Papers

This thesis investigates how superperiodicity, quasiperiodicity, and disorder shape electronic and spin transport in graphene-based systems, with an emphasis on experimentally relevant length scales and realistic atomistic modeling. Using large-scale real-space quantum-transport methods, it first establishes controlled transport fingerprints that distinguish conventional Bloch propagation in periodic structures from the anomalous dynamics induced by quasiperiodic modulations. Building on this framework, the thesis analyzes magic-angle twisted bilayer graphene and shows that, within a finite disorder window where flat-band features remain robust, moderate Anderson disorder can counterintuitively enhance the mean free path. This disorder-induced delocalization is further linked to changes in the quantum metric extracted from optical conductivity, revealing a direct connection between transport, electronic geometry, and the real-space extent of the underlying states. The study then turns to graphene quasicrystal approximants and hybrid multilayer stacks, identifying sub-ballistic transport and self-similar localization patterns as signatures of quasicrystalline order, while also demonstrating their strong fragility against disorder and interlayer proximity effects. Finally, the thesis addresses spin transport in suspended monolayer graphene, showing that atomic-scale corrugations generate short-range fluctuating Rashba fields that can limit spin lifetimes to the nanosecond range even when charge transport remains close to ballistic. Taken together, these results provide a unified picture of how geometry, disorder, and structural complexity govern transport phenomena in twisted and corrugated graphene systems.

We describe a generalization of the reciprocal theorem for particles suspended in electrolyte solutions and subjected to an electric field that could be either applied or emerged spontaneously. Attention is focused on catalytic colloids that release ions. The power of the generalization is to capture the effect of formation of a secondary cloud around a catalytic particle, which is equivalent to accounting for an excess charge $Q$ of a system. Our results show that the propulsion speed of catalytic particles has an extra contribution proportional to $Q$ and an external field $E_{\infty}$. The derived equation for $Q$ reveals that its sign is defined by the difference in the ion diffusivity and the magnitude is controlled by the average flux of ions from the surface. We demonstrate the application of the generalized theorem to electro- and diffusiophoresis of homogeneously releasing ions passive particles, as well as to a self-propulsion of inhomogeneous active particles (microswimmers). It is shown that whilst in some situations the extra term in the reciprocal theorem vanishes or has a little effect on the particle mobility, in many others it may dramatically change its magnitude, and even sign. In addition, the relevance of our results for microswimmer interactions is discussed briefly.

Logarithmic time dependences occur in many aging materials, but neither a $\ln t$ relaxation law nor a $1/t$ event rate uniquely identifies the underlying stochastic mechanism. We examine a specific log-aging process defined by iterating the age-conditioned forward-recurrence law after every event. This rule makes the event times multiplicative: the logarithmic ratios $U_n=\ln(T_{n+1}/T_n)$ are independent and identically distributed with an explicit non-exponential density. Consequently, both the mean and the variance of the event count grow linearly with $\ln(t/t_0)$, while the density of the $n$th event time has a log-normal central sector and a fixed-$n$ algebraic far tail. These clock statistics generate logarithmic drift and spreading, an Einstein relation under local detailed balance, and ultraslow transit and target-survival laws. They also separate trajectory reproducibility from ensemble–time equivalence: the relative scatter of the time-averaged mean-square displacement decays as $1/\ln(T/t_0)$, although its mean does not converge to the ensemble lag MSD. We distinguish the exact event-level construction from its diffusion-limit generalized Fokker–Planck and random-clock subordination representations, and from a generalized-Langevin closure that can match selected responses and covariances but need not reproduce event counts or rare-duration statistics. The proposed clock is therefore tested not by a single logarithmic curve, but by the joint, no-refitting consistency of multiplier, count, transport, first-passage, and finite-window observables.

