Correlation Of Energy Levels Research Articles

Scrutinizing micellar transitions and interfacial properties in mixed micelles comprising sodium dodecyl sulfate and sodium oleate: A tensiometric and scattering insight

Mixed micellar systems play a pivotal role in numerous scientific and industrial applications due to their inimitable solution properties and potential for enhancing solubilization and emulsification processes. The present study unveils the mixed micellization behavior of two anionically charged surfactants, sodium dodecyl sulfate (SDS) and sodium oleate (SO), in aqueous solutions through a combination of solution viscosity, tensiometric and small-angle neutron scattering (SANS) techniques. The dynamic changes in the interfacial properties of the mixed micellar system as a function of the SDS-to-SO ratio are evaluated from surface tension measurements. The results offer an insight into the formation of the stable mixed micelles with the alteration in the critical micelle concentration (CMC) as a function of the composition of both surfactants and the nature of the interaction. Surface tension data disclose the thermodynamic aspects of micelle formation and the influence of surfactant interactions on the surface activity of the system. Complementing the surface tension measurements, SANS analysis was conducted to clarify the structural aspects of the SDS-SO mixed micelles. SANS inferred the micellar size, shape, and aggregation number (Nagg), thereby shedding light on the nanoscale organization of the micellar aggregates in the aqueous solution. By combining SANS and surface tension data, a comprehensive understanding of the mixed micellization behavior of SDS and SO is achieved, addressing both interfacial and structural aspects. A computational simulation approach has also been employed to obtain the optimized parameters, which provide a better understanding of the correlation of SDS and SO molecular orbital energy levels. The results underscore the importance of surface tension and structural characterization techniques to comprehend the behavior of mixed micelles fully.

Investigation of statistical correlation of negative parity energy levels in Tm nucleus with A=170

In this paper, the statistical properties of 1- to 7- negative parity levels in the 170Tm nucleus are considered with emphasis on the nearest neighbor spacing distribution in the framework of random matrix theory. The latest available experimental data for different negative parity energy levels in the E≤ 3000 keV region are used to classifiy in different sequences and are analysed. The Berry – Robnik distribution function and the least square extraction method have been used to determine the parameter of distribution function in considered sequences. The results show the adaptation of the statistical behavior of all considered negative parity levels with the Wigner distribution function and therefore, the statistical correlation of such levels. Also, the strong correlations are yield for the sequences prepared by levels with odd spin values while the 2- levels show a weak correlation and a Poisson-like behavior. The dependence of the statistical behavior of the negative parity levels to the energy was investigated which suggests the maximum correlation in the 1300 <E < 2100 keV energy region.

Nonergodic extended states in the β ensemble.

Matrix models showing a chaotic-integrable transition in the spectral statistics are important for understanding many-body localization (MBL) in physical systems. One such example is the β ensemble, known for its structural simplicity. However, eigenvector properties of the β ensemble remain largely unexplored, despite energy level correlations being thoroughly studied. In this work we numerically study the eigenvector properties of the β ensemble and find that the Anderson transition occurs at γ=1 and ergodicity breaks down at γ=0 if we express the repulsion parameter as β=N^{-γ}. Thus other than the Rosenzweig-Porter ensemble (RPE), the β ensemble is another example where nonergodic extended (NEE) states are observed over a finite interval of parameter values (0<γ<1). We find that the chaotic-integrable transition coincides with the breaking of ergodicity in the β ensemble but with the localization transition in the RPE or the 1D disordered spin-1/2 Heisenberg model. As a result, the dynamical timescales in the NEE regime of the β ensemble behave differently than the latter models.

The length effect and color tuning of tetraphenylethylene functionalized oligothiophenes for effective detection of explosives

Aggregation-induced fluorescent materials are of great importance in optoelectronics and bioelectronics in solid-state devices. Herein, functionalized oligothiophenes were designed and synthesized with the tetraphenylethylene (TPE) groups to explore the length effect and color tuning for the effective detection of explosives. Remarkably, compounds 2TPE1T and 2TPE2T show an aggregation-induced emission phenomenon, while longer π–conjugated molecules 2TPE3T, 2TPE4T, TPE5T and 2TPE6T show aggregation-caused quenching character, where the reason has been explained based on UV–Vis spectra ranging from 378 to 446 nm. Furthermore, fluorescent titration experiments demonstrate that dye 2TPE1T has a better response than dye 2TPE2T for nitroaromatics. The visual detection limit of 2,6-DNT is 18.2 ng/cm2 in the test strip of 2TPE1T. In addition, there is an exquisitely linear curve between the theoretical and experimental energy levels for TPE functionalized oligothiophenes. The influence of introducing TPE end-capped on the energy gap convergence has also been discussed, showing the energy level correlation of linear fitting combined with a theoretical and experimental perspective. This result not only paves the way toward π–functional materials but also expands their applications.

