Search

The hallmark property of two-dimensional topological insulators is robustness of quantized electronic transport of charge and energy against disorder in the underlying lattice 1 . That robustness arises from the fact that, in the topological bandgap, such transport can occur only along the edge states, which are immune to backscattering owing to topological protection. However, for sufficiently strong disorder, this bandgap closes and the system as a whole becomes topologically trivial: all states are localized and all transport vanishes in accordance with Anderson localization 2,3 . The recent suggestion 4 that the reverse transition can occur was therefore surprising. In so-called topological Anderson insulators, it has been predicted 4 that the emergence of protected edge states and quantized transport can be induced, rather than inhibited, by the addition of sufficient disorder to a topologically trivial insulator. Here we report the experimental demonstration of a photonic topological Anderson insulator. Our experiments are carried out in an array of helical evanescently coupled waveguides in a honeycomb geometry with detuned sublattices. Adding on-site disorder in the form of random variations in the refractive index of the waveguides drives the system from a trivial phase into a topological one. This manifestation of topological Anderson insulator physics shows experimentally that disorder can enhance transport rather than arrest it.

We examined a one-dimensional quantum Heisenberg model that includes trimer-like correlated disordered exchange couplings and a non-uniform magnetic field. We conducted numerical experiments to study the transfer of magnons between the two ends of the chain. Using numerical methods, we calculated the time evolution of a localized magnon state at the left end of the chain. We evaluated the quality of the transfer from the left end to the right using standard tools such as fidelity and concurrence. Our calculations demonstrate the existence of magnon transfer with good fidelity for some specific energies ( E > 0 ) in the absence of a magnetic field. We also investigated the impact of the random magnetic field on our findings. [ABSTRACT FROM AUTHOR]

Purpose: The process of knowledge creation is recognized as an essential process for organizational learning and innovation. Creating knowledge to solve the problems and complexities of today's world is like opening a black box. Hence, the higher education system and universities are exploring ways to overcome the complexities and cope with global changes. In this regard, interdisciplinary collaborations and activities are crucial in creating knowledge and innovation to counter these changes. This study aimed to know the experiences of Shiraz university interdisciplinary researchers in the field of humanities and also design and explain the conceptual model of knowledge creation in interdisciplinary research teams in the field of humanities. Design/methodology/approach: In this qualitative research, grounded theory was implemented based on Strauss and Corbin's systematic approach. The sampling method was purposeful, and the participants included sixteen faculty members of shiraz university who had at least one experience of performing an interdisciplinary activity in one of the humanities fields. The first participant was selected as a pilot, and the rest were selected by snowball sampling. Semi-structured interviews were also used to collect data and continued until theoretical saturation was attained. After collecting the available information and interviewing the people, the data were organized and analyzed in three stages, open coding, axial coding, and selective coding, using the proposed framework of Strauss and Corbin. Finally, the researcher reached a final and meaningful categorization. Findings: In this research, the results were presented as a paradigm model of knowledge creation in the interdisciplinary research teams in the field of humanities. The paradigm model of the study consists of causal factors (internal and external factors), main categories (specialized competencies, scientific discourse, understanding of knowledge domains), strategies (structuring and synchronizing), context (individual and organizational), interfering factors (leadership, industry, and society), and consequences (individual and group achievement). Originality/value: The present study aimed to explore the experiences of researchers in the interdisciplinary humanities research teams on knowledge creation in qualitative research. The study used Strauss and Corbin's systematic approach to recognize the causal factors of knowledge creation and the contexts. Discovering the main category of knowledge creation in interdisciplinary research teams, the authors analyze the strategies and consequences of knowledge creation. [ABSTRACT FROM AUTHOR]

Supersymmetric (SUSY) optical structures display a number of intriguing properties that can lead to a variety of potential applications, ranging from perfect global phase matching to highly efficient mode conversion and novel multiplexing schemes. Here, we experimentally investigate the scattering characteristics of SUSY photonic lattices. We directly observe the light dynamics in such systems and compare the reflection/transmission properties of SUSY partner structures. In doing so, we demonstrate that discrete settings constitute a promising testbed for studying the different facets of optical supersymmetry.

