Non-dissipative System Research Articles

Majorana zero-modes in a dissipative Rashba nanowire

Condensed matter systems are continuously subjected to dissipation, which often has adverse effects on quantum phenomena. We focus on the impact of dissipation on a superconducting Rashba nanowire. We reveal that the system can still host Majorana zero-modes (MZMs) with a finite lifetime in the presence of dissipation. Most interestingly, dissipation can also generate two kinds of dissipative boundary states: four robust zero-modes (RZMs) and two MZMs, in the regime where the non-dissipative system is topologically trivial. The MZMs appear via bulk gap closing and are topologically characterized by a winding number. The RZMs are not associated with any bulk states and possess no winding number, but their emergence is instead tied to exceptional points. Further, we confirm the stability of the dissipation-induced RZMs and MZMs in the presence of random disorder. Our study paves the way for both realizing and stabilizing MZMs in an experimental setup, driven by dissipation.

Emulating Non-Hermitian Dynamics in a Finite Non-Dissipative Quantum System.

We discuss the emulation of non-Hermitian dynamics during a given time window using a low-dimensional quantum system coupled to a finite set of equidistant discrete states acting as an effective continuum. We first emulate the decay of an unstable state and map the quasi-continuum parameters, enabling the precise approximation of non-Hermitian dynamics. The limitations of this model, including in particular short- and long-time deviations, are extensively discussed. We then consider a driven two-level system and establish criteria for non-Hermitian dynamics emulation with a finite quasi-continuum. We quantitatively analyze the signatures of the finiteness of the effective continuum, addressing the possible emergence of non-Markovian behavior during the time interval considered. Finally, we investigate the emulation of dissipative dynamics using a finite quasi-continuum with a tailored density of states. We show through the example of a two-level system that such a continuum can reproduce non-Hermitian dynamics more efficiently than the usual equidistant quasi-continuum model.

Collapsing dynamics of relativistic fluid in modified gravity admitting a conformal Killing vector

The collapsing dynamics of relativistic fluid are explored in f(R) gravity in detailed systematic manner for the non-static spherically symmetric spacetime satisfying the equation of the conformal Killing vector. With quasi-homologous condition and diminishing complexity factor condition, exact solutions for dissipative as well as for non-dissipative system are found and the astrophysical applications of these exact solutions are discussed. Furthermore, it is demonstrated that f(R)=R, which is the extensive restriction of f(R) gravity, prior solutions of the collapsing fluid in general relativity, can be retrieved.

Rare rogue fluctuations could be generic to strongly nonlinear and non-integrable systems

We explore the possible existence of sufficiently large energy or rogue fluctuations (RFs) at late times in the strongly nonlinear regime of the classic β Fermi–Pasta–Ulam–Tsingou (FPUT) type systems. Our studies build on a study of RFs in the non-dissipative granular chain system and suggest that rare RFs could be generic to the time evolution of non-integrable strongly nonlinear systems at late enough times. Given the nonlinearity and the nonintegrability, analytical studies are largely inaccessible. The studies have hence been carried out using extensive dynamical simulations. We comment on the role of initial conditions and the surprising influence of harmonic forces on these strongly nonlinear systems. The RFs under focus here are distinct from the well known Peregrine solitons used to describe rogue waves via the weakly nonlinear Schrödinger equation.

Coupled Oscillators in an Agroecosystem: Integrating Direct and Indirect Effects.

AbstractAgricultural pests are increasingly appreciated as subjects of ecology. One particular case, a pest in coffee production, is analyzed here using the conceptual framework of complex systems, increasingly acknowledged as having an obvious home in the field of ecology, notorious for its complex structures. The particular case analyzed here arguably falls under the control of the complexity of the ecological system rather than of a simple magic bullet of population regulation. The system, which has been under study in southern Mexico for the past quarter century, is analyzed through the lens of neutral oscillations of the classical nondissipative Lotka-Volterra system. Based on three consumer/resource pairs (populations of [1] an ant, [2] a scale insect, [3] a beetle predator of the scale insect, [4] a fungal pathogen of the scale insect, and [5] a fly parasitoid of the ant), this five-dimensional system is well known qualitatively. Coupling all agents through both direct effects and trait-mediated indirect effects, the behavior of the neutral oscillation form of the system reveals a complex set of behaviors, including harmonized invariant sets, chaos, and/or quasiperiodicity. Such behaviors are well-known subjects in the science of complex systems and, it is argued, are ultimately sufficient to effect a degree of regulation on the pest, independent of explicit density-dependent feedback. Control of the system is thus seen as arguably actuated through its complexity, independent of any classic dissipative force.

