We formulate the superfluid weight in unconventional superconductors with $\mathit{k}$-dependent Cooper pair potentials based on the geometric properties of Bloch electrons. We apply the formula to a model of monolayer FeSe obtained by first-principles calculation. Our numerical calculations point to a significant enhancement of the Berezinskii-Kosterlitz-Thouless transition temperature due to the geometric contribution to the superfluid weight, which is not included in the Fermi liquid theory. The $\mathit{k}$ dependence of the gap function also stabilizes the superconducting state. Our results reveal that the geometric properties of Bloch electrons play an essential role in superconducting materials and pave the way for clarifying hidden aspects of superconductivity from the viewpoint of quantum geometry.

Transport in strongly interacting Fermi gases provides a window into the nonequilibrium behavior of strongly correlated fermions. In particular, the interface between a strongly polarized normal gas and a weakly polarized superfluid at finite temperature presents a model for understanding transport at normal-superfluid and normal-superconductor interfaces. An excess of polarization in the normal phase or a deficit of polarization in the superfluid brings the system out of equilibrium, leading to transport currents across the interface. We implement a phenomenological mean-field model of the unitary Fermi gas, and investigate the transport of spin and mass under nonequilibrium conditions. We consider independently prepared normal and superfluid regions brought into contact, and calculate the instantaneous spin and mass currents across the normal-superfluid (NS) interface. For an unpolarized superfluid, we find that spin current is suppressed below a threshold value in the driving chemical potential differences, while the threshold nearly vanishes for a critically polarized superfluid. The mass current can exhibit a threshold in cases where Andreev reflection vanishes, while in general Andreev reflection prevents the occurrence of a threshold in the mass current. Our results provide guidance to future experiments aiming to characterize spin and mass transport across NS interfaces.

We present a general quantum fluctuation theorem for the entropy production of an open quantum system coupled to multiple environments, not necessarily at equilibrium. Such a general theorem, when restricted to the weak-coupling and Markovian regime, holds for both local and global master equations, corroborating the thermodynamic consistency of local quantum master equations. The theorem is genuinely quantum, as it can be expressed in terms of conservation of a Hermitian operator, describing the dynamics of the system state operator and of the entropy change in the baths. The integral fluctuation theorem follows from the properties of such an operator. Furthermore, it is also valid when the system is described by a time-dependent Hamiltonian. As such, the quantum Jarzynski equality is a particular case of the general result presented here. Moreover, our result can be extended to nonthermal baths, as long as microreversibility is preserved. We present some numerical examples to showcase the exact results previously obtained. We finally generalize the fluctuation theorem to the case where the interaction between the system and the bath is explicitly taken into account. We show that the fluctuation theorem amounts to a relation between time-reversed dynamics of the global density matrix and a two-time correlation function along the forward dynamics involving the baths' entropy alone.

The two classes of membrane transport, namely, secondary active and passive transport, are understood as different reaction pathways in the same protein structure, described by the 16-state model in this paper. To quantify the thermodynamic difference between secondary active transport and passive transport, we extend the second law of information thermodynamics of the autonomous demon in the four-state model composed of two subsystems to the 16-state model composed of four subsystems representing the membrane transport. We reduce the 16 states to 4 states and derive the coarse-grained second law of information thermodynamics, which provides an upper bound of the free energy transport by the coarse-grained information flow. We also derive an upper bound on the free energy transport by the multi-body information flow representing the two-body or four-body correlations in the 16-state model by exploiting the cycle decomposition. The coarse-grained information flow and the multi-body information flows express the quantitative difference between secondary active and passive transport. The numerical analysis shows that the coarse-grained information flow is positive for secondary active transport and negative for passive transport. The four-body correlation is dominant in the multi-body information flows for secondary active transport. In contrast, the two-body correlation is dominant for passive transport. This result shows that both the sign of the coarse-grained information flow and the difference of the four-body correlation and the two-body correlation explain the difference of the free energy transport in secondary active and passive transport.

We investigate the relative volume of parent Hamiltonians having a target ground state up to some fixed error $\epsilon$, a quantity which sets a benchmark on the performance of quantum simulators. For vanishing error, this relative volume is of measure zero, whereas for a generic $\epsilon$ we show that it increases with the dimension of the Hilbert space. We also address the volume of parent Hamiltonians when they are restricted to be local. For translationally invariant Hamiltonians, we provide an upper bound to their relative volume. Finally, we estimate numerically the relative volume of parent Hamiltonians when the target state is the ground state of the Ising chain in a transverse field.

We use atomistic computer simulations to provide a microscopic description of the brittle failure of amorphous materials, and we assess the role of rare events and quenched disorder. We argue that brittle yielding originates at rare soft regions, similarly to Griffiths effects in disordered systems. We numerically demonstrate how localized plastic events in such soft regions trigger macroscopic failure via the propagation of a shear band. This physical picture, which no longer holds in poorly annealed ductile materials, allows us to discuss the role of finite-size effects in brittle yielding and reinforces the similarities between yielding and other disorder-controlled nonequilibrium phase transitions.

