We investigate the ratchet current (RC) in an inertial Brownian particle under the variation of mass, driving parameters, ratchet asymmetry, and temperature, modeled via the noise intensity (Q). Using stochastic simulations combined with parameter-space analysis, we show that the RC is strongly influenced by dynamical regimes, including periodic motion, chaos, bifurcations, and, most important, multistability. Notably, multistability plays a central role in the generation of temperature-induced RCs. The inclusion of Gaussian noise with arbitrarily small values of Q triggers transitions between coexisting deterministic attractors, leading to a preference for specific states. This noise-induced selection mechanism breaks velocity-space symmetry and enables directed transport. Lyapunov spectra, basins of attraction, and trajectory comparisons confirm that multistable regimes are the fundamental source of RC induced by noise. A global temperature analysis further reveals minimal RC at low Q, enhancement at intermediate Q, and suppression at high Q, while positive directed transport persists for small particle masses. These findings highlight the critical role of noise-driven transitions in deterministic multistable systems as a mechanism for controlling stochastic transport.

This Letter shows that a supersymmetric structure is inherent to the time space inverted (TSI) quantum mechanics (QM) framework, where the spatial evolution of states is generated by the operator $\hat{\mathcal{P}}^{\pm}(\hat{\mathcal{H}},\hat t;q)=\pm\sqrt{2m[\hat{\mathcal{H}}-\mathcal{\hat V}(q)]}$ [\href{https://doi.org/10.1103/PhysRevA.95.032133}{Phys. Rev. A. {\bf 95}, 032133 (2017)}], named here Momentunian, whose square-root structure that can be factorized. Such factorization leads directly to a supersymmetric algebra with supercharges and partner Hamiltonians. For the relativistic Momentunian the zero mode states are shown to be evanescent states, \textit{independent} of the physical potential. Furthermore, the existence of non-relativistic and relativistic Momentunian \textit{partners} is demonstrated, whose zero-mode states are no longer necessarily zero energies, but vanishing momenta states. The natural emergence of the $1/2$-fractional time derivatives in the TSI QM, leads to supercharges which incorporate memory effects into the supersymmetric wave functions. Results indicate that supersymmetry emerges as a structural property of the TSI QM rather than being imposed phenomenologically.

This work investigates how correlated environments influence the relative ( T_eff^(r) ) and center-of-mass ( T_eff^(R) ) effective temperatures using the Langevin description. The procedure is to consider N-identical “independent” particles, each coupled to its own thermal bath at temperature T_i ( i=1,2,… ,N ), where correlations among the baths mediate indirectly the coupling between particles. Using Jacobi coordinates, expressions for T_eff^(R) and T_eff^(r_i) are derived, and it is shown that T_eff^(R) can always be identified with the equilibrium temperature obtained from the first law of thermodynamics when N baths are put in thermal contact. The analysis demonstrates that cross correlations between the environments lead to fluctuations effects which are visible in the expression for T_eff^(R) , highlighting how microscopic noise correlations reshape macroscopic equilibration. Consequently, the procedure allows one to obtain the kind of bath cross-correlations between Langevin equations which correctly mimics the correlations involved in the first law of thermodynamics.

