Papers

Synchronization is a collective phenomenon in which interacting nonlinear oscillators develop a persistent relation between their phases and frequencies. In quantum systems, its description requires connecting the classical dynamics of limit-cycle oscillators with quantum fluctuations, dissipation, and the notion of phase. In this tutorial review, we offer a systematic framework for analyzing synchronization in classical and quantum dynamical systems. Starting from amplitude-phase dynamics, we introduce successively topics of relevance, such as phase locking, the Adler equation, Arnold tongues, and the Kuramoto model, and use these concepts to analyze coupled oscillators and their stability. We then formulate the corresponding description for quantum limit-cycle oscillators using Lindblad master equations and phase-space methods, with explicit examples of two and many coupled oscillators. We further discuss noise, synchronization measures, and the extreme quantum regime, including synchronization in spin systems. The emphasis throughout is on analytical derivations and a practical methodology for identifying synchronized states, determining their stability, and characterizing synchronization in quantum systems. The review is designed as a self-contained guide from which we hope that students can learn the essential concepts and techniques, while researchers can readily find the analytical tools and methodological insights needed to approach new synchronization problems.

Pseudo entropy extends entanglement entropy from a single quantum state to a pair of nonorthogonal states and is generally complex. Taking advantage of Cauchy-Riemann equations, Kramers-Kronig relations, and analytic continuation in state parameters, we show how and to what extent real and imaginary parts of pseudo entropy can be derived from ordinary entanglement entropy. For families with holomorphic coefficients in finite-dimensional Hilbert spaces, the reduced transition matrix equals the ordinary reduced density matrix formula evaluated at complex parameters. Then a convergent Taylor series gives the real and imaginary parts of pseudo entropy from even and odd derivatives of entanglement entropy at the real midpoint. The matrix identity also gives formulae for excess pseudo entropy and Renyi entropies, and interpolation formulae for families with polynomial coefficients. We apply these results to boundary-state quenches and thermal states in conformal field theory, and to fermionic and bosonic Gaussian states and quenches. In conformal field theory, Kramers-Kronig relations give the first moment of the imaginary part in terms of the central charge and one-point functions for boundary states.

We prove a lower comparison for disorder-averaged ferromagnetic XY correlations: independent nonnegative random couplings $K_e$ can be replaced by $-\frac12\log\mathbb{E}e^{-2K_e}$. Ginibre's inequality makes each normalized correlation convex in $1-e^{-2K_e}$, so conditional Jensen and thinning compare Bernoulli bond densities; two star-wise Jensen passes handle site dilution on bipartite graphs. Together with the phase-existence theorem of Dario and Garban, these comparisons give local Lipschitz regularity of both the averaged algebraic-phase and susceptibility-divergence thresholds throughout the supercritical density intervals on $\mathbb{Z}^2$. The clean finite-domain criterion of van Engelenburg and Lis also yields explicit finite-size susceptibility lower bounds in a weak-dilution region. For bounded centered bond noise, the possible suppression of the algebraic-phase temperature is at most quadratic in the noise amplitude. Finally, at finite positive thresholds we prove total-variation continuity for bounded iid coupling laws whose essential supremum equals the common support cap, with local Lipschitz control when the reference law has an atom at that cap.

We formulate a Maxwell-Jüttner averaged extension of relativistic nonaffine shear-viscosity theory for a classical gas of massive particles. The starting point is the relativistic nonaffine response formula derived from generalized Langevin dynamics, where proper-momentum dissipation produces a Lorentz-factor enhancement of the viscosity. Since a thermal relativistic gas is not characterized by a single Lorentz factor, we replace this scalar enhancement by an equilibrium momentum average over the Maxwell-Jüttner distribution. Within the scalar transverse mean-field closure used in this work, the minimal relativistic correction is the Maxwell-Jüttner mean of the Lorentz factor and becomes a finite-mass enhancement function of $\zeta=mc^2/(k_BT)$. In the general closure, the averaged object is the full product of the Lorentz factor, the zero-frequency memory kernel, and the nonaffine affine-force correlator. This construction separates kinematic relativistic enhancement from dynamical dissipation encoded in the bath memory and collective mode spectrum. We derive the nonrelativistic and ultrarelativistic limits, show that a specified effective hard-sphere scaling reproduces the classical square-root law as a consistency test, and identify the assumptions under which a cubic high-temperature law follows. Comparison with relativistic kinetic-theory examples clarifies that the memory kernel is not equivalent to a relaxation time unless a microscopic closure is specified. Retaining the full frequency dependence instead yields a relaxation spectrum. A single dominant pole reduces this spectrum to one shear relaxation time and gives the usual transient shear equation.