Cosmic radiation is a potential additional tool for atmospheric monitoring. High-energy cosmic rays, interacting in the atmosphere, produce secondary particles, the production and propagation of which are ruled by the state of the atmosphere. Atmospheric muons carry information on the stratosphere, as its temperature modulates their intensity. Here, we present a comprehensive investigation of the 24-year series of the muon flux recorded underground with the Large Volume Detector in the Gran Sasso Laboratory in Italy. Using advanced spectral-analysis methods, we reveal, in addition to the well-known annual cycle, two significant variations with periods of about four and ten years. These two multiannual components, however, are not present in the series of the so-called effective temperature—an average parameter commonly used to describe the entire atmospheric profile in relationship to the detected muon flux—but we find them in the series of the raw temperatures in the lower-stratospheric levels. We show that the weaker multiannual cycles emerge in the temperature series thanks to the dampening of the dominant annual radiative cycle at these levels, which are affected by higher-frequency variability related to transport and wave processes. We also show that the multiannual variations are not typical only of the Gran Sasso area but are present at large scales throughout the Northern Hemisphere. The analysis of the series of the muon flux also reveals evidence of daily to monthly scale variations, especially during the highly variable winter period. Although such short-term modulations are also found in the series of the effective temperature, we show that the variations of the two series are brought to better agreement when considering only specific layers of the atmosphere depending on the event. The amplitudes of the multiannual variations are significantly larger than those expected based on the temperature modulations. Such differences may be due to acknowledged difficulties of the adopted temperature reanalysis dataset to thoroughly represent long-term variability scales, so that long-term modulations in the raw temperature series and, consequently, in the effective temperature record would result as artificially attenuated. The muon flux therefore may be envisaged as a high time-resolution integrated proxy of lower-stratospheric temperatures.

A promising approach to useful computational quantum advantage is to use variational quantum algorithms for optimization problems. Crucial for the performance of these algorithms is to ensure that the algorithm converges with high probability to a near-optimal solution in a small time. In Barkoutsos et al. [Quantum 4, 256 (2020)], an alternative class of objective functions, called conditional value at risk (CVaR), was introduced and it was shown that they perform better than standard objective functions. Here we extend that work by introducing an evolving objective function, which we call ascending-CVaR and that can be used for any optimization problem. We test our proposed objective function in an emulation environment, using as case studies three different optimization problems: MaxCut, number partitioning, and portfolio optimization. We examine multiple instances of different sizes and analyze the performance using the variational quantum eigensolver with hardware-efficient ansatz and the quantum approximate optimization algorithm. We show that ascending-CVaR in all cases performs better than standard objective functions or the constant CVaR of Barkoutsos et al. [Quantum 4, 256 (2020)] and that it can be used as a heuristic for avoiding suboptimal minima. Our proposal achieves higher overlap with the ideal state in all problems, whether we consider easy or hard instances—on average, it gives up to ten times greater overlap at portfolio optimization and number partitioning, while it gives an 80% improvement at MaxCut. In the hard instances we consider, for the number partitioning problem, standard objective functions fail to find the correct solution in almost all cases, CVaR finds the correct solution at 60% of the cases, while ascending-CVaR finds the correct solution in 95% of the cases.

A disciplinary profile of a country is defined as the versor whose components are the number of papers produced in a given discipline divided by the overall production of the country. Starting from the Essential Science Indicators (ESI) schema of classification of subject areas, we obtained the yearly disciplinary profiles of a worldwide graph, where on each node sits a country, in the two time intervals 1988–1988 and 1992–2017, the fall of the Berlin Wall being the watershed. We analyze the empirical pairwise cross-correlation matrices of the time series of disciplinary profiles. The contrast with random matrix theory proves that, beyond measurement noise, the empirical cross-correlation matrices bring genuine information. Arising from the Shannon theorem as the least-structured model consistent with the measured pairwise correlations, the stationary probability distribution of disciplinary profiles can be described by a Boltzmann distribution related to a generalized $n_d$-dimensional Heisenberg model. The set of network interactions of the Heisenberg model has been inferred and to it, two clusterization methods, hierarchical clustering, and principal component analysis have been applied. This allows obtaining a characterization of the worldwide bilateral interactions based on physical modeling. A simple geopolitical analysis reveals the consistency of the results obtained and gives a boost to a deeper historical analysis. In order to obtain the optimal set of pairwise interactions, we used a pseudolikelihood approach. We analytically computed the pseudolikelihood and its gradient. The analytical computations deserve interest in whatever inference Bayesian problem involving an $n_d$-dimensional Heisenberg model.

