We study the influence of diffusion on NMR experiments when the molecules undergo random motion under the influence of a force field and place special emphasis on parabolic (Hookean) potentials. To this end, the problem is studied using path integral methods. Explicit relationships are derived for commonly employed gradient waveforms involving pulsed and oscillating gradients. The Bloch-Torrey equation, describing the temporal evolution of magnetization, is modified by incorporating potentials. A general solution to this equation is obtained for the case of parabolic potential by adopting the multiple correlation function (MCF) formalism, which has been used in the past to quantify the effects of restricted diffusion. Both analytical and MCF results were found to be in agreement with random walk simulations. A multidimensional formulation of the problem is introduced that leads to a new characterization of diffusion anisotropy. Unlike the case of traditional methods that employ a diffusion tensor, anisotropy originates from the tensorial force constant, and bulk diffusivity is retained in the formulation. Our findings suggest that some features of the NMR signal that have traditionally been attributed to restricted diffusion are accommodated by the Hookean model. Under certain conditions, the formalism can be envisioned to provide a viable approximation to the mathematically more challenging restricted diffusion problems.

Some immiscible blends under a strong electric field often exhibit periodic structures, bridging the gap between two electrodes. Upon shear, the structures tilt, and exhibit an elastic response which is mostly governed by the electric energy. Assuming a two-dimensional stripe structure, we calculate the Maxwell stress, and derive an expression for the shear modulus, demonstrating how it depends on the external electric field, the composition, and the dielectric properties of the blend. We also suggest the notion of effective interfacial tension, which renormalizes the effect of the electric field. This leads to a simple derivation of the scaling law for the selection of the wavelength of the structure formed under an electric field.

Active stabilization in systems with zero or negative stiffness is an essential element of a wide variety of biological processes. We study a prototypical example of this phenomenon and show how active rigidity, interpreted as a formation of a pseudowell in the effective energy landscape, can be generated in an overdamped stochastic system. We link the transition from negative to positive rigidity with time correlations in the additive noise, and we show that subtle differences in the out-of-equilibrium driving may compromise the emergence of a pseudowell.

In this paper we perform quasistatic shear simulations of model amorphous silicon bulk samples with Stillinger-Weber-type potentials. Local plastic rearrangements identified based on local energy variations are fitted through their displacement fields on collections of Eshelby spherical inclusions, allowing determination of their transformation strain tensors. The latter are then used to quantitatively reproduce atomistic stress-strain curves, in terms of both shear and pressure components. We demonstrate that our methodology is able to capture the plastic behavior predicted by different Stillinger-Weber potentials, in particular, their different shear tension coupling. These calculations justify the decomposition of plasticity into shear transformations used so far in mesoscale models and provide atomic-scale parameters that can be used to limit the empiricism needed in such models up to now.

By including the full pressure tensor dynamics in a fluid plasma model, we show that a sheared velocity field can provide an effective mechanism that makes the initial isotropic pressure nongyrotropic. This is distinct from the usual gyrotropic anisotropy related to the fluid compressibility and usually accounted for in double-adiabatic models. We determine the time evolution of the pressure agyrotropy and discuss how the propagation of “magnetoelastic perturbations” can affect the pressure tensor anisotropization and its spatial filamentation, which are due to the action of both the magnetic field and the flow strain tensor. We support this analysis with a numerical integration of the nonlinear equations describing the pressure tensor evolution.

We consider the efficiency limits of Brownian motors able to extract work from the temperature difference between reservoirs or from external thermodynamic forces. These systems can operate in a variety of modes, including as isothermal engines, heat engines, refrigerators, and heat pumps. We derive analytical results showing that certain classes of multidimensional Brownian motor, including the Smoluchowski-Feynman ratchet, are unable to attain perfect efficiency (Carnot efficiency for heat engines). This demonstrates the presence of intrinsic irreversibilities in their operating mechanism. We present numerical simulations showing that in some cases the loss process that limits efficiency is associated with vortices in the probability current.

We examine the Nagel-Schreckenberg traffic model for a variety of maximum speeds. We show that the low-density limit can be described as a dilute gas of vehicles with a repulsive core. At the transition to jamming, we observe finite-size effects in a variety of quantities describing the flow and the density correlations, but only if the maximum speed $V_{\text{max}}$ is larger than a certain value. A finite-size scaling analysis of several order parameters shows universal behavior, with scaling exponents that depend on $V_{\text{max}}$. The jamming transition at large $V_{\text{max}}$ can be viewed as the nucleation of jams in a background of freely flowing vehicles. For small $V_{\text{max}}$ no such clean separation into jammed and free vehicles is possible.