We propose a novel multi-output convolutional neural network (CNN) framework with station-specific subnets to model and analyze historical low- and high-river stages in the Negro River basin, located in northern South America. The basin is largely covered by tropical forest and experiences strong spatial and seasonal variability in rainfall. The study addresses the challenge of reconstructing accurate waterlevel time series in regions with sparse hydrological observations. Using observed data from five gauging stations—Cucuí, Serrinha, Caracaraí, Santa Maria do Boiaçú, and Moura—the study successfully reconstructs historical waterlevel time series. Quantitative evaluation shows that the subnet-based architecture achieves very low errors (MSE ≲ 0.09) and high distance correlation metrics (DC ≈ 1.00) during the 2021 flood. We also compare modelling results from subnet-based models with those obtained from individually trained station-specific networks, demonstrating that subnetworks more effectively capture both system-level and station-specific hydrological dynamics. The model captures complex temporal patterns, including sudden decreases, gradual recoveries, and flood rises, demonstrating its ability to represent station-specific hydrological dynamics and system-level responses to extreme floods and droughts. The findings highlight the broader implications of the subnet framework for hydrological prediction under climate variability, particularly for improving early-warning systems and operational monitoring in data-scarce basins. By enhancing the reconstruction of extremes and supporting gap-filling and consistency checking, the method contributes to decision-support strategies for managing future flood and drought risks in the Amazon basin. This visual summary provides a concise overview of the study’s core findings and methodologies. Water level data were collected from five gauging stations in the Negro River basin, covering regions with strong spatial and seasonal variability in rainfall. The data were preprocessed using normalization and formatting suitable for 1D convolutional layers. The study employed CNN-based subnetwork architectures integrating features from all stations, alongside independently trained CNNs for comparison, to evaluate the benefits of spatially shared learning. The graphical abstract illustrates the model’s capability to accurately reconstruct complex temporal dynamics, including sudden decreases, progressive recoveries, and repiquetes, while demonstrating superior generalization relative to individual networks across heterogeneous hydrological regimes. These results underscore the potential of the approach as a data-driven tool for flood and drought monitoring, gap-filling, and consistency checking in regions with sparse hydrological data, supporting operational applications such as early warning systems and water resource management. By leveraging subnetwork architectures, this study addresses the challenges of monitoring large and hydrologically diverse regions like the Amazon, highlighting the importance of integrative models for capturing basin-scale dynamics. CNN-based subnetworks accurately reconstruct historical low- and high-river stages in the Negro River basin. The model captures complex temporal patterns, including sudden decreases, gradual recoveries, and repiquetes. The approach supports monitoring and gap-filling in regions with sparse hydrological data. Integration of multiple stations through subnetworks enhances generalization across heterogeneous hydrological regimes. Subnetworks demonstrate potential for operational use in early warning and water resource management.

This paper investigates unbiased directed transport, known as the ratchet effect, within a system coupled to a fluid modeled by the bailout embedding technique. The system dynamics under the fluid influence are described by a four-dimensional mapping governed by parameters such as dissipation ([Formula: see text]), ratchet kicking ([Formula: see text]), and the relationship between fluid and particle densities ([Formula: see text]). We explore the behavior of the Ratchet Current (RC) in the parameter spaces [Formula: see text] and [Formula: see text], particularly focusing on the aerosol case ([Formula: see text]). Our findings reveal a complex interplay of parameters, with larger RCs observed for parameter pairs that induce periodic dynamics in the ratchet system. Furthermore, we observe RC reversal as a function of [Formula: see text] and [Formula: see text], and identify coexisting attractors (multistability) at higher [Formula: see text] values. These results shed light on the intriguing phenomenon of directed transport in fluid dynamics, offering insights that may contribute to understanding particle transport in nature, especially in the aerosol regime.

The out-of-time-order correlator (OTOC) is studied for a bosonic quantum lattice model. We gain its classical analog through the replacement of both commutators appearing in the quantum correlator by a corresponding Poisson bracket. The evaluation of the Poisson bracket is then performed in a complex-valued description of the Hamiltonian dynamics and, for the initial choice of quantum operators to be site-specific annihilators, turns out to be given by the expectation value of the absolute square of a specific element of the complex-valued monodromy matrix. The growth rate of this expectation value is compared to a typical chaos indicator, the mean finite-time Lyapunov exponent (FTLE). In both cases the numerical phase-space average is weighted by a Wigner function corresponding to a multimode coherent state. For a three-well Bose-Hubbard model in the Mott insulator regime, it is found that although, on the level of single trajectories, FTLE and classical OTOC show similar long-time behavior, after averaging, they exhibit a marked difference [which for purely chaotic initial conditions is close to ln(sqrt[2])], rooting in the different order the logarithm and the average are taken. This observation is an example of the relevance of the fluctuations of the FTLE to correctly explain the quantitative difference between OTOC growth rate and FTLE in a prototypical many-body system.