The slow energy relaxation in quenched glasses is a ubiquitous yet poorly understood phenomenon. Despite extensive study, the microscopic origin of the observed power-law decay remains debated, with proposed mechanisms ranging from saddle-point slowdown and marginal stability to coarsening of localized excitations and phonon dynamics. Here, by simulating gradient descent in archetypal structural glass formers, we show that none of these scenarios can account for our data. Instead, the power-law behavior emerges from a remarkably simple caging effect: each particle experiences an effective stiffening potential that arises from many-body confinement and diverges at a characteristic cage size. This mechanism analytically yields the observed power-law decay and is quantitatively reproduced by a minimal single-particle cage model with fixed neighbours, demonstrating that collective relaxation modes are not essential. The dynamics is punctuated by fluctuations as the system rolls through inflection points on the energy landscape, which act as `speed bumps' but do not affect the overall power-law behaviour. In contrast to mean-field spin glass theory, we find no characteristic temperature that separates distinct dynamical regimes; state following within a given glass basin occurs universally for all initial temperatures whenever the system is sufficiently close to the inherent structure. Our results establish a complete physical picture of gradient descent dynamics in typical structural glasses.

Twisted graphene layers host van Hove singularities (vHSs), peaks in the electronic density of states, thought to drive exotic phases in moiré materials, but their effect on thermal transport has remained unclear. Here we show that vHSs in twisted double bilayer graphene (tDBLG) generate an unusually large Nernst signal-the transverse voltage produced by a longitudinal temperature gradient in a magnetic field. The pronounced Nernst peaks at the vHSs of the conduction and valence bands of tDBLG are tunable by an electric field with a maximum value of $\sim 40$ $\mu V K^{-1} T^{-1}$ at $\sim 1$ $K$, which is comparable to the best-known Nernst materials. Our theoretical calculations show that the large enhancement of the Nernst signal arises from the Lifshitz transitions around the vHSs. These findings establish the Nernst effect as a sensitive probe of Fermi-surface topology in moiré materials, and identify a universal thermoelectric signature of van Hove singularities.

Mapping quantum phase diagrams through classical simulation is notoriously resource-intensive, as even small systems far from the thermodynamic limit demand prohibitive computational effort. The variational quantum eigensolver (VQE) offers a compelling alternative, exploiting approximate ground states to distinguish phases. An appealing proposal, dubbed as Delta-VQE, determines critical points by contrasting variational energies optimized from reference states of distinct phases. Intriguingly, the diagnostic sharpens as circuit depth decreases, highlighting its promise as a resource-conscious probe of quantum criticality. To probe the broader applicability and underlying mechanisms of this approach, we investigate the one-dimensional transverse-field Ising model with a three-spin cluster interaction, a setting in which the Ising transitions are generally situated beyond the self-dual line. We demonstrate that, whenever dual ansätze are employed, Delta-VQE invariably detects the self-dual points rather than the true criticality. In contrast, when ansätze are carefully tailored to embody the competing phases across the boundary, the genuine Ising critical point can be successfully identified with only minor finite-size effects. Our results establish that, while Delta-VQE provides a resource-efficient probe of quantum criticality without requiring precise ground-state preparation, its diagnostic power is fundamentally contingent upon the judicious selection of physically representative ansätze.

Why do ChatGPT-like AIs, despite major architectural and training differences, unexpectedly tip to undesirable content (e.g. harmful, misleading, repetitive) even under deterministic greedy decoding? We show that a broad class of such tippings is caused by the many-body interactions between tokens (spins) as they cross the finite-layer system. Tipping emerges as a dynamical first passage process between competing output basins. Attention disorder controls the transport toward, away from, or along the basins' boundary. A few-basin reduction yields a closed finite-layer threshold, whose coarse-grained predictions show good agreement across ChatGPT-like families. These results suggest that a broad class of AI failures represents 'foreseeable engineering risk' rather than inherently unpredictable behavior, with important implications for legal and societal assessments of AI harm.

