$ for $\Delta_{\phi^2}$, and $18.77\%$ for $\nu$, demonstrating sub-percent agreement in the fundamental-field sector while revealing substantially larger deviations in the composite and correlation-length sectors within the leading-order truncation.

To explore the applicability of orbital-free density functional theory (OF-DFT) in nuclear physics, we perform a systematic benchmark of 36 one-point kinetic energy density functionals, which are originally developed for electron systems in condensed matter physics. It is found that the direct use of the original parameters for electron systems leads to inconsistent performance, with certain functionals exhibiting physically unacceptable asymptotic behaviors. However, through parameter re-optimization targeting nuclear densities, different mathematical forms of generalized gradient approximation (GGA) functionals converge to a consistent root-mean-square error of approximately 13 MeV. From a physical perspective, this consistent behavior signifies that the optimized semi-local GGAs have successfully captured the macroscopic, liquid-drop-like background of the nucleus, while the residual deviations appear as periodic oscillations at the magic numbers that could reflect the quantum shell effects.

We study the ground-state density patterns of a population-imbalanced two-component dipolar Bose-Einstein condensate confined in a circular quasi-two-dimensional box. Using a mean-field model, we map out phase diagrams as functions of the axial confinement, interaction imbalance, and population ratio. The system supports a rich sequence of stationary morphologies, including a nearly uniform pancake state, pancake-droplet and ring-droplet coexistence states, droplet arrays, and concentric rings. These patterns show a close structural correspondence to microphase-separated morphologies in diblock-copolymer systems, with the population imbalance acting as an effective volume fraction that selects the pattern topology. Analysis of the density profiles and structure factors reveals that the modulated states possess an intrinsic nonzero characteristic wave vector, which remains essentially unchanged when the box size is varied. We also find that the characteristic pattern spacing scales linearly with the axial confinement length, indicating that the transverse thickness of the condensate controls the effective in-plane length scale. In a finite circular box, this smooth scaling is interrupted by discrete steps, reflecting geometric frustration and the integer locking of the number of rings or droplets. Our results show that box-trapped dipolar mixtures provide a controllable platform for studying finite-size pattern selection and nonlocal microphase formation in quantum fluids.

We develop a systematic perturbation theory for the Helmholtz free energy of a classical $N$-body system within the mesoscopic framework of~\cite{OsanoMeso,OsanoExtensivity}. The combined coarse-graining operator $\mathcal{C}=\mathcal{C}_x\circ\mathcal{C}_p$ acting on single-particle phase space partitions it into product cells $C_{i,\alpha}=V_i\times\Pi_\alpha$ and generates a mesoscopic partition function $\mathcal{Z}_{\rm meso}(\lambda)$ whose reference level factorises by the multinomial theorem: $\mathcal{Z}_{\rm meso}^{(0)}=(Z_1^{(0)})^N$. Perturbation theory for $\mathcal{F}_{\rm meso}(\lambda)=-k_BT\ln\mathcal{Z}_{\rm meso}(\lambda)$ in the inter-cell perturbation $\mathcal{V}_{\rm meso}$ yields the mesoscopic Gibbs–Bogoliubov inequality and an exact coupling-parameter integration formula. The full free energy satisfies \begin{equation*} F(\lambda)=\mathcal{F}_meso(\lambda)-k_BT\!\sum_{i<j}I(i,j;\lambda)+O\!\left(|\Lambda|\ell^{-d}e^{-2\ell/\xi}\right), \end{equation*} where the inter-cell mutual informations $I(i,j;\lambda)$ are the corrections identified in the extensivity analysis. The first-order theory recovers the van der Waals equation and the Barker–Henderson result; the second-order term converges to the structure-factor formula in the fine-cell limit. For long-range interactions, factorisation fails, and the mutual-information corrections quantify the resulting non-extensivity.