All-dielectric apodized photonic crystals: A nondissipative pseudo-Hermitian system hosting multiple exceptional points

Optical systems obeying non-Hermitian dynamics have been the subject of intense and concerted investigation over the last two decades owing to their broad implications in photonics, acoustics, electronics as well as atomic physics. A vast majority of such investigations rely on a dissipative, balanced loss-gain system which introduces unavoidable noise and consequently, this limits the coherent control of propagation dynamics. Here, we show that an all-dielectric, non-dissipative photonic crystal (PC) could host, at least two exceptional points in its eigenvalue spectrum. By introducing optimum apodization in the PC architecture, namely 1D-APC, we show that such a configuration supports a spectrum of exceptional points which distinctly demarcates the PT-symmetric region from the region where PT -symmetry is broken in the parameter space. The analytical framework allows us to estimate the geometric phase of the reflected beam and derive the constraint that governs the excitation of topologically-protected optical Tamm-plasmon modes in 1D-APCs.

Dissipation driven degeneracies

Dissipation alone can produce counterintuitive topological wave transport that is otherwise absent in a non-dissipative system. This work demonstrates the influence of dissipation on degeneracies that arise in the context of elastic wave transport. The conditions on the parameters necessary to observe non-Hermitian degeneracies in the Bloch spectrum are precisely derived. It will be shown—contrary to the expectation from singularity theory of a linear eigenvalue problem—that a proportionally damped system with commutative damping does not exhibit non-Hermitian degeneracies. The necessity of a non-commutative and non-proportional dissipation model to observe non-Hermitian degeneracies (or exceptional points) is emphasized. Non-proportional dissipation is used to induce a non-Hermitian degeneracy in a local resonance sub-Bragg bandgap of a linear chain, without using negative damping. While Bloch waves are chosen to illustrate the influence of dissipation, the results readily extend to waves in non-periodic media as well as other wave and vibration transport problems.

The role of time integration in energy conservation in Smoothed Particle Hydrodynamics fluid dynamics simulations

The choice of a time integration scheme is a crucial aspect of any transient fluid simulation, and Smoothed-Particle Hydrodynamics (SPH) is no exception. The influence of the time integration scheme on energy balance is here addressed. To do so, explicit expressions allowing to compute the deviations from the energy balance, induced by the time integration scheme, are provided. These expressions, computed a posteriori, are valid for different integration methods. Besides, a new formulation that improves energy conservation by enhancing stability, based on an implicit integration scheme, is proposed. Such formulation is tested with the simulation of a two-dimensional non-viscous impact of two jets, with no artificial dissipation terms. To the best of our knowledge, this is the first stable simulation of a non-dissipative system with a weakly-compressible SPH method. A viscous case, the Taylor–Green vortex, has also been simulated. Results show that an implicit time integration scheme also behaves better in a viscous context.

Complexity of dynamical cylindrical system in f(G, T) gravity

The purpose of this paper is to formulate a complexity factor for a non-static cylindrical structure in the background of [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] represent the Gauss–Bonnet term and trace of the energy–momentum tensor, respectively. Different physical factors such as inhomogeneous energy density, anisotropic pressure, heat dissipation and modified terms are considered as candidates of complexity. In order to determine a complexity factor encompassing the essential aspects of the system, we apply the technique of orthogonal splitting to the Riemann tensor. We also study evolution of the cylinder through two modes: homologous and homogeneous. Further, we utilize the complexity-free and homologous conditions to examine the dissipative and non-dissipative self-gravitating system. Finally, the factors responsible for inducing complexity during the evolution system are inspected. We deduce that the modified terms in [Formula: see text] gravity make the system more complex.

Spin-current instability at a magnetic domain wall in a ferromagnetic superfluid: A generation mechanism of eccentric fractional skyrmions

Spinful superfluids of ultracold atoms are ideal for investigating the intrinsic properties of spin current and texture because they are realized in an isolated, nondissipative system free from impurities, dislocations, and thermal fluctuations. This study theoretically reveals the impact of spin current on a magnetic domain wall in spinful superfluids. An exact wall solution is obtained in the ferromagnetic phase of a spin-1 Bose-Einstein condensate with easy-axis anisotropy at zero temperature. The bosonic-quasiparticle mechanics analytically show that the spin current along the wall becomes unstable if the velocity exceeds the critical spin-current velocities, leading to complicated situations because of the competition between transverse magnons and ripplons. Our direct numerical simulation reveals that this system has a mechanism to generate an eccentric fractional skyrmion, which has a fractional topological charge, but its texture is not similar to that of a meron. This mechanism is in contrast to the generation of conventional skyrmions in easy-axis magnets. The theoretical findings can be examined in the same situation as in a recent experiment on ultracold atoms. In terms of the universality of spontaneous symmetry breaking, unexplored similar phenomena are expected in different physical systems with the same broken symmetry.