We investigate a spin-degenerate Fermi gas coupled to a high-finesse optical cavity, where the competition between scalar and vectorial couplings is controlled by the relative polarization angle of the pump and cavity fields. We find that the phase transition threshold is synergistically determined by the scalar-vectorial coupling weight and Pauli blocking, with the latter dictating the critical pump lattice depth required for the onset of superradiance. For a two-component Fermi gas with opposite spins, the population ratio drives two distinct types of phase transitions corresponding to real-space phase separation: continuous and discontinuous. Nevertheless, the boundary of the phase transition remains fundamentally governed by the scalar-vectorial coupling competition. We clarify the impact of the relative polarization angle on phase transitions of the system; these results also apply to bosonic systems. Our results provide valuable theoretical insights for future experimental realizations.

Low-temperature magnetoresistance loops of compacted CrO2 powders become strongly nonmonotonic when electrical transport is dominated by a small number of spin-dependent intergranular tunnelling paths. We reanalyse previously reported data for undoped CrO2 and Fe-containing Cr1-xFexO2, focusing on additional branch crossings beyond the conventional low-field hysteresis. In the Fe-containing specimen, the resistance decreases, passes through a minimum, rises over an extended field interval, and then decreases again at higher field. This nonmonotonic hysteretic feature is strongly reduced when the magnetic-field sweep is slowed. Digitization of the three fastest sweeps shows that the field at which the resistance starts to recover shifts approximately linearly with sweep rate, corresponding to an effective magnetotransport relaxation time of about 3 s. This scale is attributed not to microscopic spin flips but to the slow evolution of local moment and domain configurations at the intergranular contacts dominating the current. The observations are consistent with conventional negative tunnelling magnetoresistance superimposed on a slower resistance-increasing contribution associated with transient local magnetic disorder. Fe increases coercivity and interfacial magnetic heterogeneity while reducing the overall negative magnetoresistance. The results support a transport-weighted magnetic-reconfiguration mechanism for the unusual hysteresis shape.

Entanglement carries universal content that labels phases and critical points. We study the entanglement entropy of the steady states of critical non-Hermitian free-fermion chains. It scales logarithmically with subsystem size, but the coefficients vary continuously with the parameters and form a Rényi family that no single central charge can reproduce. We trace this anomaly to an “imaginary” Dirac point, a crossing in the imaginary part of the energy where the occupied state switches between two Bloch states. Their nonorthogonality weakens the occupation discontinuity and lowers the logarithmic coefficient. A low-energy expansion yields closed-form coefficients in excellent agreement with lattice numerics in various one-dimensional critical steady states. Remarkably, weak real onsite disorder leaves this logarithmic scaling intact and enhances the entanglement. Our results provide a generic understanding of entanglement in critical non-Hermitian free-fermion steady states.

We report profound impacts of the stacking sequence of triangular lattices of magnetic transition metal ions intercalated between the layers of the van der Waals material NbS$_2$. Using single crystal x-ray and neutron diffraction, and transport and magnetization measurements, we show there are two distinct polytypes of $\rm V_{1/3}NbS_2$ with disparate easy axes of magnetization and different anomalous Hall responses. Self-consistent analysis of inelastic neutron scattering data provides evidence for oscillatory RKKY interactions that extend to 1 nm and stabilize quasi-collinear A-type altermagnetic orders in both polytypes though with perpendicular easy axes. The detailed stacking sequence of a bulk polytype crystal dramatically impact its macroscopic anomalous Hall response and magnetism, which suggests a new path to engineer the bulk properties of a layered three dimensional solid.

Spin, pseudospin, valley, polarization, and other two-component degrees of freedom share the geometry of SU(2), yet their topological manifestations are usually discussed as separate phenomena. This review develops a common geometric language for their winding in momentum and real space,beginning with Berry phase and the Dirac Hamiltonian and extending to graphene, topological insulators, Weyl semimetals, and magnetic skyrmions. We argue that the common thread is not merely topology itself, but the continuity constraints imposed on two-component wavefunctions. Whenever the relevant symmetry is preserved, winding determines which states can continuously connect across an interface or deformation, thereby governing transmission, torque generation, optical selection rules, and other physical responses. We then ask a practical question: what does topology buy an engineer? In skyrmions, winding partitions magnetic configuration space and stabilizes ultrasmall information carriers with tunable dynamics. In graphene, pseudospin matching governs Klein tunneling, enabling a gate-controlled transmission gap without sacrificing the massless Dirac dispersion. In topological insulators and Weyl semimetals, spin-momentum locking and Berry-curvature engineering generate electrically selectable spin currents, while helicity-dependent optical transitions produce circular photogalvanic responses. Together, these examples suggest that topology is not merely a classification of quantum matter, but a design language in which symmetry-protected wavefunction continuity can be engineered for memory, switching, actuation, and sensing.