From Anderson localization on random regular graphs to many-body localization

The article reviews the physics of Anderson localization on random regular graphs (RRG) and its connections to many-body localization (MBL) in disordered interacting systems. Properties of eigenstate and energy level correlations in delocalized and localized phases, as well at criticality, are discussed. In the many-body part, models with short-range and power-law interactions are considered, as well as the quantum-dot model representing the limit of the “most long-range” interaction. Central themes – which are common to the RRG and MBL problems – include ergodicity of the delocalized phase, localized character of the critical point, strong finite-size effects, and fractal scaling of eigenstate correlations in the localized phase.

Superatomic Signature and Reactivity of Silver Clusters with Oxygen: Double Magic Ag 17 – with Geometric and Electronic Shell Closure

Understanding the stability and reactivity of silver clusters toward oxygen provides insights to design new materials of coinage metals with atomic precision. Herein, we report a systematic study o...

Quantum engine based on many-body localization

Many-body-localized (MBL) systems do not thermalize under their intrinsic dynamics. The athermality of MBL, we propose, can be harnessed for thermodynamic tasks. We illustrate this ability by formulating an Otto engine cycle for a quantum many-body system. The system is ramped between a strongly localized MBL regime and a thermal (or weakly localized) regime. The difference between the energy-level correlations of MBL systems and of thermal systems enables mesoscale engines to run in parallel in the thermodynamic limit, enhances the engine's reliability, and suppresses worst-case trials. We estimate analytically and calculate numerically the engine's efficiency and per-cycle power. The efficiency mirrors the efficiency of the conventional thermodynamic Otto engine. The per-cycle power scales linearly with the system size and inverse-exponentially with a localization length. This work introduces a thermodynamic lens onto MBL, which, having been studied much recently, can now be considered for use in thermodynamic tasks.

Statistics of eigenstates near the localization transition on random regular graphs

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the Anderson transition and the delocalized phase. In the delocalized phase near the transition point, the observables show a broad critical regime for system sizes $N$ below the correlation volume $N_{\xi}$ and then cross over to the ergodic behavior. Eigenstate correlations allow us to visualize the correlation length $\xi \sim \log N_{\xi}$ that controls the finite-size scaling near the transition. The critical-to-ergodic crossover is very peculiar, since the critical point is similar to the localized phase, whereas the ergodic regime is characterized by very fast "diffusion" which is similar to the ballistic transport. In particular, the return probability crosses over from a logarithmically slow variation with time in the critical regime to an exponentially fast decay in the ergodic regime. Spectral correlations in the delocalized phase near the transition are characterized by level number variance $\Sigma_2(\omega)$ crossing over, with increasing freqyency $\omega$, from ergodic behavior $\Sigma_2=\left(2/\pi^2\right)\ln\omega/\Delta$ to $\Sigma_2\propto \omega^2$ at $\omega_c\sim (N N_{\xi})^{-1/2}$ and finally to Poissonian behavior $\Sigma_2 = \omega/\Delta$ at $\omega_{\xi}\sim N_{\xi}^{-1}$. We find a perfect agreement between results of exact diagonalization and those resulting from the solution of the self-consistency equation obtained within the saddle-point analysis of the effective supersymmetric action. We show that the RRG model can be viewed as an intricate $d\to\infty$ limit of the Anderson model in $d$ spatial dimensions.

Energy-level statistics in strongly disordered systems with power-law hopping.

Motivated by neutral excitations in disordered electronic materials and systems of trapped ultracold particles with long-range interactions, we study energy-level statistics of quasiparticles with the power-law hopping Hamiltonian in a strong random potential. In solid-state systems such quasiparticles, which are exemplified by neutral dipolar excitations, lead to long-range correlations of local observables and may dominate energy transport. Focussing on the excitations in disordered electronic systems, we compute the energy-level correlation function in a finite system in the limit of sufficiently strong disorder. At small energy differences the correlations exhibit Wigner-Dyson statistics. In particular, in the limit of very strong disorder the energy-level correlation function is given by for small frequencies and for large frequencies , where is the characteristic matrix element of excitation hopping in a system of volume , and , and are coefficient of order unity which depend on the shape of the system. The energy-level correlation function, which we study, allows for a direct experimental observation, for example, by measuring the correlations of the ac conductance of the system at different frequencies.