δ-AlOOH (δ) is a high-pressure hydrous phase that participates in the deep geological water cycle. At 0 GPa, δ has asymmetric hydrogen bonds (H bonds). Under pressure, it exhibits H-bond disordering, tunneling, and finally, H-bond symmetrization at ∼18 GPa. This study investigates these 300 K pressure-induced state changes in δ with ab initio calculations. H-bond disordering in δ was modeled using supercell multiconfiguration quasiharmonic calculations. We examine (a) energy barriers for proton jumps, (b) the pressure dependence of phonon frequencies, (c) 300 K compressibility, (d) neutron diffraction pattern anomalies, and (e) compare ab initio bond lengths with measured ones. Such thorough and systematic comparisons indicate that (a) proton “disorder” has a restricted meaning when applied to δ. Nevertheless, H bonds are disordered between 0 and 8 GPa, and a gradual change in H-bond configuration results in enhanced compressibility. (b) Several structural and vibrational anomalies at ∼8 GPa are consistent with the disappearance of a particular (HOC-12) H-bond configuration and its change into another one (HOC-11*). (c) Between 8 and 11 GPa, H-bond configuration (HOC-11*) is generally ordered, at least in short- to midrange scale. (d) Between 11.5 and 18 GPa, H-bond lengths approach a critical value that impedes compression, resulting in decreased compressibility. In this pressure range, especially approaching H-bond symmetrization at ∼18 GPa, anharmonicity and tunneling should play an essential role in the proton dynamics. Further simulations accounting for these effects are desirable to clarify the protons' state in this pressure range.

A new class of atomic interferences using ultranarrow optical transitions are pushing quantum engineering control to a very high level of precision for the next generation of sensors and quantum gate operations. In such context, we propose a new quantum engineering approach to Ramsey-Bordé interferometry introducing multiple composite laser pulses with tailored pulse duration, Rabi field amplitude, frequency detuning and laser phase step. We explore quantum metrology with hyper-Ramsey and hyper-Hahn-Ramsey clocks below the ${10}^{-18}$ level of fractional accuracy by fine-tuning control of light excitation parameters leading to spinor interferences protected against light-shift coupled to laser-probe field variation. We review cooperative composite pulse protocols to generate robust Ramsey-Bordé, Mach-Zehnder, and double-loop atomic sensors shielded against measurement distortion related to Doppler and light shifts coupled to pulse area errors. Fault-tolerant autobalanced hyperinterferometers are introduced eliminating several technical laser pulse defects that can occur during the entire probing interrogation protocol. Quantum sensors with composite pulses and ultracold atomic sources should offer a new level of high accuracy in the detection of acceleration and rotation inducing phase shifts, a strong improvement in tests of fundamental physics with hyperclocks while paving the way to a new conception of atomic interferometers tracking space-time gravitational waves with very high sensitivity.

We investigate steady state entanglement (SSE) between two nitrogen-vacancy (NV) center defects in a diamond host on an ultrathin yttrium iron garnet (YIG) strip. We determine the dephasing and dissipative interactions of the qubits with the quanta of spin waves (magnon bath) in the YIG depending on the qubit positions on the strip. We show that the magnon's dephasing effect can be eliminated, and we can transform the bath into a multimode displaced thermal state using external magnetic fields. Entanglement dynamics of the qubits in such a displaced thermal bath have been analyzed by deriving and solving the master equation. An additional electric field is considered to engineer the magnon dispersion relation at the band edge to control the Markovian character of the open system dynamics. We determine the optimum geometrical parameters of the system of distant qubits and the YIG strip to get SSE. Furthermore, parameter regimes for which the shared displaced magnon bath can sustain significant SSE against the local dephasing and decoherence of NV centers to their nuclear spin environments have been determined. Along with SSE, we investigate the steady state coherence (SSC) and explain the physical mechanism of how delayed SSE appears following a rapid generation and sudden death of entanglement using the interplay of decoherence-free subspace states, system geometry, displacement of the thermal bath, and enhancement of the qubit dissipation near the magnon band edge. A nonmonotonic relation between bath coherence and SSE is found, and critical coherence for maximum SSE is determined. Our results illuminate the efficient use of system geometry, band edge in bath spectrum, and reservoir coherence to engineer system-reservoir interactions for robust SSE and SSC.