We study Hilbert-space fragmentation and thermalization in a one-dimensional dipole-conserving Bose-Hubbard chain. By analyzing the structure of the Hamiltonian matrix in the Fock basis, we show that the system exhibits weak Hilbert-space fragmentation. We further construct an exponentially large family of frozen product states and derive analytical upper and lower bounds on their number. Using exact diagonalization, we examine the consequences of weak fragmentation for eigenstate half-chain entanglement, density relaxation dynamics, and level statistics. All these quantities reveal a transition from a weak eigenstate thermalization regime to a nonergodic regime with increasing on-site interaction strength. These results show that weak Hilbert-space fragmentation does not preclude quantum chaos or thermalization, and provides a minimal platform for studying the interplay of dipole conservation, weak fragmentation, and ergodicity breaking.

We present a comprehensive theoretical investigation of the superconducting (SC) properties of hexagonal HfRuAs ($h$-HfRuAs) by solving anisotropic Migdal–Eliashberg (ME) equations with the inputs from ab initio calculations of electronic structure, phonon dispersion and electron phonon coupling matrix elements. The calculated Eliashberg spectral function reveals strong electron–phonon coupling (EPC) with a constant $\lambda \approx 1.56$, dominated by low-frequency phonon modes associated primarily with Hf and Ru vibrations. The SC state is characterized by a single anisotropic gap with overall $s$-wave symmetry, as evidenced by the fully gapped quasiparticle density of states. The momentum-resolved EPC and SC gap exhibit pronounced anisotropy across different Fermi surface sheets, with the largest variations occurring on the hole-like bands. The SC gap is centered around $\Delta \approx 2.9$ meV with a spread of $\sim 0.8$ meV, indicating significant multiband anisotropy. The resulting gap ratio $2\Delta(0)/k_B T_c \approx 4.2$ exceeds the BCS weak-coupling limit, establishing $h$-HfRuAs as a strong-coupling superconductor. The calculated transition temperature, $T_c$, agrees in the order of magnitude with experiments. Overall, our results identify $h$-HfRuAs as a phonon-mediated, strongly coupled anisotropic superconductor and provide detailed insights into the role of momentum-dependent electron–phonon interactions in determining its SC properties.

The Korteweg-De Vries (KdV) equation is a paradigmatic model of integrable classical fields, with solitonic solutions where localised profiles interact by elastic, factorised scattering. When solitons interact, their shapes are modified, and individual solitons cannot be identified. This is a key problem in soliton gas where one needs a density of solitons per unit distance: can we locate asymptotic objects, quasiparticles, even at finite times in the macroscopic limit? Quasiparticles' positions should satisfy locality properties, the field in mesoscopic regions being determined by quasiparticles lying there. We solve this problem for the KdV equation. We define solitons' positions as functions of spectral and impact parameters via an expansion bijection generalising that of hard rods. These “KdV rods” solve the semiclassical Bethe equations, implementing the collision rate ansatz, and satisfy a repulsion condition generalising the rods' lengths to the KdV scattering shifts and related to the condensate condition. This gives an explicit characterisation of multi-soliton fields in terms of solitons' positions instead of impact parameters. We construct fluid-cell projections, that project out solitons lying outside mesoscopic regions: the resulting field is unchanged in this region and supported there up to small corrections. We show that in the weak limit, conserved densities are given by the empirical density for these solitons' positions. Thus we have associated a kinetic theory of quasiparticles to the KdV equation. The results hold under natural assumptions on spectral and impact parameters, and no randomness is required. Our proof is based on novel solitonic tau functions. This is a crucial step towards rigorously deriving the kinetic equation of the KdV soliton gas, first proposed by Gennady El in 2003. We believe the methods are generalisable to other solitonic models.

We study fractional quantum Hall states with quasihole excitations, on Riemann surfaces of arbitrary genus. For configurations with $m$ quasiholes we construct a vector bundle above the $m$-th symmetric power of the curve so that the fiber at a point $\lbrace w_1,\dots,w_m \rbrace$ corresponds to the state with quasiholes localized at these positions. We determine the Chern character of this bundle via the Grothendieck-Riemann-Roch theorem and show that in the completely filled state, i.e. when the number of particles is maximal, the vector bundle is compatible with the condition of projective flatness. Furthermore, we obtain a generalization of this result to the case of multiple layers and multiple quasihole types. In genus zero and one, we construct explicit wave-functions and verify that the curvature of the associated Chern connection reproduces the predicted Chern classes. The Chern classes obtained match, term by term, the predicted decomposition of the Berry phase under quasihole exchange, into an extensive Aharonov–Bohm contribution and a fractional statistical contribution.