A Mechanical Feedback Classification of Linear Mechanical Control Systems

We give a classification of linear nondissipative mechanical control system under mechanical change of coordinates and feedback. First, we consider a controllable case that is somehow a mechanical counterpart of Brunovský classification, then we extend the result to all linear nondissipative mechanical systems (not necessarily controllable) which leads to a mechanical canonical decomposition. The classification of Lagrangian systems is given afterwards. Next, we show an application of the classification results to the stability and stabilization problem and illustrate them with several examples. All presented results in this paper are expressed in terms of objects on the configuration space Rn only, while the state-space of a mechanical control system is Rn×Rn consisting of configurations and velocities.

Applications of the (G′/G2)-Expansion Method for Solving Certain Nonlinear Conformable Evolution Equations

The core objective of this article is to generate novel exact traveling wave solutions of two nonlinear conformable evolution equations, namely, the (2+1)-dimensional conformable time integro-differential Sawada–Kotera (SK) equation and the (3+1)-dimensional conformable time modified KdV–Zakharov–Kuznetsov (mKdV–ZK) equation using the (G′/G2)-expansion method. These two equations associate with conformable partial derivatives with respect to time which the former equation is firstly proposed in the form of the conformable integro-differential equation. To the best of the authors’ knowledge, the two equations have not been solved by means of the (G′/G2)-expansion method for their exact solutions. As a result, some exact solutions of the equations expressed in terms of trigonometric, exponential, and rational function solutions are reported here for the first time. Furthermore, graphical representations of some selected solutions, plotted using some specific sets of the parameter values and the fractional orders, reveal certain physical features such as a singular single-soliton solution and a doubly periodic wave solution. These kinds of the solutions are usually discovered in natural phenomena. In particular, the soliton solution, which is a solitary wave whose amplitude, velocity, and shape are conserved after a collision with another soliton for a nondissipative system, arises ubiquitously in fluid mechanics, fiber optics, atomic physics, water waves, and plasmas. The method, along with the help of symbolic software packages, can be efficiently and simply used to solve the proposed problems for trustworthy and accurate exact solutions. Consequently, the method could be employed to determine some new exact solutions for other nonlinear conformable evolution equations.

Driven Qubit by Train of Gaussian-Pulses

The simplest non-dissipative 2-level atom system, a qubit, excited by a train of resonant n-Gaussian laser pulses is investigated. This concerns examination of the averaged atomic variables, the intensity-intensity correlation function, and the transient fluorescent radiation. Analytical formulas for the above expressions are obtained. Computational results show that the transient spectra with the initial ground and coherent atomic states exhibit asymmetric Mollow structure with dip structure, dense oscillation, and narrowing, and depends on the pulse number (n), the repetition time (τR), and the observed time.

Role of higher-order inertia in modulating elastic wave dispersion in materials with granular microstructure

(Meta-) materials with granular microstructures exhibit nonlinear dispersive wave propagation, which is typically attributed to the presence of a microstructure. However, this behavior can arise from two additional sources in a linear non-dissipative system – the grain-scale or micromechanical characteristics and the grain-scale or micro-inertial characteristics. The microstructure, the grain-scale mechanical and the grain-scale inertial properties in combination may be designated as micro-mechano-morphology. From a continuum modeling viewpoint, the observed dispersion behavior that accounts for micro-mechano-morphology of materials with granular microstructures can be described using a granular micromechanics based micromorphic model (Nejadsadeghi and Misra 2019b, Misra and Poorsolhjouy 2016). Following the approach outlined in these works, we elaborate on the effect of micro-scale inertia upon the wave propagation behavior. The work is motivated by the observation of negative group velocity of optical waves seen in simulations using discrete models of granular media. We show that higher-order inertia is necessary for describing this phenomena using continuum models. We further show that this phenomena can be modulated by micro-scale mass density distributions, thus affecting the widths of potential frequency band-gaps, including the negative group velocity of the acoustic branch.

Symmetry of linear dielectric response tensors: Dispersion models fulfilling three fundamental conditions

Physically correct dispersion models must fulfill three fundamental conditions (time-reversal symmetry, Kramers–Kronig consistency, and conformity with sum rules). The application of these conditions on systems exhibiting low crystal symmetry, spatial dispersion, and/or magneto-optic effects is a non-trivial task. The aim of this contribution is to present an approach using decomposition of dielectric tensors into a set of independent spectral functions. For the derivation, the most general case of anisotropic dielectric response with optical activity is considered. The contribution discusses both the natural optical activity exhibiting spatial dispersion and the local magneto-optic effect of rotation of the plane of polarization induced by the external magnetic field. If the response tensor is expressed up to the term linear in the direction of the wave vector, then its symmetry can be classified into 16 types. Formulas expressing each type of the dielectric tensor using independent spectral functions are presented (the most complex case with the lowest symmetry requires 15 spectral functions). The symmetry for different internal and external conditions is demonstrated with the help of several simple models based on solving the classical equations of motion. It is shown that interpreting free particles in the magnetic field as bound particles is not correct. Instead, the Landau levels in a non-dissipative system must be interpreted as splitting of diamagnetic part of the dielectric response, rather than energy of bound states.

