Papers

For nonautonomous open systems described by macroscopic stochastic thermodynamics, we derive an emergent second law that constrains time-dependent macroscopic fluctuations by the entropy production along the most probable evolution under the time-reversed driving protocol. We show that this bound can be understood as a macroscopic consequence of the fluctuation theorem: the time reverse of this evolution provides a possible fluctuation path under the forward dynamics. In the linear-response and slow-driving regime, the bound becomes an equality to first order and generalizes the McLennan-Zubarev formula to the time-dependent probability density of nonautonomous systems with weak nonconservative affinities. We illustrate our results in a bistable system under sudden quenches and periodic driving.

Network Hamiltonian Models (NHMs) provide an efficient framework for modeling the aggregation of interacting particles (e.g., the condensation of proteins into gel-like, oligomeric, or fibrillar states), representing the system as a network whose edges represent bound interactions. Terms within the network Hamiltonian represent multi-body interactions governing aggregation behavior, and are specified via topological degrees of freedom. Because motional degrees of freedom are not explicitly represented within the NHM, their influence must be indirectly accounted for by introduction of corresponding terms to the Hamiltonian. Here, we describe specifications for terms representing motional degrees of freedom of two, three, and four-body interactions. We also consider the impact of these terms on the aggregation states of a minimal system governed only by a pairwise edge potential, showing that three and four-body interactions favor condensation of the system into small droplet-like structures at low temperature.

We find that the measurement-induced phase transition generated by deterministic global measurements, previously observed in the integrable transverse-field Ising model (TFIM), persists in non-integrable variants of the same. To address this question, we consider the TFIM with longitudinal field and the axial next-nearest-neighbor Ising (ANNNI) model. We show that both the survival probability and the bipartite entanglement entropy consistently capture a transition between area-law and volume-law entangled phases for two distinct initial states: a product state with all spins polarized along the transverse direction and a Greenberger-Horne-Zeilinger (GHZ) state. Finite-size scaling reveals a pronounced initial state dependence: for the polarized product state, the transition point follows an inverse-square-root scaling with system size in both non-integrable models, consistent with the integrable TFIM, whereas for the GHZ initial state, it deviates from this scaling and approaches zero considerably more slowly in the non-integrable models than in the integrable TFIM. These results establish the robustness of measurement-induced transitions under deterministic measurements against integrability breaking while highlighting the crucial role of the initial state in governing their scaling behavior.

Modern quantum experiments can probe many-body wavefunctions through projective measurements, providing snapshots of individual many-body configurations. A fundamental question is whether the intrinsic structure of their measurement distributions can reveal quantum dynamics beyond predefined observables. Here, we address this question at the many-body ergodicity-breaking transition using two complementary characteristics of nonequilibrium wavefunction snapshots: their binary intrinsic dimension (BID) and the topology of wavefunction networks constructed from Hamming distances. We show that the critical point is characterized by an extensive but submaximal BID, and scale-free network connectivity with highly connected hubs. These signatures distinguish the ergodic, critical, and nonergodic regimes, and provide experimentally accessible probes of ergodicity breaking from projective measurement snapshots.

The heat capacity of a system quantifies how it energetically responds to changes in temperature at equilibrium. Whilst this quantity is positive and even additive for non-interacting systems, self-gravitating systems such as stars or subsystems of strongly interacting quantum systems are known to have negative or anomalous specific heat capacities. In this work, we investigate how the presence of entanglement at equilibrium can influence how an interacting system responds energetically to changes in temperature. We examine the local heat capacity of interacting quantum systems providing an analytical understanding for when anomalies occur. Most interestingly, we find a connection between local heat capacity anomalies and entanglement by deriving a separability bound based on the fluctuations of local and interaction energies. We illustrate our results with two examples (i) a nearest neighbour spin-1/2 chain and (ii) two coupled quantum harmonic oscillators. Lastly, we provide an information-theoretic formula connecting mutual information and athermality to the non-additivity of the heat capacity. Our results provide model-independent thermodynamic entanglement detection bounds and insight into the relationship between quantum correlations and the heat capacity of quantum systems.

