We delve into growing open chemical reaction systems (CRSs) characterized by autocatalytic reactions within a variable volume, which changes in response to these reactions. Understanding the thermodynamics of such systems is crucial for comprehending biological cells and constructing protocells because it sheds light on the physical conditions necessary for their self-replication. Building on our recent work, where we developed a thermodynamic theory for growing CRSs featuring basic autocatalytic motifs with regular stoichiometric matrices, we now expand this theory to include scenarios where the stoichiometric matrix has a nontrivial left kernel space. This extension introduces conservation laws, which limit the variations in chemical species due to reactions, thereby confining the system's possible states to those compatible with its initial conditions. By considering both thermodynamic and stoichiometric constraints, we clarify the environmental and initial conditions that dictate the CRSs' fate—whether they grow, shrink, or reach equilibrium. We also find that the conserved quantities significantly influence the equilibrium state achieved by a growing CRS. These results are derived independently of specific thermodynamic potentials or reaction kinetics, therefore underscoring the fundamental impact of conservation laws on the growth of the system.

We put forward four schemes of a coupled-qubit quantum Otto machine, a generalization of the single-qubit quantum Otto machine, based on work and heat transfer between an internal system consisting of a coupled pair of qubits and an external environment consisting of two heat baths and two work storages. The four schemes of our model are defined by the positions of attaching the heat baths, which play a key role in the power of the coupled-qubit engine. First, for the single-qubit heat engine, we find a maximum-power relation, and the fact that its efficiency at the maximum power is equal to the Otto efficiency, which is greater than the Curzon-Ahlborn efficiency. Second, we compare the coupled-qubit engines to the single-qubit engine from the point of view of achieving the maximum power based on the same energy-level change for work production and find that the coupling between the two qubits can lead to greater powers but the system efficiency at the maximum power is lower than the single-qubit system's efficiency and the Curzon-Ahlborn efficiency.

The quantum alternating operator ansatz (QAOA) is a generalized approach for solving challenging optimization problems that builds on the alternating structure of the quantum approximate optimization algorithm. Finding high-quality parameters efficiently for QAOA remains a major challenge in practice. In this work, we introduce a classical strategy for parameter setting, suitable for cases in which the number of distinct cost values grows only polynomially with the problem size, such as is common for constraint-satisfaction problems. The crux of our strategy is that we replace the cost function expectation value step of QAOA with a classical model that can be efficiently evaluated classically and has parameters which play an analogous role to the QAOA parameters. This model is based on empirical observations that, in some QAOA states, variable configurations with the same cost have the same amplitudes from step to step. We define this class of states as homogeneous states. For problems with particular symmetries, QAOA states are guaranteed to be homogeneous. More generally, high overlaps between QAOA states and homogeneous states have been empirically observed in a number of settings. Building on this idea, we define a classical homogeneous proxy for QAOA in which this property holds exactly and which yields information describing both states and expectation values. We then classically determine high-quality parameters for this proxy and then use these parameters in QAOA, an approach we label the homogeneous heuristic for parameter setting. We numerically examine this heuristic for MaxCut on unweighted Erdős-Rényi random graphs. For up to three QAOA levels we demonstrate that the heuristic is easily able to find parameters that match approximation ratios corresponding to previously found globally optimized approaches. For levels up to 20 we obtain parameters using our heuristic with approximation ratios monotonically increasing with depth, while a strategy that uses parameter transfer instead fails to converge with comparable classical resources. These results suggest that our heuristic may find good parameters in regimes that are intractable with noisy intermediate-scale quantum devices. Finally, we outline how our heuristic may be applied to wider classes of problems.

