Regular and chaotic dynamics in time-dependent relativistic mean-field theory

Nucleon escape widths of the giant dipole resonances in spherical nuclei

The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by using time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.

We discuss some problems of dissipative chaos for open quantum systems in the\nframework of semiclassical and quantum distributions. For this goal, we propose\na driven nonlinear oscillator with time-dependent coefficients, i.e. with\ntime-dependent Kerr-nonlinearity and time-modulated driving field. This model\nshowing both regular and chaotic dynamics in the classical limit is realized in\nseveral experimental schemes. Quantum dissipative chaos is analyzed on the base\nof numerical method of quantum trajectories. Three quantities are studied: the\nWigner function of oscillatory mode from the point of view of quantum-assemble\ntheory and both semiclassical Poincare section and quantum Poincare section\ncalculated on a single quantum trajectory. The comparatively analysis of these\ndistributions for various operational chaotic regimes of the models is\nperformed, as well as scaling invariance in dissipative chaos and quantum\ninterference effects assisted by chaos are discussed.\n

Antiferromagnets have attracted significant attention because of their considerable potential in engineering high-density and ultrafast memory devices, a crucial and increasingly demanded component of contemporary high-performance information technology. Theoretical and experimental investigations are actively progressing to provide the capability of efficient switching and precise control of the Néel vector, which is crucial for the intended practical applications of antiferromagnets. Recently, a time-dependent Schwinger boson mean-field theory has been successfully developed to study the sublattice magnetization switching in anisotropic quantum antiferromagnets [K. Bolsmann et al ., PRX Quantum , vol. 4, 2023, Art. no. 030332]. Here we use a complementary exact diagonalization method to study such sublattice magnetization switching, but in small-cluster quantum antiferromagnets, by means of an external magnetic field. Furthermore, this article aims to support the findings of the Schwinger boson approach. We show that the results of both approaches are consistent at short time scales, with only about 12.5 % deviations. The consistency of the outcomes obtained through this alternative exact approach demonstrates that the time-dependent Schwinger boson mean-field theory is a versatile framework to capture the essentials of the switching process in quantum antiferromagnets. Thereby, the findings of current article pave the way for further theoretical and computational progress in the study of antiferromagnets for engineering spintronic devices with ultrahigh density and ultrafast speed.

In this contribution we study the onset of chaos via type-II intermittency within the framework of Horizontal Visibility graph theory. We construct graphs associated to time series generated by an iterated map close to a Neimark–Sacker bifurcation and study, both numerically and analytically, their main topological properties. We find well defined equivalences between the main statistical properties of intermittent series (scaling of laminar trends and Lyapunov exponent) and those of the resulting graphs, and accordingly construct a graph-theoretical description of type-II intermittency. We finally recast this theory into a graph-theoretical renormalization group (RG) framework, and show that the fixed point structure of RG flow diagram separates regular, critical and chaotic dynamics.

Hostile space weather is one of the principal threats to modern human technology because of the dependency of our lives on satellites. Solar coronal mass ejections, solar flares, and high‐speed solar wind streams often cause some sequences of damaging disturbances within the Earth's magnetosphere, in the atmosphere, and even on the Earth's surface. The time‐varying Sun, as the main source of space weather causes geomagnetic storms and substorms in many ways with coronal mass ejections (CME) being possibly the most harmful among them. CMEs cause transient magnetized plasma flows as interplanetary consequences, which drive the geomagnetic storms and substorms in the Earth's magnetosphere. It is shown that the cyclic solar activity has chaotic characteristics. It seems that the chaotic modeling of solar and geomagnetic activity indices is an important approach for analysis and prediction of the solar extreme events. This is particularly useful for engineers and designers interested in space weather prediction and its applications. One of the most important tools for eliciting the chaotic trends is the “Lyapunov exponents,” which is a useful measure of the stability of a dynamic system. This paper analyzes the variation of Lyapunov exponents (LE) for three solar and geomagnetic activity indices during CMEs: the sunspot number, disturbance storm time, and proton temperature. The analysis has been carried out using the technique of adaptive LE estimation adopted from previous works; the suitable window for which has been determined via trial and error. It is shown that the LE of these solar and geomagnetic activity indices varies rapidly during CMEs. The variation in LEs creates a pattern as a precursor for the forthcoming CME. This precursor, which is an oscillation in the values of Les, begins several steps sooner than the CME's occurrence. Then, during the CME, the LEs decrease to a small positive or a negative value, which demonstrates that during an anomaly such as a CME the chaotic characteristics of solar and geomagnetic activity indices decrease and solar and geomagnetic activity indices follow more regular dynamics.

An extended time-dependent mean-field theory for strongly correlated nuclear systems

Periodic and chaotic current oscillations are observed during electrodissolution of copper in a pH 3.5 sodium acetate/ acetic acid buffer under potentiostatic conditions using a rotating copper disk electrode. Periodic or chaotic oscillations are observed depending on the applied potential and electrode rotation rate. The oscillations arise after the formation and dissolution of an acetate salt film precursor to oxide passivation. The nature and composition of the surface films were examined using scanning electron microscopy and x‐ray powder diffraction data. Nonlinear dynamic analysis methods have been used to show the existence of deterministic chaos. Time series data of the chaotic oscillations were used to generate a return map that appears to be one‐dimensional. The chaotic attractor was reconstructed in a three‐dimensional state space using the method of time delays and the largest Lyapunov exponent was calculated and was positive for the chaotic oscillations indicating a sensitive dependence on initial conditions characteristic of deterministic chaos.