We formulate planetary sustainability as a minimal nonequilibrium problem for coupled finite stocks and fluxes, using the operational language of closed life-support systems: inventories, flux balances, recycling efficiencies, processing capacities, reserve times and failure thresholds. Rather than asserting that waste is universally more limiting than resources, we propose a reserve-time principle: the binding constraint is whichever buffer becomes critical first. A nonlinear model coupling a regenerative resource stock, an accumulated waste stock and an activity variable exhibits a soft threshold, where waste suppresses growth while processing remains formally capable, and a hard threshold, where waste production exceeds maximal processing capacity. With immediate waste feedback, activity settles globally at the soft threshold; the hard threshold is crossed only transiently or under exogenous forcing. A resource-side threshold completes the picture. We extend the model to recycling and to multiple resource and waste classes, give a numerical example, situate the four-function description of life against the origin of life, viruses and aging, contrast the biosphere's two long-term failure modes, and relate the approach to Spaceship Earth, planetary boundaries, Limits to Growth, System Dynamics and stock-pollution economics.

When only local observables of a many-body quantum system are of interest, it is desirable to formulate a reduced description within the Hilbert space of the corresponding subsystem, with the remaining degrees of freedom traced out and acting as an environment. Assuming initially uncorrelated states and Gaussian environments, we develop a framework for reconstructing the local dynamical generator of noninteracting quantum chains, with polynomial computational complexity. As an application, we consider two representative models: a bipartitioned Kitaev chain and a Kitaev chain boundary-coupled to a fully connected free-fermion environment. In both models, strong subsystem-environment coupling leads to non-Markovian dynamics characterized by ballistic spreading of the Lindblad dissipator support within the subsystem. On the other hand, weak coupling to a fully connected environment yields predominantly boundary-localized, Markovian dissipation. Our work highlights the implications of subsystem-environment correlations on the generator of local dynamics, beyond the conventional weak-coupling approximations.

These notes accompany lectures given in June 2025 at the summer school Fundamental Problems in Statistical Physics XVI. They offer a short introduction to random quantum circuits as simple models for generic many-body quantum systems. They give an outline of the motivation for introducing these models, starting from ideas of random matrix theory. They also provide a sketch of calculations of some of the quantities of most physical interest, based on an average over an ensemble of systems. These quantities give insights into operator spreading, entanglement dynamics and spectral correlations.

We study the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice with ferromagnetic nearest-neighbor couplings fixed at $J_1=1$ and strong antiferromagnetic next-nearest-neighbor interactions, i.e., $J_2 \leq -1/4$. Little is known for this range of $J_2$, whereas for less negative values of $J_2$ the system orders ferromagnetically at low temperatures and appears to remain in the Ising universality class. In previous work it was shown that the model has a largely degenerate ground state, and it was conjectured that there is some kind of phase transition. We introduce a complex-valued nematic order parameter, which can differentiate between the high-temperature paramagnetic phase and the observed partially-disordered stripe phase at lower temperatures. Configurations in this phase consist of stripes of spins parallel with respect to one lattice direction, which collectively meander along the remaining two, producing partially disordered ground states. The sharp peaks in the specific heat observed in earlier work only appear when using periodic boundary conditions and are absent for free boundaries. Additionally, we reveal a striking dependence of the behavior on the aspect ratio of the considered samples. Ultimately, even a careful finite-size scaling analysis for $J_2 = -0.5$ and $J_2 = -1$ is unable to clearly discern between a crossover without any singularities and some form of continuous transition, including the possibility of an infinite-order transition of the Berezinskii-Kosterlitz-Thouless (BKT) type. For $J_2=-1/4$ we find that the system remains disordered at all temperatures and that it exhibits a finite ground-state entropy per site, for which our simulations provide the accurate asymptotic estimate $S(T=0)/N = 0.230\,960\,93(14)$ in the thermodynamic limit $N\rightarrow\infty$.