Twisted two-dimensional semiconductors provide a route to flat and topological moiré minibands, but systematic principles for organizing their material dependence have remained unclear. Here, we establish a high-throughput framework that integrates structural relaxation, first-principles electronic structure calculations, and moiré band topology. We apply this framework to 43 experimentally realized monolayers and 91 symmetry-inequivalent bilayer prototypes, yielding over 1,000 angle-resolved moiré electronic band structures. This database reveals that the low-energy moiré electronic structure is organized primarily by the valley character of the parent band edge together with stacking symmetry. In $\Gamma$-valley systems, the miniband width usually follows a nearly quadratic twist-angle scaling, consistent with a folding-dominated kinetic-energy scale. In $K$-valley systems, stacking-controlled interlayer hybridization governs whether parent Berry curvature is redistributed into isolated valley Chern minibands. By contrast, $M$-valley systems form a more material-specific class associated with anisotropic and symmetry-constrained band folding. The same valley-and-stacking hierarchy rationalizes the emergence or suppression of $\mathbb{Z}_2$ minibands, and surface termination in Janus bilayers provides a microscopic knob for changing the relevant valley character. These results establish a materials-level organizing principle for designing flat and topological moiré bands in twisted semiconductors.

We present a fast Stokesian dynamics (FSD) framework for the dynamics and rheology of suspensions of rigid aggregates. The method extends the sphere-level formulation of Fiore and Swan (2019) to multi-bead rigid bodies. Rigidity is enforced implicitly through geometric constraints, enabling stable and efficient time integration. We develop a block-triangular factorization preconditioner for the resulting saddle-point system. The approach combines an approximate inverse of the far-field mobility with a block-diagonal approximation of the Schur complement, enabling independent inversion of each aggregate sub-block via LU decomposition. The method is implemented as an open-source plugin for the HOOMD-blue software suite, and validated against benchmark problems, including doublet dynamics in shear flow, pair sedimentation, Brownian diffusion, and suspension rheology across dilute and structured regimes, accurately capturing both deterministic and stochastic behavior. The framework is further validated against experimental rheology of carbon black slurries, explicitly accounting for van der Waals cohesion, Hertzian contact, and tangential friction via enhanced lubrication. The simulations accurately reproduce the shear-thinning and high-shear viscous regimes. The method exhibits favorable GPU scaling for small system sizes, with decreasing runtime per bead prior saturation. A size-dependent Ewald splitting parameter accelerates simulations at low volume fractions, yielding up to an order-of-magnitude speedup compared to constant Ewald splitting. For larger systems, a constant Ewald splitting produces linear scaling with particle number, whereas the size-dependent choice leads to quadratic scaling due to increased far-field cost. Overall, the proposed framework enables accurate and scalable simulation of rigid aggregate suspensions in Stokes flow.