Cold shock proteins from the mesophilic organism Bacillus subtilis (BsCSP), the thermophilic organism Bacillus caldolyticus (BcCSP), and the hyperthermophilic organism Thermotoga maritima (TmCSP) are homologous proteins with similar native structure but quite different thermal stabilities, which makes them promising candidates for investigating the general and specific aspects the folding and unfolding dynamics of proteins and free-energy landscapes. In this study, we employed magnetic tweezers to explore the force-dependent folding and unfolding rates of BsCSP, BcCSP, and TmCSP at forces from several pN to tens of pN. Our results indicate similar force-dependent folding rates for these three proteins, while the unfolding rate of BsCSP, BcCSP, and TmCSP decreases sequentially, consistent with previous biochemical findings. Comparing with TmCSP, BcCSP shows lower but sufficient stability with folding free energy of 8.0 $k_{B}T$, and its force-dependent unfolding rates exhibit tremendous nonlinear behavior deviated from Bell's model like TmCSP. BsCSP has very low stability with folding free energy of only 3.9 $k_{B}T$, and its force-dependent unfolding rates at 3–10 pN exhibit almost linear behavior. Comprehensive free-energy landscapes are constructed, revealing common barriers that governs folding and unfolding dynamics for BcCSP and TmCSP but a wide merged barrier for BsCSP. Our findings provide valuable insights into the folding and unfolding mechanisms of these CSPs, shedding light on the relationship between protein structure, stability, and mechanical properties.

We study three aspects of work statistics in the context of the fluctuation theorem for quantum spin chains up to 1024 sites by numerical methods based on matrix-product states (MPSs). First, we use our numerical method to evaluate the moments/cumulants of work done by the sudden quench process on the Ising or Haldane spin chains, and we study their behaviors across the quantum phase transitions. Our results show that, up to the fourth cumulant, the work statistics can indicate the quantum phase transition characterized by the local order parameters but barely for purely topological phase transitions. Second, we propose to use the fluctuation theorem, such as Jarzynski's equality, which relates the real-time correlator to the ratio of the thermal partition functions, as a benchmark indicator for the numerical real-time evolving methods. Third, we study the passivity of ground and thermal states of quantum spin chains under some cyclic impulse processes. We show that the passivity of thermal states and ground states under the Hermitian actions is ensured by the second laws and variational principles, respectively, and we also verify this by numerical calculations. In addition, we also consider the passivity of ground states under non-Hermitian actions, for which the variational principle cannot be applied. Despite that, we find no violation of passivity from our numerical results for all the cases considered in the Ising and Haldane chains. Overall, we demonstrate that the work statistics for the sudden quench and impulse processes can be evaluated precisely by the numerical MPS method to characterize quantum phase transitions and examine the passivity of quantum states. We also propose to exploit the universality of the fluctuation theorem to benchmark the numerical real-time evolutions in an algorithmic and model-independent way.

We investigate the transport and energy spectrum properties of a three-dimensional high-order topological structure formed by stacking two-dimensional square diatomic Chern insulator lattices. Electron-hole symmetry and the energy spectrum degeneracy at individual points in the semimetallic phase are proven to be due to chiral and antiunitary symmetries in the periodic system. Additionally, we explore the influence of boundary conditions in a slab system with varying surface atom connectivity, and we demonstrate analytically the presence of zero-energy surface states in specific configurations. Moreover, we describe the emergence of two chiral hinge states driven by a perpendicular phase in the nanowire geometry. Next, the quantum Hall resistance is computed in the cross-configuration of a four-lead device. In this paper, we demonstrate that the trajectories of hinge states, determined by the number of layers in parallelepiped finite structure, give rise to fractional Hall plateaus.

Materials typically fail under complex stress states, essentially involving dilatational (volumetric) components that eventually lead to material decohesion/separation. It is therefore important to understand dilatational irreversible deformation—i.e., dilatational plasticity—en route to failure. In the context of glasses, much focus has been given to shear (volume-preserving) plasticity, both in terms of the stress states considered and the corresponding material response. Here, using a recently developed methodology and extensive computer simulations, we shed basic light on the elementary processes mediating dilatational plasticity in glasses. We show that plastic instabilities, corresponding to singularities of the glass Hessian, generically feature both dilatational and shear irreversible strain components. The relative magnitude and statistics of the strain components depend both on the symmetry of the driving stress (e.g., shear versus hydrostatic tension) and on the cohesive (attractive) part of the interatomic interaction. We further show that the tensorial shear component of the plastic strain is generally nonplanar and also extract the characteristic volume of plastic instabilities. Elucidating the fundamental properties of the elementary micromechanical building blocks of plasticity in glasses sets the stage for addressing larger-scale, collective phenomena in dilatational plasticity such as topological changes in the form of cavitation and ductile-to-brittle transitions. As a first step in this direction, we show that the elastic moduli markedly soften during dilatational plastic deformation approaching cavitation.