Originally developed in the context of quantum field theory, the concept of supersymmetry can be used to systematically design a new class of optical structures. In this work, we demonstrate how key features arising from optical supersymmetry can be exploited to control the flow of light for mode-division multiplexing applications. Superpartner configurations are experimentally realized in coupled optical networks, and the corresponding light dynamics in such systems are directly observed. We show that supersymmetry can be judiciously used to remove the fundamental mode of a multimode optical structure while establishing global phase-matching conditions for the remaining set of modes. Along these lines, supersymmetry may serve as a promising platform for versatile optical components with desirable properties and functionalities.

We investigate the interplay of Bloch oscillations and Anderson localization in optics. Gradual washing out of Bloch oscillations and the formation of nearly stationary averaged intensity distributions, which are symmetric for narrow and strongly asymmetric for broad input excitations, are observed experimentally in laser-written waveguide arrays. At large disorder levels Bloch oscillations are completely destroyed and both narrow and wide excitations lead to symmetric stationary averaged intensity distributions with exponentially decaying tails.

We show, numerically and experimentally, that the presence of weak disorder results in an enhanced energy distribution of an initially localized wave-packet, in one- and two-dimensional finite lattices. The addition of a focusing nonlinearity facilitates the spreading effect even further by increasing the wave-packet effective size. We find a clear transition between the regions of enhanced spreading (weak disorder) and localization (strong disorder).

A non-unitary transformation leading to a Hatano–Nelson problem is performed on an array of equally-spaced optical waveguides. Such transformation produces a non-reciprocal system of waveguides, as the corresponding Hamiltonian becomes non-Hermitian. This may be achieved by judiciously choosing an attenuation (amplification) of the injected (or exciting) field. The non-Hermitian transport induced by such transformation is studied for several cases and closed analytical solutions, not present in the available literature, are straightforwardly obtained. The corresponding non-Hermitian Hamiltonian may represent an open system that interacts with the environment, either loosing to or being provided with energy from the exterior. [ABSTRACT FROM AUTHOR]

Amorphous photonic structures are mesoscopic optical structures described by electrical permittivity distributions with underlying spatial randomness. They offer a unique platform for studying a broad set of electromagnetic phenomena, including transverse Anderson localization, enhanced wave transport, and suppressed diffusion in random media. Despite this, at a more practical level, there is insufficient work on both understanding the nature of optical transport and the conditions conducive to vector-wave localization in these planar structures, as well as their potential applications to photonic nanodevices. In this study, we fill this gap by investigating experimentally and theoretically the characteristics of optical transport in a class of amorphous photonic structures and by demonstrating their use to some basic waveguiding nanostructures. We demonstrate that these 2-D structures have unique isotropic and asymmetric band gaps for in-plane propagation, controlled from first principles by varying the scattering strength and whose properties are elucidated by establishing an analogy between photon and carrier transport in amorphous semiconductors. We further observe Urbach band tails in these random structures and uncover their relation to frequency- and disorder-dependent Anderson-like localized modes through the modified Ioffe-Regel criterion and their mean free path - localization length character. Finally, we illustrate that our amorphous structures can serve as a versatile platform in which photonic devices such as disorder-localized waveguides can be readily implemented. Editors Summary: Amorphous photonic structures offer a unique platform for studying unique optical transport phenomena in random media. The authors examine both experimentally and theoretically TE (in-plane) polarized near-infrared light in amorphous structures, demonstrating isotropic and asymmetric bandgaps, Anderson-like localized states at the midgap, and readily available practical waveguide structures. [ABSTRACT FROM AUTHOR]

The study of noise assisted-transport in quantum systems is essential in a wide range of applications, from near-term NISQ devices to models for quantum biology. Here, we study a generalized XXZ model in the presence of stochastic collision noise, which allows describing environments beyond the standard Markovian formulation. Our analysis through the study of the local magnetization, the inverse participation ratio (IPR) or its generalization, and the inverse ergodicity ratio (IER) showed clear regimes, where the transport rate and coherence time could be controlled by the dissipation in a consistent manner. In addition, when considering various excitations, we characterized the interplay between collisions and system interactions, identifying regimes in which transport was counterintuitively enhanced when increasing the collision rate, even in the case of initially separated excitations. These results constitute an example of an essential building block for the understanding of quantum transport in structured noisy and warm-disordered environments. [ABSTRACT FROM AUTHOR]