This work investigates how locally persistent crystal-like ordering in liquids influences the Debye-Waller factor. We have developed a theoretical framework based on liquid-phonon theory which introduces a phonon relaxation time, expressed as the ratio of shear viscosity to infinite-frequency shear modulus. These values are obtained using the Yukawa one-component plasma model. Within this framework, we establish expressions for the heat capacity at constant pressure and the Debye-Waller factor for the liquid state. These expressions explicitly introduce additional temperature dependence arising from the finite phonon lifetime. Anharmonicity is accounted for within the quasi-particle approximation. We compare our heat capacity results with values measured by Gathers for aluminum and copper, finding good agreement when assuming partial local crystal-type order. Comparisons with experimental heat capacities serve to validate the approach prior to its application to the study of electrical resistivity, the principal objective of this work. Using liquid-phonon Debye-Waller factors in the methodology developed earlier in [Phys. Rev. E 102, 053209 (2020)] for electrical resistivity in dense matter, and comparing with experimental resistivities from Gathers, we elucidate the character of the locally persisting crystal order in liquid aluminum and liquid copper. These results indicate that the electrical resistivity measurements can serve as a valuable probe for determining both the extent and the nature of crystalline order in the liquid state.

For a quantum Gibbs sampler whose mixing bottleneck is a weakly broken symmetry, I show that the correct initialization is determined by representation theory. I first prove a general speedup-versus-prefactor dichotomy: by exactly eliminating slow-mode overlap, I convert a nominal prefactor reduction into a fundamental, asymptotic acceleration of the system's mixing time. I then show that when the bottleneck is a weakly broken symmetry, the otherwise exponentially expensive bottleneck eigenvector is the symmetry charge.For a non-Abelian group $G$, I prove that the correct initialization target is the group-averaging asymmetry. Projecting this asymmetry out requires a $G$-invariant input. Partial, subgroup-invariant inputs produce a cascade of mixing-time speedups indexed by the subgroup lattice. Conversely, matching first moments alone is provably insufficient.The asymmetry is a directly measurable initialization target. I verify these results analytically and numerically in an $SU(2)$ Davies sampler where total-spin multiplets constitute the slow modes. The predicted speedup cascade emerges with relaxation rates scaling linearly with the symmetry-breaking parameter. Finally, the model maps the boundaries of the asymmetry target, illustrating where the separate matching of conserved logical data becomes necessary.

An isolated small system consisting of a movable shell and a finite number of internal particles is considered. Exact distributions of the shell coordinates and momenta are obtained for various types of internal particle motion under the conditions of conservation of the total energy and momentum of the system. The coordinate distribution consists of a finite number of branches and may contain plateau regions. The momentum distribution corresponds to a non-uniform distribution of energy among the degrees of freedom of the system. It is shown that the coordinate distribution depends on the number of internal particles and remains unchanged when the dimensionality of their motion varies, whereas the momentum distribution depends on the number of degrees of freedom. Consequently, comparison of the coordinate and momentum distributions of the shell makes it possible to draw conclusions about the internal structure of the system. The chaotic motion of the shell caused by impacts from the internal particles is analyzed; unlike Brownian motion, it persists even in the absence of an external medium. A universal expression for the root-mean-square deviation of the shell is obtained explicitly, depending on the number of internal particles and their masses.

Parametric resonance underpins the operation of a wide range of physical systems, from nanomechanical resonators to quantum-information systems and Ising machines. As an archetypal class of driven-dissipative systems, parametric oscillators are generally expected to exhibit a single pair of stable period-two states with opposite phases. This bistable behavior enables both the simulation of spin Hamiltonians and the preparation of superconducting cat states. Whether multiple pairs of such states can coexist in a single oscillator, however, remains an open question. Here, we show experimentally and theoretically that conventional controlled nonlinear friction can induce the coexistence of two distinct pairs of period-two states in a micromechanical oscillator. The friction is implemented via a canonical approach, utilizing a drive-induced resonant coupling that transfers two vibrational quanta from the oscillatory mode to a faster decaying mode. We demonstrate that the onset of multistability is governed by a swallowtail catastrophe and quantitatively map the associated bifurcation structure. Our results broaden the understanding of parametric resonance and establish micro- and nano-mechanical oscillators as a versatile platform for studying catastrophe theory and multistable nonequilibrium dynamics.