Brain functions, such as perception, motor control and learning, and decision making, have been explained based on a Bayesian framework, i.e., to decrease the effects of noise inherent in the human nervous system or external environment, our brain integrates sensory and a priori information in a Bayesian optimal manner. However, it remains unclear how Bayesian computations are implemented in the brain. Herein, I address this issue by analyzing a Mexican-hat-type neural network, which was used as a model of the visual cortex, motor cortex, and prefrontal cortex. I analytically demonstrate that the dynamics of an order parameter in the model corresponds exactly to a variational inference of a linear Gaussian state-space model, a Bayesian estimation, when the strength of recurrent synaptic connectivity is appropriately stronger than that of an external stimulus, a plausible condition in the brain. This exact correspondence can reveal the relationship between the parameters in the Bayesian estimation and those in the neural network, providing insight for understanding brain functions.

A unique type of quasi-two-dimensional complex plasma system was observed which consisted of monodisperse microspheres and their binary agglomerations (dimers). The particles and their dimers levitated in a plasma sheath at slightly different heights and formed two distinct sublayers. The system did not crystallize and may be characterized as a disordered solid. The dimers were identified based on their characteristic appearance in defocused images, i.e., rotating interference fringe patterns. The in-plane and interplane particle separations exhibit nonmonotonic dependence on the discharge pressure.

The multiagent evolutionary games on a lattice are equivalent to a kinetic Ising model if the uniform pair interactions are defined by a two-strategy coordination game and the logit rule controls the strategy updates. Now we extend this model by allowing the players to use additional neutral strategies that provide zero payoffs for both players if one of them selects one of the neutral strategies. In the resulting $n$-strategy evolutionary games the analytical methods and numerical simulations indicate continuous order-disorder phase transitions when increasing the noise level if $n$ does not exceed a threshold value. For larger $n$ the system exhibits a first order phase transition at a critical noise level decreasing asymptotically as $2/\ln \left(n\right)$.

Extensive Monte Carlo simulations are performed to investigate the critical properties of a special singular point usually known as the Landau point. The singular behavior is studied in the case when the order parameter is a tensor of rank 2. Such an order parameter is associated with a nematic-liquid-crystal phase. A three-dimensional lattice dispersion model that exhibits a direct biaxial nematic-to-isotropic phase transition at the Landau point is thus chosen for the present study. Finite-size scaling and cumulant methods are used to obtain precise values of the critical exponent $\nu =0.713\left(4\right)$, the ratio $\gamma /\nu =1.85\left(1\right)$, and the fourth-order critical Binder cumulant $U^{*}=0.6360\left(1\right)$. Estimated values of the exponents are in good agreement with renormalization-group predictions.

We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which directed long-range connections are randomly added according to the probability $P_{ij}\sim r^{-\alpha }$, where $r_{ij}$ is the Manhattan distance between nodes $i$ and $j$, and the exponent $\alpha$ is a controlling parameter [J. M. Kleinberg, Nature (London) 406, 845 (2000)]. Our results show that the collective behavior of this system exhibits a continuous order-disorder phase transition at a critical parameter, which is a decreasing function of the exponent $\alpha$. Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the system undergoes a crossover among distinct universality classes. For $\alpha \le 3$ the critical behavior is described by mean-field exponents, while for $\alpha \ge 4$ it belongs to the Ising universality class. Finally, in the region where the crossover occurs, $3<\alpha <4$, the critical exponents are dependent on $\alpha$.

The temperature dependence of DNA flexibility is studied in the presence of stretching and unzipping forces. Two classes of models are considered. In one case the origin of elasticity is entropic due to the polymeric correlations, and in the other the double-stranded DNA is taken to have an intrinsic rigidity for bending. In both cases single strands are completely flexible. The change in the elastic constant for the flexible case due to thermally generated bubbles is obtained exactly. For the case of intrinsic rigidity, the elastic constant is found to be proportional to the square root of the bubble number fluctuation.

Photon impingement is capable of liberating electrons in electronic devices and driving the electron flux from the lower chemical potential to higher chemical potential. Previous studies hinted that the thermodynamic efficiency of a nanosized photoelectric converter at maximum power is bounded by the Curzon-Ahlborn efficiency ${\eta }_{\text{CA}}$. In this study, we apply quantum effects to design a photoelectric converter based on a three-level quantum dot (QD) interacting with fermionic baths and photons. We show that, by adopting a pair of suitable degenerate states, quantum coherences induced by the couplings of QDs to sunlight and fermion baths can coexist steadily in nanoelectronic systems. Our analysis indicates that the efficiency at maximum power is no longer limited to ${\eta }_{\text{CA}}$ through manipulation of carefully controlled quantum coherences.