Spurred by the recent development of fracton topological phases, unusual topological phases possessing fractionalized quasiparticles with mobility constraints, the concept of symmetries has been renewed. In particular, in accordance with the progress of multipole symmetries, associated with conservation of multipoles, such as dipole or quadruple moments as well as global charges, there have been proposed topological phases with such symmetries. These topological phases are unconventional because excitations are subject to mobility constraints corresponding to the multipole symmetries. We demonstrate a way to construct such phases by preparing layers of symmetry protected topological (SPT) phases and implementing gauging a global symmetry. After gauging, the statistics of a fractional excitation is altered when crossing the SPT phases, resulting in topological phases with the multipole symmetries. The way we construct the phases allows us to have a comprehensive understanding of field theories of topological phases with the multipole symmetries and other fracton models.

We present a theoretical model of matter-wave diffraction through a material nanostructure. This model is based on the numerical solution of the time-dependent Schrödinger equation, which goes beyond the standard semiclassical approach. In particular, we consider the dispersion force interaction between the atoms and the material, which is responsible for high energy variations. The effect of such forces on the quantum model is investigated, along with a comparison with the semiclassical model. In particular, for atoms at low velocity and close to the material surface, the semiclassical approach fails, while the quantum model accurately describes the expected diffraction pattern. This description is thus relevant for slow and cold atom experiments where increased precision is required, e.g., for metrological applications.

We show that energy relaxation causes a point defect in the uniaxial-nematic phase of a spin-2 Bose-Einstein condensate to deform into a spin-Alice ring that exhibits a composite core structure with distinct topology at short and long distances from the singular line. An outer biaxial-nematic core exhibits a spin half-quantum vortex structure with a uniaxial-nematic inner core. By numerical simulation, we demonstrate a dynamical oscillation between the spin-Alice ring and a split-core hedgehog configuration via the appearance of ferromagnetic rings with associated vorticity inside an extended core region. We further show that a similar dynamics is exhibited by a spin-Alice ring surrounding a spin-vortex line resulting from the relaxation of a monopole situated on a spin-vortex line in the biaxial-nematic phase. In the cyclic phase, similar states are shown instead to form extended phase-mixing cores containing rings with fractional mass circulation or cores whose spatial shape reflects the order-parameter symmetry of a cyclic inner core, depending on the initial configuration.