We present a novel parameterized 4-qubit Eisert-Wilkens-Lewenstein (EWL) quantum game circuit for recommender systems in quadruple helix innovation ecosystems (academia, industry, government, and civil society). The local strategy operators $U_{i} = R_y(\theta_{i})$ for each helix actor are directly tuned by normalized dominance weights extracted from real participant funding data (\texit{ecContribution}) in the European Commission CORDIS Horizon Europe database (project COVend, ID 101045956). The circuit employs a multi-qubit EWL entangler followed by parameterized local rotations, inverse entangler, and full measurement, achieving only 22 gates and circuit depth 11 while scaling as $O(n)$ for $n$-round helix communications. Measurement probabilities after the quantum game serve as recommender scores for disruptive versus sustaining innovation trends. These scores are subsequently mapped into the diagonal Dirac potential of a Dirac-Solow-Swan Hamiltonian, enabling time-evolution simulation of capital accumulation and bifurcation dynamics under disruptive innovation. Numerical experiments on real CORDIS quadruple-helix collaboration networks demonstrate the circuit's NISQ compatibility and its ability to forecast disruptive capital trajectories with high fidelity. The proposed framework bridges quantum game theory, parameterized quantum circuits, and relativistic economic growth models, offering a computationally efficient tool for innovation policy and strategic decision-making in complex socio-economic ecosystems. Complexity analysis and reproducibility are provided through open Qiskit implementations.

We present a theoretical framework for unidirectional electromagnetohydrodynamic flow of dilute electrolytes under perpendicular magnetic fields. Starting from the Navier–Stokes equation coupled with the Poisson–Nernst–Planck formulation, we show that the problem admits a sequential decoupling: the Stokes equation is solved first to obtain the velocity profile, which defines a hydrodynamic potential entering the Nernst–Planck description of ions. This Lorentz-force-induced potential competes with electrostatic attraction and significantly alters ionic distributions. We analyze this mechanism in two canonical geometries. In planar Couette shear, it produces a Manning–Oosawa-like condensation transition in one dimension, a phenomenon absent in classical electrostatics. We derive an eigenvalue equation predicting a sharp threshold between counterion enrichment and depletion at the charged wall. In cylindrical Taylor–Couette flow, the same effect shifts the classical Manning criterion by a magnetic parameter, enabling tunable control of condensation. These findings extend Manning–Oosawa phenomenology to driven, non-equilibrium systems and provide a basis for magnetic manipulation of screening in electrolytes, with implications for microfluidics, electrochemical systems, and nonlinear boundary-value theory.

We study localization in a one-dimensional quasiperiodic lattice obtained by extending the Aubry-André model with an additional $N$th-neighbor hopping term of strength $J_{N}$. This long-range tunneling couples successive windings of an effective helical chain and introduces a second control parameter beyond the quasiperiodic potential strength $\Delta$. Working with noninteracting fermions (typically at half filling), we diagnose the delocalization-localization transition using extensions of the modern theory of polarization. Specifically, we compute the polarization amplitudes of the many-body Slater-determinant ground state and construct a geometric Binder cumulant from polarization amplitudes. The critical potential where the localization transition happens is extracted from the sign change (zero crossing) of the geometric Binder cumulant. We map critical potential as a function of $J_N$ and the helical range $N$, finding that stronger helical hopping generally stabilizes the extended phase (shifting critical potential upward), while the $N$-dependence can display pronounced commensurability-induced spikes. We further compare the geometric Binder cumulant with the Fermi gap, which remains near zero at small values of potential and opens in the same parameter regime where the geometric Binder cumulant departs from extended phase. Finally, to take a controlled thermodynamic limit along Fibonacci system sizes, we employ a Zeckendorf-shift construction that fixes the many-body sector consistently as system size goes to infinity.