We consider the Ornstein-Uhlenbeck process with a broad initial probability distribution (Lévy distribution), which exhibits so-called nonspectral modes. The relaxation rate of such modes differs from those determined from the parameters of the corresponding Fokker-Plank equation. The first nonspectral mode is shown to govern the relaxation process and allows for estimation of the initial distribution's Lévy index. A method based on continuous wavelet transformation is proposed to extract both (spectral and nonspectral) relaxation rates from a stochastic data sample.

We study numerically the two-dimensional Ising model with nonconserved dynamics quenched from an initial equilibrium state at the temperature $T_i\ge T_c$ to a final temperature $T_f$ below the critical one. By considering processes initiating both from a disordered state at infinite temperature $T_i=\infty$ and from the critical configurations at $T_i=T_c$ and spanning the range of final temperatures $T_f\in [0,T_c[$ we elucidate the role played by $T_i$ and $T_f$ on the aging properties and, in particular, on the behavior of the autocorrelation $C$ and of the integrated response function $\chi$. Our results show that for any choice of $T_f$, while the autocorrelation function exponent ${\lambda }_C$ takes a markedly different value for $T_i=\infty$ [${\lambda }_C(T_i=\infty )\simeq 5/4$] or $T_i=T_c$ [${\lambda }_C(T_i=T_c)\simeq 1/8$] the response function exponents are unchanged. Supported by the outcome of the analytical solution of the solvable spherical model we interpret this fact as due to the different contributions provided to autocorrelation and response by the large-scale properties of the system. As changing $T_f$ is considered, although this is expected to play no role in the large-scale and long-time properties of the system, we show important effects on the quantitative behavior of $\chi$. In particular, data for quenches to $T_f=0$ are consistent with a value of the response function exponent ${\lambda }_{\chi }=\frac{1}{2}{\lambda }_C(T_i=\infty )=5/8$ different from the one [${\lambda }_{\chi }\in (0.5–0.56)$] found in a wealth of previous numerical determinations in quenches to finite final temperatures. This is interpreted as due to important preasymptotic corrections associated to $T_f>0$.

We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions $N$ and $M$. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish, for arbitrary $N\le M$, a general relation between the $n$-point densities and the cross moments of the eigenvalues of the reduced density matrix, i.e., the so-called Schmidt eigenvalues, and the analogous functionals of the eigenvalues of the Wishart-Laguerre ensemble of the random matrix theory. This allows us to derive explicit expressions for two-level densities, and also an exact expression for the variance of von Neumann entropy at finite $N,M$. Then, we focus on the moments $\mathbb{E}\left\{K^a\right\}$ of the Schmidt number $K$, the reciprocal of the purity. This is a random variable supported on $[1,N]$, which quantifies the number of degrees of freedom effectively contributing to the entanglement. We derive a wealth of analytical results for $\mathbb{E}\left\{K^a\right\}$ for $N=2$ and 3 and arbitrary $M$, and also for square $N=M$ systems by spotting for the latter a connection with the probability $P(x_{\text{min}}^{\text{GUE}}\ge \sqrt{2N}\xi )$ that the smallest eigenvalue $x_{\text{min}}^{\text{GUE}}$ of an $N\times N$ matrix belonging to the Gaussian unitary ensemble is larger than $\sqrt{2N}\xi$. As a by-product, we present an exact asymptotic expansion for $P(x_{\text{min}}^{\text{GUE}}\ge \sqrt{2N}\xi )$ for finite $N$ as $\xi \to \infty$. Our results are corroborated by numerical simulations whenever possible, with excellent agreement.

We consider nonlinear rate equations appropriate for a quantum cascade laser subject to optical feedback. We analyze the conditions for a Hopf bifurcation in the limit of large values of the delay. We obtain a simple expression for the critical feedback rate that highlights the effects of key parameters such as the linewidth enhancement factor and the pump. All our asymptotic approximations are validated numerically by using a path continuation technique that allows us to follow Hopf bifurcation points in parameter space.

When identical oscillators are coupled together in a network, dynamical steady states are often assumed to reflect network symmetries. Here, we show that alternative persistent states may also exist that break the symmetries of the underlying coupling network. We further show that these symmetry-broken coexistent states are analogous to those dubbed “chimera states,” which can occur when identical oscillators are coupled to one another in identical ways.