Photoexcited charge carriers in topological insulators display anomalously long-range transport at cryogenic temperatures, but the underlying mechanism remains under debate. Here we use a transverse electric field as a discriminating probe of photocarrier dynamics in bulk-insulating Sb-doped Bi2Se3 nanoribbons, combining scanning photocurrent microscopy (SPCM) with ultrafast transient photovoltage (TPV) measurements. SPCM shows that suppression of the photocurrent requires a transverse electric field nearly 50 times larger than that needed to deflect free carriers, yet comparable to the expected exciton dissociation field. TPV measurements at 12 K and low excitation fluence reveal that the photocarrier diffusivity exceeds the value implied by the Einstein relation and the measured drift mobility by more than an order of magnitude, a bound that holds even at the lower end of the fitting uncertainty. Together, these observations indicate that the long-range photoresponse is not carried by free charge carriers but by a charge-neutral correlated state.

Electrical contacts between metals and two-dimensional (2D) semiconductors such as molybdenum disulfide (MoS2) critically govern device performance, yet their microscopic nature remains difficult to disentangle using any single characterization technique. Here we present an integrated experimental framework that combines current-voltage (IV) characterization, laser beam induced current (LBIC) mapping, and bias-dependent Kelvin probe force microscopy (KPFM) to comprehensively resolve the contact properties of few-layer MoS2-based two-terminal devices under ambient conditions. IV measurements deliver macroscopic transport characteristics as a function of bias voltage and illumination conditions. LBIC maps the local photocurrent response with micrometer spatial resolution, revealing the position and nature of internal electric fields at MoS2-metal interfaces. KPFM, operated under an applied static bias rather than in the conventional work-function mode, provides nanoscale-resolved potential distributions that quantify the relative magnitudes and spatial locations of contact barriers. We apply this framework to three representative devices - one exhibiting ohmic-like and two exhibiting diode-like contact behavior - and demonstrate that the combined analysis can unambiguously identify whether the dominant barrier is of Schottky or tunnel type and determine the asymmetry between the two contacts. We further demonstrate that thermal annealing significantly reduces the total resistance, while contact barriers remain the dominant source of resistance. The methodology is directly transferable to other 2D semiconductor-metal systems and provides a practical yet comprehensive route toward a quantitative microscopic understanding of 2D device contacts.

Charge transport governs organic transistors and photovoltaics, yet predicting it from atomic structure remains challenging. Electron–phonon interactions span disparate frequencies, strengths and spatial ranges, and collectively generate nonperturbative carrier dynamics. Existing methods regain tractability only by assuming a mechanism or reducing electron–phonon coupling to a few modes. We introduce a parameter-free framework that instead computes transport from ab initio electron–phonon Hamiltonians, propagating carriers across hundreds-of-molecule domains with the full phonon spectrum and letting transport regimes and bottlenecks emerge from nonperturbative Green–Kubo dynamics. Across five representative crystals, it captures measured mobilities, temperature exponents, and optical-conductivity fingerprints. Our results overturn the prevailing microscopic mechanism for DNTT, tracing its transient localization to correlated on-site disorder from acoustic phonons rather than independent hopping fluctuations. The resulting two-axis transport map provides design principles and highlights the underexplored phenacene family, exemplified by the high-mobility picene, as a promising direction.

The discovery of ferroelectric nematic phase opened new directions in the field of soft matter chemistry and physics. In this paper, we have modified a previously reported ferroelectric nematogen based on molecular structure with dimethylamino-terminated part. We have prepared two new homologues by prolonging a side chain and investigated the effect of its length on the mesomorphic properties. While previously reported homologues exhibited a direct phase transition from the isotropic (Iso) to the ferroelectric nematic phase (NF), for prolonged alkyl chain there is a narrow nematic phase (N) in between. For new compounds, we have established their mesomorphic and material properties. We have confirmed ferroelectricity of the NF phase by the polarization, SHG signal and permittivity. Finally, we have compared these parameters with respect to the side-chain length and discussed new effects, discovered for prolonged homologues due to the presence of an additional N phase.