Scale-invariant avalanche dynamics are commonly associated with criticality and robust, universal size exponents. Dissipation is generally expected to drive the system away from the critical point, progressively suppressing large events. The Olami–Feder–Christensen (OFC) model challenges this picture: in its non-conservative regime, the avalanche-size exponent is non-universal and can exceed the mean-field value $\tau=3/2$, while system-spanning events persist even at large dissipation. Here, we show that these apparently anomalous features are also observed experimentally in a two-dimensional granular system displaying scale-invariant avalanche dynamics. By increasing interparticle friction, and therefore dissipation, the avalanche-size exponent increases from $\tau=1.58$ to $\tau=1.83$, while the upper cutoff remains proportional to the system size. We further identify similarities between experiment and the OFC model in their memory effects, local dynamics, and the emergence of better-than-random predictability of large events. The latter indicates that the system does not remain permanently critical, but instead evolves through configurations with different propensities to generate extreme events. Our results suggest that OFC-like dynamics are not merely an anomalous feature of a particular model, but may provide a relevant framework for understanding scale-invariant dynamics with $\tau>3/2$ in real dissipative systems.

Buckled colloidal monolayers constitute a versatile soft-matter platform for engineering artificial spin lattices, with each particle serving as a single Ising spin. While the average Ising coupling energy has been approximately derived for perfect particle lattices, extracting the complete set of coupling parameters from real samples remains inaccessible. Here, we apply an inverse method to reconstruct all nearest-neighbor effective Ising coupling energies from measured colloidal spin configurations. We design multiple experimental protocols to control the thermodynamic state of the colloidal system, from isotropic compression and shear deformation to modulation of interparticle attraction, each giving rise to distinct spin configurations. Using spin configuration data, we reconstruct all nearest-neighbor effective Ising coupling energies using maximum likelihood estimation. To assess inference reliability without ground-truth model parameters, we propose to use the convergence of the standard deviation of the estimated couplings as a practical, ground-truth-free criterion, and validate its reliability using simulation data with known parameters. The extracted spatially resolved couplings reveal how each control protocol influences the sign, magnitude, statistical distribution, and spatial arrangement of the microscopic coupling parameters: isotropic compression strengthens antiferromagnetic couplings and enhances quenched disorder; shear deformation generates direction-dependent anisotropic couplings; and increased interparticle attraction drives a crossover from antiferromagnetic to paramagnetic and then to ferromagnetic couplings. This work establishes a practical inference framework for estimating effective model parameters of colloidal artificial spin lattices.

We analyze how an arbitrary observation mask on a finite periodic ring of equally spaced sensors affects the posterior covariance, Fourier-mode coupling, and normalized posterior trace in Gaussian-process reconstruction. Under a rotationally stationary prior and homogeneous independent measurement noise, complete observation gives independent scalar posterior formulas for the Fourier modes. For an arbitrary mask, however, the matrix $Q_M=F D_MF^\ast$ is generally non-diagonal; its off-diagonal entries are finite Fourier components of the realized mask and couple modes in the posterior precision. Consequently, masks with the same unavailable-channel fraction can have different normalized posterior traces because their geometries differ. A dimensionless 64-channel synthetic benchmark illustrates this finite-matrix effect. A circumferential array of equally spaced wall-mounted microphones at a fixed axial station of a circular fan or compressor duct provides one concrete mechanical-engineering interpretation: failed, saturated, corrupted, or dropped-out channels form the observation mask. The analysis is a finite-dimensional reference calculation under the stated rotational-stationarity and common-noise assumptions, not a performance claim for a nonuniform or unequally instrumented operating duct.

