Physical Review E最新文献

A quantum walk (QW) utilizes its internal quantum states to decide the displacement, thereby introducing single-particle entanglement between the internal and positional degrees of freedom. By simulating three variants of QWs with the conventional, symmetric, and split-step translation operators with or without classical randomness in the coin operator, we show the entanglement is robust against both time- and spatially dependent randomness, which can cause localization transitions of QWs. We propose a classical quantity called overlap, which literally measures the overlap between the probability distributions of the internal states as a proxy of entanglement. The overlap is associated with the off-diagonal terms of the reduced density matrix in the internal space, which then reflects its purity. Therefore, the overlap captures the inverse behavior of the entanglement entropy in most cases. We test the limitation of the classical proxy by constructing a special case with high population imbalance between the internal states to blind the overlap. Possible implications and experimental measurements are also discussed.

When nodes in excitable system are stimulated, the system tends to form traveling waves or self-organized spiral waves, such as electrical signals in the heart and the spread of epidemics. Networks composed of these nodes can be influenced by higher-order interactions. We utilized the FitzHugh-Nagumo (FHN) model for nodes to construct a three-layer lattice network, incorporating higher-order interactions applicable to neuronal models. We found that higher-order interactions have a suppressive effect on spiral waves, which exhibit various dynamics such as stable rotation, drifting, and dissipation under different influences of these interactions. There exists a critical threshold at which the spiral waves transition from stable rotation to dissipation. We aim to investigate real systems, such as the brain or heart, to explore this type of excitable media and provide theoretical insights into the propagation of excitation within networks.

We generalize a semiclassical path integral approach originally introduced by Giachetti and Tognetti [Phys. Rev. Lett. 55, 912 (1985)0031-900710.1103/PhysRevLett.55.912] and Feynman and Kleinert [Phys. Rev. A 34, 5080 (1986)0556-279110.1103/PhysRevA.34.5080] to time-dependent Hamiltonians, thus extending the scope of the method to the pricing of financial derivatives. We illustrate the accuracy of the approach by presenting results for the well-known, but analytically intractable, Black-Karasinski model for the dynamics of interest rates. The accuracy and computational efficiency of this path integral approach make it a viable alternative to fully numerical schemes for a variety of applications in derivatives pricing.

We consider the information fiber optical channel modeled by the nonlinear Schrodinger equation with additive Gaussian noise. Using path-integral approach and perturbation theory for the small dimensionless parameter of the second dispersion, we calculate the conditional probability density functional in the leading and next-to-leading order in the dimensionless second dispersion parameter associated with the input signal bandwidth. Taking into account the specific filtering of the output signal by the output signal receiver, we calculate the mutual information in the leading and next-to-leading order in the dispersion parameter and at large signal-to-noise ratio (SNR). Further, we find the explicit analytical expression for the mutual information in the case of the modified Gaussian input signal distribution taking into account the limited frequency bandwidth of the input signal. We explain the behavior of the mutual information as a function of the average input signal power and the input signal bandwidth in connection with the frequency broadening in the presence of small dispersion.

The self-organization of active particles on a two-dimensional single-occupancy lattice is investigated, with an emphasis on the effects of boundary confinement and the influence of an external mean fluid flow. The study examines collective behaviors, particularly the transition from a disordered phase to the formation of orientationally ordered patterns, and their impact on particle transport and flux. In the absence of fluid flow, confinement causes particles to accumulate near the walls, leading to clogs or obstructions that hinder movement, or to the formation of bands aligned with the channel. Although these bands limit the particles' ability to freely self-propel, they still result in a net flux along the channel. The introduction of an external Poiseuille fluid flow induces vorticity, shifts the phase transition to higher alignment sensitivities, and promotes particle clustering at the channel center, significantly enhancing overall flux.