Group theoretical analysis of the [formula omitted] reaction

The H3++H2→H2+H3+ proton transfer reaction is complicated due to the proton scrambling from the large amplitude motions in the H5+ intermediate. In order to understand this reaction, high-resolution spectroscopic studies are necessary for the reactants/products and the intermediate, and the group theoretical analysis is an essential aspect in the prediction and interpretation of these spectra. With five indistinguishable protons, H5+ is characterized using the G240 complete nuclear permutation-inversion (CNPI) group. For most of the configurations sampled by the reaction path, the feasible permutations depend on the distance between the H3+ and H2 fragments. Subgroups of G240 can be used to describe these feasible permutations. Specifically, we consider two limits of the molecular configurations. The equilibrium structure of H5+, i.e., [H2-H-H2]+, can be described using the G16 molecular symmetry group, while the dissociation products, i.e., H3+⋯H2, require the G24 molecular symmetry group. In the present study, a group theoretical analysis is performed for both limits, providing the symmetries for the nuclear spins and rovibrational wave functions. Also, spectroscopic properties for [H2-H-H2]+, particularly rovibrational couplings and electric dipole selection rules, as well as correlations of energy levels between [H2-H-H2]+ and H3+⋯H2, are obtained.

Hydrogen gas sensing feature of polyaniline/titania (rutile) nanocomposite at environmental conditions

The resistance-based sensors of polyaniline/titania (rutile) nanocomposite (TPNC) were prepared by spin coating technique onto an epoxy glass substrate with Cu-interdigited electrodes to study their hydrogen (H2) gas sensing features. Our findings are that the change of the surface morphology, porosity and wt% of titania in TPNCs have a significant effect on H2 gas sensing of sensors. All of the sensors had a reproducibility response toward 0.8vol% H2 gas at room temperature, air pressure and 50% relative humidity. A sensor with 40wt% of titania nanoparticles had better response/recovery time and the response than other sensors. Moreover, H2 gas sensing mechanism of TPNC sensors based contact areas and the correlation of energy levels between PANI chains and the titania grains were studied.

Interplay of slow bath fluctuations and energy transfer in 2D spectroscopy of the FMOlight-harvesting complex: benchmarking of simulation protocols

Recently developed approaches to simulate environment-induced fluctuation effects in two-dimensional (2D) spectroscopy of excitons are compared for the Fenna-Matthews-Olson light-harvesting complex. Fast fluctuations induce population redistribution between exciton energy-levels and raise homogeneous line widths of various peaks in 2D spectra. These effects are easily accounted for in sum-over-eigenstates (SOS) approach and the quasi-particle (QP) scattering approach through relaxation and dephasing rate constants. Slow fluctuations cause correlations of energies at various delay times in 2D photon-echo spectra. These may be calculated either by doing cumulant expansion in SOS techniques or by statistical averaging over static disorder in SOS and QP approaches. We compare the 2D photon-echo signal simulated using two levels of cumulant expansion approaches and two statistical averaging approaches for the same system. These levels differ by the treatment of energy-level correlations at different delay times and give rise to different cross-peak shapes: the cross-peaks retain their original diagonally elongated shapes when correlations are included, while they are more spherically broadened when correlations are neglected. Statistical averaging over disorder give very similar results but requires much higher computational effort. The peak redistribution timescales are very similar for all levels of theory. The spectral signatures at these different levels of theory are compared and simulation cost is estimated. Approaches which do require statistical averaging over disorder are orders of magnitude slower.

Valence Electronic Structure of Benzo-2,1,3-chalcogenadiazoles Studied by Photoelectron Spectroscopy and Density Functional Theory

The He I photoelectron spectra of benzo-2,1,3-thia-, selena-, and telluradiazole were measured, and the observed ionization bands were assigned by comparison with the results of DFT calculations. Whereas the B3LYP exchange-correlation functional provided orbital energies that permitted a preliminary assignment by application of Koopman's theorem, a more-accurate interpretation was established by calculation of the vertical ionization energies with the PW91 functional and analysis of the correlation of energy levels along the homologous series. This strategy clarified earlier disagreements in the assignment of the spectrum of benzo-2,1,3-thiadiazole.

Energy level promotion in the correlation from the tunnelling-doubled harmonic oscillator to the bi-rotor: application to internal rotation in molecules

A surprisingly rich variety of phenomena are revealed in the energy level correlation between the limits of a tunnelling doubled harmonic oscillator and a bi-rotor. Some levels are found to have their vibrational quantum number "promoted" upon removal of the barrier to rotation, other levels, which we dub "invariant", are found to be completely independent of the barrier, while yet other levels exhibit a smooth transition between these limits. The general nature of these features can be understood in terms of the different degeneracies of the limiting cases. The elucidation of these effects aids the understanding of the rotational-vibrational energy levels of molecules having two internal rotor moieties.

