Symmetry Of States Research Articles

Controlling the optical output of arylamino-dibenzothiophene systems by sulphur oxidation state

Six arylamino-dibenzothiophene (Ary-DBTs) derivatives (with D-π-D or D-π pattern) were synthesized in order to investigate how the symmetry and different oxidation states, sulfide (Ary-DBT, Ary2-DBT), sulfoxide (Ary-DBTSO, Ary2-DBTSO) and sulfone (Ary-DBTSO2, Ary2-DBTSO2) affect the optical properties of these compounds, respectively. To unravel the complexity of their photophysics, extensive characterization was carried out, including UV–Vis and fluorescence spectroscopy both in different solvents at room temperature and in rigid matrix at 77 K. In addition to the presence of various singlet states, this study has brought to light the existence, in rigid conditions, of radiative triplet states responsible for phosphorescence phenomena. This interesting architecture of triplet states was investigated using the time-resolved EPR (TREPR) technique and further supported by TDDFT calculations. This approach allows us to obtain a complete photophysical view of the generation and decay of excited states and how molecular geometry influences it.

Analytic computation of the entanglement of formation for bipartite isotropic states using their symmetry

It is well-known that computing the entanglement of formation of a general bipartite state is a difficult task. We use the local symmetry of bipartite isotropic states in arbitrary dimensions to compute their entanglement of formation analytically. Our computation is an explicit and detailed version of the computation performed by Terhal et al [B. M. Terhal and K. G. H. Vollbrecht, Phys. Rev. Lett. 85, 2625 (2000)]. However, it is not just a review but we also have our contribution and novelty. For instance, we provide a rigorous proof for the entanglement of formation of two qutrit isotropic states and notably we give a proof supporting the conjecture proposed by Terhal et al about the entanglement of formation of bipartite isotropic states for the last range of allowed parameter values.

Formation of Delocalized Linear M-B-M Covalent Bonds: A Combined Experimental and Theoretical Study of BM2(CO)8+ (M = Co, Rh, Ir) Complexes.

Investigations of transition-metal boride clusters not only lead to novel structures but also provide important information about the metal-boron bonds that are critical to understanding the properties of boride materials. The geometric structures and bonding features of heteronuclear boron-containing transition metal carbonyl cluster cations BM(CO)6+ and BM2(CO)8+ (M = Co, Rh, and Ir) are studied by a combination of the infrared photodissociation spectroscopy and density functional calculations at B3LYP/def2-TZVP level. The completely coordinated BM2(CO)8+ complexes are characterized as a sandwich structure composed of two staggered M(CO)4 fragments and a boron cation, featuring a D3d symmetry and 1Eg electronic ground state as well as metal-anchored carbonyls in an end-on manner. In conjunction with theoretical calculations, multifold metal-boron-metal bonding interactions in BM2(CO)8+ complexes involving the filled d orbitals of the metals and the empty p orbitals of the boron cation were unveiled, namely, one σ-type M-B-M bond and two π-type M-B-M bonds. Accordingly, the BM2(CO)8+ complexes can be described as a linear conjugated (OC)4M═B═M(CO)4 skeleton with a formal B-M bond index of 1.5. The three delocalized d-p-d covalent bonds render compensation for the electron deficiency of the cationic boron center and endow both metal centers with the favorable 18-electron structure, thus contributing much to the overall structural stability of the BM2(CO)8+ cations. As a comparison, the saturated BRh(CO)6+ and BIr(CO)6+ complexes are determined to be a doublet Cs-symmetry structure with an unbridged (OC)2B-M(CO)4 pattern, involving a two-center σ-type (OC)2B → M(CO)4+ dative single bond along with a weak covalent B-M half bond. This work offers important insight into the structure and bonding of late transition metal boride carbonyl cluster cations.

Uniform descriptions of pseudospin symmetries in bound and resonant states

As a continuation of our previous work on the conservation and breaking of the pseudospin symmetry (PSS) in resonant states [Phys. Lett. B 847, 138320 (2023)], in this work, the PSS in nuclear single-particle bound and resonant states are investigated uniformly within a relativistic framework by exploring the poles of the Green's function in spherical Woods-Saxon potentials. As the potential depths increase from zero to finite depths, the PS partners evolve from resonant states to bound states. In this progress, the PSS is broken gradually with energy, width, and density splittings. Specially, the energy and width splittings for the resonant and bound states are directly determined by the ratio of the pseudo spin-orbit potentials between the PS partners. Obvious threshold effect is observed for the energy splitting at a critical potential depth, with which one PS partner has become a quasi-bound state inside the centrifugal barrier while the other one is still a high-energy resonant state outside the centrifugal barrier. The differences in the density distributions of the lower component between the PS partners are manifested in the phase shift for the resonant states and amplitudes for bound states.