Alloying Ag into Cu(In,Ga)Se$_2$ has enabled record solar-cell efficiencies ($\sim23.6\%$), yet their long-term stability remains in question because initio calculations predict a Ag-Cu miscibility gap near ambient temperature. By off-lattice Monte-Carlo simulations using a newly developed machine learning (ML) interatomic potential we show that the presence of coherency strain is resolving the controversy between experimental observations and the predicted phase stability. Incorporating elastic energy contributions present in a coherent setup results in complete Ag-Cu miscibility, whereas the expected phase separation occurs in the absence of coherency strains with respect to the end boundary phases, which are mimicked by an incoherent interface with misfit dislocations. The developed ML-MC framework provides a novel approach for resolving discrepancies in thermodynamic stability for systems where mechanical and chemical effects compete.

Recently, magnetic 2-dimensional (2D) van der Waals (vdW) materials have garnered tremendous attention. The vdW ferromagnet Fe5Ge1Te2 has a Curie temperature Tc of ~ 270 K, which is tailorable by tuning the stoichiometry and the Fe deficiency to reach room temperature. To explore the expanded compositional space, we implemented combinatorial synthesis and high-throughput characterization to investigate the structural phase distribution and ferromagnetism of a Fe-Ge-Te thin film library. The library was prepared by magnetron co-sputtering followed by annealing in vacuum or in an inert environment. Composition and structural phase distribution of the 177 pads in the library were characterized using high-throughput wavelength dispersive spectroscopy (WDS), X-ray diffraction (XRD), and two-point probe resistance measurements. We leverage unsupervised machine learning to cluster the XRD dataset into groups of compositions with similar structural phases, and further study the ferromagnetic properties via SQUID magnetometry and X-ray magnetic circular dichroism (XMCD) across different clusters. The results are compared against magnetization and structural models calculated using DFT. Our results demonstrate that the hexagonal crystal structure is a critical prerequisite for ferromagnetism in this system, and that unexplored materials adopting this structure can be efficiently identified as possible ferromagnetic materials using our high-throughput, ML-assisted framework. This workflow based on the combinatorial strategy allows us to rapidly capture the composition-structure-magnetic property map across a broad compositional landscape of novel magnetic materials.

Autonomous labs enable the integration of automated experiment execution, data analysis and decision making. The main challenge remains the integration of diverse data streams from multiple instruments, where the data is often heterogeneous and unsynchronized. The standard learning process of undetermined synthesis-process-structure-property relationships (SPSPR) usually relies on post-experiment analysis after data is fully collected, not during live experiments, and decision making is carried out independently across characterization equipment. Here, we demonstrate the Multi-instrument Autonomous Discovery (MAD) framework – combining structural property mapping and functional property optimization simultaneously in a closed-loop manner. As an example, we applied MAD to phase change memory (PCM) materials, and, in particular on the Mn-Sb-Te ternary, a previously unexplored materials system for PCM. A multi-output model is employed to merge data from x-ray diffraction (XRD) and electrical resistance measurements simultaneously through a co-regionalization kernel that models the relationship between them. The output probabilistic posterior and uncertainty quantification facilitate decision making with shared knowledge, while the goals are different across tasks. We aimed to maximize the knowledge of crystal structure distribution using non-negative matrix factorization (NMF), while in parallel, we find the composition with the maximum resistance value, an important figure of merit for PCM. Leveraging MAD, we found promising electrical PCMs and identified the SPSPR within 25 closed-loop iterations, corresponding to a seven-fold speed-up. The framework opens a new path of study in large-scale autonomous facilities, where future experiments can be run in parallel together, not independently.

