Search Results (99)

We explore the capability of a Large Language Model (LLM) to perform specific computations in mathematical physics: the task is to compute the coordinate Bethe Ansatz solution of selected integrable spin chain models. We select three integrable Hamiltonians for which the solutions were unpublished; two of the Hamiltonians are actually new. We observed that the LLM semi-autonomously solved the task in all cases, with a few mistakes along the way. These were corrected after the human researchers spotted them. The results of the LLM were checked against exact diagonalization (performed by separate programs), and the derivations were also checked by the authors. The Bethe Ansatz solutions are interesting in themselves. Our second model manifestly breaks left–right invariance, but it is PT-symmetric; therefore its solution could be interesting for applications in Generalized Hydrodynamics. And our third model is solved by a special form of the nested Bethe Ansatz, where the model is interacting, but the nesting level has a free fermionic structure lacking $U\left(1\right)$-invariance. This structure appears to be unique and it was found by the LLM. We used ChatGPT 5.2 Pro and 5.4 Pro by OpenAI. Full article

The universal operator-growth hypothesis (OGH) states that, in a closed chaotic system, the Lanczos coefficients grow linearly, $b_n\simeq \alpha n$. We ask how this structure is modified when the system is coupled to a Markovian environment, so that the generator becomes non-Hermitian. Applying the Arnoldi recursion to the vectorized Lindbladian in the infinite-temperature Wightman inner product, we organize the resulting pair of growth rates ${\alpha }_{\mathbb{C}}\equiv {\alpha }_R+i{\alpha }_I$—defined as effective slopes of the sub-diagonal and diagonal Arnoldi coefficients over a pre-registered fit window—around two statements whose logical status we delimit precisely. First, whenever the dissipator acts as $\mathcal{D}=-2\gamma \widehat{G}$ with $\widehat{G}$, a Hermitian grading (all dephasing-type baths), the diagonal obeys the identity $\mathrm{Re}{a}_n=-2\gamma {⟨\widehat{G}⟩}_n$: the imaginary rate measures how fast the growing operator accumulates weight in the dissipation channels. Second, we prove a conditional parity theorem: if the Hamiltonian, jump operators, and seeds can be made simultaneously real in some basis (an antiunitary condition), then $b_n$ is even, and $\mathrm{Re}{a}_n$ is odd in $\gamma$ exactly, so ${\alpha }_R$ is renormalized only at $O\left({\gamma }^2\right)$, and ${\alpha }_I=2{\kappa }_0\gamma$ follows from closed-system data alone. We exhibit a one-qubit Lindbladian that satisfies the often-assumed generator symmetry ${\mathcal{G}}^{†}\left(\gamma \right)=-\mathcal{G}(-\gamma )$ yet violates parity ($b_1=|1-\gamma |$), showing that the extra condition is essential; all models studied here satisfy it bit-exactly. For large-q SYK, these ingredients predict ${\alpha }_{\mathbb{C}}=\mathcal{J}-2i(q-2)\gamma$, whose imaginary part is fixed solely by the interaction range; the first ladder step is exact, and the multi-step increments approach $q-2$ with system size ($1.92\pm 0.04$ at $N=12$, $q=4$). Under a common fit protocol, the closed-system rates saturate by $N=10$ (${\alpha }_R\left(0\right)\to 0.437$, $2{\kappa }_0\to 0.224$). The imaginary rate is not an independent observable at leading order—its content is its sign, which resolves how the growing operator meets its environment (opposite for spin chains and SYK). Full article

Hybrid organic–inorganic composites based on biopolymers and nanoclays are attracting increasing interest for the development of functional materials in biomedical and agricultural applications. In this work, elongated alginate/halloysite nanotube (Alg/HNT) composite filaments were fabricated through a wet-spinning process assisted by syringe-based extrusion. Alg/HNT dispersions with different inorganic/organic ratios were first screened in terms of colloidal stability and injectability in order to identify suitable formulations for extrusion. The influence of key processing parameters, including the extrusion flow rate and calcium chloride concentration in the coagulation bath, was then systematically investigated to elucidate their effect on filament morphology and structure. Optical and scanning electron microscopy revealed that filament diameter can be tuned by varying the CaCl₂ concentration, while partial alignment of alginate chains along the extrusion direction was observed. Halloysite nanotubes were homogeneously distributed within the polymer matrix, mainly as micro-sized aggregates. Finally, the nanotubes were chemically functionalized with caffeine, as a model molecule, and incorporated into the alginate filaments, demonstrating the feasibility of introducing specific functionalities into wet-spun Alg/HNT composite fibers. These results establish a reproducible strategy for the fabrication of alginate/HNT filaments with tunable morphology and functionalizable nanotube interfaces, providing a versatile platform for the development of sustainable hybrid biopolymer materials. Full article