The superconducting (SC) cuprate ${\mathrm{HgBa}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_8$ (Hg1223) has the highest SC transition temperature $T_c$ among cuprates at ambient pressure $P_{\mathrm{amb}}$, namely, $T_c^{\mathrm{opt}}\simeq 138$ K experimentally at the optimal hole doping concentration. $T_c^{\mathrm{opt}}$ further increases under pressure $P$ and reaches 164 K at optimal pressure $P_{\mathrm{opt}}\simeq 30$ GPa, then $T_c^{\mathrm{opt}}$ decreases with increasing $P>P_{\mathrm{opt}}$ generating a dome structure [Gao et al., Phys. Rev. B 50, 4260(R) (1994)]. This nontrivial and nonmonotonic $P$ dependence of $T_c^{\mathrm{opt}}$ calls for a theoretical understanding and mechanism. To answer this open question, we consider the ab initio low-energy effective Hamiltonian (LEH) for the antibonding (AB) $\mathrm{Cu}3d_{x^2-y^2}/\mathrm{O}2p_{\sigma }$ band derived generally for the cuprates. In the AB LEH for cuprates with $N_{\ell }\le 2$ laminated ${\mathrm{CuO}}_2$ planes between block layers, it was proposed that $T_c^{\mathrm{opt}}$ is determined by a universal scaling $T_c^{\mathrm{opt}}\simeq 0.16\left|t_1\right|F_{\mathrm{SC}}$ [Schmid et al., Phys. Rev. X 13, 041036 (2023)], where $t_1$ is the nearest-neighbor hopping, and the SC order parameter at optimal hole doping $F_{\mathrm{SC}}$ mainly depends on the ratio $u=U/|t_1|$ where $U$ is the onsite effective Coulomb repulsion: The $u$ dependence of $F_{\mathrm{SC}}$ has a peak at $u_{\mathrm{opt}}\simeq 8.5$ and a steep decrease with decreasing $u$ in the region $u<u_{\mathrm{opt}}$ irrespective of materials dependent on other ab initio parameters. In this paper, we show that $|t_1|$ increases with $P$, whereas $u$ decreases with $P$ in the ab initio Hamiltonian of Hg1223. Based on these facts, we show that the domelike $P$ dependence of $T_c^{\mathrm{opt}}$ can emerge at least qualitatively if we assume Hg1223 with $N_{\ell }=3$ follows the same universal scaling for $T_c^{\mathrm{opt}}$, and Hg1223 is located at the slightly strong coupling region $u\gtrsim u_{\mathrm{opt}}$ at $P_{\mathrm{amb}}$ and $u\simeq u_{\mathrm{opt}}$ at $P_{\mathrm{opt}}$ by taking account of expected corrections to our ab initio calculation. The consequence of these assumptions is the following: With increasing $P$ within the range $P<P_{\mathrm{opt}}$, the increase in $T_c^{\mathrm{opt}}$ is accounted for by the increase in $|t_1|$, whereas $F_{\mathrm{SC}}$ is insensitive to the decrease in $u$ around $\simeq u_{\mathrm{opt}}$ and hence to $P$ as well. At $P>P_{\mathrm{opt}}$, the decrease in $T_c^{\mathrm{opt}}$ is accounted for by the decrease in $u$ below $u_{\mathrm{opt}}$, which causes a rapid decrease in $F_{\mathrm{SC}}$ dominating over the increase in $|t_1|$. We further argue the appropriateness of these assumptions based on the insight from studies on other cuprate compounds in the literature. In addition, we discuss the dependencies of $u$ and $|t_1|$ on each crystal parameter (CP), which provides hints for design of even higher $T_c^{\mathrm{opt}}$ materials.

We study the effects of the interplay of weak disorder and weak coupling in a system of parametric micromechanical oscillators. Each oscillator is bistable, enabling the mapping of its stable states onto spin states. The coupling changes the rate of interstate switching of an oscillator depending on the state of other oscillators. We demonstrate that the change is exponentially strong and therefore manifests even for weak coupling. Difference in the oscillator eigenfrequencies translates into disorder in the system. The analysis and the experiment show that disorder leads to a nontrivial stationary state that displays current. The system provides a well-controlled and fully characterized implementation of the asymmetric Ising model, in which coupled spins affect each other differently. This model plays an important role in physics and biology. Our findings open the possibilities of constructing and exploring asymmetric Ising systems with controlled parameters and connectivity.

Through the analysis of the spatial correlations of local stress, we detect the propagation of long-ranged liquid-elasticity-mediated shear stress waves in polymeric and low-molecular weight liquids. The propagation of shear waves is effectively planar; i.e., ${\sigma }_{\alpha \beta }$ propagates in the $\alpha \beta$ plane. The autocorrelation functions of the local stress of a region are affected by both the relaxation of stress in that region and the propagation of stress from the region to the rest of the sample. However, due to the planar propagation of shear waves, the transfer of ${\sigma }_{\alpha \beta }$ from those slices of the simulation box that are periodic in the $\alpha \beta$ plane is negligible. This allows direct probing of the position-dependent local stress relaxation modulus of liquid in the vicinity of a confining surface.