Nonreciprocal many-body dynamics can develop a swap phase characterized by spontaneous global oscillations far from equilibrium. To determine how local nonreciprocal interactions predict global oscillations and how broadly this prediction applies, we compare mean-field theory, independent-node theory, and nearest-neighbor spin-coupling theory for a two-spin nonreciprocal Ising model on networks of fixed coordination number (\(z=4\)). Nearest-neighbor spin-coupling theory retains nine independent joint edge probabilities. Monte Carlo benchmarks show that it predicts the oscillation amplitude, angular momentum, and period on edge-swapped networks with a 2.1% aggregate mean absolute relative error. We then extend the square lattice to degree-preserving edge-swapped networks and find sharply different behavior. With increasing system size, the oscillation amplitude and angular momentum decay strongly on the periodic square lattice but remain nearly size independent on edge-swapped networks. These results show that identical local parameters do not determine the macroscopic phase. The contrasting finite-size trends identify network geometry as a key determinant of collective oscillations at fixed local interaction parameters.

We propose a new product entropy, defined as the Rényi (or von Neumann) entropy of a normalized product operator constructed from two density matrices. We establish a duality showing that the SVD entanglement entropy of a subsystem for two pure states is exactly equivalent to the product entropy of the complementary subsystem. This connection provides both a transparent physical interpretation in terms of the spectral diversity of the subsystem state product and a computationally efficient route that bypasses the reduced transition matrix. For low-lying eigenstates, we derive analytical expressions for the subsystem product entropy between the ground state and primary excitations in two-dimensional conformal field theories, explicitly verified against the critical Ising chain. In quantum quench dynamics, the quasiparticle picture yields time evolution in the scaling limit: following a global quench, the subsystem product entropy exhibits distinct sequences of thermalization and revivals, whereas under a local operator quench, it develops characteristic plateaus whose constant values are determined by the inserted operator. Extensive numerical calculations on the critical Ising chain confirm the analytical predictions with excellent accuracy.

Recent studies have shown that classical LiF simulations can reproduce low-temperature experimental spectra when performed at a simulation temperature $T^*$ higher than the physical temperature $T$. We show that the characteristic scale of this rescaling follows naturally from quantum vibrational statistics. An effective temperature $T_{\rm eff}(T)$ is obtained by matching classical and quantum harmonic energies and is evaluated using an analytic acoustic-optical model and a first-principles LiF vibrational density of states $D(\varepsilon)$. The resulting temperature reproduces the low-temperature scale of the reported spectral temperature and approaches the physical temperature in the classical regime. Our results identify zero-point motion and Planck-Bose-Einstein statistics as the origin of the reported temperature scale.

Open quantum systems describe quantum systems that interact unavoidably with their environments. These notes introduce the physical origins of decoherence and dissipation in realistic settings, developing the theoretical framework of reduced dynamics and quantum master equations within the connection to thermodynamics in the quantum regime. Additionally, a set of relevant exercises are proposed to reinforce the acquisition of knowledge. The text equips readers with the tools to model and analyze open quantum dynamics.

We investigate the thermodynamic geometry of an ideal quantum gas obeying inclusion statistics, characterized by a negative statistical parameter $g < 0$. In this framework the grand-canonical partition function admits a finite maximum fugacity, and the thermodynamic scalar curvature $R$ is strictly positive for all $g < 0$, reflecting effective attractive statistical interactions analogous to those of a bosonic system. As the fugacity approaches its maximum value, $R$ diverges, signaling a phase transition of the Bose-Einstein condensation type. A key distinction from the ordinary ideal Bose gas is that the condensation temperature is elevated relative to the bosonic case, and finite-temperature condensation occurs even in the dimensional regime $1/2 < D/\sigma \leq 1$ where standard bosons do not condense, while for $D/\sigma \leq 1/2$ the transition temperature vanishes. Three independent criteria; divergence of $R$, the maximum fugacity singularity, and the non-analytic cusp in the specific heat, coincide at the same condensation point, confirming the thermodynamic consistency of the transition.

We consider two canonical market-microstructure regularities: the long-memory of trade signs and the square-root law of meta-order impact. The point is not to propose new empirical laws, but to separate the clocks on which existing laws are defined. The sign-memory law is an event-time statement about the ordering and fragmentation of hidden orders. The square-root impact law is an operational-time statement about front motion in a locally linear latent order book. Starting from a discrete-time random-walk bid/ask reaction–diffusion order book with a separate event clock, we identify an event-time imbalance reduction, derive the operational-time front and impact equations in the locally linear regime, and then subordinate both sign and impact observables to calendar time. Fractional or tempered clock effects enter through this event-to-calendar projection, not through a different operational-time impact mechanism. This gives a compact clock-aware framework in which event-time sign persistence, operational-time square-root impact, and anomalous calendar-time effects appear as distinct but compatible consequences of a common order-book representation.