Metabolic networks play pivotal roles in understanding the evolution of organisms, microbiome dynamics and disease prevention and treatment. This study presents a comprehensive analysis of metabolic network properties across 10912 organisms spanning Bacteria, Archaea, and Eukarya domains. A novel method for the network construction is introduced, emphasizing the chemical transformations of metabolites. Unlike conventional approaches that link every substrate to every product in all chemical reactions, this method aligns more closely with metabolic pathways, linking products only to their generating substrates. Emphasis is placed on investigating the community structure within metabolic networks, employing the Surprise quality function that better addresses some limitations of previous approaches. Through comparisons between real and randomized versions of the networks, we identify characteristics that cannot be explained solely by the network degree distribution, thus identifying topological properties and community structures that arise from additional evolutionary pressures. This highlights the need for evolutionary models to incorporate additional mechanisms beyond the replication of the degree distribution.

We study quantum dynamics through the lens of entanglement generation and characterize the underlying unitary evolution by the distinct signatures it imprints on the time-dependent entangling power. For a unitary operator, we characterize ergodicity by the equality between its long-time-averaged entangling power and the Haar-averaged linear entropy. We define mixing more stringently as the convergence of the time-dependent entangling power itself to the Haar value at long times. Within this framework, we establish the ergodic hierarchy of dynamical behavior, showing in particular that mixing implies ergodicity, whereas ergodicity does not necessarily imply mixing. As an application, we find that two-qubit unitary gates are neither ergodic nor mixing: their long-time-averaged entangling power can take only four discrete values, none of which coincides with the Haar average. We then investigate many-body dynamics using the kicked Ising chain and find that the long-time-averaged entangling power converges to the Haar value in both integrable and nonintegrable cases, indicating ergodicity. Remarkably, however, the nonintegrable chain exhibits mixing, whereas the integrable chain, despite being ergodic, is demonstrably nonmixing. We also introduce a Lyapunov-like exponent to characterize the rate at which the time-dependent entangling power approaches its saturation value. We find that this exponent increases systematically with the degree of integrability breaking in the many-body system. Our results establish entanglement generation as a useful framework for characterizing dynamical systems and reveal qualitatively different signatures of integrability beyond conventional diagnostics.

We study the semidefinite programs (SDPs) of quantum information whose variables are density operators, measurement operators, or unbounded positive semidefinite operators, together with their thermodynamic regularizations by the von Neumann, Fermi-Dirac, and Bose-Einstein entropies, which have been associated with Boltzmann, Fermi-Dirac, and Bose-Einstein statistics, respectively. We find that this correspondence is exact: the Fermi-Dirac and Bose-Einstein regularized SDPs coincide with the constrained free-energy minimization of an ideal Fermi or Bose gas whose Hamiltonian and non-commuting charges are the second quantizations of the SDP data and whose one-body density matrix is the SDP variable, while the Boltzmann framework corresponds to the single-particle case. We show that the three frameworks can be unified under one framework, in which each entropy-regularized dual is, up to a term linear in the chemical potentials, the grand potential of the corresponding system; the duals are unconstrained and concave in the chemical-potential vector, with gradient and Hessian given by thermal expectation values that hybrid quantum-classical algorithms can estimate. We further identify the Fermi-Dirac and Bose-Einstein relative entropies with the Umegaki relative entropy between quasi-free states, which yields their monotonicity under gauge-covariant Gaussian channels. The result places a wide class of SDPs and their solvers within the thermodynamics of ideal quantum gases and points to extensions to interacting gases.