I analyze the nonlinear Hamiltonian equations of motion for a one-dimensional chain of transverse magnetic nano-islands, seeking solutions for different types of static domain walls (DWs) connecting uniform static states. The system of elongated magnetic islands oriented transverse (y-direction) to the chain direction (x-direction) experiences an applied magnetic field transverse to the chain. The macro-spin model includes dipole interactions between islands, their uniaxial and easy-plane anisotropies, and Oersted energy of the applied field. DWs can form most easily between pairs of degenerate uniform states, described by their local magnetizations as oblique, y-parallel, and y-alternating. The DWs between oblique states are well described with scalar ${\phi }^4$ theory. General DW structures are found via a numerical energy relaxation scheme. At some anisotropy and field parameters, nearest-neighbor dipole interactions drive antiferromagnetic order inside the DW itself. Full article

The discovery of dynamical quantum phase transitions (DQPTs) has fundamentally challenged the traditional view that phase transitions only occur in thermal equilibrium. Experimental platforms and 1D numerical methods, like matrix product states (MPS), have made great progress. However, exploring true 2D DQPTs remains difficult due to finite-size limitations and the geometric biases of quasi-1D cylinder mappings. Here, we bypass these limitations by deploying a tree tensor network (TTN) approach. This allows us to directly compute the quench dynamics of the transverse-field Ising model (TFIM) on an open 2D square lattice. Because the TTN architecture naturally mirrors 2D lattice connectivity, we can extract the global Loschmidt echo. Our simulations reveal that while deep quenches yield standard DQPTs, quenching within the ferromagnetic phase produces an anomalous dynamical response. In this regime, the rate function exhibits sharp non-analytic peaks even as the macroscopic order parameter maintains its initial sign. This decoupled behavior strongly indicates that local spin excitations drive 2D DQPTs, rather than the macroscopic domain-wall motions seen in 1D chains. These results provide a quantitative numerical baseline for understanding non-equilibrium quantum matter in higher dimensions. Full article

We investigate a random field of mutually dependent random variables (“spins”), indexed by a finite one-dimensional lattice, called in physical sciences the one-dimensional Ising model, in which the random variables can take only ±1 values (see the text for a precise definition). One of the couplings, termed a “bond,” that describes the mutual influence of two adjacent random variables is altered—it does not equal the others, thereby introducing a single “defect” bond. This defect bond represents a localised perturbation within an otherwise uniform system. Utilising the recurrence relations of Chebyshev polynomials and the bijective map between the number of spins and the polynomial index, we present a new method for calculations and systematically explore, using it, the system’s properties across different chain lengths and boundary conditions. As an application, we derive analytical expressions for the dependence of the average values of the random variables on their position within the chain, which we refer to as the “local magnetisation profile”. From the findings related to the system with a defect bond, we present a novel result for this profile under free (Dirichlet) boundary conditions and re-derive the corresponding result for antiperiodic boundary conditions. Full article

Sodium-pumping NADH: ubiquinone oxidoreductase (Na⁺-NQR) is an important component of the aerobic respiratory chain of Vibrio cholerae. It oxidizes NADH, reduces ubiquinone, and uses the free energy of this redox reaction to move sodium across the cell membrane. The enzyme is a membrane complex of six subunits, two 2Fe−2S centers, and four flavins. Both the oxidized and reduced forms of Na⁺-NQR exhibit EPR signals due to flavin semiquinone radicals. It has been shown that in the oxidized form of the enzyme, the radical is a neutral flavin, while in the NADH-reduced form, the radical is an anionic flavin. Electron Spin Echo Envelope Modulation Spectroscopy (ESEEM) was used to probe the presence of the magnetic nucleus ²³Na in the immediate vicinity of the paramagnetic centers. The contribution of the ²³Na nucleus was observed only in the ESEEM spectra of the anionic flavin semiquinone previously assigned to FMN_NqrB. Analysis shows that the Na⁺ ion is within ~3–4 Å of the flavin radical. This distance is consistent with two models: (i) complexation of the Na⁺ ion with the carbonyl group of CO4; or alternatively, (ii) a “cation-π interaction,” between Na⁺ and the electron-rich π-system of the flavin aromatic rings. Full article