Statistical physicists have long studied systems where the variable of interest spans many orders of magnitude, the classic example is the relaxation times of glassy materials, which are often found to follow power laws. A power-law dependence has been found for the probability of transmission of COVID-19, as a function of length of time a susceptible person is in contact with an infected person. This is in data from the United Kingdom's COVID-19 app. The amount of virus in infected people spans many orders of magnitude. Inspired by this, I assume that the power-law behavior found in COVID-19 transmission is due to the effective transmission rate varying over orders of magnitude from one contact to another. I then use a model from statistical physics to estimate that if a population all wear FFP2/N95 masks, this reduces the effective reproduction number for COVID-19 transmission by a factor of approximately nine.

We investigate the overdamped dynamics of a "passive" particle driven by nonreciprocal interaction with a "driver" Brownian particle. When the interaction between them is short-ranged, the long-time behavior of the driven particle is remarkably universal-the mean-squared displacement (MSD) and the typical position of the driven particle exhibit the same qualitative behaviors independent of the specific form of the potential. In particular, the MSD grows as t^{1/2} in one dimension and logt in two spatial dimensions. We compute the exact scaling functions for the position distribution in d=1 and 2. These functions are universal when the interaction is short-ranged. For long-ranged interactions, the MSD of the driven particle grows as t^{ϕ} with exponent ϕ depending on the tail of the potential.

We consider the critical behavior of two-dimensional Potts models in the presence of a bond disorder in which the correlation decays as a power law. In some recent work the thermal sector of this theory was investigated by a renormalization group computation based on perturbed conformal field theory. Here we apply the same approach to study instead the magnetic sector. In particular, we compute the leading corrections to the Potts spin scaling dimension. Our results include as a special case the long-range disorder Ising model. We compare our prediction to Monte Carlo simulations. Finally, by studying the magnetization scaling function, we show a clear numerical evidence of a cross-over between the long-range and the short-range class of universality.

We discuss the spectral properties of microwave networks and quantum graphs with preserved and partially violated T invariance (time-reversal invariance) under an edge swap transformation. A chaotic tetrahedral quantum graph was simulated by the tetrahedral microwave network in which the swap transformation was realized by replacing one pair of edges {e_{i}} and {e_{j}} adjacent to different vertices {v_{i}} and {v_{j}}. We show that the spectra {ν_{n}}_{n=1}^{∞} and {ν[over ̃]_{n}}_{n=1}^{∞} before and after an edge swap operation are level-2 interlaced. The experimental distribution P(ΔN) of the spectral shift ΔN=N(ν)-N[over ̃](ν), where N(ν) and N[over ̃](ν) are the counting functions for the original and swapped networks, was confirmed in the numerical calculations. For chaotic systems with partially violated T invariance, the cases of level-2 interlacing (ΔN=±2) appear less frequently than for the systems with time reversal symmetry. Furthermore, the widths of the overlapping areas with ΔN=±2 are getting narrower than for the system with preserved T invariance. The smaller susceptibility to the swap operation for networks and graphs with partially violated T invariance is likely caused by the stronger level repulsion in their spectra than in the systems with preserved T invariance leading to smaller rigidity of their spectra.

Finding index-1 saddle points is crucial for understanding phase transitions. In this work, we propose a simple yet efficient approach, the spring pair method (SPM), to accurately locate saddle points. Without requiring the Hessian information, the SPM evolves a single pair of spring-coupled particles on an energy surface. By designing complementary drifting and climbing dynamics based on gradient decomposition, the spring pair converges onto the minimum energy path (MEP) and spontaneously aligns its orientation with the MEP tangent, providing a reliable ascent direction for efficient convergence to saddle points. The SPM fundamentally differs from traditional surface walking methods that rely on the eigenvectors of the Hessian, which may deviate from the MEP tangent and potentially lead to convergence failure or undesired saddle points. The efficiency of the SPM for finding saddle points is verified by ample examples, including Lennard-Jones clusters, Morse clusters, water clusters, and the Landau energy functional involving quasicrystal phase transitions.