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We take non-Hermitian Aubry–André–Harper models and quasiperiodic Kitaev chains as examples to demonstrate the equivalence and superposition of real and imaginary quasiperiodic potentials (QPs) on inducing localization of single-particle states. We prove this equivalence by analytically computing Lyapunov exponents (or inverse of localization lengths) for systems with purely real and purely imaginary QPs. Moreover, when superposed and with the same frequency, real and imaginary QPs are coherent on inducing the localization, in a way which is determined by the relative phase between them. The localization induced by a coherent superposition can be simulated by the Hermitian model with an effective strength of QP, implying that models are in the same universality class. When their frequencies are different and relatively incommensurate, they are incoherent and their superposition leads to less correlation effects. Numerical results show that the localization happens earlier and there is an intermediate mixed phase lacking of mobility edge.

Photoluminescent zero-dimensional (0D) quantum dots (QDs) derived from transition metal dichalcogenides, particularly molybdenum disulfide, are presently in the spotlight for their advantageous characteristics for optoelectronics, imaging, and sensors. Nevertheless, up to now, little work has been done to synthesize and explore photoluminescent 0D WS 2 QDs, especially by a bottom-up strategy without using usual toxic organic solvents. In this work, we report a facile bottom-up strategy to synthesize high-quality water-soluble tungsten disulfide (WS 2 ) QDs through hydrothermal reaction by using sodium tungstate dihydrate and l -cysteine as W and S sources. Besides, hybrid carbon quantum dots/WS 2 QDs were further prepared based on this method. Physicochemical and structural analysis of QD hybrid indicated that the graphitic carbon quantum dots with diameters about 5 nm were held onto WS 2 QDs via electrostatic attraction forces. The resultant QDs show good water solubility and stable photoluminescence (PL). The excitation-dependent PL can be attributed to the polydispersity of the synthesized QDs. We found that the PL was stable under continuous irradiation of UV light but can be quenched in the presence of hydrogen peroxide (H 2 O 2 ). The obtained WS 2 -based QDs were thus adopted as an electrodeless luminescent probe for H 2 O 2 and for enzymatic sensing of glucose. The hybrid QDs were shown to have a more sensitive LOD in the case of glucose sensing. The Raman study implied that H 2 O 2 causes the partial oxidation of QDs, which may lead to oxidation-induced quenching. Overall, the presented strategy provides a general guideline for facile and low-cost synthesis of other water-soluble layered material QDs and relevant hybrids in large quantity. These WS 2 -based high-quality water-soluble QDs should be promising for a wide range of applications in optoelectronics, environmental monitoring, medical imaging, and photocatalysis.

Superlattice materials have emerged as promising candidates for water electrocatalysis due to their tunable crystal structures, electronic properties, and potential for interface engineering. However, the catalytic activity of transition metal‐based superlattice materials for the hydrogen evolution reaction (HER) is often constrained by their intrinsic electronic band structures, which can limit charge carrier mobility and active site availability. Herein, a highly efficient electrocatalyst based on a VS2‐VS heterodimensional (2D‐1D) superlattice with sulfur vacancies is designed addressing the limitations posed by the intrinsic electronic structure. The enhanced catalytic performance of the VS2‐VS superlattice is primarily attributed to the engineered heterojunction, where the work function difference between the VS2 layer and VS chain induces a charge separation field that promotes efficient electron‐hole separation. Introducing sulfur vacancies further amplifies this effect by inducing quantum localization of the separated electrons, thereby significantly boosting HER activity. Both theoretical and experimental results demonstrate that the superlattice achieves a ΔGH* of −0.06 eV and an impressively low overpotential of 46 mV at 10 mA·cm−2 in acidic media, surpassing the performance of commercial Pt/C while maintaining exceptional stability over 15 000 cycles. This work underscores the pivotal role of advanced material engineering in designing catalysts for sustainable energy applications. In this study, the VS2‐VS heterodimensional superlattice electrocatalyst with sulfur vacancies is designed to overcome the intrinsic electronic constraints. The engineered heterojunction between the VS2 layer and the VS chain creates a charge separation field that enhances electron‐hole separation, while sulfur vacancies contribute to quantum localization, significantly boosting HER activity.