In Artificial Colloidal Ice (ACI), paramagnetic colloidal particles are confined in double-well traps and interact via repulsive, isotropic, magnetic dipole-dipole interactions that can be controlled by an external magnetic field. In this paper, we dynamically introduce anisotropic interactions to ACI by rotating the external magnetic field, which, in equilibrium, makes the system go from a charge-free 2-in, 2-out ice rule state, to a charged 4-in, 4-out state. We observe a strong dependence of the final configuration on the field's rotation rate $\omega$: at high angular velocity, the system achieves a defect free final state via a difussionless transformation from the initial ground state. However, counterintuitively, at slow rotation rates, ergodicity breaks down, trapping the system in a partially ordered metastable state.

Today the Citrine Platform regularly powers data-driven materials discovery across industries, having moved beyond one-off demonstrations into routine industrial practice. Getting there required solving a core set of recurring obstacles: experimental data are scarce, costly, and published in formats that resist reuse; conventional accuracy metrics overstate model performance under the extrapolative conditions that define discovery; and realistic design spaces are bounded by physics, manufacturability, supply, and cost. Developed over more than a decade as an integrated response to these obstacles, the Citrine Platform is organized as four cooperating stages within a closed sequential learning loop. Stage 1 ingests and featurizes data through the Graphical Expression of Materials Data (GEMD) model, which treats process history, measurement uncertainty, and provenance as first-class features. Stage 2 builds machine learning models with well-calibrated uncertainty, including multivariate prediction intervals for correlated objectives, and validates them with extrapolative cross-validation and dynamic discovery metrics rather than random held-out splits. Stage 3 encodes compositional, physical, processing, and economic constraints directly into the design space, and Stage 4 applies the FUELS sequential learning framework with uncertainty-aware acquisition functions to navigate large constrained spaces under tight evaluation budgets. Published case studies spanning organic semiconductors, autonomous nanoparticle synthesis, and benchmark optimization tasks demonstrate two- to nine-fold reductions in experimental effort relative to random search, illustrating a stack in which data, modeling, and design-space layers continuously co-evolve.

We investigate the properties of the largest eigenvalue of correlation matrices within the framework of Wishart ensembles. In this work, we propose the largest eigenvalue as an effective empirical order parameter for detecting phase transitions in chaotic and spin systems, drawing an analogy between its derivatives and thermodynamic response functions derived from the free energy, however not necessarily linked to a critical divergence originally observed in the context of phase transitions theory.

Predicting the properties of multicomponent molten salts using density functional theory (DFT) remains challenging because the spatial and temporal scales required to evaluate transport properties and phase behavior are computationally prohibitive. In this work, we develop a moment tensor potential trained using a a DFT dataset of NaCl, KCl, NaCl-KCl mixtures, and the NaK alloy, enabling large-scale molecular dynamics simulations across wide ranges of temperatures and compositions. We systematically evaluate the effect of D3 dispersion corrections and apply the resulting potential to predict liquid densities, diffusion coefficients, radial distribution functions, heat capacities, thermal conductivities, and the NaCl-KCl phase diagram. The model successfully reproduces many temperature- and composition-dependent trends. However, systematic deviations in several absolute properties persist, highlighting the importance of experimental validation and calibration. These findings support a hybrid modeling framework in which first-principles-informed machine-learning potentials provide transferable predictive capability and mechanistic insight, while experimental data incorporated during model development or subsequent engineering assessments is necessary to improve quantitative accuracy.

We employ a generalized approach to the master equation for driven open $N$-level ($N>2$) quantum systems using Lewis-Riesenfeld invariants, which avoids the driving-strength restrictions inherent to conventional approaches. We show that the invariant-based master equation provides a unifying generalized framework, which reduces to the frequently employed laboratory-frame master equations and the less frequently employed rotating-frame master equation framework under appropriate simplifications. Extending the prototypical two-level system, we show that the inclusion of another state coupled to the ground state via reservoir-induced dephasing gives rise to qualitatively new dissipative behaviors that are, in general, not captured by standard approximations. We also apply the invariant-based master equation framework to a driven quantum dot coupled to a leaky cavity, demonstrating the framework's ability to capture relevant dissipative dynamics without additional assumptions. Our work paves the way for quantum-control applications in the presence of dissipation.

