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Furthermore, we investigate their spectral properties, in particular, to find out whether not only their eigenvalues but also the fluctuations in their spectra and their length spectra differ.Although the nonequilibrium-relaxation (NER) method has been widely used in Monte Carlo studies on phase transitions in classical spin systems, such studies have been quite limited in quantum phase transitions. The reason is that the relaxation process based on cluster-update quantum Monte Carlo (QMC) algorithms, which are now standards in Monte Carlo studies on quantum systems, has been considered "too fast" for such analyses. Recently, the present authors revealed that the NER process in classical spin systems based on cluster-update algorithms is characterized by stretched-exponential critical relaxation, rather than conventional power-law relaxation in local-update algorithms. In the present article, we show that this is also the case in quantum phase transitions analyzed with the cluster-update QMC. As the simplest example of isotropic quantum spin models that exhibit quantum phase transitions, we investigate the Néel-dimer quantum phase transition in the two-dimensional S=1/2 columnar-dimerized antiferromagnetic Heisenberg model with the continuous-time loop algorithm, and we confirm stretched-exponential critical relaxation consistent with the three-dimensional classical Heisenberg model in the Swendsen-Wang algorithm.We show that the Wang-Landau algorithm can be formulated as a stochastic gradient descent algorithm minimizing a smooth and convex objective function, of which the gradient is estimated using Markov chain Monte Carlo iterations. The optimization formulation provides us another way to establish the convergence rate of the Wang-Landau algorithm, by exploiting the fact that almost surely the density estimates (on the logarithmic scale) remain in a compact set, upon which the objective function is strongly convex. The optimization viewpoint motivates us to improve the efficiency of the Wang-Landau algorithm using popular tools including the momentum method and the adaptive learning rate method. We demonstrate the accelerated Wang-Landau algorithm on a two-dimensional Ising model and a two-dimensional ten-state Potts model.Electronic parametric instabilities of an ultrarelativistic circularly polarized laser pulse propagating in underdense plasmas are studied by numerically solving the dispersion relation which includes the effect of the radiation reaction force in laser-driven plasma dynamics. Emphasis is placed on studying the different modes in the laser-plasma system and identifying the absolute and convective nature of the unstable modes in a parameter map spanned by the normalized laser vector potential and the plasma density. Implications for the ultraintense laser-plasma experiments are pointed out.The unique spatial and temporal properties of relativistic high harmonics generated from a laser-driven plasma surface allow them to be coherently focused to an extremely high intensity reaching the Schwinger limit. The ultimately achievable intensity is limited by the harmonic wavefront distortions during the interactions. Here we demonstrate experimentally that the harmonic divergence can be controlled by an optically shaped plasma surface with a prepulse that has the same spatial and temporal distribution as the main laser pulse. Simulations are also performed to explain the experimental observation, and we find that the harmonic wavefront curvature from a dented surface can be precompensated by a convex plasma. Our work suggests an active approach to control the harmonic divergence and wavefront by an optically shaped target. This can be critical for further high harmonics applications.The bending of nanostructures (NSs), such as nanopillars and nanowires, caused by cell adhesion is an interesting phenomenon and is important for the measurements of cellular forces, understanding the biological behavior of cells, and disease diagnosis. However, which factors are related to the bending of NSs and how the factors affect bending displacement are still not well understood. Here, we establish an analytic thermodynamic theory to study the bending mechanism of NSs caused by cellular force during the cell adhesion process, and analyze the factors affecting bending displacement. It is found that the bending of NSs is determined by the competition between the stretching energy of the membrane and the strain energy of the NSs. The bending displacement can be evaluated based on our model.We show that a commonly accepted transparency threshold for a thin foil in a strong circularly polarized normally incident laser pulse needs a refinement. We present an analytical model that correctly accounts for laser absorption. The refined threshold is determined not solely by the laser amplitude, but by other parameters that are equally or even more important. Our predictions are in perfect agreement with particle-in-cell simulations. The refined criterion is crucial for configuring laser plasma experiments in the high-field domain. 5-HT 5-HT Receptor agonist In addition, an opaque foil steepens the pulse front, which can be important for numerous applications.If a static perturbation is applied to a liquid crystal, then the director configuration changes to minimize the free energy. If a shear flow is applied to a liquid crystal, then one might ask Does the director configuration change to minimize any effective potential? To address that question, we derive the Leslie-Ericksen equations for dissipative dynamics and determine whether they can be expressed as relaxation toward a minimum. The answer may be yes or no, depending on the number of degrees of freedom. Using theory and simulations, we consider two specific examples, reverse tilt domains under simple shear flow and dowser configurations under plane Poiseuille flow, and we demonstrate that each example shows relaxation toward the minimum of an effective potential.We numerically estimate the leading asymptotic behavior of the length L_n of the longest increasing subsequence of random walks with step increments following Student's t-distribution with parameters in the range 1/2≤ν≤5. We find that the expected value E(L_n)∼n^θlnn, with θ decreasing from θ(ν=1/2)≈0.70 to θ(ν≥5/2)≈0.50. For random walks with a distribution of step increments of finite variance (ν>2), this confirms previous observation of E(L_n)∼sqrt[n]lnn to leading order. We note that this asymptotic behavior (including the subleading term) resembles that of the largest part of random integer partitions under the uniform measure and that, curiously, both random variables seem to follow Gumbel statistics. We also provide more refined estimates for the asymptotic behavior of E(L_n) for random walks with step increments of finite variance.
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