Integrated Jx photonic lattices, inspired by the quantum harmonic oscillator and due to their equidistant eigenvalue spectrum, have proven extremely useful for various applications, such as perfect imaging and coherent transfer of quantum states. However, to date their large‐scale implementation remains challenging. This study applies concepts from supersymmetry (SUSY) to construct two‐dimensional (2D) systems with spectra identical to that of one‐dimensional (1D) Jx lattices. While exhibiting different dynamics, these 2D equivalent systems retain the key imaging and state transfer properties of their 1D Jx counterpart. The method extends to all systems with separable spectra and facilitates experimental fabrication of large‐scale photonic circuits. [ABSTRACT FROM AUTHOR]

The quantum Zeno effect refers to the slowdown of the decay of a quantum system due to frequent measurements. It has been extended beyond quantum systems, manifesting itself in such phenomena as the suppression of output beam decay by sufficiently strong absorption introduced in guiding optical systems. In this case, the phenomenon is termed as macroscopic Zeno effect. Here the observation of the macroscopic Zeno effect in a topological photonic system is reported. The phenomenon is based on the suppression of decay for only a subspace of edge modes that can propagate in the system and does not rely on the existence of exceptional points. By introducing controlled losses in one of the arms of a topological insulator comprising two closely positioned Su–Schrieffer–Heeger arrays, the macroscopic Zeno effect is demonstrated, which manifests itself in an increase of the transparency of the system with respect to the topological modes created at the interface between two arrays. The phenomenon remains robust against disorder in the non‐Hermitian topological regime. In contrast, coupling a topological array with a non‐topological one results in a monotonic decrease in output power with increasing absorption. [ABSTRACT FROM AUTHOR]

Controlling topological phases of light allows the observation of abundant topological phenomena and the development of robust photonic devices. The prospect of more sophisticated control with topological photonic devices for practical implementations requires high-level programmability. Here we demonstrate a fully programmable topological photonic chip with large-scale integration of silicon photonic nanocircuits and microresonators. Photonic artificial atoms and their interactions in our compound system can be individually addressed and controlled, allowing the arbitrary adjustment of structural parameters and geometrical configurations for the observation of dynamic topological phase transitions and diverse photonic topological insulators. Individual programming of artificial atoms on the generic chip enables the comprehensive statistical characterization of topological robustness against relatively weak disorders, and counterintuitive topological Anderson phase transitions induced by strong disorders. This generic topological photonic chip can be rapidly reprogrammed to implement multifunctionalities, providing a flexible and versatile platform for applications across fundamental science and topological technologies., (© 2024. The Author(s).)

We propose generation and entanglement detection schemes for generalized N-mode single-photon perfect W-states. These states are suitable for perfect teleportation and superdense coding. Based on the evolution of single-photon wavefunction in scalable integrated photonic lattices, we present schemes to generate these states using both planar and ring type waveguide structures. The integrated waveguide structures can be precisely fabricated, offer low photon propagation losses and can be integrated on a chip. In addition, we derive set of generalized entanglement conditions using the sum uncertainty relations of generalized su(2) algebra operators. We show that any given genuinely entangled N-mode single-photon state is a squeezed state of a specific su(2) algebra operator and can be expressed as superposition of a pair of orthonormal generalized N-mode single-photon perfect W-states which are eigenstates of that specific su(2) algebra operator. Within the single-photon subspace, the generalized entanglement condition reduces to a simplified single-photon separability condition. Detection of entanglement of single-photon states, using this single-photon separability condition, requires finding fidelity with two pairs of orthonormal generalized N-mode single-photon perfect W-states and hence more suitable for our purpose. Finally, we propose an experimental scheme to verify the entanglement using the proposed conditions. This scheme uses a photonic circuit consisting of directional couplers and phase shifters. The same photonic circuit can also be used to generate generalized N-mode single-photon perfect W-states. [ABSTRACT FROM AUTHOR]

The unique properties of light underpin the visions of photonic quantum technologies, optical interconnects and a wide range of novel sensors, but a key limiting factor today is losses due to either absorption or backscattering on defects. Recent developments in topological photonics have fostered the vision of backscattering-protected waveguides made from topological interface modes, but, surprisingly, measurements of their propagation losses were so far missing. Here we report on measurements of losses in the slow-light regime of valley-Hall topological waveguides and find no indications of topological protection against backscattering on ubiquitous structural defects. We image the light scattered out from the topological waveguides and find that the propagation losses are due to Anderson localization. The only photonic topological waveguides proposed for materials without intrinsic absorption in the optical domain are quantum spin-Hall and valley-Hall interface states, but the former exhibit strong out-of-plane losses, and our work, therefore, raises fundamental questions about the real-world value of topological protection in reciprocal photonics. This work investigates the real-world value of topological protection in reciprocal photonics. Measurements of propagation losses in the slow-light regime of valley-Hall topological waveguides yield no indications of topological protection against backscattering on structural defects. [ABSTRACT FROM AUTHOR]