High-pressure experiments on Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi-2212) have reported apparently conflicting evolutions of the superconducting transition temperature $T_c$, ranging from weak enhancement to strong suppression and even a proposed second superconducting dome. To clarify the origin of these discrepancies, we combine first-principles density functional theory calculations with a pressure-dependent low-energy bilayer model solved by the slave-boson mean-field method together with a Berezinskii-Kosterlitz-Thouless estimate of phase coherence. Our results show that hydrostatic pressure induces a pronounced self-doping effect in Bi-2212: holes are transferred from the Bi-O charge-reservoir layers to the CuO$_2$ superconducting planes, leading to a systematic increase in the effective CuO$_2$-plane hole concentration $\delta_x$. At the same time, pressure enhances the pairing scale through the renormalization of the hopping and superexchange parameters. As a consequence, the pressure evolution of $T_c$ is governed by the competition between pressure-enhanced pairing and pressure-driven motion along the common $T_c$-$\delta_x$ dome, making $T_c(P)$ highly sensitive to the initial doping state. Even samples with very similar ambient-pressure $T_c$ but slightly different initial doping can therefore display qualitatively different pressure responses. This provides a unified interpretation of a large part of the disparate high-pressure behavior reported for Bi-2212 and suggests that slightly underdoped samples are more favorable than ambient-pressure optimal samples for achieving improved superconducting performance under pressure.

Spintronics has advanced through discoveries of various electrically-driven spin dynamics in nanomagnets. Here, we report a novel switching dynamics of spin systems driven by spin-orbit torque, using a noncollinear antiferromagnetic nanodot. With electric pulses spanning a wide range of durations and amplitudes, we find an unconventional insensitivity of a threshold current density to pulse duration in switch-back events. This observation is attributed to a previously unrecognized process, in which the noncollinear antiferromagnetic order undergoes multiple rotations before completing reversal, a phenomenon we term multi-rotational switching. Our theoretical analysis reveals that multi-rotational switching arises from the interplay of three key factors: current-driven coherent rotation of the noncollinear antiferromagnetic order, field-induced reorientation of the uncompensated net magnetization, and thermal fluctuations. These findings establish a microscopic mechanism governing current-induced switching in noncollinear antiferromagnets, a topic of growing interest for next-generation spintronics technologies, opening a new route to controlling antiferromagnetic order in nanodevices.

We give an exact form of the density matrix of the spin-1/2 Kitaev spin liquid represented in terms of spin operators and study the entanglement structures of the Kitaev honeycomb model within the spin framework. We show that the density matrix is naturally organized by equivalence classes of string operators associated with the underlying gauge structure of the model. With the explicit form of the density matrix, plus the exact Gauss law of the emergent gauge theory and the exact 1-form Wilson symmetry in the Kitaev model, we demonstrate the existence of the underlying symmetry-resolved block-diagonal structure of the reduced density matrix, which gives rise to the extensive degeneracy in the entanglement spectrum. The block-diagonal structure is then proven to be responsible for the separability of the entanglement entropy into the gauge and matter parts. Furthermore, we extend the formalism to subsystems with an odd number of lattice sites, revealing a relation between the entanglement spectrum and the fermion parity that is seldom mentioned in the literature.

We performed high-precision magnetization measurements up to 120~T on three compositions of the newly discovered kagome antiferromagnet YCu$_3$(OD)$_{7-x}$Br$_{2+x}$ (YCOB), revealing a previously unobserved 5/9 fractional magnetization plateau. All YCOB samples with different Br$^-$ concentrations exhibit nearly identical magnetization curves below 60~T, whereas the 5/9 plateau appears at markedly different fields in the ultrahigh-field regime. By modeling the experimental data using tensor-network calculations, we derive the effective spin Hamiltonians for the YCOB family with three spatially anisotropic Heisenberg couplings (the 3$J$-type model), which quantitatively reproduces the measured magnetization processes and captures the composition-dependent evolution of the 5/9 plateau. Furthermore, our theoretical analysis suggests the emergence of a spin supersolid phase in the field window between the 1/3 and 5/9 plateaus, which is sensitive to spin exchange parameters and accounts for the significant variation in the critical fields of the 5/9 plateau observed among different YCOB compositions.