We study the far-from-equilibrium dynamics of domain-wall initial states in the integrable lattice Landau–Lifshitz spin chain. Building on the linear spin-wave description of domain-wall spreading, we derive the long-wavelength magnon dispersion directly from the microscopic integrable Hamiltonian and use it to characterize the propagation and broadening of the resulting wavefronts. The dispersion interpolates between a quadratic form at the isotropic point and a linear form in the easy-plane regime. In the isotropic limit, the quadratic dispersion leads to diffusive broadening, whereas in the easy-plane regime the domain-wall front propagates ballistically. Keeping the leading nonlinear correction to the linear dispersion gives a cubic dispersive term, which produces a characteristic $t^{1/3}$ broadening of the ballistic front. We further show that the sign of this cubic correction changes at a critical anisotropy, leading to a reversal of the dispersive wake from trailing to advancing. The resulting critical point occurs at $\Delta_c=1/7$, corresponding to $\gamma_c\simeq 1.047$. Numerical simulations of the full nonlinear spin dynamics confirm the analytical scaling and demonstrate the coexistence of the amplitude-independent spin-wave front with amplitude-dependent nonlinear soliton propagation.

It is now well-established that classical statistical mechanics emerges from the entanglement structure of quantum chaotic systems, as quantified by the (subsystem) eigenstate thermalization hypothesis (ETH). While this statement rests on the well-studied bipartite entanglement of the eigenstates of such systems, recent years have shown that many-body states are often characterized by multipartite entanglement, raising the question: what are the universal multipartite entanglement features of chaotic eigenstates? We answer this question in part by studying a tripartite generalization of the ergodic bipartition ansatz through the lens of two tripartite entanglement probes, the Rényi tripartite multi-entropy and the Rényi reflected entropy. We derive leading-order analytical expressions for the ensemble averages of both quantities using a saddle-point analysis. Beyond these measures, we obtain the average of the Rényi-2 reflected density matrix, $\rho_{AA^*}^{(2)}$,which controls the Rényi-2 reflected entropy. We show that $\rho_{AA^*}^{(2)}$ in a chaotic eigenstate is well-described by this ensemble average which, unlike an ordinary reduced density matrix, takes three qualitatively distinct forms across subsystem-size regimes, which may be viewed as a tripartite generalization of subsystem ETH. We benchmark our analytical predictions against exact diagonalization of the mixed-field Ising model.

We study the bulk phase behavior of a polydisperse liquid crystal fluid made of biaxial boards with restricted orientations using both fundamental measure theory and Monte Carlo computer simulations. The continuous polydispersity is included in the intermediate particle length of the boards via a truncated Schulz distribution. By calculating several phase diagrams across a range of polydispersity coefficients, we find that polydispersity (i) enhances demixing between two uniaxial nematic phases and (ii) expands the stability region of the biaxial phase. Although metastable with respect to non-uniform phases, we identify certain mixtures exhibiting two-phase coexistence paths involving uniaxial-uniaxial and uniaxial-biaxial phase separations. Whether these paths can be completed depends on the precise shape of the parent distribution function. Monte Carlo simulations performed for a representative case exhibit the same phase diagram topology predicted by theory, thereby validating the theoretical approach. The main difference between both approaches lies in quantitative agreement, with simulated phase transitions systematically occurring at higher packing fractions than those predicted theoretically. Our combined theoretical and simulation results may prove relevant to the design and interpretation of sedimentation experiments on colloidal suspensions of polydisperse anisotropic particles.

How rapidly does order give way to randomness, and can quantum coherence accelerate this process? We address these questions through the paradigmatic problem of card shuffling, formulated as a random walk on the symmetric group $S_n$. We first recast the random-transposition walk studied by Diaconis and Shahshahani, as well as more general walks generated by conjugacy classes of $S_n$, in continuous time. We then identify the transition matrix of each classical walk with a permutation Hamiltonian generating a corresponding unitary quantum walk. Purely unitary evolution, however, does not generically converge to the uniform distribution in the classical sense of mixing: coherence preserves information rather than erasing it. We therefore embed the problem into a quantum stochastic walk, where coherent dynamics competes with the dissipative process responsible for classical mixing. In this setting, quantum coherence assists randomization. We prove that it can only decrease the distance from the uniform distribution in the computational basis and can therefore accelerate mixing. An analysis of the slowest mode yields a criterion for the coupling strength required to produce an appreciable speedup. Finally, numerical results reveal a scaling collapse of the ratio between quantum and classical mixing times onto a simple one-parameter form. Our results illustrate how coherence and dissipation can cooperate in the emergence of randomness in walks on permutation groups.