Semiclassical theory for parametric correlation of energy levels

Parametric energy-level correlation describes the response of the energy-level statistics to an external parameter such as the magnetic field. Using semiclassical periodic-orbit theory for a chaotic system, we evaluate the parametric energy-level correlation depending on the magnetic field difference. The small-time expansion of the spectral form factor K(τ) is shown to be in agreement with the prediction of parameter dependent random matrix theory to all orders in τ.

Cross correlation of low-lying levels of even–even nuclei

We consider the cross correlations of low-lying energy levels of nuclei belonging to small intervals of the excitation-energy ratio R 4 / 2 of the first 4 + to 2 + states. The mean value of the cross-correlation coefficients, plotted as a function of R 4 / 2 has deep minima at values of R 4 / 2 = 2.2 and 2.9, which correspond to the critical dynamical symmetries of the interacting Boson model. The distribution of the calculated coefficients for nuclei belonging to different R 4 / 2 classes has different pattern.

Vibrational dynamics of the floppy LiNC∕LiCN molecular system

Modern spectroscopical techniques allow the efficient experimental investigation of highly excited vibrational states in molecular systems. On the theoretical side, powerful computational methods have also been developed for the calculation of the corresponding energy levels and wave functions, and their interpretation. In this paper we use a combination of two such methods, namely, the distribution of zeroes in the Husimi function and energy-level correlation diagrams, to discuss a classification scheme, for the lowest hundred vibrational levels of the LiNC/LiCN floppy molecular system, based on their dynamical characteristics.

Classical and quantum mechanics of diatomic molecules in tilted fields

We investigate the classical and quantum mechanics of diatomic molecules in noncollinear (tilted) static electric and nonresonant linearly polarized laser fields. The classical diatomic in tilted fields is a nonintegrable system, and we study the phase space structure for physically relevant parameter regimes for the molecule KCl. While exhibiting low-energy (pendular) and high-energy (free-rotor) integrable limits, the rotor in tilted fields shows chaotic dynamics at intermediate energies, and the degree of classical chaos can be tuned by changing the tilt angle. We examine the quantum mechanics of rotors in tilted fields. Energy-level correlation diagrams are computed, and the presence of avoided crossings quantified by the study of nearest-neighbor spacing distributions as a function of energy and tilting angle. Finally, we examine the influence of classical periodic orbits on rotor wave functions. Many wave functions in the tilted field case are found to be highly nonseparable in spherical polar coordinates. Localization of wave functions in the vicinity of classical periodic orbits, both stable and unstable, is observed for many states.

Pendular-limit representation of energy levels and spectra of symmetric- and asymmetric-top molecules

We report theoretical investigations pertaining to spectroscopy of pendular-state molecules, which are subjected to the large electrostatic interaction between the molecular dipole and a strong external field. After an appropriate coordinate transformation and a power-series expansion with an order parameter $\ensuremath{\lambda}$ that represents the degree of pendular condition, the zeroth-order Hamiltonian for the pendular limit has been derived. Motions of asymmetric tops in a high field are well described as two-dimensional anisotropic harmonic oscillations, and pendular-state quantum numbers have been introduced to label the energy levels. By using perturbative treatments, energies up to the ${\ensuremath{\lambda}}^{0}$ order are represented analytically with the pendular-state quantum numbers. Symmetry considerations are also accomplished by using the group theory appropriate to dipolar rigid bodies of symmetric and asymmetric tops in a uniform electric field. Energy levels and wave functions are classified into irreducible representations of the groups and selection rules for optical transitions are described. Energy-level correlations between the field-free and pendular conditions are also discussed on the basis of the group theoretical considerations. For symmetric and asymmetric tops, pendular-limit selection rules on the quantum numbers are derived by expanding the transition-dipole operators on $\ensuremath{\lambda}$, and transition strengths are analytically evaluated for all the excitation configurations with each of the transition types. Utilities of the present formulation have been verified by the comparison with exact model calculations based on the matrix diagonalization with a free-rotation basis set.

A random matrix approach to the crossover of energy-level statistics from Wigner to Poisson

We analyze a class of parametrized random matrix models, introduced by Rosenzweig and Porter, which is expected to describe the energy level statistics of quantum systems whose classical dynamics varies from regular to chaotic as a function of a parameter. We compute the generating function for the correlations of energy levels, in the limit of infinite matrix size. The crossover between Poisson and Wigner statistics is measured by a renormalized coupling constant. The model is exactly solved in the sense that, in the limit of infinite matrix size, the energy-level correlation functions and their generating function are given in terms of a finite set of integrals.