Thermal fluctuations can drive an interface when bulk fluctuation amplitudes differ between two phases. We study how shear flow modifies this mechanism using a stochastic non-conserved order- parameter model. For a planar interface parallel to the imposed shear, we derive its propagation velocity in the weak-noise and small-bias regime. The driving force comprises a shear-modified entropic contribution determined by bulk fluctuation spectra and a non-equilibrium contribution arising from the breaking of time-reversal symmetry. At low shear rates, the entropic term provides the dominant contribution to the velocity of an interface near the zero-velocity plane of the shear flow, and the shear-induced change in the velocity scales as the 4/3 power of the shear rate. At high shear rates, two-dimensional simulations show that the measured velocity is largely accounted for by the modified bulk entropic contribution.

Mobility links an applied force to the resulting motion and is generally positive near equilibrium. Far from equilibrium, however, internal energy input can reverse this response. Here we show that information feedback provides a distinct route to negative mobility. We consider an overdamped dimer consisting of a run-and-tumble particle coupled by a spring to a passive Brownian particle. Information enters through periodic measurements of the relative displacement, which are processed to reset the active polarity. Although the unloaded dimer has no net drift, an applied force biases its internal configuration, and an information-mechanical feedback amplifies and converts this bias into active propulsion against the force, producing negative mobility. We develop an analytical theory that captures this mechanism and yields a feedback-gain criterion for response reversal. Including the information-processing cost reveals a tradeoff: rapid feedback enhances reverse transport but incurs a growing informational cost, yielding an optimal finite feedback rate for information-inclusive efficiency. These results show that information can reshape nonequilibrium response by controlling how internally supplied energy is converted into macroscopic transport.

Quantum wake dynamics in quantum magnets have recently been inferred from the dynamical spin structure factor, which probes only a restricted class of local perturbations. Here, we show that resonant inelastic x-ray scattering (RIXS) selection rules act as an operator filter on fractionalized excitations, producing distinct quantum wakes in the spin-$\frac{1}{2}$ Heisenberg antiferromagnetic chain. Using explicit real-time evolution of single-spin and spin-conserving bond correlators, we find that the conventional spin response propagates up to the maximum spinon velocity, $v_s=\frac{\pi}{2} J$, whereas the bond channels concentrate their spectral weight into a slower dominant wake with $v\simeq 0.92 J$, while weaker components remain bounded by the full spinon light cone. The corresponding momentum- and frequency-resolved responses map onto experimentally accessible RIXS channels, demonstrating that different spectroscopic perturbations resolve complementary pathways of many-body propagation beyond the neutron-scattering spin structure factor. Their inelastic spectral weights further provide access to quantum Fisher information, while equal-time bond sum rules connect the same spectroscopic channels to the ground-state energy. Because the same correlators can be prepared and measured on quantum hardware, they also define direct, experimentally anchored benchmarks for quantum simulations, particularly in frustrated and higher-dimensional magnets where controlled classical real-time calculations become challenging.

We present a comprehensive Monte Carlo study of two-dimensional bond percolation with algebraically decaying connection probabilities $p(r)\propto 1/r^{2+\sigma}$, establishing the universality diagram in the long-range (LR) regime for $\sigma\le2$. Using the event-based ensemble method, we simulate systems with linear sizes up to $L=16384$ and investigate three universality regimes: LR Wilson–Fisher (WF) A ($1<\sigma\le2$), LR Wilson–Fisher B ($2/3<\sigma\le1$), and LR mean-field (MF) ($0<\sigma\le2/3$). In the LR-WF-B regime, the anomalous dimension is consistent with $\eta=2-\sigma$, in agreement with mathematical results for $2/3<\sigma<1$, while the correlation-length exponent $\nu(\sigma)$ exhibits nontrivial, non-Gaussian variation. In the LR-WF-A regime, although $\eta$ remains close to $2-\sigma$ for smaller $\sigma$, statistically resolvable deviations $\delta\eta(\sigma)=\eta-(2-\sigma)>0$ start to appear near $\sigma\simeq3/2$ and grow toward the short-range crossover at $\sigma=2$. Finally, by complementing the event-based simulations with conventional ensemble simulations, we reveal the coexistence of complete-graph asymptotics and LR Gaussian-fixed-point scaling in the LR-MF regime. These results further clarify the critical properties in long-range percolation and provide crucial benchmarks for long-range statistical systems.