Sequential circuits provide an optimal linear-depth route to unitarily preparing long-range ordered quantum states, but circuit-level noise can be far more damaging than noise applied after preparation: local errors may be propagated by subsequent gates into nonlocal defects that destroy the target order. In this work, we present classes of unitary sequential circuits that prepare certain non-trivial orders in the presence of Pauli noise. Our constructions exploit the spatial structure of the syndromes of the target state, which in certain cases allows us to systematically suppress the propagation of errors using strictly local gates. The strategy can be applied both to symmetry-breaking order, for which we present a 3D example, and to topological order, which we showcase on a 4D version of the toric code. We also highlight how this stability against errors necessitates non-Clifford gates, and how measurement-feedback loops can be used to stabilize lower-dimensional states as well.

We determine the conditions under which the nonlinear Maxwell-Cattaneo theory of charge transport admits a local Gaussian Schwinger-Keldysh embedding with a particular modified dynamical KMS symmetry. We show that treating the additional vector as intrinsically dissipative fundamentally modifies the entropy-current analysis: the hydrostatic generating functional no longer fixes all entropy-current improvements, which must instead be supplied independently. Subsequently we discuss the additional constraints not contained in the hydrodynamic analysis that are imposed by the modified KMS transformation becoming a symmetry of the action. We both interpret and supply the corresponding stochastic quasi-hydrodynamics.

We introduce a general mechanism for engineering moment-selective temporal designs with hierarchically structured aperiodic drives. At special control settings where the driven dynamics is constrained by a finite symmetry group, lower-order moments can already reproduce Haar statistics while a selected higher-order deviation remains nonzero. A small static detuning from such a setting generically produces an exponentially long lifetime whose exponent scales inversely with the square of the detuning. We illustrate this mechanism in qubit systems through exact Fibonacci and silver-mean constructions with tetrahedral and icosahedral resonances, for which the first retained non-Haar moments occur at orders $3$ and $6$, respectively. We further show that stochastic control fluctuations produce a qualitatively different cutoff from coherent detuning. Finally, we propose a finite-time signature of the long-lived moment that can be measured without requiring observations over exponentially long times.

We introduce an on-lattice minimal model of two-dimensional melting, a clock model with vacancies with control parameters temperature, chemical potential and external field. We study the full phase diagram using cluster Monte Carlo, Tensor Network Renormalisation Group and selfconsistent mean field methods. A non-universal ensemble of melting scenarios is observed including the KTHNY scenario of two Berezinskii-Kosterlitz-Thouless phase transitions delimiting a quasilong-range ordered phase. The upper transition evolves into first-order transition in analogy with simulations on hard and soft discs and at low chemical potential there is a single transition between ordered high density and disordered low density phases. The evolution is via a special tricritical point that is accessed in detail. This work therefore provides a framework for understanding the crossover between 2D melting scenarios and offers insights into the behavior of realistic systems.

Magic, or nonstabilizerness, is the resource that promotes stabilizer operations to universal quantum computation. For bipartite pure states, its component intrinsic to the correlations between the subsystems, the nonlocal magic, is obtained by minimizing a magic measure over local unitaries. For the stabilizer Rényi entropy (SRE), the minimum is conjectured to be attained by the computational-basis (CB) representative, the state obtained by assigning the Schmidt coefficients in decreasing order to matching computational-basis labels. We prove this conjecture for two families of states at every system size and bipartition: states with dyadic-staircase Schmidt spectra and states of Schmidt rank at most six. For arbitrary bipartite pure states, we show that the CB value exceeds the nonlocal SRE by at most $4$, fixing the leading term of any divergent scaling of nonlocal SRE. We further show that the nonlocal SRE grows at most logarithmically with the entanglement entropy. Consequently, one-dimensional area-law states have bounded nonlocal SRE, while critical states with logarithmic entanglement entropy permit at most doubly logarithmic growth with system size. We apply these results to the transverse-field Ising chain, where we tightly bound the nonlocal SRE in the gapped phases and identify its double-logarithmic growth at criticality.