Nanoimprint lithography (NIL) master fidelity is governed by coupled variations beginning with resist spin-coating, proceeding through electron beam exposure, and culminating in anisotropic etch transfer. We present an integrated, physics-based simulation chain. First, it includes a spin-coating thickness model that combines Emslie–Meyerhofer scaling with a Bornside edge correction. The simulated wafer-scale map at 4000 rpm exhibits the canonical center-rise and edge-bead profile with a 0.190–0.206 μm thickness range, while the locally selected 600 nm × 600 nm tile shows <0.1 nm variation, confirming an effectively uniform region for downstream analysis. Second, it couples an e-beam lithography (EBL) module in which column electrostatics and trajectory-derived spot size feed a hybrid Gaussian–Lorentzian proximity kernel; under typical operating conditions (${\sigma }_{traj}$ ≈ 2–5 nm), the model yields low CD bias (ΔCD = 2.38/2.73 nm), controlled LER (2.18/4.90 nm), and stable NMSE (1.02/1.05) for isolated versus dense patterns. Finally, the exposure result is passed to a level set reactive ion etching (RIE) model with angular anisotropy and aspect ratio-dependent etching (ARDE), which reproduces density-dependent CD shrinkage trends (4.42% versus 7.03%) consistent with transport-limited profiles in narrow features. Collectively, the simulation chain accounts for stage-to-stage propagation—from spin-coating thickness variation and EBL proximity to ARDE-driven etch behavior—while reporting OPC-aligned metrics such as NMSE, ΔCD, and LER. In practice, mask process correction (MPC) is necessary rather than optional: the simulator provides the predictive model, metrology supplies updates, and constrained optimization sets dose, focus, and etch set-points under CD/LER requirements. Full article

Gap-protected topological channels are a promising way to realize robust and high-fidelity state transfer in quantum networks. Although various topological transfer protocols based on the Su-Schrieffer-Heeger (SSH) model or its variants have been proposed, the phase accumulation during the evolution, as an essential aspect, is underestimated. Here, by numerically studying the phase information of quantum state transfer (QST) in one-dimensional (1D) topological spin chains, we uncover a universal phase correction ${\varphi }_0=(N-1)\pi /2$ for both adiabatic and diabatic topological schemes. Interestingly, the site-number-dependent phase correction satisfies ${\mathbb{Z}}_4$ symmetry and is equally effective for perfect mirror transmission in spin chains. Our work reveals a universal phase correction in 1D topologically protected QST, which will prompt a reevaluation of the topological protection mechanism in quantum systems. Full article

Heme enzymes that bind and reduce O₂ are susceptible to poisoning by NO. The high reactivity and affinity of NO for ferrous heme produces stable ferrous-NO complexes, which in theory should preclude O₂ binding and turnover. However, NO inhibition is often competitive with respect to O₂ and rapidly reversible, thus providing cellular and organismal survival advantages. This kinetic paradox has prompted a search for mechanisms for reversal and hence resistance. Here, I critically review proposed resistance mechanisms for NO dioxygenase (NOD) and cytochrome c oxidase (CcO), which substantiate reduction or oxidation of the tightly bound NO but nevertheless fail to provide kinetically viable solutions. A ferrous heme intermediate is clearly not available during rapid steady-state turnover. Reversible inhibition can be attributed to NO competing with O₂ in transient low-affinity interactions with either the ferric heme in NOD or the ferric heme-cupric center in CcO. Toward resolution, I review the underlying principles and evidence for kinetic control of ferric heme reduction via an O₂-triggered ferric heme spin crossover and an electronically-forced motion of the heme and structurally-linked protein side chains that elicit electron transfer and activate O₂ in the flavohemoglobin-type NOD. For CcO, kinetics, structures, and density functional theory point to the existence of an analogous O₂ and reduced oxygen intermediate-controlled electron-transfer gate with a linked proton pump function. A catalytic cycle and mechanism for CcO is finally at hand that links each of the four O₂-reducing electrons to each of the four pumped protons in time and space. A novel proton-conducting tunnel and channel, electron path, and pump mechanism, most notably first hypothesized by Mårten Wikström in 1977 and pursued since, are laid out for further scrutiny. In both models, low-energy spin-orbit couplings or ‘spintronic’ interactions with O₂ and NO or copper trigger the electronic motions within heme that activate electron transfer to O₂, and the exergonic reactions of transient reactive oxygen intermediates ultimately drive all enzyme, electron, and proton motions. Full article