Observation and all-optical manipulation of replica symmetry breaking dynamics in a multi-Stokes-involved Brillouin random fiber laser photonic system

In this paper, we propose and demonstrate an all-optical control of RSB transition in a multi-wavelength Brillouin random fiber laser (MWBRFL). Multi-order Stokes light components can be subsequently generated by increasing the power of the Erbium-doped fiber amplifier (EDFA) inside the MWBRFL, providing additional disorder as well as multiple Stokes-involved interplay. It essentially allows diversified laser mode landscapes with adjustable average mode lifetime and random mode density of the 1st order Stokes, which benefits the switching between replica symmetry breaking (RSB) and replica symmetry (RS) states in an optically controlled manner. Results show that the average mode lifetime of the 1st order Stokes component gradually decreases from 250.0 ms to 1.2 ms as high orders from the 2nd to the 5th of Stokes components are activated. Meanwhile, the order parameter q of the 1st order Stokes random lasing emission presents distinct statistical distributions within the selective sub-window under various EDFA optical powers. Consequently, all-optical dynamical control of the 1st Stokes random laser mode landscapes with adjustable average mode lifetime turns out to be attainable, facilitating the RSB transition under an appropriate observation time window. These findings open a new avenue for exploring the underlying physical mechanisms behind the occurrence of the RSB phenomenon in photonic complex systems.

Gauge symmetry of excited states in projected entangled-pair state simulations

Gauge symmetry of excited states in projected entangled-pair state simulations

Probing the electronic structure and ground state symmetry of gas phase C60+ via VUV photoionization and comparison with theory.

Recently, some of us reviewed and studied the photoionization dynamics of C60 that are of great interest to the astrochemical community as four of the diffuse interstellar bands (DIBs) have been assigned to electronic transitions in the C60+ cation. Our previous analysis of the threshold photoelectron spectrum (TPES) of C60 [Hrodmarsson et al., Phys. Chem. Chem. Phys. 22, 13880-13892 (2020)] appeared to give indication of D3d ground state symmetry, in contrast to theoretical predictions of D5d symmetry. Here, we revisit our original measurements taking account of a previous theoretical spectrum presented in the work of Manini et al., Phys. Rev. Lett. 91(19), 196402 (2003), obtained within a vibronic model parametrized on density functional theory/local-density approximation electronic structure involving all hg Jahn-Teller active modes, which couple to the 2Hu components of the ground state of the C60+ cation. By reanalyzing our measured TPES of the ground state of the C60 Buckminsterfullerene, we find a striking resemblance to the theoretical spectrum calculated in the work of Manini et al., Phys. Rev. Lett. 91(19), 196402 (2003), and we provide assignments for many of the hg modes. In order to obtain deeper insights into the temperature effects and possible anharmonicity effects, we provide complementary modeling of the photoelectron spectrum via classical molecular dynamics (MD) involving density functional based tight binding (DFTB) computations of the electronic structure for both C60 and C60+. The validity of the DFTB modeling is first checked vs the IR spectra of both species which are well established from IR spectroscopic studies. To aid the interpretation of our measured TPES and the comparisons to the abinitio spectrum we showcase the complementarity of utilizing MD calculations to predict the PES evolution at high temperatures expected in our experiment. The comparison with the theoretical spectrum presented in the work of Manini et al., Phys. Rev. Lett. 91(19), 196402 (2003), furthermore, provides further evidence for a D5d symmetric ground state of the C60+ cation in the gas phase, in complement to IR spectroscopy in frozen noble gas matrices. This not only allows us to assign the first adiabatic ionization transition and thus determine the ionization energy of C60 with greater accuracy than has been achieved at 7.598 ± 0.005eV, but we also assign the two lowest excited states (2E1u and 2E2u) which are visible in our TPES. Finally, we discuss the energetics of additional DIBs that could be assigned to C60+ in the future.

Friction tensor for an ellipsoid enclosed in a rarefied gas

This research renders calculations of rotranslational friction and diffusion tensors in a rarefied gas, considering both specular and diffuse reflection off ellipsoidal particles. Calculations were conducted in a spherical polar coordinate system, revealing the dynamic nature of these off-diagonal tensors. The tensor elements were determined analytically, intending to compute the surface integrals. All diagrams, and pictures of two-dimensional surfaces were obtained by the numerical integration process in MATLAB. Additionally, we performed calculations without using the time parameter and time derivatives in the relevant relations. Deviations from the state of spherical symmetry were observed in the results for an ellipsoid and show that the tensors are dynamic quantities. Therefore, it is necessary to provide average values. We established that the non-zero elements of the friction tensor for an ellipsoid represent the directions of linear momentum transfer. Also, the non-zero components of the diffusion tensor signify the extent of fluctuations in relevant momentum transfers in corresponding directions.

Electronic Coherences Excited by an Ultra Short Pulse Are Robust with Respect to Averaging over Randomly Oriented Molecules as Shown by Singular Value Decomposition.