We describe how strong vorticity fluctuations appear in three-dimensional incompressible turbulence driven by a large-scale random force. By combining analytical and numerical methods, we construct a vorticity instanton: the most probable force history driving the flow to a prescribed large vorticity at a given point and time. We show how the smooth, large-scale force produces a long vortex filament with a thin, viscous-scale core. Our main finding is that the standard mechanism of amplifying a vortex tube through radial compression and axial stretching is only effective up to a threshold value. Producing vorticity above the threshold requires an additional ingredient: vorticity waves propagating along the tube. The final vorticity is the result of two colliding waves. This mechanism has striking similarities to the one recently suggested by OpenAI for creating infinite vorticity in finite-time Navier–Stokes blow-up.

Urban street networks are modeled as spatial graphs whose geometry reflects planning, history, and physical constraints. Global orientation measures describe the overall order of a city but do not reveal how street directions form coherent neighborhoods. Here we introduce bearings communities—spatially connected domains whose streets share a common orientation—and analyze them using concepts from the physics of polycrystalline materials. Across $1025$ large cities worldwide, these domains are almost perfectly ordered: their mean coherence is $0.964$ and varies by only $1.4\%$ from one city to the next, far above the value expected for randomly oriented streets. Every city is therefore a mosaic of well-ordered orientational grains, differing only in their number, size, and mutual alignment. Because the grains are equally regular everywhere, a city's global order is set mainly by how many of them it averages over: a city appears ordered because it is built from a few large grains, not because its fabric is locally more regular. A null model in which grain orientations are randomized confirms this grain-counting mechanism. Finally, the interface fraction $\gamma$ measures how strongly domains interlock, yielding a morphology diagram that organizes cities continuously between grid-like, polycrystalline, and fragmented limits.

As a simple model of interacting systems of excitable degrees of freedom, we consider a threshold contact process on various lattices and networks, in which a successful activation event requires the presence of more than one active neighbors. We show by combining numerical simulations and a phenomenological theory that, in the two-phase coexistence region and for a sufficiently low initial activity, a slower-than-exponential temporal decay of the global density emerges, caused by the spontaneous formation of slowly vanishing and non-communicating clusters of activity. This slow-decay phenomenon is found to appear generally for regular lattices and also for finite-dimensional random lattices such as the Voronoi-Delaunay network. However, the slow-decay is impeded by small-world property, as demonstrated by simulations on random-regular networks. In the case of a power-law decay of the order parameter, which is valid among others on two-dimensional regular lattices, our phenomenological theory points out that the decaying state is stable against unbounded nucleation only if the decay exponent exceeds $1/2$. Besides the well-known Griffiths effects of quenched random systems, this slow-decay phenomenon rooted in the threshold condition provides an alternative mechanism of off-critical but scale-free dynamics, occurring also in the absence of disorder.

Time evolution of tensor-network states is a central tool for studying nonequilibrium dynamics in strongly correlated quantum systems. In the past decade, using the time-dependent variational principle (TDVP) discretized by projector-splitting has become the gold standard for evolving matrix product states (MPS) with long-range Hamiltonians. More recently, a conceptually different class of discretizations of the TDVP, the class of Basis Update and Galerkin (BUG) integrators, has been developed within the framework of dynamical low-rank approximation, offering an alternative, more flexible approach. In this work, we formulate two BUG integrators explicitly for MPS. The BUG integrators result in "single-site" MPS integrators that are robust with respect to small singular values, avoid backward-in-time substeps, and naturally allow for the adaptive choice of bond dimensions. We consider the augmented BUG integrator of first order and the midpoint BUG integrator of second order and clarify their relation to the projector-splitting discretization of the TDVP. Using representative models of strongly correlated quantum systems, like the XY spin model with long-range interaction and two-dimensional lattice models of fermions and spins of various lengths, we perform a systematic numerical comparison between BUG and projector-splitting time discretizations of the continuous-time TDVP, focusing on scalability, numerical complexity, and accuracy. We find that BUG integrators, due to their reduced numerical cost and the flexibility of the concept, provide a competitive and, in certain regimes, advantageous alternative to the well-established time-stepping by projector-splitting in TDVP, especially in models with large local dimensions, and in cases where observables are extracted with high temporal resolution.

