In living cells, the bistable switches involving phosphorylation-dephosphorylation (PdP) cycles, operate far from thermodynamic equilibrium and consume hydrolysis free energy to perform ultrasensitive response and exhibit strong robustness against noise. Here, we focus on the distinct roles of cellular ATP levels ([ATP]) and hydrolysis free energy ($\mathrm{\Delta }\mu$) in bistable switches with different structures of reaction network. Specifically, we herein propose thermodynamically consistent models of single- and double-PdP-cycle bistable switches to study the relationship between network structures and the interplay between [ATP] and $\mathrm{\Delta }\mu$. We demonstrate that [ATP] and $\mathrm{\Delta }\mu$ act cooperatively to promote the activation of switches in identical networks wherein all phosphorylations promote target production, irrespective of different feedback mechanisms. On the other hand, the competition between [ATP] and $\mathrm{\Delta }\mu$ found in the nonidentical, or reversed, networks can enhance the robustness of bistability. We also discuss special network structures inducing multistability or nonmonotonic functions of $\mathrm{\Delta }\mu$. Our results gain insight into the relationship between network structures and the roles of [ATP] and $\mathrm{\Delta }\mu$ in bistable switches, potentially guiding the future design of synthetic biochemical switches.

To successfully navigate chemical gradients, microorganisms need to predict how the ligand concentration changes in space. Due to their limited size, they do not take a spatial derivative over their body length but rather a temporal derivative, comparing the current signal with that in the recent past over the so-called adaptation time. This strategy is pervasive in biology, but it remains unclear what determines the accuracy of such measurements. Using a generalized version of the previously established sampling framework, we investigate how resource limitations and the statistics of the input signal set the optimal design of a well-characterized network that measures temporal concentration changes: the Escherichia coli chemotaxis network. Our results show how an optimal adaptation time arises from the trade-off between the sampling error, caused by the stochastic nature of the network, and the dynamical error, caused by uninformative fluctuations in the input. A larger resource availability reduces the sampling error, which allows for a smaller adaptation time, thereby simultaneously decreasing the dynamical error. Similarly, we find that the optimal adaptation time scales inversely with the gradient steepness, because steeper gradients lift the signal above the noise and reduce the sampling error. These findings shed light on the principles that govern the optimal design of the E. coli chemotaxis network specifically, and any system measuring temporal changes more broadly.

Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics was recently proposed that can generate high velocity gradients from a smooth-in-space forcing term. It is based on a linear partial differential equation stirred by an additive random forcing term that is $\delta$-correlated in time. The underlying proposed deterministic mechanism corresponds to a transport in Fourier space that aims to transfer energy injected at large scales towards small scales. The key role of the random forcing is to realize these transfers in a statistically homogeneous way. Whereas at finite times and positive viscosity the solutions are smooth, a loss of regularity is observed for the statistically stationary state in the inviscid limit. We present here simulations, based on finite volume methods in the Fourier domain and a splitting method in time, which are more accurate than the pseudospectral simulations. We show that our algorithm is able to reproduce accurately the expected local and statistical structure of the predicted solutions. We conduct numerical simulations in one, two, and three spatial dimensions, and we display the solutions both in physical and Fourier space. We additionally display key statistical quantities such as second-order structure functions and power spectral densities at various viscosities.

We present a detailed derivation of the elastic energy of a homogeneous, isotropic linear elastic medium consisting of different coherent martensite variants or phases and its mapping to an Ising model, as required for an efficient quantum annealing determination of the equilibrium microstructure. The approach is demonstrated for a sample with a large number of grains with a tetragonal eigenstrain. Furthermore, we illustrate how the elastic effects may lead to the formation of ion conducting channels in the doped solid electrolyte ${\mathrm{Li}}_7{\mathrm{La}}_3{\mathrm{Zr}}_2{\mathrm{O}}_{12}$ (LLZO). Apart from bulk elastic and chemical effect we demonstrate how to include interfacial effects into the quantum annealing approach and emphasize the importance of high precision elastic calculations.