This study examines the nonlinear stability of trajectories under coordinate contraction and dilatation in three dynamical systems: the discrete-time dissipative H & eacute;non map, and the conservative, non-integrable, continuous-time H & eacute;non-Heiles and diamagnetic Kepler problems. The nonlinear stability analysis uses the q-deformed Jacobian and q-derivative, with trajectory stability assessed for q > 1 (dilatation) and q < 1 (contraction). It is shown that q-deformed Jacobian adds nonlinear terms to the linear Lyapunov stability analysis, and is named here as q-stability. Analytical curves in the parameter space mark boundaries of distinct low-periodic motions in the H & eacute;non map. Numerical simulations compute the maximal Lyapunov exponent across the parameter space, in Poincar & eacute; surfaces of section, and as a function of total energy in the conservative systems. Simulations show that contraction (dilatation) of coordinates generally decreases (increases) q-stability exponent when compared to the q = 1 case with positive Lyapunov exponents. Dilatation and contraction tend to increase the q-stability exponent for Lyapunov stable orbits. Some exceptions to this trend remain unexplained regarding Kolmogorov-Arnold-Moser (KAM) tori stability.

Time continues to be an intriguing physical property in the modern era. On the one hand, we have the classical and relativistic notion of time, where space and time have the same hierarchy, essential in describing events in spacetime. On the other hand, in quantum mechanics, time appears as a classical parameter, meaning that it does not have an uncertain relation with its canonical conjugate. In this work we use a recent spacetime-symmetric proposal [Phys. Rev. A 95 , 032133 (2017)] that tries to solve the unbalance in nonrelativistic quantum mechanics by extending the usual Hilbert space: the time parameter t and the position operator X in one subspace, and the position parameter x and time operator T in the other subspace. Time as an operator is better suited for describing tunneling processes. We then solve the 1/2 / 2-fractional integrodifferential equation for a particle subjected to strong and weak potential limits and obtain an analytical expression for the tunneling time through a rectangular barrier. Using a Gaussian energy distribution, we demonstrate that for wave packets well resolved in time, the expectation value of the operator T is the energy average of the classical time T class = a S /a E , where S is the classical action, which can be real or imaginary. The imaginary classical time does not contribute to the traveling time. Furthermore, we apply our results to a Gaussian energy distribution and compare them to previous works. This work is a correction of a previous paper [Phys. Rev. A 107, , 052220 (2023)].

In this work, we consider an application of fractional derivatives to realistic physical situations, namely the elastic collision of particles and the nonintegrable diamagnetic Kepler problem. The origin of fractional dynamics can be nonlocal interacting dynamics, memory effects, environments with fractal interacting properties, and relaxation processes, among others. In the case of collisions, considering identical and distinguishable particles, additional solutions appear compared to non-fractional dynamics. For specific velocities of one particle before the collision, several velocities of the other particle are allowed after the collision. Consequently, novel velocity distributions emerge. For the diamagnetic Kepler problem, the fractional dynamic strongly affects the regular and quasi-regular regimes of motion, while the completely chaotic motion remains essentially unaltered. Besides, we derive a fractional momentum-like integral of motion for the pure fractional Kepler problem.

Received 2 April 2024DOI:https://doi.org/10.1103/PhysRevA.109.049903©2024 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum formalismQuantum foundationsAtomic, Molecular & Optical

We investigate a monolayer graphene chip's relativistic ratchet current (RRC). Our findings indicate that thermal noise can paradoxically amplify dynamics, in contrast to its conventional inhibitory role. Under noise, temperature (T) activation of the RRC remains stable over a broader range of T values, and an increased number of RRCs reversals are observed as a function of T and relevant parameters of the external electric field. The results regarding structural changes and symmetry breaking of the dissipative attractors can be understood. The observed activation and reversal of RRCs under a variation of external parameters unveil the diverse and complex behavior of the charge carrier transport on the graphene chip. Understanding this behavior allows for generating specific RRCs values, properties and effects for the charge carriers, offering a variety of possibilities for application and control of the graphene chip device.