We construct representation-independent families of solutions of the non-braided scalene Yang–Baxter equation from quadratic noncommutative algebras. Beginning with two anticommuting generators, we obtain a continuous deformation in terms of quantum-plane algebras and extend the construction to an arbitrary number of generators. In the latter case the scalene Yang–Baxter relation fixes the multiparameter exchange matrix to an exact multiplicative form, thereby selecting a distinguished subclass of multiparameter quantum affine spaces. We construct finite-dimensional realizations using singular matrices and finite Heisenberg–Weyl operators, as well as infinite-dimensional realizations in terms of bilateral weighted shifts and multiplicative-shift operators. The explicit realizations are generically purely scalene: although the ordered triple satisfies the scalene Yang–Baxter equation, its individual constituent operators do not satisfy the ordinary non-braided Yang–Baxter equation. These results provide a representation-independent algebraic framework for constructing Yang–Baxter-irreducible scalene triples and a starting point for investigating their possible applications to quantum integrability.

We investigate the Lee–Yang zeros (LYZ) of inhomogeneous anisotropic XY spin chains with Dzyaloshinskii–Moriya (DM) interactions in the complex transverse-field plane, focusing on their fundamental connection to quantum phase transitions. We systematically study uniform chains, period-2 and period-3 modulated chains, and Fibonacci quasiperiodic chains of lengths 5 and 8. As the DM coupling strength $D$ increases, the LYZ exhibit qualitatively distinct topological evolutions on the complex plane: the complex zeros of the uniform chain collapse toward the real axis; periodic chains feature either bifurcation of closed zero contours before all zeros become real or a single re-emergence of complex zeros; quasiperiodic chains exhibit repeated annihilation and revival of complex zeros. Analytical derivations demonstrate that this diverse behavior originates from DM-induced shifts of folded bands and the modulation of zero positions by anisotropic pairing at particle–hole band crossings. Our results establish a direct correspondence between LYZ topology and band deformation: isolated contact points of zeros with the real axis correspond to discrete quantum critical fields, while continuous real-zero intervals directly identify gapless chiral phases. Accordingly, beyond locating phase boundaries, LYZ can distinguish characteristic phases and serve as an intuitive probe for band folding and phase diagram restructuring.

A power series for the Wigner-Kirkwood pair commutation function for quantum statistical mechanics in classical phase space is given with terms automatically generated by recursion. The calculated second virial coefficient agrees with the measured values of helium for temperatures greater than 65 K. Prospects for a general quantum Monte Carlo algorithm are discussed.

We determine the aging phase diagram of mixed spherical $(p+s)$-spin glasses quenched from random configurations to zero temperature. Solving the asymptotic dynamical equations of Cugliandolo and Kurchan, we find transitions between aging states with one, two, and continuously many effective temperatures, including phases in which discrete and continuous hierarchies coexist. We obtain analytic expressions for the energies reached asymptotically by the dynamics. In models combining pairwise and higher-order interactions, and sufficiently separated interaction orders ($s>3$), a fully continuous phase exists, where the gradient descent relaxation converges to the algorithmic energy lower bound. Instead, in mixed models with only high-order interactions ($p\ge3$) the energy relaxation remains strictly above it. Numerical integration of the dynamical equations is consistent with the predicted two-step and mixed discrete–continuous aging states.

