Since the problem of the residual entropy of square ice was exactly solved, exact solutions for two-dimensional realistic ice models have been of interest. In this work, we study the exact residual entropy of ice hexagonal monolayer in two cases. In the case that the external electric field along the $z$-axis exists, we map the hydrogen configurations into the spin configurations of the Ising model on the kagome lattice. By taking the low temperature limit of the Ising model, we derive the exact residual entropy, which agrees with the result determined previously from the dimer model on the honeycomb lattice. In another case that the ice hexagonal monolayer is under the periodic boundary conditions in the cubic ice lattice, the residual entropy has not been studied exactly. For this case, we employ the six-vertex model on the square lattice to represent the hydrogen configurations obeying the ice rules. The exact residual entropy is obtained from the solution of the equivalent six-vertex model. Our work provides more examples of the exactly soluble two-dimensional statistical models.

Based on large-scale density matrix renormalization group techniques, we investigate the critical behaviors of quantum three-state Potts chains with long-range interactions. Using fidelity susceptibility as an indicator, we obtain a complete phase diagram of the system. The results show that as the long-range interaction power $\alpha$ increases, the critical points $f_c^{*}$ shift towards lower values. In addition, the critical threshold ${\alpha }_c(\approx 1.43$) of the long-range interaction power is obtained for the first time by a nonperturbative numerical method. This indicates that the critical behavior of the system can be naturally divided into two distinct universality classes, namely the long-range ($\alpha <{\alpha }_c$) and short-range ($\alpha >{\alpha }_c$) universality classes, qualitatively consistent with the classical ${\varphi }^3$ effective field theory. This work provides a useful reference for further research on phase transitions in quantum spin chains with long-range interaction.

In order to reveal mechanisms to control and manipulate spin currents, we perform a detailed investigation of the dephasing effects in the open $XX$ model with a Lindblad dynamics involving global dissipators and thermal baths. Specifically, we consider dephasing noise modeled by current-preserving Lindblad dissipators acting on graded versions of these spin systems, that is, systems in which the magnetic field and/or the spin interaction are growing (decreasing) along the chain. In our analysis, we study the nonequilibrium steady state via the covariance matrix using the Jordan-Wigner approach to compute the spin currents. We find that the interplay between dephasing and graded systems gives rise to a nontrivial behavior: When we have homogeneous magnetic field and graded interactions we have rectification enhancement mechanisms, and when we have fully graded systems we can control the spin current in order to keep the direction of the particle and/or spin flow even with inverted baths. We describe our result in detailed numerical analysis and we see that rectification in this simple model indicates that the phenomenon may generally occur in quantum spin systems.

In this paper, we solve the inverse problem for the cubic mean-field Ising model. Starting from configuration data generated according to the distribution of the model, we reconstruct the free parameters of the system. We test the robustness of this inversion procedure both in the region of uniqueness of the solutions and in the region where multiple thermodynamics phases are present.

The Dicke model is a fundamental model in quantum optics, which describes the interaction between quantum cavity field and a large ensemble of two-level atoms. In this work, we propose an efficient charging quantum battery achieved by considering an extension Dicke model with dipole-dipole interaction and an external driving field. We focus on the influence of the atomic interaction and the driving field on the performance of the quantum battery during the charging process and find that the maximum stored energy exhibits a critical phenomenon. The maximum stored energy and maximum charging power are investigated by varying the number of atoms. When the coupling between atoms and cavity is not very strong, compared to the Dicke quantum battery, such quantum battery can achieve more stable and faster charging. In addition, the maximum charging power approximately satisfies a superlinear scaling relation $P_{\max }\propto \beta N^{\alpha }$, where the quantum advantage $\alpha =1.6$ can be reached via optimizing the parameters.