In this paper, we investigate a seven-parameter, five-dimensional dynamical system, specifically a unidirectional coupling of two FitzHugh-Nagumo neuron models, with one neuron being sinusoidally driven. This master-slave configuration features neuron N1 as the master, subjected to an external sinusoidal electrical current, and neuron N2 as the slave, interacting with N1 through an electrical force. We report numerical results for three distinct scenarios where N1 operates in (i) periodic, (ii) quasiperiodic, and (iii) chaotic regimes. The primary objective is to explore how the dynamics of the master neuron N1 influence the coupled system's behavior. To achieve this, we generated cross sections of the seven-dimensional parameter space, known as parameter planes. Our findings reveal that in the periodic regime of N1, the coupled system exhibits period-adding sequences of Arnold tongue-like structures in the parameter planes. Furthermore, regions of multistability can also be identified in these parameter planes of the coupled system. In the quasiperiodic regime, regions of periodic motion are absent, with only regions of quasiperiodic and chaotic dynamics present. In the chaotic regime of N1, the parameter planes display regions of chaos, hyperchaos, and transient hyperchaos.

Using the position as an independent variable, and time as the dependent variable, we derive the function ${\cal P}^{(\pm)}=\pm\sqrt{2m({\cal H}-{\cal V}(q))}$, which generates the space evolution under the potential ${\cal V}(q)$ and Hamiltonian ${\cal H}$. No parametrization is used. Canonically conjugated variables are the time and minus the Hamiltonian ($-{\cal H}$). While the classical dynamics do not change, the corresponding quantum operator ${\cal \hat P}^{(\pm)}$ naturally leads to a $1/2-$fractional time evolution, consistent with a recent proposed spacetime symmetric formalism of the quantum mechanics. Using Dirac's procedure, separation of variables is possible, and while the two-coupled position-independent Dirac equations depend on the $1/2$-fractional derivative, the two-coupled time-independent Dirac equations (TIDE) lead to positive and negative shifts in the potential, proportional to the force. Both equations couple the ($\pm$) solutions of ${\cal \hat P}^{(\pm)}$ and the kinetic energy ${\cal K}_0$ (separation constant) is the coupling strength. Thus, we obtain a pair of coupled states for systems with finite forces, not necessarily stationary states. The potential shifts for the harmonic oscillator (HO) are $\pm\hbar\omega/2$, and the corresponding pair of states are coupled for ${\cal K}_0\ne 0$. No time evolution is present for ${\cal K}_0=0$, and the ground state with energy $\hbar\omega/2$ is stable. For ${\cal K}_0>0$, the ground state becomes coupled to the state with energy $-\hbar\omega/2$, and \textit{this coupling} allows to describe higher excited states in the HO. Energy quantization of the HO leads to the quantization of ${\cal K}_0=k\hbar\omega$ ($k=1,2,\ldots$). For the one-dimensional Hydrogen atom, the potential shifts become imaginary and position-dependent. Decoupled case ${\cal K}_0=0$ leads to plane-waves-like solutions at the threshold. Above the threshold (${\cal K}_0>0$), we obtain a plane-wave-like solution, and for the bounded states (${\cal K}_0<0$), the wave-function becomes similar to the exact solutions but squeezed closer to the nucleus.