Granovetter's threshold model provides a classical framework for social mobilization, where collective action spreads through cascades as individuals join once movement size reaches their personal threshold. Here, we characterize social tipping points-the minimum seed required for global mobilization-using the initial fraction of instigators, $\rho_0$, as a control parameter. For a finite population of size $N$ with Beta-distributed thresholds $(\alpha, \beta)$, we present an exact analytical study of the cascade dynamics. By evaluating the asymptotic active fraction $\rho_\infty$, we map the thermodynamic phase diagram separating partial cascades ($\rho_0 \le \rho_\infty < 1$) from complete mobilization ($\rho_\infty = 1$), revealing continuous and discontinuous transition lines that meet seamlessly at a critical endpoint. For interior-peaked distributions ($\alpha > 1, \beta > 1$), the regimes are separated by a hybrid phase transition combining a first-order discontinuity with second-order bottleneck singularities. Combining exact finite-$N$ combinatorial formulations with large-deviation theory, we establish how finite-size fluctuations smooth these singularities. For power-law thresholds ($\alpha > 1, \beta = 1$), the critical scaling window shrinks as $N^{-1/3}$, while the expected inactive fraction vanishes as $N^{-1/3}$ at criticality. For interior-peaked distributions ($\beta > 1$), the order parameter is bimodally distributed: realizations either achieve full mobilization or stall near a bottleneck $\rho^*$. Excluding fully mobilized trajectories, $\rho^* - \langle \rho_\infty \rangle$ vanishes as $N^{-1/4}$ and the scaling window compresses to $N^{-1/2}$. Together, these results establish an exact finite-size scaling theory for threshold-driven tipping phenomena.

We study the ground-state properties of linear chains of dipolar planar rotors hindered by a six-fold on-site potential, a model motivated by water molecules confined in the hexagonal cavities of beryl. Using density matrix renormalization group (DMRG) calculations, we locate the quantum phase transition between the disordered and ferroelectrically ordered phases using the von Neumann entanglement entropy and the Binder ratio of the polarization. A sweep of the six-fold pinning strength shows that increasing hindrance shifts the critical dipolar coupling gc to smaller values. These results suggest that crystal-field hindrance can promote, rather than suppress, dipolar ordering. This work has implications for ferroelectricity and quantum-device tuning in confined molecular rotors

Modern experiments often record nonequilibrium dynamics as sequences of discrete events whose rates depend on the realized past. We develop a fluctuation-response theory for such non-Markovian jump processes directly on the observed event record. Memory can destroy a closed master equation for the state probabilities. Each transition count nevertheless obeys an exact stochastic equation. After the history-dependent mean event tendency is subtracted, the remaining random increment is a martingale increment–the part of the event that cannot be predicted from the past. Martingale increments associated with different transitions and different times are orthogonal. These increments form a complete orthogonal basis for the random deviation of any observable measured from the record, such as a current, occupation time, or event count. The coefficient of a given increment is the event-consequence kernel. It measures how that event changes the predicted final observable, relative to continuing without the event, for the particular history already realized. Multiplying this kernel by the event intensity gives the history-conditioned response to perturbing the corresponding transition rate. Thus, the intensity-normalized response is exactly the expansion coefficient of that event in the observable fluctuation. This identification yields exact finite-time and finite-frequency fluctuation-response relations. Averaging over histories leaves a nonnegative response-heterogeneity gap. The gap measures how strongly the consequence of the same event varies across histories and tests whether a proposed memory coordinate is response-sufficient. Finite-history versions can be estimated from spontaneous trajectories. Bounding the logarithmic rate sensitivity further gives response-kinetic uncertainty relations controlled by dynamical activity.