Chromatinized DNA is targeted by proteins and small molecules to regulate chromatin function. For example, anthracycline cancer drugs evict nucleosomes in a mechanism that is still poorly understood. We here developed a flexible method for specific isotope labeling of nucleosomal DNA enabling NMR studies of such nucleosome interactions. We describe the synthesis of segmental one-strand 13 C-thymidine labeled 601-DNA, the assignment of the methyl signals, and demonstrate its use to observe site-specific binding to the nucleosome by aclarubicin, an anthracycline cancer drug that intercalates into the DNA minor grooves. Our results highlight intrinsic conformational heterogeneity in the 601 DNA sequence and show that aclarubicin binds an exposed AT-rich region near the DNA end. Overall, our data point to a model where the drug invades the nucleosome from the terminal ends inward, eventually resulting in histone eviction and nucleosome disruption., (© 2024 The Authors. ChemBioChem published by Wiley-VCH GmbH.)

We have designed and fabricated a kind of supersymmetric slotted Fabry–Perot semiconductor laser near 1550 nm to achieve a single-mode, high-power, and narrow-linewidth operation. The structure of the laser is composed of an electrically pumped broad ridge waveguide in the middle to provide optical gain, a group of periodic slots etched near the front facet to suppress the extra longitudinal modes and achieve a narrow linewidth, and a pair of passive superpartner waveguides located on both sides to filter out the high-order lateral modes in the broad waveguide. The device measured under the temperature of 25 °C shows an output power of 113 mW, a single-lobe lateral far-field distribution with the full width at half maximum of 7.8°, a peak wavelength of 1559.7 nm with the side-mode suppression ratio of 48.5 dB, and an intrinsic linewidth of 230 kHz at the bias current of 800 mA. The device is a promising candidate for cost-effective light sources for coherent communication systems and LiDARs. [ABSTRACT FROM AUTHOR]

We study a single-particle continuous-time quantum walk on a one-dimensional spatial lattice with complex nearest neighbour (NN) and next-nearest neighbour (NNN) hopping amplitudes. We show that the model allows for controlled information transfer and directional biasing without a biased initial state. Specifically, we show that for an unbiased initial state, complex couplings lead to chiral propagation and a causal cone structure asymmetric about the origin. We provide a hydrodynamic description for the dynamics in the large space–time limit. We obtain a global ‘quasi-stationary state’ which can be described in terms of the local quasi-particle densities satisfying Euler type of hydrodynamic equations and characterized by an infinite set of conservation laws. Further, we show that higher-order hydrodynamic equations can be used to describe the anomalous sub-diffusive scaling near the extremal fronts. The long-time behaviour for any complex NNN hopping with a nonzero real component is similar to that of purely real hopping; at a critical coupling strength, there is a Lifshitz transition where the topology of the causal structure changes from a regime with one causal cone to a regime with two nested (asymmetric) causal cones. For purely imaginary NNN hopping, there is a transition from one causal cone to a regime with two partially overlapping cones which can be attributed to the existence of degenerate maximal fronts. Both the nature of the Lifshitz transition and the scaling behaviour at the critical coupling are different in the two cases. We also discuss possible experimental realizations of such a model. [ABSTRACT FROM AUTHOR]

Disorder and non-Hermiticity dramatically impact the topological and localization properties of a quantum system, giving rise to intriguing quantum states of matter. The rich interplay of disorder, non-Hermiticity, and topology is epitomized by the recently proposed non-Hermitian topological Anderson insulator that hosts a plethora of exotic phenomena. Here we experimentally simulate the non-Hermitian topological Anderson insulator using disordered photonic quantum walks, and characterize its localization and topological properties. In particular, we focus on the competition between Anderson localization induced by random disorder, and the non-Hermitian skin effect under which all eigenstates are squeezed toward the boundary. The two distinct localization mechanisms prompt a non-monotonous change in profile of the Lyapunov exponent, which we experimentally reveal through dynamic observables. We then probe the disorder-induced topological phase transitions, and demonstrate their biorthogonal criticality. Our experiment further advances the frontier of synthetic topology in open systems. The authors report an experimental observation of a non-Hermitian topological Anderson insulator using photonic quantum walks, revealing the competition between Anderson localization induced by random disorder and the non-Hermitian skin effect. [ABSTRACT FROM AUTHOR]