Lithium tantalate is technologically one of the most important ferroelectric materials with a low poling field that has several applications in the field of photonics and memory switching devices. In a Hamiltonian system, such as dipolar system, the polarization behavior of such ferroelectrics can be well-modeled by Klein–Gordon (K-G) equation. Due to strong localization coupled with discreteness in a nonlinear K-G lattice, there is a formation of breathers and multi-breathers that manifest in the localization peaks across the domains in polarization–space–time plot. Due to the presence of nonlinearity and also impurities (as antisite tantalum defects) in the structure, dissipative effects are observed and hence dissipative breathers are studied here. To probe the quantum states related to discrete breathers, the same K-G lattice is quantized to give rise to quantum breathers (QBs) that are explained by a periodic boundary condition. The gap between the localized and delocalized phonon-band is a function of impurity content that is again related to the effect of pinning of domains due to antisite tantalum defects in the system, i.e., a point of easier switching within the limited amount of data on poling field, which is related to Landau coefficient (read, nonlinearity). Secondly, in a non-periodic boundary condition, the temporal evolution of quanta shows interesting behavior in terms of ‘critical’ time of redistribution of quanta that is proportional to QB’s lifetime in femtosecond having a possibility for THz applications. Hence, the importance of both the methods for characterizing quantum breathers is shown in these perspectives.

A bstract In AdS/CFT we consider a class of bulk geometric quantities inside the entanglement wedge called reflected minimal surfaces. The areas of these surfaces are dual to the entanglement entropy associated to a canonical purification (the GNS state) that we dub the reflected entropy . From the bulk point of view, we show that half the area of the reflected minimal surface gives a reinterpretation of the notion of the entanglement wedge cross-section. We prove some general properties of the reflected entropy and introduce a novel replica trick in CFTs for studying it. The duality is established using a recently introduced approach to holographic modular flow. We also consider an explicit holographic construction of the canonical purification, introduced by Engelhardt and Wall; the reflected minimal surfaces are simply RT surfaces in this new spacetime. We contrast our results with the entanglement of purification conjecture, and finally comment on the continuum limit where we find a relation to the split property: the reflected entropy computes the von Neumann entropy of a canonical splitting type-I factor introduced by Doplicher and Longo.

A bstract Quantum complexity, suitably defined, has been suggested as an important probe of late-time dynamics of black holes, particularly in the context of AdS/CFT. A notion of quantum complexity can be effectively captured by quantifying the spread of an operator in Krylov space as a consequence of time evolution. Complexity is expected to behave differently in chaotic many-body systems, as compared to integrable ones. In this paper we investigate Krylov complexity for the case of interacting integrable models at finite size and find that complexity saturation is suppressed as compared to chaotic systems. We associate this behavior with a novel localization phenomenon on the Krylov chain by mapping the theory of complexity growth and spread to an Anderson localization hopping model with off-diagonal disorder, and find that localization is enhanced in the integrable case due to a stronger disorder in the hopping amplitudes, inducing an effective suppression of Krylov complexity. We demonstrate this behavior for an interacting integrable model, the XXZ spin chain, and show that the same behavior results from a phenomenological model that we define: this model captures the essential features of our analysis and is able to reproduce the behaviors we observe for chaotic and integrable systems via an adjustable disorder parameter.

A bstract The SYK model is a quantum mechanical model that has been proposed to be holographically dual to a 1 + 1-dimensional model of a quantum black hole. An emergent “gravitational” mode of this model is governed by an unusual action that has been called the Schwarzian action. It governs a reparametrization of a circle. We show that the path integral of the Schwarzian theory is one-loop exact. The argument uses a method of fermionic localization, even though the model itself is purely bosonic.

We propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and particles) are emergent in the form of joint probability amplitudes for position and time of events. Textbook relativistic quantum mechanics and quantum field theory can be recovered by dividing the event Hilbert spaces into space and time (a foliation) and then conditioning the event states onto the time part. Our theory satisfies the full Lorentz symmetry as a ‘geometric’ unitary transformation, and possesses relativistic observables for space (location of an event) and time (position in time of an event).

Universal quantum computers are potentially an ideal setting for simulating many-body quantum dynamics that is out of reach for classical digital computers. We use state-of-the-art IBM quantum computers to study paradigmatic examples of condensed matter physics—we simulate the effects of disorder and interactions on quantum particle transport, as well as correlation and entanglement spreading. Our benchmark results show that the quality of the current machines is below what is necessary for quantitatively accurate continuous-time dynamics of observables and reachable system sizes are small comparable to exact diagonalization. Despite this, we are successfully able to demonstrate clear qualitative behaviour associated with localization physics and many-body interaction effects.