We consider locally driven-dissipative quantum spins that undergo a continuous weak measurement of their collective spin. We show that such a system can exhibit full spin-synchronization in trajectories corresponding to the same measurement record. Mathematically, we demonstrate that this is a general consequence of the irreducibility of the quantum Markov semigroup generated by the Lindbladian, in combination with a transitive symmetry, in particular spin-permutation symmetry. When breaking the irreducibility, e.g. in the absence of local dissipation, the system can exhibit a weaker form of partial synchronization. Given the general origin, this measurement-induced phenomenon arises in a broad class of many-body systems.

We consider defect conformal field theories (DCFTs) at finite temperature, where a $p$-dimensional conformal defect wraps the thermal circle. Extending the previous study of line defects to defects of general dimensions, we determine the general forms of the thermal one-point functions of bulk scalars, conserved currents and the stress tensor by imposing the residual symmetry and the conservation laws. The low temperature expansion of the thermal one-point functions is shown to be reproduced by the bulk-defect operator expansion, allowing us to read off the thermal one-point coefficients of defect operators. We examine the general results in four classes of examples with free bulk theories: the trivial defect, free scalar and fermion theories with a boundary, the free scalar theory with a localized $\phi$ deformation in $d=2\,p+2$ dimensions and the free $\mathrm{O}(N)$ model with a localized $\phi^2$ deformation in $d=p+2-\epsilon$ dimensions. In the last example with $\epsilon = 1$, where the defect becomes an interface, we find that the thermal one-point functions coincide with those of the free scalar theory with the Dirichlet boundary condition, in accordance with the conjectured factorization of an interface CFT into two decoupled boundary CFTs.

Recent studies of "deep thermalization" have revealed universal physics in quantum many-body dynamics beyond equilibration towards Gibbs states: maximally random quantum state ensembles can emerge on local subsystems, generated by measurements on their complement. In this work, we further identify a new form of universality exhibited in the "finer fingerprints" of quantum dynamics for local subsystems, induced by global unitary time-evolution. Specifically, we consider the projected Kraus ensemble, an ensemble of Kraus operators obtained by unraveling the quantum channel on a small subsystem with respect to knowledge of the classical configurations of its complement. Our central result is a one-parameter random matrix Ansatz that captures the ensemble's emergent statistical behavior along particular spacetime scalings, valid for generic 1D circuit dynamics without conservation laws: the ensemble is described by the product of a complex Ginibre random matrix and an independent log-normal random real scalar. The former encodes scrambling within the subsystem, captured by rotational invariance of the Ginibre measure, whereas the latter encodes fluctuations in the Born probabilities, arising from locality of the underlying dynamics. Our Ansatz can be established in the special cases of dynamics generated by global Haar random unitaries and dual-unitary circuits, while we motivate it for generic circuits using arguments of spacetime duality and the multiplicative ergodic theorem on long products of spatial transfer matrices. Extensive numerical simulations for random and Floquet circuit models verify these predictions. This universality in Kraus operators also provides a microscopic mechanism for deep thermalization in generic 1D quantum circuit dynamics, and has implications for local quantum information recoverability involving classical side information tied to knowledge of the bath.

Chirality, a systematic rotational bias in the motion of a particle, arises in a wide range of physical and biological systems, from charged colloids in magnetic fields to swimming bacteria near surfaces. While its effects in homogeneous environments are well understood, the interplay between chirality and structural disorder has remained largely unexplored. Here we investigate the chiral random walk on two-dimensional percolation clusters above the percolation threshold, combining numerical simulations with an analytically tractable annealed-disorder approximation. We find that the long-time diffusion coefficient depends non-monotonically on both the chirality parameter and the obstacle density: for every obstacle density above the percolation threshold, there exists an optimal chirality that enhances diffusion relative to the achiral walk. We show that the optimal chirality is set by an edge-adhering mechanism: maximum diffusion is achieved when the persistence length of the wall-adhering motion matches half the typical obstacle cluster perimeter. This yields a closed-form prediction for the optimal chirality in terms of geometric properties of the medium alone, which we verify across the full range of obstacle densities studied. The enhancement extends to first-passage statistics, where chirality shortens typical search times at strong disorder while lengthening them at weak disorder, with direct implications for biological navigation in disordered environments.