In this paper, we analyze the dynamic effect of a reservoir computer (RC) on its performance. Modified Kuramoto's coupled oscillators are used to model the RC, and synchronization, Lyapunov spectrum (and dimension), Shannon entropy, and the upper bound of the Kolmogorov-Sinai entropy are employed to characterize the dynamics of the RC. The performance of the RC is analyzed by reproducing the distribution of random, Gaussian, and quantum jumps series (shelved states) since a replica of the time evolution of a completely random series is not possible to generate. We demonstrate that hyperchaotic motion, moderate Shannon entropy, and a higher degree of synchronization of Kuramoto's oscillators lead to the best performance of the RC. Therefore, an appropriate balance of irregularity and order in the oscillator's dynamics leads to better performances.

An essential action in quantum information processing is the manipulation (control) of a single qubit, ideally a closed two-level system. However, in realistic applications, quantum processes are often under the influence of the external environment, e.g., presenting some degree of dissipation and decoherence. In this paper we address the emerging difficulties in the (tracking) quantum control of a two-level system under the influence of both Markovian and non-Markovian noise. We employ a same framework to treat both situations, a Lindblad-type equation, but considering that for the former (latter) case, the decay rate ⠂ is time independent (dependent). We discuss the conditions leading to a breakdown of the quantum control and eventual ways to overcome the problem, like employing a fast control scheme or controlling the off-diagonal terms of the system density matrix. Surprisingly, for Markovian noise such breakdown time decreases with ⠂ not as an exponential but as a power law. This indicates that the quantum control should be possible for a coupling between the system and the environment stronger than previously expected. Moreover, we find that for non-Markovian noise, the breakdown time is longer when there is backflow, i.e., ⠂(t) can be negative. The present theoretical results point to certain favorable scenarios to operate qubits even in a noisy medium.

Using the example of the city of São Paulo (Brazil), in this paper, we analyze the temporal relation between human mobility and meteorological variables with the number of infected individuals by the COVID-19 disease. For the temporal relation, we use the significant values of distance correlation t0(DC), which is a recently proposed quantity capable of detecting nonlinear correlations between time series. The analyzed period was from February 26, 2020 to June 28, 2020. Fewer movements in recreation and transit stations and the increase in the maximal temperature have strong correlations with the number of newly infected cases occurring 17 days after. Furthermore, more significant changes in grocery and pharmacy, parks, and recreation and sudden changes in the maximal pressure occurring 10 and 11 days before the disease begins are also correlated with it. Scanning the whole period of the data, not only the early stage of the disease, we observe that changes in human mobility also primarily affect the disease for 0-19 days after. In other words, our results demonstrate the crucial role of the municipal decree declaring an emergency in the city to influence the number of infected individuals.

Using the position as an independent variable, and time as the dependent variable, we derive the function P^(±), which generates the space evolution under the potential V(q) and Hamiltonian H. Canonically conjugated variables are the time and minus the Hamiltonian. While the classical dynamics do not change, the corresponding quantum operator naturally leads to a 1/2-fractional time evolution, consistent with a recently proposed spacetime symmetric formalism of quantum mechanics. Using Dirac's procedure, separation of variables is possible, and while the coupled position-independent Dirac equations depend on the 1/2-fractional derivative, the coupled time-independent Dirac equations (TIDE) lead to positive and negative shifts in the potential, proportional to the force. Both equations couple the (±) solutions of P̂^(±) and the kinetic energy K_0 is the coupling strength. We obtain a pair of coupled states for systems with finite forces. The potential shifts for the harmonic oscillator (HO) are ±ħω/2, and the corresponding pair of states are coupled for K_0 0. No time evolution is present for K_0=0, and the ground state with energy ħω/2 is stable. For K_0>0, the ground state becomes coupled to the state with energy -ħω/2, and this coupling allows to describe higher excited states. Energy quantization of the HO leads to quantization of K_0=kħω (k=1,2,…). For the one-dimensional Hydrogen atom, the potential shifts become imaginary and position-dependent. Decoupled case K_0=0 leads to plane-waves-like solutions at the threshold. Above the threshold, we obtain a plane-wave-like solution, and for the bounded states the wave-function becomes similar to the exact solutions but squeezed closer to the nucleus.