Reconstructing Hamiltonians from local measurements is key to enabling reliable quantum simulations: both validating the implemented model and identifying any leftover terms with sufficient precision is a problem of increasing importance. Here we propose a deep-learning-assisted variational algorithm for Hamiltonian reconstruction by preprocessing a dataset that is diagnosed to contain thermal measurements of local operators. We demonstrate the efficient and precise reconstruction of local Hamiltonians, while long-range interacting Hamiltonians are reconstructed approximately. Away from equilibrium, for periodically and random multipolar driven systems, we reconstruct the effective Hamiltonian widely used for Floquet engineering of metastable steady states. Moreover, our approach allows us to reconstruct an effective quasilocal Hamiltonian even in the heating regime beyond the validity of the prethermal plateau, where perturbative expansions fail.

Quantum state engineering plays a vital role in various applications in the field of quantum information. Different strategies, including drive-and-dissipation, adiabatic cooling, and measurement-based steering, have been proposed for state generation and manipulation, each with its upsides and downsides. Here, we address a class of measurement-based state engineering protocols where a sequence of generalized measurements is employed to steer a quantum system toward a desired (pure or mixed) target state. Previously studied measurement-based protocols relied on idealized procedures and avoided exploration of the effects of various errors stemming from imperfections of experimental realizations and external noise. We employ the quantum trajectory formalism to provide a detailed analysis of the robustness of these steering protocols against multiple classes of errors. We study a set of realistic errors that can be classified as dynamic or static, depending on whether they remain unchanged while running the protocol. More specifically, we investigate the impact of the erroneous choice of detector-system coupling, erroneous re-initialization of the detector state following a measurement step, fluctuating steering directions, and environmentally induced errors in the detector-system interaction. We show that the protocol remains fully robust against the erroneous choice of detector-system coupling parameters and presents reasonable robustness against other types of errors. Our analysis employs various quantifiers such as fidelity, trace distance, and linear entropy to characterize the protocol's robustness and provide analytical results for these quantifiers against various errors. We introduce averaging hierarchies of stochastic equations describing individual quantum trajectories associated with detector readouts. Subsequently, we demonstrate the commutation between the classical expectation value and the time-ordering operator of the exponential of a Hamiltonian with multiplicative white noise, as well as the commutation of the expectation value and the partial trace with respect to detector outcomes. Our ideas are implemented and demonstrated for a specific class of steering platforms, addressing a single qubit.

Anisotropic environmental signals or polarized membrane ion/solute carriers can generate spatially varying intracellular gradients, leading to polarized cell dynamics. For example, the directional migration of neutrophils, galvanotaxis of glioblastoma, and water flux in kidney cells all result from the polarized distribution of membrane ion carriers and other intracellular components. The underlying physical mechanisms behind how polarized ion carriers interact with environmental signals are not well studied. Here, we use a physiology-relevant, physics-based mathematical model to reveal how ion carriers generate intracellular ion and voltage gradients. The model can discern the contribution of individual ion carriers to the intracellular pH gradient, electric potential, and water flux. We discover that an extracellular pH gradient leads to an intracellular pH gradient via chloride-bicarbonate exchangers, whereas an extracellular electric field leads to an intracellular electric potential gradient via passive potassium channels. In addition, mechanical-biochemical coupling can modulate actin distribution and flow, creating a biphasic dependence of cell speed on water flux. Moreover, we find that F-actin interaction with NHE alone can generate cell movement, even when other ion carriers are not polarized. Taken together, the model highlights the importance of cell ion dynamics in modulating cell migration and cytoskeletal dynamics.

The equipartition theorem is a fundamental law of classical statistical physics, which states that every degree of freedom contributes $k_{\mathrm{B}}T/2$ to the energy, where $T$ is the temperature and $k_{\mathrm{B}}$ is the Boltzmann constant. Recent studies have revealed the existence of a quantum version of the equipartition theorem. In the present work, we focus on how to obtain the quantum counterpart of the generalized equipartition theorem for arbitrary quadratic systems in which the multimode Brownian oscillators interact with multiple reservoirs at the same temperature. An alternative method of deriving the energy of the system is also discussed and compared with the result of the quantum version of the equipartition theorem, after which we conclude that the latter is more reasonable. Our results can be viewed as an indispensable generalization of recent works on a quantum version of the equipartition theorem.