We report the theoretical prediction and experimental observation of a new class of four-dimensional (4D) tensor singularities and their three-dimensional (3D) Euler-class descendants, protected by chiral and spacetime inversion symmetries on a superconducting circuit platform. The 4D point-like singularity/monopole, characterized by the Dixmier-Douady class of a real bundle gerbe associated with tensor gauge fields, is observed to evolve into a nodal ring carrying an additional first Euler class charge under symmetry-preserving perturbations. Dimensional reduction reveals 3D Euler and Euler curvature dipoles, exhibiting nontrivial Euler topology and a topological sum rule that ensures zero-energy flat bands inherit nontrivial topology even without interactions. Crucially, these high-dimensional degenerate systems are mapped and reconstructed using a hybrid analog-digital protocol designed for non-Abelian quantum geometry measurement within a superconducting qubit array. Our work not only expands the family of topological monopoles but also establishes a robust experimental framework for exploring high-order gauge theory and real-bundle topology across diverse quantum platforms.

Thermodynamic extensivity is commonly introduced as a postulate – the homogeneity of degree one in thermodynamic potentials. We provide a constructive derivation of this property from microscopic conditions on the pair potential, without assuming it. Working with the one- and two-particle reduced densities of the $N$-body canonical Gibbs state, we introduce a combined coarse-graining operator $\mathcal{C}$ on single-particle phase space $\mathcal{M}=\Lambda\times\mathbb{R}^3$, producing dimensionless mesoscopic probabilities over spatial–momentum cells $\{V_i\times\Pi_\alpha\}$. Under three conditions on the pair potential – stability, temperedness, and exponential cluster decomposition with correlation length $\xi$ – we show, using the Ursell cluster expansion, that the coarse-grained entropy satisfies \[S_{\mathrm{CG}}=\sum_i S_i+O\!\left(\frac{|\Lambda|}{\ell^d}e^{-\ell/\xi}\right),\] where $\ell\gg\xi$ is the cell diameter. The correction is exponentially suppressed per cell, making entropy additive and recovering the thermodynamic limit of Ruelle and Fisher in explicit operator language. For systems with long-range interactions, where temperedness fails, the correction does not vanish, and non-additivity is quantified through inter-cell mutual information. We further show that spatial averaging does not commute with nonlinear thermodynamic functionals such as the entropy density – a thermodynamic analogue of the cosmological averaging problem – and we derive the generalised Euler relation with explicit surface corrections.

Anderson localization is fundamentally controlled by dimensionality, yet the nature of the Anderson transition in continuously tunable noninteger dimensions remains largely unexplored. Here, we introduce a family of three-dimensional fractal lattices with continuously tunable spectral dimension $d_s\in[2,3]$, providing a controlled platform for studying localization physics beyond integer dimensions and across the lower critical dimension $d_s=2$. Using large-scale finite-size scaling analysis, we systematically investigate the Anderson transition and identify mobility edges throughout the fractal family. The critical disorder strength evolves continuously from $0$ to $16.6$ as the spectral dimension increases from $2$ to $3$. We show that the spectral dimension predominantly governs the universality class of the transition, while the precise critical point is additionally influenced by microscopic geometric details of the underlying fractal lattice. The critical exponent exhibits an approximate inverse dependence on $d_s$, providing quantitative insight into scaling theory in noninteger dimensions. Our results establish tunable fractal lattices as a versatile framework for exploring localization and quantum critical phenomena beyond conventional integer-dimensional systems.