Localization of plastic flow into a narrow shear band is a fundamental and ubiquitous nonequilibrium phenomenon in amorphous solids. Because of the intrinsic entangling of three types of elementary local atomic motion—shear, dilatation, and rotation—the precise physical process of shear band emergence is still an enigma. Here, to unveil this mystery, we formulate a theoretical protocol covering both affine and nonaffine components of deformation, to decode these three highly entangled local atomic-scale events. In contrast to the broad concept of the shear transformation zone, the plastic behavior can be demonstrated comprehensively as the operative manipulation of more exact shear-dominated zones, dilatation-dominated zones, and rotation-dominated zones. Their spatiotemporal evolution exhibits a transition from synchronous motion to separate distribution at the onset of the shear band. The hidden mechanism is then revealed with the help of extreme value theory and percolation analysis. Numerical evidence from extreme value theory indicates that dilatation is the dominant mode at the embryonic stage of the initial plastic units, as evidenced through the larger degree of dilatation localization compared with shear and rotation. The percolation analysis points towards the critical power-law scaling nature at the transition from stochastic activation to percolation of plastic regions. Then the comprehensive picture underlying shear banding emergence is uncovered. Firstly, dilatation triggers initial shear and rotation in soft regions, leading to the embryos of the initial flow units, which are followed by the secondary activation of rotation in neighboring hard material, thus causing an alternating distribution of rotation and shear-dilatation regions. Such rotation activation contributes to further perturbation in these regions and ultimately leads to percolation transition and shear band formation. Our findings also reinforce that the discussion of plastic behavior in disordered materials must take into account both affine and nonaffine component deformation.

Quantitative descriptions of strongly correlated materials pose a considerable challenge in condensed matter physics and chemistry. A promising approach to address this problem is quantum embedding methods. In particular, the dynamical mean-field theory (DMFT) maps the original system to an effective quantum impurity model comprising correlated orbitals embedded in an electron bath. The biggest bottleneck in DMFT calculations is numerically solving the quantum impurity model, i.e., computing the Green's function. Past studies have proposed theoretical methods to compute the Green's function of a quantum impurity model in polynomial time using a quantum computer. So far, however, efficient methods for computing the imaginary-time Green's functions have not been established despite the advantages of the imaginary-time formulation. We propose a quantum-classical hybrid algorithm for computing imaginary-time Green's functions on quantum devices with limited hardware resources by applying the variational quantum simulation. Using a quantum circuit simulator, we verified this algorithm by computing Green's functions for a dimer model as well as a four-site impurity model obtained by DMFT calculations of the single-band Hubbard model, although our method can be applied to general imaginary-time correlation functions.

The purpose of this paper is to present the concept of an autonomous Stirling-like engine powered by anisotropy of thermodynamic fluctuations. Specifically, simultaneous contact of a thermodynamic system with two heat baths along coupled degrees of freedom generates torque and circulatory currents—an arrangement referred to as a Brownian gyrator. The embodiment that constitutes the engine includes an inertial wheel to sustain rotary motion and average out the generated fluctuating torque, ultimately delivering power to an external load. We detail an electrical model for such an engine that consists of two resistors in different temperatures and three reactive elements in the form of variable capacitors. The resistors generate Johnson-Nyquist current fluctuations that power the engine, while the capacitors generate driving forces via a coupling of their dielectric material with the inertial wheel. A proof-of-concept is established via stability analysis to ensure the existence of a stable periodic orbit generating sustained power output. We conclude by drawing a connection to the dynamics of a damped pendulum with constant torque and to those of a macroscopic Stirling engine. The sought insights aim at nanoengines and biological processes that are similarly powered by anisotropy in temperature and chemical potentials.

The Carnot theorem, one expression of the second law of thermodynamics, places a fundamental upper bound on the efficiency of heat engines operating between two heat baths. The Carnot theorem can be stated in a more generalized form for heat engines operating with multiple heat baths, where the maximum efficiency is achieved for reversible heat engines operating quasistatically between two heat baths. In this study, we determine the irreversible efficiency of heat engines operating with multiple heat baths in a linear response regime, i.e., under small temperature differences and a slow variation of the control parameters, by quantifying the impact of the dissipation by irreversible operations. The Carnot theorem is derived as a natural consequence of it. Because the result obtained is based on the linear response relation and fluctuation-dissipation theorem in the universal framework of linear response theory, it has wide applicability to irreversible heat engines operating in the linear response regime.

Accurate simulation of the time evolution of a quantum system under the influence of an environment is critical to making accurate predictions in chemistry, condensed-matter physics, and materials sciences. Whereas there has been a recent surge in interest in quantum algorithms for the prediction of nonunitary time evolution in quantum systems, few studies offer a direct quantum analog to the Lindblad equation. Here, we present a quantum algorithm—utilizing a decomposition of nonunitary operators approach—that models dynamic processes via the unraveled Lindblad equation. This algorithm is employed to probe both a two-level system in an amplitude damping channel as well as the transverse field Ising model in a variety of parameter regimes; the resulting population dynamics demonstrate excellent agreement with classical simulation, showing the promise of predicting population dynamics utilizing quantum devices for a variety of important systems in molecular energy transport, quantum optics, and other open quantum systems.