Measure synchronization and clustering in a coupled-pendulum system suspended from a common beam.

In this paper, we investigate measure synchronization (MS) in a nondissipative coupled-pendulum system suspended from a common beam. The system consists of several identical pendula hanging from a common beam that are indirectly coupled through the movements of the beam. We find that as the ratio R of the mass of the common beam to the mass of each pendulum decreases, which, in turn, increases the coupling strength between the pendula, the coupled-pendulum can achieve MS, including partial MS and complete MS, below certain threshold values of Rc. The energy characteristics of the MS are discussed. It is found that the pendula reach frequency locking at the MS transitions. Furthermore, by employing Poincaré section analysis, we reveal the dynamical mechanism of MS transitions.

Non-dissipative System as Limit of a Dissipative One: Comparison of the Asymptotic Regimes

Let $$\Omega \subset \mathbb {R}^n$$ be a bounded smooth domain in $$\mathbb {R}^n$$. Given $$u_0\in L^2(\Omega )$$, $$g\in L^\infty (\Omega )$$ and $$\lambda \in \mathbb {R}$$, consider the family of problems parametrised by $$p \searrow 2$$, $$\begin{aligned} \left\{ \begin{array}{llll} &{}&{} \dfrac{\partial u}{\partial t} - \Delta _p u = \lambda u + g, \, \text { on } \quad (0,\infty )\times \Omega , \\ &{}&{} u = 0, \qquad \qquad \qquad \quad \quad \;\, \text { in } \quad (0,\infty )\times \partial \Omega , \\ &{}&{} u(0, \cdot ) = u_0, \qquad \qquad \quad \,\text { on } \quad \Omega , \end{array} \right. \end{aligned}$$where $$\Delta _p u:=\mathrm {div}\big (|\nabla u|^{p-2}\nabla u\big )$$ denotes the p-laplacian operator. Our aim in this paper is to describe the asymptotic behavior of this family of problems comparing compact attractors in the dissipative case $$p>2$$, with non-compact attractors in the non-dissipative limiting case $$p=2$$ with respect to the Hausdorff semi-distance between then.

Stability Analysis of a Simple Strut with Elastic Springs Through Sensitivity Surfaces and Gradients

The global elastic stability of a strut supported by three inclined springs is studied using the exact displacement geometry. The discrete phenomenological model in the theory of stability, described by Thompson and Gaspar, exhibits different postbuckling behaviors, depending on the initial geometry for large imperfections, and this has various applications in engineering. Using the total potential energy method, a system of nonlinear algebraic equations is derived for the nondissipative system. The arc length method is adopted to solve the system of nonlinear equations, considering the stability of equilibrium points at each position, while detecting and traversing the critical points with the possibility of intervention. The characteristic equilibrium paths and their corresponding trajectories are shown and compared with the asymptotic solutions at the first critical point. A parametric analysis is performed, and sensitivity surfaces are constructed for several initial positions of the springs, represented by the initial angle in the horizontal plane. A wide range of independent imperfections with large amplitudes in two directions is considered. The concept of load capacity gradient functions of sensitivity surfaces is introduced and used to qualitatively and quantitatively analyze the stability behavior of the system located far away from the initial position. A few interesting observations and conclusions are obtained from the sensitivity analysis of a simple strut in the postcritical region. The critical combinations of imperfections for each static system are determined through analysis of the gradients. Further, the “stable” and “unstable” regions of the sensitivity surfaces are identified, with some observations made. Finally, the applications of load capacity gradient functions in structural optimization and form findings are reviewed.

Nonreciprocal Single Photon Frequency Conversion via Chiral Coupling between a V-Type System and a Pair of Waveguides**Supported by the Anhui Provincial Natural Science Foundation under Grant No 1608085MA09, and the National Natural Science Foundation of China under Grant Nos 11774262, 61675006, 11474003 and 61472282.

The single photon frequency conversion is investigated theoretically in the system composed of a V-type system chiral coupling to a pair of waveguides. The single photon scattering amplitudes are obtained using the real-space Hamiltonian. The calculated results show that the probability of single photon frequency down- or up-conversion can reach a unit by choosing appropriate parameters in the non-dissipative system with perfect chiral coupling. We present a nonreciprocal single photon beam splitter whose frequency of the output photon is different from that of the input photon. The influences of dissipations and non-perfect chiral coupling on the single frequency conversion are also shown. Our results may be useful in designing quantum devices at the single-photon level.

Energy transfer by a wave transmitted from one nondissipative system to another

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