Electronic-structure calculations based on Kohn-Sham density functional theory remain indispensable in computational materials science and chemistry. Their computational cost, however, limits accessible system sizes and simulation times. At the same time, conventional machine-learning interatomic potentials (MLIPs), which are becoming the workhorse of large-scale materials modeling, usually target only energies and forces. They therefore leave out the quantum-operator-level information required to reconstruct band structures, densities of states, spatial charge distributions, and other electronic observables. Mandala fills this methodological gap. It is a modular software framework for learning block-sparse electronic-structure matrices with E(3)-equivariant graph neural networks. The framework is built around a unified representation of atom-resolved Hamiltonian, overlap, and density matrices, together with reusable abstractions for basis conversion, sparse block handling, irreducible representation mapping, graph construction, model definition, and training. This design allows Mandala to support heterogeneous chemical compositions, a wide range of neural architecture variants within one workflow, and multiple electronic-structure backends. Mandala evaluates selected observables directly from the predicted operators, including band energy, electron count, density of states, and band structure. This connects electronic-structure learning and observable-guided modeling while retaining a representation tied to quantum-mechanical operators rather than only scalar or vector targets as in MLIPs. In this form, Mandala is intended to complement atomistic interatomic potential workflows by resolving electronic structure and operator-derived observables within one scalable implementation.

Kirchhoff's law fundamentally relates thermal emission to absorption. For linear, static, reciprocal media, it equates the emissivity and absorptivity for each direction and frequency, while in nonreciprocal systems emission and absorption are equal when the bias is time-reversed. In time-varying media, however, temporal modulation breaks time-translation invariance, converts frequencies, and enables energy exchange with the modulation drive. As a result, a same-frequency relation between absorptivity and emissivity can no longer be expected. Here, we derive a generalized Kirchhoff's law for linear time-varying Floquet media. We show that the emissivity at a given frequency equals a weighted sum of harmonic-resolved absorptivities of the adjoint system, with weights accounting for thermal occupation and photon-flux conversion. This relation has both practical and fundamental consequences. In practical terms, it allows emissivity to be calculated from absorption, simplifying the design of time-varying thermal emitters. More fundamentally, it reveals thermal radiation regimes inaccessible in static media. In particular, we identify time-varying structures that exhibit strong emission with negligible absorption at the same frequency for all directions, yielding a near-maximal violation of the conventional form of Kirchhoff's law.

The Mafia game, also known as Werewolf, describes a competition between a coordinated minority whose identities are concealed and a larger good faction composed primarily of uninformed civilians attempting to identify and eliminate them. We introduce an agent-based formulation in which the daytime decision is not represented by uniform random voting. Instead, randomly paired agents modify player-specific public suspicion scores according to their roles, and one surviving player is subsequently eliminated with probability proportional to their accumulated suspicion. These scores persist throughout the game, producing a history-dependent stochastic process with two competing absorbing outcomes: elimination of the mafia or numerical parity between the mafia and the good faction. We investigate the effects of population size, initial mafia size, and the presence of perfectly informed detectives through extensive Monte Carlo simulations. In the absence of detectives, a random-execution approximation predicts that, in the dilute-mafia and early-time regime, the cumulative probability of mafia extinction behaves as $F(\tau)\sim (\tau/N)^{N_m}$, in agreement with simulations as $N_m/N$ decreases. The winning-probability curves also exhibit an empirical finite-size crossover characterized by a population scale $N_c$. Rescaling the population by $N_c$ approximately collapses the curves obtained for different initial mafia populations. Perfectly informed detectives substantially shorten mafia-survival times and introduce an additional dependence on population composition for which the same one-parameter rescaling is insufficient. The model provides a minimal connection between microscopic histories of accusation and the macroscopic absorption statistics of hidden-role games.