The intermediate-energy double pendulum is a prototypical chaotic system. Despite its irregular motion, it exhibits recurrent flips - events in which one of the arms passes over the top. We develop a statistical prediction for the mean flip rate in terms of phase space flux. Applying this flux-based approach to the equal-mass, equal arm ("egalitarian") double pendulum, we find excellent agreement between the statistical prediction and numerical simulations: ensemble-averaged flip rates agree at about the 1% level, while even the statistics of individual chaotic trajectories agree at the few-percent level, quantifying the validity of the ergodic approximation. This agreement holds for flips of either arm and over a broad range of energies. This flux-based approach is closely related to that used for the egalitarian three-body system. A central role is played by the saddle orbits: periodic orbits that tend to the stable saddle eigenmode as the energy approaches the saddle energy from above and approximately follow the ridge of the potential at higher energies. These orbits provide a natural dividing surface for defining flips while avoiding recrossings. Indeed, the resulting distribution of crossing times exhibits a distinct gap. We also present two alternative simplified dividing surfaces, one of which is based on an accurate analytic approximation to the saddle orbits.

We investigate nonlinear Drude weights (NLDWs) in the one-dimensional repulsive Hubbard model at zero temperature by combining exact Bethe-ansatz calculations with low-energy effective field theory. At quarter filling, we first derive the strong-coupling expansion of the NLDWs and confirm it numerically over a wide range of interaction strength. We then compare the numerical results with the prediction of the Tomonaga-Luttinger liquid (TLL) description including irrelevant perturbations. While band-curvature corrections yield finite contributions to higher-order NLDWs, the Umklapp interaction predicts divergent NLDWs when the order $n$ of the Drude weight exceeds a threshold determined by the TLL parameter. In contrast, finite-size scaling of the exact Bethe-ansatz results indicates that all calculated NLDWs remain finite in the thermodynamic limit, revealing a discrepancy between the exact results and the predictions of the low-energy effective field theory. At half filling, we analyze the finite-size scaling of the NLDWs across the Mott metal-insulator transition. We derive their asymptotic behavior in the insulating phase and propose a hyperscaling ansatz for NLDWs near the critical point, which is verified numerically. Our results clarify the interaction dependence and critical scaling of nonlinear transport coefficients in the one-dimensional Hubbard model and highlight limitations of the conventional low-energy effective description for higher-order transport.

Motivated by a previous Ising study, we identify a ${\it higher}$ Nishimori line in the learning phase diagram of the $2D$ $q$-state Potts model $(2 < q\leq 4)$ under bond-energy measurements. This ${\it higher}$ Nishimori line meets the critical temperature line of the Potts model, in a ${\it higher}$ Nishimori critical point – a tricritical point at finite inference strength that separates a paramagnetic, a ferromagnetic and a 'spin-glass' phase. With analytical tools, we discuss the general structure of the rich phase diagram, which contains two unstable and three stable fixed points, and obtain a number of exact results for universal quantities, including the decay exponent of the Edwards-Anderson correlator, using a Gaussian measurement protocol which allows for exact calculations. Using extensive numerical tools, we confirm these statements for a generic, discrete $q$-state measurement protocol and determine precise numerical estimates for the location of higher and ordinary Nishimori critical points as well as RG flows between the various fixed points. We also discuss the Casimir effective central charges of the critical points in the learning phase diagram, and their monotonic ${\it decrease}$ along measurement-induced RG flows, as established non-perturbatively by the c-effective theorem and its extensions, and contrast it to the monotonic increase along the corresponding RG flows in the random-bond Potts model. Finally, we discuss a general argument based on ${\it Elitzur's \; theorem}$ that establishes stability of the ordinary Nishimori critical points in their respective learning phase diagrams. Equivalently, our results describe a monitored deformed $\mathbb{Z}_q$ toric code where the tricritical ${\it higher}$ Nishimori point is an 'information' critical point that separates stable quantum, classical, and no memory phases.