Strain-controlled isotropic compression gives rise to jammed packings of repulsive, frictionless disks with either positive or negative global shear moduli. We carry out computational studies to understand the contributions of the negative shear moduli to the mechanical response of jammed disk packings. We first decompose the ensemble-averaged, global shear modulus as $\langle G\rangle =(1-{\mathcal{F}}_{-})\langle G_{+}\rangle +{\mathcal{F}}_{-}\langle G_{-}\rangle$, where ${\mathcal{F}}_{-}$ is the fraction of jammed packings with negative shear moduli and $\langle G_{+}\rangle$ and $\langle G_{-}\rangle$ are the average values from packings with positive and negative moduli, respectively. We show that $\langle G_{+}\rangle$ and $\langle \left|G_{-}\right|\rangle$ obey different power-law scaling relations above and below $p{N}^2\sim 1$. For $p{N}^2>1$, both $\langle G_{+}\rangle N$ and $\langle |G_{-}|\rangle N\sim {\left(p{N}^2\right)}^{\beta }$, where $\beta \sim 0.5$ for repulsive linear spring interactions. Despite this, $\langle G\rangle N\sim {\left(p{N}^2\right)}^{{\beta }^{\prime }}$ with ${\beta }^{\prime }\gtrsim 0.5$ due to the contributions from packings with negative shear moduli. We show further that the probability distribution of global shear moduli $\mathcal{P}\left(G\right)$ collapses at fixed $p{N}^2$ and different values of $p$ and $N$. We calculate analytically that $\mathcal{P}\left(G\right)$ is a $\mathrm{\Gamma }$ distribution in the $p{N}^2\ll 1$ limit. As $p{N}^2$ increases, the skewness of $\mathcal{P}\left(G\right)$ decreases and $\mathcal{P}\left(G\right)$ becomes a skew-normal distribution with negative skewness in the $p{N}^2\gg 1$ limit. We also partition jammed disk packings into subsystems using Delaunay triangulation of the disk centers to calculate local shear moduli. We show that the local shear moduli defined from groups of adjacent triangles can be negative even when $G>0$. The spatial correlation function of local shear moduli $C\left(\vec{r}\right)$ displays weak correlations for $p{n}_{\mathrm{sub}}^2<{10}^{-2}$, where $n_{\mathrm{sub}}$ is the number of particles within each subsystem. However, $C\left(\vec{r}\right)$ begins to develop long-ranged spatial correlations with fourfold angular symmetry for $p{n}_{\mathrm{sub}}^2\gtrsim {10}^{-2}$.

We study two-dimensional random sequential adsorption (RSA) of flat polygons and rounded squares aligned in parallel to find a transition in the asymptotic behavior of the kinetics of packing growth. Differences in the kinetics for RSA of disks and parallel squares were confirmed in previous analytical and numerical reports. Here, by analyzing the two classes of shapes in question we can precisely control the shape of the packed figures and thus localize the transition. Additionally, we study how the asymptotic properties of the kinetics depend on the packing size. We also provide accurate estimations of saturated packing fractions. The microstructural properties of generated packings are analyzed in terms of the density autocorrelation function.

In inhomogeneous media, electromagnetic-wave rays deviate from the trajectories predicted by the leading-order geometrical optics. This effect, called the spin Hall effect of light, is typically neglected in ray-tracing codes used for modeling waves in plasmas. Here, we demonstrate that the spin Hall effect can be significant for radiofrequency waves in toroidal magnetized plasmas whose parameters are in the ballpark of those used in fusion experiments. For example, an electron-cyclotron wave beam can deviate by as large as 10 wavelengths ($\sim 0.1$ m) relative to the lowest-order ray trajectory in the poloidal direction. We calculate this displacement using gauge-invariant ray equations of extended geometrical optics, and we also compare our theoretical predictions with full-wave simulations.

Stochastic differential equations projected onto manifolds occur in physics, chemistry, biology, engineering, nanotechnology, and optimization, with interdisciplinary applications. Intrinsic coordinate stochastic equations on the manifold are sometimes computationally impractical, and numerical projections are therefore useful in many cases. In this paper a combined midpoint projection algorithm is proposed that uses a midpoint projection onto a tangent space, combined with a subsequent normal projection to satisfy the constraints. We also show that the Stratonovich form of stochastic calculus is generally obtained with finite bandwidth noise in the presence of a strong enough external potential that constrains the resulting physical motion to a manifold. Numerical examples are given for a wide range of manifolds, including circular, spheroidal, hyperboloidal, and catenoidal cases, higher-order polynomial constraints that give a quasicubical surface, and a ten-dimensional hypersphere. In all cases the combined midpoint method has greatly reduced errors compared to other methods used for comparison, namely, a combined Euler projection approach and a tangential projection algorithm. We derive intrinsic stochastic equations for spheroidal and hyperboloidal surfaces for comparison purposes to verify the results. Our technique can handle multiple constraints, which allows manifolds that embody several conserved quantities. The algorithm is accurate, simple, and efficient. A reduction of an order of magnitude in the diffusion distance error is found compared to the other methods and an up to several orders of magnitude reduction in constraint function errors.

Inhomogeneous environments are rather ubiquitous in nature, often implying anomalies resulting in deviation from Gaussianity of diffusion processes. While sub- and superdiffusion are usually due to contrasting environmental features (hindering or favoring the motion, respectively), they are both observed in systems ranging from the micro- to the cosmological scale. Here we show how a model encompassing sub- and superdiffusion in an inhomogeneous environment exhibits a critical singularity in the normalized generator of the cumulants. The singularity originates directly and exclusively from the asymptotics of the non-Gaussian scaling function of displacement, and the independence from other details confers it a universal character. Our analysis, based on the method first applied by Stella et al. [Phys. Rev. Lett. 130, 207104 (2023)], shows that the relation connecting the scaling function asymptotics to the diffusion exponent characteristic of processes in the Richardson class implies a nonstandard extensivity in time of the cumulant generator. Numerical tests fully confirm the results.