Hilbert-space fragmentation provides a mechanism for ergodicity breaking in quantum many-body systems even in the absence of disorder, leading to dynamically disconnected sectors and strong memory of initial conditions. However, identifying such structures is often challenging and typically relies on prior knowledge of conservation laws or model-specific analytical insight. Here we introduce an unbiased approach based on spectral graph theory and, within this framework, formulate the concept of nearly fragmented systems, in which perturbative processes couple otherwise fragmented sectors while preserving their dynamical imprint. By representing basis states as vertices and Hamiltonian matrix elements as edges, we map the connectivity structure of the many-body Hilbert space onto a graph and analyze it using tools such as the Laplacian spectrum, Fiedler vectors, and modularity. Exact fragmentation corresponds to disconnected graph components, while nearly fragmented systems manifest as weakly connected communities whose structure can still be resolved spectrally. Applying this framework to the one-dimensional $t$-$J$ model and its perturbations, we demonstrate that graph-theoretic diagnostics reliably identify both fragmented and nearly fragmented Hilbert-space structures and capture the hierarchy of dynamical time scales that governs the system's evolution. We further show that the method extends beyond kinetically constrained models by applying it directly to the Hubbard chain, where it reveals the emergence of nearly decoupled subspaces associated with doublon dynamics and spin configurations. Our results establish the spectral graph analysis as a general and scalable tool for diagnosing fragmentation and approximate dynamical constraints in complex quantum many-body systems.

Hydrodynamic heat flow, where out-of-equilibrium phonons collectively drift in response to a temperature gradient, has attracted renewed interest following its experimental observation in graphite from cryogenic to room temperatures. To rapidly screen for other materials exhibiting this unconventional non-Fourier regime, the computationally inexpensive thermal conductivity ratio $\kappa_{LPBE}/\kappa_{RTA}$ obtained from a complete solution of the linearized Peierls-Boltzmann equation (LPBE) for phonon transport and the relaxation time approximation (RTA) for phonon decay, has often been used as an indicator for phonon hydrodynamics. Yet, a clear connection between $\kappa_{LPBE}/\kappa_{RTA}$ and the signatures of drifting hydrodynamic phonon populations has not been established in the literature. Here we show that $\kappa_{LPBE}/\kappa_{RTA}$ directly correlates with the microscopic hydrodynamic signatures arising from the spectral properties of the phonon collision operator, which is often computationally expensive to compute, thus establishing the former as a reliable low-cost indicator for phonon hydrodynamics. On the other hand, other indicators in the literature that are derived only from the phonon scattering rates do not correlate with $\kappa_{LPBE}/\kappa_{RTA}$, and so, are inadequate to predict phonon hydrodynamics. Our study also reveals that $\kappa_{LPBE}/\kappa_{RTA}$, and therefore the strength of hydrodynamic signatures, decrease with increasing Brillouin zone (BZ) sampling density for several ultrahigh-$\kappa$ materials at low temperatures, thus underscoring the need for careful BZ sampling for robust predictions of phonon hydrodynamics. Our work justifies the use of $\kappa_{LPBE}/\kappa_{RTA}$ as a computationally inexpensive indicator of phonon hydrodynamics, thus enabling accelerated search for new materials that exhibit such unconventional heat flow regimes.

We investigate the transport properties of a superfluid Fermi gas confined in a ring trap with a moving potential barrier across the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover. Employing time-dependent Bogoliubov–de Gennes (BdG) equations, we simulate the dynamics of a Josephson junction biased by both DC and AC currents. Over a wide range of interaction strengths, the barrier-velocity dependence of the chemical potential difference exhibits low-order plateau structures, consistent with Shapiro steps, with fitted levels close to integer multiples of $\hbar\omega/2$ within the phase-coherent regime. This factor of $1/2$ reflects our convention of defining the chemical potential per single fermion in the BdG framework. Microscopic analysis reveals that these fundamental steps originate from synchronized phase slips mediated by periodic soliton generation at the barrier. Our findings clarify the role of interaction regimes in the nonequilibrium phase dynamics of ring-trapped fermionic superfluids and provide microscopic insights relevant to future studies of atomtronic systems with nontrivial topology.