The clogging transition of granular flow through a disordered porous structure is investigated by three-dimensional discrete element simulations. Results reveal the existence of an intermittent flow state, which has been already observed for active particles or agitated grains, but is absent in single-pore flows of passive particles. Interestingly, the analysis of the intermittent dynamics shows similar attributes to the bottleneck flow of active grains, i.e., exponential distribution of flowing intervals and power-law tails for the clogging times. Precisely, based on the exponent of the power-law tail, a clogging phase diagram for porous structures is proposed in the plane of the scaled pore size $D/d_p$ and the friction coefficient ${\mu }_s$. Then, we demonstrate that the intermittency arises from a delay in the dissipation of particles' kinetic energy after clogging imposed by the porous structure. Finally, the maximum achievable particle flow rate driven by gravity is predicted from the Froude number ${\mathrm{Fr}}_m$, which linearly scales with the pore size and the friction coefficient.

When a measurement observable does not commute with a quantum system's Hamiltonian, the energy of the measured system is typically not conserved during the measurement. Instead, energy can be transferred between the measured system and the meter. In this work, we experimentally investigate the energetics of noncommuting measurements in a circuit quantum electrodynamics system containing a transmon qubit embedded in a 3D microwave cavity. We show through spectral analysis of the cavity photons that a frequency shift is imparted on the probe, in balance with the associated energy changes of the qubit. Our experiment provides new insights into foundations of quantum measurement, as well as a better understanding of the key mechanisms at play in quantum energetics.

Collective light emission and multiqubit dynamics of solid-state quantum emitters are affected both by their coupling to the light field and to lattice vibrations. The effect of phonons on quantum emitters is twofold: polaron formation is described by ultrafast non-Markovian dynamics, while slower dephasing is well described by exponential decay. Of the two temperature-dependent processes, the effect of the former on the collective emission and the entanglement decay of emitters is usually not modeled, and also the latter is sometimes neglected. Here we propose and compare two methods that are efficient also for several emitters: the first method concatenates the fast and slow phonon dynamics, and the second is the polaron method. For a single quantum emitter, we show that the dynamical equations are identical in both methods, while predictions for two or more emitters also agree very well. Both of our methods incorporate non-Markovian dynamics due to phonons demonstrating the temperature sensitivity of the collective photon emission. Utilizing a simplified Markovian model instead may not be accurate enough especially for quantum information applications: for example, we show how the Markovian model may considerably overestimate the two-emitter concurrence, except at very low temperatures. Our concatenation and polaron methods can be applied to an arbitrary number and type of quantum emitters, and beyond the bulk GaAs environment that we consider here. Especially the concatenation method can take phonon effects into account at the same computational cost as modeling the emitter-photon interaction alone. Finally, we present approximate analytical expressions for the collective emission spectrum for $N$ emitters on a one-dimensional chain.

The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this paper, we provide a family of versatile generalizations of this relation. Our proof methods build on a deep connection between entropic uncertainties and interpolation inequalities for the doubly stochastic map that links probability distributions in two measurement bases. In contrast to the original relation, our generalization also incorporates the von Neumann entropy of the underlying quantum state. These results can be directly used to bound the extractable randomness of a source-independent quantum random number generator in the presence of fully quantum attacks, to certify entanglement between trusted parties, or to bound the entanglement of a system with an untrusted environment.

Searching via quantum walk is a topic that has been extensively studied. Most previous results provide approximate solutions, while in this paper we prove an algorithm that can find a marked vertex certainly. We adopt the coined discrete-time quantum walk (DTQW) model with adjusted operators and prove that, on complete bipartite graphs, when parameters are set properly, coined DTQW can deterministically find a marked vertex, i.e., the success probability is exactly 1. Before this paper there have been results of an alternating continuous-time quantum walk method that achieve deterministic spatial search, but this paper provides a deterministic quantum spatial search result via DTQW, while maintaining a quadratic speedup compared to classical algorithms. We also provide the quantum circuit implementation.

Normalizing flows (NF) are powerful generative models with increasing applications in augmenting Monte Carlo algorithms due to their high flexibility and expressiveness. In this work we explore the integration of NF in the diagrammatic Monte Carlo (DMC) method, presenting an architecture designed to sample the intricate multidimensional space of Feynman's diagrams through dimensionality reduction. By decoupling the sampling of diagram order and interaction times, the flow focuses on one interaction at a time. This enables one to construct a general diagram by employing the same unsupervised model iteratively, dressing a zero-order diagram with interactions determined by the previously sampled order. The resulting NF-augmented DMC method is tested on the widely used single-site Holstein polaron model in the entire electron-phonon coupling regime. The obtained data show that the model accurately reproduces the diagram distribution by reducing sample correlation and observables' statistical error, constituting the first example of global sampling strategy for connected Feynman's diagrams in the DMC method.