Chirality has been considered as one of the key factors in the evolution of life in nature. It is important to uncover how chiral potentials of molecular systems play vital role in fundamental photochemical processes. Here, we investigate the role of chirality in photoinduced energy transfer in a model dimeric system, where the monomers are excitonically coupled. To observe transient chiral dynamics and energy transfer, we employ circularly polarized laser pulses in two-dimensional electronic spectroscopy to construct the two-dimensional circular dichroism (2DCD) spectral maps. Tracking time-resolved peak magnitudes in 2DCD spectra allows one to identify chirality induced population dynamics. The dynamics of energy transfer is revealed by the time-resolved kinetics of cross peaks. However, the differential signal of 2DCD spectra shows the magnitude of cross peaks is dramatically reduced at initial waiting time, which indicates the weak chiral interactions between two monomers. The downhill energy transfer is resolved by presenting a strong magnitude of cross peak in 2DCD spectra after long waiting time. The chiral contribution towards coherent and incoherent energy-transfer pathways in the model dimer system is further examined via control of excitonic couplings between two monomers. Applications are made to study the energy-transfer process in the Fenna-Matthews-Olson complex. Our work uncovers the potential of 2DCD spectroscopy to resolve the chiral-induced interactions and population transfers in excitonically coupled systems.

We study a model of a lipid bilayer membrane described by two order parameters: the chemical composition described using the Gaussian model and the spatial configuration described with the elastic deformation model of a membrane with a finite thickness or, equivalently, for an adherent membrane. We assume and explain on physical grounds the linear coupling between the two order parameters. Using the exact solution, we calculate the correlation functions and order parameter profiles. We also study the domains that form around inclusions on the membrane. We propose and compare six distinct ways to quantify the size of such domains. Despite its simplicity, the model has many interesting features like the Fisher-Widom line and two distinct critical regions.

The climate is a complex nonequilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the possible steady states under different forcing is the bifurcation diagram, which reveals the regions of multistability, the position of tipping points, and the range of stability of each steady state. However, its construction is highly time consuming in climate models with a dynamical deep ocean, whose relaxation time is of the order of thousand years, or other feedback mechanisms that act on even longer time scales, like continental ice or carbon cycle. Using a coupled setup of the MIT general circulation model, we test two techniques for the construction of bifurcation diagrams with complementary advantages and reduced execution time. The first is based on the introduction of random fluctuations in the forcing and permits to explore a wide part of phase space. The second reconstructs the stable branches using estimates of the internal variability and of the surface energy imbalance on each attractor, and is more precise in finding the position of tipping points.

In this paper, we show that the destruction of the main Kolmogorov-Arnold-Moser (KAM) islands in two-degree-of-freedom Hamiltonian systems occurs through a cascade of period-doubling bifurcations. We calculate the corresponding Feigenbaum constant and the accumulation point of the period-doubling sequence. By means of a systematic grid search on exit basin diagrams, we find the existence of numerous very small KAM islands (“islets”) for values below and above the aforementioned accumulation point. We study the bifurcations involving the formation of islets and we classify them in three different types. Finally, we show that the same types of islets appear in generic two-degree-of-freedom Hamiltonian systems and in area-preserving maps.

The interest in active matter stimulates the need to generalize thermodynamic description and relations to active matter systems, which are intrinsically out of equilibrium. One important example is the Jarzynski relation, which links the exponential average of work done in an arbitrary process connecting two equilibrium states with the difference of the free energies of these states. Using a simple model system, a single thermal active Ornstein-Uhlenbeck particle in a harmonic potential, we show that if the standard stochastic thermodynamics definition of work is used, the Jarzynski relation is not generally valid for processes connecting stationary states of active matter systems.

We present the diffusiophoresis of ellipsoidal particles induced by ionic solute gradients. Contrary to the common expectation that diffusiophoresis is shape independent, here we show experimentally that this assumption breaks down when the thin Debye layer approximation is relaxed. By tracking the translation and rotation of various ellipsoids, we find that the phoretic mobility of ellipsoids is sensitive to the eccentricity and the orientation of the ellipsoid relative to the imposed solute gradient, and can further lead to nonmonotonic behavior under strong confinement. We show that such a shape- and orientation-dependent diffusiophoresis of colloidal ellipsoids can be easily captured by modifying theories for spheres.