These ground-state perturbations in terms of the eigenvalue shift and profile deformation of the SUSY Hamiltonian then allow for the series of SUSY transformations (Figure 2), which leads to a family of quasi-isospectral potentials with different landscapes [[17], [20], [35]]. Keywords: Darboux transformation; dimensionality; Householder transformation; isospectrality; Lanczos transformation; supersymmetry EN Darboux transformation dimensionality Householder transformation isospectrality Lanczos transformation supersymmetry 2763 2778 16 05/19/22 20220601 NES 220601 1 Introduction A light wave is characterized by multiple physical quantities defined in spatial and temporal domains, their reciprocal spaces, and the other intrinsic spaces of photons such as polarization [[1]]. The SUSY transformation can also be applied to other 1D problems, such as the conservation of scattering properties for any angle of incidence [[20], [46]], the control of orbital angular momenta in SUSY-transformed structures with rotational symmetry (Figure 3e and f) [[20], [47]], and the topological transition using the QR-factorized SUSY transformation [[38]]. 3 Isospectrality in supersymmetric photonics Supersymmetry (SUSY) is an intriguing conjecture that implies a hidden connection between integer spin bosons and half-integer spin fermions in particle physics [[13]]. [Extracted from the article]

Thanks to the topological protection, photonic topological edge states can move along the edges of photonic crystals without radiating into the bulk or reflecting when encountering disorders or defects. The valley Hall effect helps obtain topological edge states without breaking the time-reversal symmetry but breaking the inversion symmetry of the system, which means that the valley Hall edge state is independent of the magnetic field. Thus, with two inversion symmetry-broken photonic lattices, a domain wall that supports valley Hall edge states can be established. Generally, the zigzag-type domain wall is likely to support topological valley Hall edge states. However, in this work we investigate the valley Hall edge state on the armchair-type domain wall in a honeycomb lattice and demonstrate that armchair-type valley Hall edge states can also circumvent sharp corners with tiny reflection. The armchair-type domain wall, with the refractive index change being staggered, supports not only the bright but also the dark valley Hall edge solitons, and even the vector valley Hall edge solitons. Our results deepen the understanding of topological valley Hall edge states on different types of domain walls and may find applications in developing techniques of manipulating light fields for fabricating on-chip optical functional devices. [ABSTRACT FROM AUTHOR]

Anderson localization derived from randomness plays a crucial role in various kinds of phase transitions. Although treated as a free variable parameter in theory, randomness in electronic materials is hard to control experimentally owing to the coexisting Coulomb interaction. Here we demonstrate that the intrinsic anion disorder in a mixed-anion system of SrNbO2N induces a significant random potential that overwhelms the Coulomb potential while maintaining the lattice structure. A metal-to-insulator transition is triggered by a chemical modulation of the electron density where the critical electron density is more than three orders of magnitude greater than that predicted by the well-known Mott criterion. The localized electrons show characteristic electrical properties such as temperature-dependent multiple crossovers of conduction mechanisms and a positive magnetoresistance above 50% at low temperature. The large magnetoresistance is attributed to wave-function shrinkage of the localized states and clearly visualizes the anisotropy in the band structure, which indicates a compatibility of the periodicity and randomness. Anderson localisation is a well-known phenomenon in condensed-matter physics, which is driven by disorder and can be an important factor in the low-temperature properties for a wide range of systems. Here, the authors describe how a metal-insulator transition can be induced by anion disorder in the perovskite oxynitride SrNbO2N. [ABSTRACT FROM AUTHOR]