We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior, raising the question of whether a measure of complexity can track this process. In addition to examining observable equilibration, we extend our analysis to study how the complexity of the quantum states evolves, providing insight into the transition from initial coherence to equilibrium. We define a classical statistical complexity measure based on observable entropy and deviation from equilibrium, which captures the dynamical progression towards equilibration and effectively distinguishes between complex and non-complex trajectories. In particular, our measure is sensitive to non-complex dynamics. Such dynamics include the quasi-periodic behavior exhibited by low-dimensional initial states, where the system explores a limited region of Hilbert space while preserving coherence. Numerical simulations of an Ising-like non-integrable Hamiltonian spin-chain model support these findings. Our work provides new insight into the emergence of equilibrium behavior from unitary dynamics and advances complexity as a meaningful tool in the study of the emergence of classicality in microscopic systems. Full article

We present a numerical investigation comparing two entanglement generation protocols in finite XX spin chains with varying spin magnitudes ($s=1/2,1,3/2$). Protocol 1 (P1) relies on staggered couplings to steer correlations toward the ends of the chain. At the same time, Protocol 2 (P2) adopts a dual-port architecture that uses optimized boundary fields to mediate virtual excitations between terminal spins. Our results show that P2 consistently outperforms P1 in all spin values, generating higher-fidelity entanglement in shorter timescales when evaluated under the same system parameters. Furthermore, P2 exhibits superior robustness under realistic imperfections, including diagonal and off-diagonal disorder, as well as dephasing noise. To further assess the resilience of both protocols in experimentally relevant settings, we employ the pseudomode formalism to characterize the impact of non-Markovian noise on the entanglement dynamics. Our analysis reveals that the dual-port mechanism (P2) remains effective even when memory effects are present, as it reduces the excitation of bulk modes that would otherwise enhance environment-induced backflow. Together, the scalability, efficiency, and noise resilience of the dual-port approach position it as a promising framework for entanglement distribution in solid-state quantum information platforms. Full article

We present a model of classical binary time series derived from a matrix product state (MPS) Ansatz widely used in one-dimensional quantum systems. We discuss how this quantum Ansatz allows us to generate classical time series in a sequential manner. Our time series are built in two steps: First, a lower-level series (the driving noise or the increments) is created directly from the MPS representation, which is then integrated to create our ultimate higher-level series. The lower- and higher-level series have clear interpretations in the quantum context, and we elaborate on this correspondence with specific examples such as the spin-1/2 Ising model in a transverse field (ITF model), where spin configurations correspond to the increments of discrete-time, discrete-level stochastic processes with finite or infinite autocorrelation lengths, Gaussian or non-Gaussian limit distributions, nontrivial Hurst exponents, multifractality, asymptotic self-similarity, etc. Our time series model is a parametric model, and we investigate how flexible the model is in some synthetic and real-life calibration problems. Full article

We investigate the entanglement properties in semiconductor quantum dot systems modeled by the extended Hubbard model, focusing on the impacts of potential energy variations and electron interactions within a four-site quantum dot spin chain. Our study explores local and pairwise entanglement across configurations with electron counts $N=4$ and $N=6$, under different potential energy settings. By adjusting the potential energy in specific dots and examining the entanglement across various interaction regimes, we identify significant variations in the ground states of quantum dots. We extend this analysis to larger systems with $L=6$ and $L=8$, comparing electron counts $N=L$ and $N=L+2$, revealing sharper entanglement transitions and reduced finite-size effects as the system size increases. Our results show that local potential shifts and the Coulomb interaction strength lead to notable redistributions of the electron configurations in the quantum dot spin chain, significantly affecting the entanglement properties. These changes are depicted in phase diagrams that highlight entanglements’ dependencies on the interaction strengths and potential energy adjustments, illustrating complex entanglement dynamics shifts triggered by interdot interactions. Full article

The cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics are its underlying ontological states that evolve by permutations. They do not create would-be quantum mechanical superposition states. We review this with a classical automaton consisting of an Ising spin chain which is then related to the Weyl equation in the continuum limit. Based on this and generalizing, we construct a new “Necklace of Necklaces” automaton with a torus-like topology that lends itself to represent the Dirac equation in 1 + 1 dimensions. Special attention has to be paid to its mass term, which necessitates this enlarged structure and a particular scattering operator contributing to the step-wise updates of the automaton. As discussed earlier, such deterministic models of discrete spins or bits unavoidably become quantum mechanical, when only slightly deformed. Full article