Time continues to be an intriguing physical property in the modern era. On the one hand, we have the classical and relativistic notions of time, where space and time have the same hierarchy, which is essential in describing events in spacetime. On the other hand, in quantum mechanics time appears as a classical parameter, meaning that it does not have an uncertainty relation with its canonical conjugate. In this work, we use a recent spacetime-symmetric proposal [Phys. Rev. A 95, 032133 (2017)] that tries to solve the unbalance in nonrelativistic quantum mechanics by extending the usual Hilbert space, having the time parameter t and the position operator (X) over cap in one subspace and the position parameter x and time operator T in the other subspace. Time as an operator is better suitable for describing tunneling processes. We then solve the 1/2-fractional integrodifferential equation for a particle subjected to strong and weak potential limits and obtain an analytical expression for the tunneling time through a rectangular barrier. Using a Gaussian energy distribution, we demonstrate that, for wavepackets well resolved in time, the expectation value of the operator T is the energy average of the classical time Tclass = 8S/8E, where S is the classical action, which can be real or imaginary. For wavepackets not well resolved in time, the contribution of Tclass consistently vanishes, and solely properties of the energy distribution contribute to T. We show that the time of travel for nontunneling particles is purely real. When tunneling is involved, complex arrival times emerge, becoming a signature of tunneling. Furthermore, we apply our results to a constant energy distribution, obtaining pure imaginary times for energies below the barrier while obtaining complex times for particles with a wavepacket spreading energies below and above the barrier, and show a comparison to previous works.

Oseledec’s theorem provides the necessary conditions for the existence of the decomposition of the tangent bundle called Oseledec’s splitting and the formal definition of the Lyapunov exponents. Using the concept of τ-domination of expansion or contraction rates of invariant subspaces after a time τ, together with the Oseledec theorem, we propose three quantifiers of τ-domination and τ-non-domination, which can be used to study the complex dynamics of physical systems. The interpretation of the Oseledec τ-domination in terms of the finite-time Lyapunov exponents is of great advantage for this purpose. Numerical results for the quantifiers are presented using the conservative standard map in a regime with mixed phase-space dynamics. Distinct typical regions in the phase-space are chosen, two containing a completely chaotic motion and two containing regularity islands. Results show that all quantifiers recognize that regions close to hyperbolic periodic points have a larger Oseledec τ-domination than regions around islands of regularity. Furthermore, Oseledec τ-non-dominated regions are also identified and are mostly close to regularity islands. We found a relation between the mean of expansion rates between the Oseledec subspaces and the mean of the angles between them.

Time continues to be an intriguing physical property in the modern era. On the one hand, we have the Classical and Relativistic notion of time, where space and time have the same hierarchy, which is essential in describing events in spacetime. On the other hand, in Quantum Mechanics, time appears as a classical parameter, meaning that it does not have an uncertainty relation with its canonical conjugate. In this work, we use a recent proposed spacetime-symmetric formalism~\href{https://doi.org/10.1103/PhysRevA.95.032133}{[Phys.~Rev.~A {\bf 95}, 032133 (2017)]} that tries to solve the unbalance in nonrelativistic Quantum Mechanics by extending the usual Hilbert space. The time parameter $t$ and the position operator $\hat{X}$ in one subspace, and the position parameter $x$ and time operator $\mathbb{T}$ in the other subspace. Time as an operator is better suitable for describing tunnelling processes. We then solve the novel $1/2$-fractional integrodifferential equation for a particle subjected to strong and weak potential limits and obtain an analytical expression for the tunnelling time through a rectangular barrier. We compare to previous works, obtaining pure imaginary times for energies below the barrier and a fast-decaying imaginary part for energies above the barrier, indicating the anti-hermiticity of the time operator for tunnelling times. We also show that the expected time of arrival in the tunnelling problem has the form of an energy average of the classical times of arrival plus a quantum contribution.