Nuclear charge radius differences in the silver isotopic chain have been reported through different combinations of experiment and theory, exhibiting a tension of two combined standard errors. This study investigates this issue by combining high-accuracy calculations for six low-lying states of atomic silver with an improved measurement of the $5s{}^2{S}_{1/2}-5p{}^2{P}_{3/2}$ transition optical isotope shift. Our calculations predict measured electronic transition energies in Ag i at the 0.3% level, the highest accuracy achieved in this system so far. We calculate electronic isotope shift factors by employing analytical response relativistic coupled-cluster theory and find that a consistent charge radius difference between ${}^{107,109}\mathrm{Ag}$ is returned when combining our calculations with the available optical isotope shift measurements. We therefore recommend an improved value for the mean-squared charge radius difference between ${}^{107}\mathrm{Ag}$ and ${}^{109}\mathrm{Ag}$ as 0.207(6) ${\mathrm{fm}}^2$, within one combined error from the value derived from muonic Ag experiments, and an updated set of charge radii differences across the isotopic chain.

Disorder can fundamentally modify the transport properties of a system. A striking example is Anderson localization, suppressing transport due to destructive interference of propagation paths. In inhomogeneous many-body systems, not all particles are localized for finite-strength disorder, and the system can become partially diffusive. Unraveling the intricate signatures of localization from such observed diffusion is a longstanding problem. Here, we experimentally study a degenerate, spin-polarized Fermi gas in a disorder potential formed by an optical speckle pattern. We record the diffusion through the disordered potential upon release from an external confining potential. We compare different methods to analyze the resulting density distributions, including a new approach to capture particle dynamics by evaluating absorption-image statistics. Using standard observables, such as diffusion exponent and coefficient, localized fraction, or localization length, we find that some show signatures for a transition to localization above a critical disorder strength, while others show a smooth crossover to a modified diffusion regime. In laterally displaced disorder, we spatially resolve different transport regimes simultaneously, which allows us to extract the subdiffusion exponent expected for weak localization. Our work emphasizes that the transition toward localization can be investigated by closely analyzing the system's diffusion, offering ways of revealing localization effects beyond the signature of exponentially decaying density distribution.

We propose and experimentally demonstrate an analog scheme for generating XY-type ($J_{ij}^x{\sigma }_x^i{\sigma }_x^j+J_{ij}^y{\sigma }_y^i{\sigma }_y^j$) Hamiltonians on trapped ion spins with independent control over the $J_{ij}^x$ and $J_{ij}^y$ terms. The Ising-type interactions ${\sigma }_x^i{\sigma }_x^j$ and ${\sigma }_y^i{\sigma }_y^j$ are simultaneously generated by employing two spin-dependent forces operating in parallel on the same set of normal modes. We analytically calculate the region of validity of this scheme, and provide numerical and experimental validation with ${}^{171}\mathrm{Yb}^{+}$ ions. This scheme inherits the programmability and scalability of the Ising-type interactions with trapped ions that have been explored in numerous quantum simulation experiments. Our approach extends the capabilities of existing trapped ion quantum simulators to access a large class of spin Hamiltonians relevant for exploring exotic quantum phases such as superfluidity and spin liquids.

We present the irreversibility generated by a stationary cavity magnomechanical system composed of a yttrium iron garnet (YIG) sphere with a diameter of a few hundred micrometers inside a microwave cavity. In this system, the magnons, i.e., collective spin excitations in the sphere, are coupled to the cavity photon mode via magnetic dipole interaction and to the phonon mode via magnetostrictive force (optomechanical-like). We employ the quantum phase-space formulation of the entropy change to evaluate the steady-state entropy production rate and associated quantum correlation in the system. We find that the behavior of the entropy flow between the cavity photon mode and the phonon mode is determined by the magnon-photon coupling and the cavity photon dissipation rate. Interestingly, the entropy production rate can increase/decrease depending on the strength of the magnon-photon coupling and the detuning parameters. We further show that the amount of correlations between the magnon and phonon modes is linked to the irreversibility generated in the system for small magnon-photon coupling. Our results demonstrate the possibility of exploring irreversibility in driven magnon-based hybrid quantum systems and open a promising route for quantum thermal applications.