We investigate the interplay of geometric symmetry, size, and external magnetic fields in regulating individual skyrmion states within magnetic nanostructures. By analyzing nanodisks, nanosquares, and nanorectangles, we demonstrate that rotational symmetry in nanodisks enables rich topological phase transitions, from ferromagnetic states to skyrmions, skyrmioniums, and multi-states, as their diameter increases. In contrast, square and rectangular structures exhibit suppressed topological complexity due to corner-induced demagnetization effects and reduced symmetries. Under perpendicular magnetic fields, nanodisks show field-driven transitions between skyrmionium and skyrmion states. By leveraging asymmetry, square and rectangular nanostructures stabilize skyrmions over a broader parameter range than nanodisks. These findings highlight geometric symmetry as a critical design parameter for tailoring skyrmion stability and functionality in spintronic applications such as multi-state memory and reconfigurable logic devices.

Single-channel resonances are fundamental processes in scattering of atoms, yet their occurrence is largely incidental and lacks systematic control. In this Letter, we propose a mechanism to realize a continuously tunable single-channel resonance by controlling the temperature of the heteronuclear mixture. By extending the Casimir-like mediated interaction to finite temperature, we demonstrate that thermal smearing of the Fermi surface reshapes the effective potential between impurities, giving rise to a temperature-controlled resonance (TCR) over a wide parameter range. As a direct consequence, the resonance position shifts systematically with temperature variation, providing a clear experimental signature of this mechanism. We further investigate the quench dynamics of a Bose gas immersed in a Fermi sea and demonstrate that the observed temperature-dependent loss features in recent experiments are consistent with the TCR mechanism. Our results establish temperature as a simple and experimentally accessible control knob for single-channel resonances in ultracold quantum gases.

We review the theoretical development and modern applications of the Evans-Sackmann hydrodynamic model for lateral transport in supported fluid membranes. We first cover the original formulation, emphasizing the linear momentum decay term that captures membrane-substrate coupling mediated by a thin lubricating fluid layer. This coupling term enables quantitative interpretation of tracer diffusion measurements in supported bilayers. Building on this foundation, we survey theoretical extensions that relax standard boundary conditions at the inclusion perimeter, where inclusions refer to embedded objects such as proteins, lipid domains, or tracer particles within the membrane. We discuss the drag of a disk and a liquid domain, as well as the dynamics of membrane phase separation. We further highlight how the supported-membrane mobility tensor serves as a unifying tool for systematic treatments of correlated diffusion, polymer dynamics, phase separation kinetics, and many-body interactions in quasi-two-dimensional environments. Finally, we discuss recent extensions to active and chiral membranes, where odd viscosity provides a transverse hydrodynamic response and offers a possible route for detecting chirality in two-dimensional fluids.

The quantum Mpemba effect concerns with anomalous relaxation of quantum states that evolves either under unitary or non-unitary dynamics. In the context of open quantum systems, while most studies focus on quantum states evolving under completely positive trace-presing dynamics described by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, we demonstrate that an analogous effect can arise at the level of operators. In particular, we show that operators that evolves under the adjoint Liouvillian – despite not being a trace-preserving map – can still exhibit a genuine Mpemba effect. We derive general conditions under which this phenomenon can occur and validate our predictions for three different open quantum setups. Our results broaden the scope of the Mpemba effect in quantum systems and provide a framework for controlling the relaxation of physically relevant observables.

There is considerable current interest in the emergence of statistical correlations within a population of otherwise non-interacting Brownian particles subject to a common fluctuating environment or drive. Examples include global stochastic resetting, switching confining potentials, fluctuating diffusivities, and stochastically gated boundaries. Most studies have focused on the analytical structure of the stationary joint probability density (assuming it exists). In this paper, we extend previous work on the exit statistics of multiple particles in stochastically gated domains to the case of global resetting in an interval with absorbing boundaries at both ends. First, we use a generalised Itô's lemma to derive a hierarchy of boundary value problems (BVPs) for the joint splitting probability that all particles exit from the same end of the interval. The BVPs form a nested sequence with respect to the initial number of particles $M$. We explicitly solve the BVP for a pair of particles ($M=2$) and use this to illustrate the emergence of pairwise correlations. Second, we show how the BVP for the splitting probability of $M$ Brownian particles can be mapped onto the $M$th order moment equation of a stochastic diffusion equation with resetting. We thus establish a general mathematical framework to study exit problems for globally-driven particle systems.