The broken and unbroken phases of PT and supersymmetry in optical systems are explored for a complex refractive index profile in the form of a Scarf potential, under the framework of supersymmetric quantum mechanics. The transition from unbroken to the broken phases of PT -symmetry, with the merger of eigenfunctions near the exceptional point is found to arise from two distinct realizations of the potential, originating from the underlying supersymmetry. Interestingly, in PT -symmetric phase, spontaneous breaking of supersymmetry occurs in a parametric domain, possessing non-trivial shape invariances, under reparametrization to yield the corresponding energy spectra. One also observes a parametric bifurcation behaviour in this domain. Unlike the real Scraf potential, in PT -symmetric phase, a connection between complex isospecrtal superpotentials and modified Korteweg-de Vries equation occurs, only with certain restrictive parametric conditions. In the broken PT -symmetry phase, supersymmetry is found to be intact in the entire parameter domain yielding the complex energy spectra, with zero-width resonance occurring at integral values of a potential parameter. [ABSTRACT FROM AUTHOR]

In 1878, Lord Rayleigh observed the highly celebrated phenomenon of sound waves that creep around the curved gallery of St Paul’s Cathedral in London1,2. These whispering-gallery waves scatter efficiently with little diffraction around an enclosure and have since found applications in ultrasonic fatigue and crack testing, and in the optical sensing of nanoparticles or molecules using silica microscale toroids. Recently, intense research efforts have focused on exploring non-Hermitian systems with cleverly matched gain and loss, facilitating unidirectional invisibility and exotic characteristics of exceptional points3,4. Likewise, the surge in physics using topological insulators comprising non-trivial symmetry-protected phases has laid the groundwork in reshaping highly unconventional avenues for robust and reflection-free guiding and steering of both sound and light5,6. Here we construct a topological gallery insulator using sonic crystals made of thermoplastic rods that are decorated with carbon nanotube films, which act as a sonic gain medium by virtue of electro-thermoacoustic coupling. By engineering specific non-Hermiticity textures to the activated rods, we are able to break the chiral symmetry of the whispering-gallery modes, which enables the out-coupling of topological ‘audio lasing’ modes with the desired handedness. We foresee that these findings will stimulate progress in non-destructive testing and acoustic sensing.An acoustic topological gallery insulator constructed from sonic crystals made of thermoplastic rods decorated with carbon nanotube films enables the out-coupling of amplified and focused sound at audible frequencies. [ABSTRACT FROM AUTHOR]

A Majorana fermion is the single fermionic particle that is its own antiparticle. Its dynamics is determined by the Majorana equation, where the spinor field is by definition equal to its charge‐conjugate field. In this paper, we investigated Shannon's entropy of linear Majorana fermions to understand how this quantity is modified due to an external potential of the linear type linear. Subsequently, we turn our attention to the construction of an ensemble of these Majorana particles to study the thermodynamic properties of the model. Finally, we show how Shannon's entropy and thermodynamic properties are modified under the linear potential action. [ABSTRACT FROM AUTHOR]

Anderson's groundbreaking discovery that the presence of stochastic imperfections in a crystal may result in a sudden breakdown of conductivity1 revolutionized our understanding of disordered media. After stimulating decades of studies2, Anderson localization has found applications in various areas of physics3–12. A fundamental assumption in Anderson's treatment is that no energy is exchanged with the environment. Recently, a number of studies shed new light on disordered media with dissipation14–22. In particular it has been predicted that random fluctuations solely in the dissipation, introduced by the underlying potential, could exponentially localize all eigenstates (spectral localization)14, similar to the original case without dissipation that Anderson considered. We show in theory and experiment that uncorrelated disordered dissipation can simultaneously cause spectral localization and wave spreading (dynamical delocalization). This discovery implies the breakdown of the commonly known correspondence between spectral and dynamical localization known from the Hermitian Anderson model with uncorrelated disorder. Experimental and theoretical results of wave propagation in a disordered system with non-Hermitian disorder are presented, showing that wave spreading occurs in the parameter regime where all eigenstates are expected to be localized. [ABSTRACT FROM AUTHOR]

We present trapped solitary wave solutions of a coupled nonlinear Schrödinger (NLS) system in 1 + 1 dimensions in the presence of an external, supersymmetric and complex -symmetric potential. The Schrödinger system this work focuses on possesses exact solutions whose existence, stability, and spatio-temporal dynamics are investigated by means of analytical and numerical methods. Two different variational approximations are considered where the stability and dynamics of the solitary waves are explored in terms of eight and twelve time-dependent collective coordinates (CCs). We find regions of stability for specific potential choices as well as analytic expressions for the small oscillation frequencies in the CC approximation. Our findings are further supported by performing systematic numerical simulations of the NLS system. [ABSTRACT FROM AUTHOR]