We study the translocation of a polymer chain through a nanopore where the chain length fluctuates stochastically due to the polymerization-depolymerization processes at the chain ends. We map this process to an equivalent representation where the pore performs a stochastic random-walk-like process on a line in the presence of two diffusing sinks on either side of it with diffusion constants $D_1$ and $D_3$ respectively. The translocation process terminates when the pore hits either of the two outer diffusing sinks. In the case where the pore motion itself is diffusive with diffusion constant $D_2$, we compute exactly the splitting probability that the pore hits the left (right) sink before hitting the right (left) sink. We show that the splitting probability in the presence of mobile sinks is rather nontrivial compared to the classical case of immobile sinks (the latter corresponds to the case when the chain length is fixed). Furthermore, we also compute exactly the probability distribution of the translocation time and that of the chain length at the completion time of the translocation. We show that both distributions have power law tails with exponents that depend continuously on the diffusion constants $D_1$, $D_2$ and $D_3$. We validate our analytical predictions via numerical simulations. We then present numerical results for the case when the pore performs a fractional Brownian motion with Hurst exponent $0<H<1$, while the sinks are still diffusive.

Near $(1+1)$-dimensional [$(1+1)$D] Ising criticality, a magnetic perturbation induces confinement and produces a cascade of bound-state excitations known as mesons. Here we show these mesons share a universal mass scaling after independently rescaling the model-dependent microscopic couplings. The number of stable mesons is controlled by the lightest two-meson threshold, while the lightest-meson mass follows a continuous trajectory characterized by a single scaling parameter. Using Hamiltonian truncation method, we obtain the trajectory numerically in both Ising field theory and the near-critical mixed-field Ising chain (MFIC). Under the rescaling, the trajectory and stable-meson-count crossover windows of MFIC both collapse onto the field-theory results. To further demonstrate the above universal organization of the meson spectra, we consider a class of four-periodic spin-$1/2$ Heisenberg-Ising chains under transverse fields, whose parameter space contains a family of quantum Ising critical points. The Hamiltonian family includes effective spin models for the quasi-one-dimensional antiferromagnets Ba(Sr)Co$_2$V$_2$O$_8$. Using tensor-network calculations, we obtain the corresponding lightest-meson mass trajectory for BaCo$_2$V$_2$O$_8$ and find that it also collapse onto the same universal curve given by field-theory result. Our results suggest that the universal scaling structure of quantum Ising criticality extends into the nearby confining regime, governing the organization of the meson spectrum. They thereby provide a practical criterion for interpreting excitations of quasi-1D Ising-like magnets in mixed fields beyond $E_8$ integrability.

We extend the analysis of the class of quantum phase transitions (QPTs) that can be interpreted as condensations in state space, first introduced in [M. Ostilli and C. Presilla, J. Phys. A 54, 055005 (2021)], by generalizing the arguments of [M. Ostilli and C. Presilla, Phys. Rev. Lett. 127, 040601 (2021)] to prove the existence and determine the location (via simple bounds) of QPTs in general one-parameter lattice Hamiltonians. Unlike our original formulation, this extension also encompasses second-order QPTs, for which we provide the explicit example of the transverse-field Ising model. Our analysis suggests that, under conditions typically satisfied in physical contexts, any QPT taking place in lattice systems can be interpreted as a condensation in state space.

Nano- or micro-particle rotation driven by light has been well known in the fields of optical manipulation and optical physics since the end of the last century. It is viewed as a sort of angular-momentum transfer from light to material, but its microscopic analysis based on the Hamiltonian or the equation of motion has been less developed. We model this rotation with a simple setup of an electrically dipolar or multipolar particle irradiated by circularly polarized laser and comprehensively analyze the Langevin-type equation of motion by using the Floquet theory for dissipative classical systems and the mode separation method. Furthermore, we numerically compute the time evolution of the particle. As a result, we accurately estimate the dependence of the laser-frequency, laser-intensity, particle mass, temperature, and friction (dissipation) on the laser-driven rotation. We determine the “nonequilibrium phase diagram” of the laser-driven rotation in a broad parameter regime, which consists of three regimes: the rotation frequency $\Omega\propto\omega^{-1}$, $\Omega\propto\omega^{-3}$, or $\Omega=\omega$ ($\omega$ is the laser frequency). Comparing our theoretical result with some experiments, we show that the result of the overdamped Langevin equation is qualitatively consistent with the experiments.