We employ Onsager's second virial density functional theory combined with the Parsons-Lee theory within the restricted orientation (Zwanzig) approximation to examine the phase structure of hard square boards of dimensions $\left(L\times D\times D\right)$ uniaxially confined in narrow slabs. Depending on the wall-to-wall separation ($H$), we predict a number of distinctly different capillary nematic phases, including a monolayer uniaxial or biaxial planar nematic, homeotropic with a variable number of layers, and a $T$-type structure. We determine that the favored phase is homotropic, and we observe first-order transitions from the homeotropic structure with $n$ layers to $n+1$ layers as well as from homeotropic surface anchoring to a monolayer planar or $T$-type structure involving both planar and homeotropic anchoring at the pore surface. By increasing the packing fraction, we further demonstrate a reentrant homeotropic-planar-homeotropic phase sequence in a particular range (i.e., $\frac{H}{D}=1.1$ and $0.25\le \frac{L}{D}<0.26$). We find that the $T$-type structure is more stable when the pore is wide enough with respect to the planar phase. The enhanced stability of the mixed-anchoring $T$-structure is unique for square boards and becomes manifest at pore width exceeding $L+D$. More specifically, the biaxial $T$-type structure emerges directly from the homeotropic state without intervention of a planar layer structure as observed for other convex particle shapes.

Quantum chaos plays a significant role in understanding several important questions of recent theoretical and experimental studies. Here, by focusing on the localization properties of eigenstates in phase space (by means of Husimi functions), we explore the characterizations of quantum chaos using the statistics of the localization measures, that is the inverse participation ratio and the Wehrl entropy. We consider the paradigmatic kicked top model, which shows a transition to chaos with increasing the kicking strength. We demonstrate that the distributions of the localization measures exhibit a drastic change as the system undergoes the crossover from integrability to chaos. We also show how to identify the signatures of quantum chaos from the central moments of the distributions of localization measures. Moreover, we find that the localization measures in the fully chaotic regime apparently universally exhibit the beta distribution, in agreement with previous studies in the billiard systems and the Dicke model. Our results contribute to a further understanding of quantum chaos and shed light on the usefulness of the statistics of phase space localization measures in diagnosing the presence of quantum chaos, as well as the localization properties of eigenstates in quantum chaotic systems.

We propose an approach combining the continuum theory and molecular-statistical approach for a suspension of carbon nanotubes based on a negative diamagnetic anisotropy liquid crystal. Using the continuum theory, we show that in the case of an infinite sample in suspension it is possible to observe peculiar magnetic Fréedericksz-like transitions between three nematic phases: planar, angular, and homeotropic with different mutual orientations of liquid-crystal and nanotube directors. The transition fields between these phases are found analytically as functions of material parameters of the continuum theory. To account for the effects associated with temperature changes, we propose a molecular-statistical approach that allows obtaining the equations of orientational state for the orientation angles of the main axes of the nematic order, i.e., the liquid-crystal and carbon-nanotube directors in a similar form as was obtained within the continuum theory. Thus, it is possible to relate the parameters of the continuum theory, such as the surface-energy density of a coupling between molecules and nanotubes, to the parameters of the molecular-statistical model and the order parameters of the liquid crystal and carbon nanotubes. This approach allows determining the temperature dependencies of the threshold fields of transitions between different nematic phases, which is impossible in the framework of the continuum theory. In the framework of the molecular-statistical approach we predict the existence of an additional direct transition between the planar and homeotropic nematic phases of the suspension, which cannot be described based on the continuum theory. As the main results, the magneto-orientational response of the liquid-crystal composite is studied and a possible biaxial orientational ordering of the nanotubes in the magnetic field is shown.

In this paper, using a shell model, we simulate highly turbulent stably stratified flow for weak to moderate stratification at unitary Prandtl number. We investigate the energy spectra and fluxes of velocity and density fields. We observe that for moderate stratification, in the inertial range, the kinetic energy spectrum $E_u\left(k\right)$ and the potential energy spectrum $E_b\left(k\right)$ show dual scaling—Bolgiano-Obukhov scaling $[E_u\left(k\right)\sim k^{-11/5}$ and $E_b\left(k\right)\sim k^{-7/5}]$ for $k<k_B$, where $k_B$ is the Bolgiano wave number, and Kolmogorov scaling $(\sim k^{-5/3})$ for $k>k_B$. In addition, we find that the mixing efficiency ${\eta }_{\mathrm{mix}}$ varies as ${\eta }_{\mathrm{mix}}\sim \mathrm{Ri}$ for weak stratification, whereas ${\eta }_{\mathrm{mix}}\sim {\mathrm{Ri}}^{1/3}$ for moderate stratification, where $\mathrm{Ri}$ is the Richardson number.