We carry out a systematic investigation on the low-energy electric dipole strength, which is often called pygmy dipole resonances (PDR), using the canonical-basis time-dependent Hartree-Fock-Bogoliubov (Cb-TDHFB) method. The Cb-TDHFB is a new method which is derived from TDHFB with an approximation analogous to the BCS theory that the pair potential is assumed to be diagonal in the time-dependent canonical basis. We apply the method to linear-response calculation for even-even nuclei. We report the neutron-number dependence of PDR in light (A < 70) and heavy isotopes (A > 100) around N = 82.

The time-dependent self-consistent field method (TDSCF) is formulated and applied to the study of intramolecular dynamics and unimolecular decomposition processes. The method is illustrated by calculations on vibrational predissociation in van der Waals molecules, such as I2(v)Ne→I2(v′)+Ne. The TDSCF has the advantage of achieving formal separability of the modes by associating a time-dependent Hamiltonian with each mode, while permitting (possibly extensive) energy transfer among the modes via the time-dependent mean potential which acts on each mode. We present quantal, semiclassical, and classical versions of the method; a proper classical limit of the quantum TDSCF replaces the averages over wave functions by averages over self-consistently obtained bundles of trajectories. In all three versions, considerable computational economy is retained in comparison with full dynamics calculation. A detailed study is made of those properties which can be correctly obtained in such a time-dependent mean field theory. Attention is drawn to problems such as the occurrence of spurious states in the asymptotic region, and a simple method for avoiding them is suggested. We find for the I2(v)Ne vibrational predissociation that the TDSCF compares well with corresponding full dynamics calculations for average single mode properties such as dissociation lifetimes and the translational energy release. Moreover, comparison with classical trajectory calculations shows that the TDSCF method reproduces the essential dynamical mechanism of the dissociation (in-phase impulsive I⋅⋅⋅Ne collision following several ineffective vibrations). The self-consistent bundle trajectories and the time-dependent mean fields are analyzed, and provide insight into the process dynamics. It is concluded that the TDSCF approach in both quantal and quasiclassical versions is a potentially powerful tool in the study of intramolecular energy transfer and unimolecular dissociation.

Relativistic mean-field description of small- and large-amplitude collective motion in nuclei

The new approach for combinatorial optimization problems using chaotic dynamics is discussed. We show effectiveness of chaotic neuro dynamics for solving combinatorial optimization problems by applying the chaotic neural network to traveling salesman problems. In this paper, we adopt the chaotic neural network model with two internal states, corresponding to mutual interactions which minimize an energy function and refractoriness which induce chaotic dynamics. We investigate relationships between solving abilities and different model parameters such as decay parameters of two internal states, Lyapunov exponents and first order statistics of firing patterns.

We discuss application of contemporary methods of the theory of dynamical systems with regular and chaotic hyperbolic dynamics to investigation of topological structure of magnetic fields in conducting media. For substantial classes of magnetic fields, we consider well-known physical models allowing us to reduce investigation of such fields to study of vector fields and Morse-Smale diffeomorphisms as well as diffeomorphisms with nontrivial basic sets satisfying the A axiom introduced by Smale. For the point-charge magnetic field model, we consider the problem of separator playing an important role in the reconnection processes and investigate relations between its singularities. We consider the class of magnetic fields in the solar corona and solve the problem of topological equivalency of fields in this class. We develop a topological modification of the Zeldovich funicular model of the nondissipative cinematic dynamo, constructing a hyperbolic diffeomorphism with chaotic dynamics that is conservative in the neighborhood of its transitive invariant set.

Quantum chaos cannot develop faster than &amp;#x03BB;&amp;#x2264;2&amp;#x03C0;/(&amp;#x210F;&amp;#x03B2;) for systems in thermal equilibrium [Maldacena, Shenker &amp; Stanford, JHEP (2016)]. This `MSS bound' on the Lyapunov exponent &amp;#x03BB; is set by the width of the strip on which the regularized out-of-time-order correlator is analytic. We show that similar constraints also bound the decay of the spectral form factor (SFF), that measures spectral correlation and is defined from the Fourier transform of the two-level correlation function. Specifically, the inflection exponent&amp;#x03B7;, that we introduce to characterize the early-time decay of the SFF, is bounded as &amp;#x03B7;&amp;#x2264;&amp;#x03C0;/(2&amp;#x210F;&amp;#x03B2;). This bound is universal and exists outside of the chaotic regime. The results are illustrated in systems with regular, chaotic, and tunable dynamics, namely the single-particle harmonic oscillator, the many-particle Calogero-Sutherland model, an ensemble from random matrix theory, and the quantum kicked top. The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.

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