We report a methodology for averaging quantum photoexcitation vibronic dynamics over the initial orientations of the molecules with respect to an ultrashort light pulse. We use singular value decomposition of the ensemble density matrix of the excited molecules, which allows the identification of the few dominant principal molecular orientations with respect to the polarization direction of the electric field. The principal orientations provide insights into the specific stereodynamics of the corresponding principal molecular vibronic states. The massive compaction of the vibronic density matrix of the ensemble of randomly oriented pumped molecules enables a most efficient fully quantum mechanical time propagation scheme. Two examples are discussed for the quantum dynamics of the LiH molecule in the manifolds of its electronically excited Σ and Π states. Our results show that electronic and vibrational coherences between excited states of the same symmetry are resilient to averaging over an ensemble of molecular orientations and can be selectively excited at the ensemble level by tuning the pulse parameters.

Keldysh crossover in one-dimensional Mott insulators

Recent advancements in pulse laser technology have facilitated the exploration of nonequilibrium spectroscopy of electronic states in the presence of strong electric fields across a broad range of photon energies. The Keldysh crossover serves as an indicator that distinguishes between excitations resulting from photon absorption triggered by near-infrared multicycle pulses and those arising from quantum tunneling induced by terahertz pulses. Using a time-dependent density-matrix renormalization group, we investigate the emergence of the Keldysh crossover in a one-dimensional (1D) Mott insulator. We find that the Drude weight is proportional to photo-doped doublon density when a pump pulse induces photon absorption. In contrast, the Drude weight is suppressed when a terahertz pulse introduces doublons and holons via quantum tunneling. The suppressed Drude weight accompanies glassy dynamics with suppressed diffusion, which is a consequence of strong correlations and exhibits finite polarization decaying slowly after pulse irradiation. In the quantum tunneling region, entanglement entropy slowly grows logarithmically. These contrasting behaviors between the photon-absorption and quantum tunneling regions are a manifestation of the Keldysh crossover in 1D Mott insulators and provide a novel methodology for designing the localization and symmetry of electronic states called subcycle-pulse engineering.

Mqdtfit: A collection of Python functions for empirical multichannel quantum defect calculations

The Python functions distributed with this article can be used for calculating the parameters of multichannel quantum defect theory models describing excited bound states of complex atoms. These parameters are obtained by fitting a model to experimental data provided by the user. The two main formulations of the theory are supported, namely the one in which the parameters of the model are a set of eigen channel quantum defects and a transformation matrix, and the one where these parameters are the elements of a reactance matrix. The distribution includes programs for calculating theoretical energy levels, calculating mixing coefficients and channel fractions and producing Lu-Fano plots. Program summaryProgram Title: mqdtfitCPC Library link to program files:https://doi.org/10.17632/nzgygzd96c.1Developer's repository link:https://github.com/durham-qlm/mqdtfitLicensing provisions: BSD 3-clause.Programming language: Python 3.Nature of problem: Multichannel quantum defect theory aims at giving a unified description of the excited states of multielectron systems whereby the properties of entire series can be predicted from models involving a relatively small number of parameters. These parameters are obtained by fitting theory to experimental data, in the empirical version of the theory. The present programs specifically concern the application of this theory to the bound states of complex atomic systems, such as divalent atoms, for which spectroscopic series are often perturbed by isolated states of a different symmetry, making a multichannel description necessary.Solution method: The functions forming this library are grouped and linked to each other into a single Python module. They can be used to calculate the parameters of a given multichannel quantum defect theory model by fitting the model to experimental data provided by the user. These parameters are either a set of eigen channel quantum defects and a transformation matrix, in the eigenchannel parametrization of the theory, or the elements of an orthogonal matrix, in the reactance matrix parametrization of the theory. Given these parameters, this software can also be used to calculate theoretical energy levels, calculate coefficients describing the mixing between the channels considered and produce Lu-Fano plots.

Eigenvalue-based quantum state verification of three-qubit W class states

In quantum many-body systems, W class states are typical examples of states with genuine multipartite entanglement. They have been found to be valuable resources in many quantum information processing tasks. However, the characterization and verification of W class states still remains an intractable problem. Here we first propose an eigenvalue-based verification protocol consisting of four practical adaptive local projective measurement tests, and obtain the optimal test probabilities with particle swarm optimization algorithm. The efficiency achieved by this protocol is far from satisfactory when compared with the theoretical upper bound. Then by utilizing the symmetry of the target states and a class of specific unitaries, we optimize the original verification strategy based on group theory. In this case, our new protocol can realize the efficient verification of three-qubit W class states.

Fuzzy Mandelbric Set and Its Perturbations by Dynamical Noises

In this paper, we introduce a membership function used to form the fuzzy Mandelbric set and investigate the structural effects of additive and multiplicative dynamic noises on it. The newly defined membership function of this fuzzy set and its perturbations is a generalization of the indicator function for the classical Mandelbric set. We present an algorithm for detecting each complex number’s fuzzy membership degree. Through the use of the membership degrees of each complex number and experimental mathematics based on the visualizations of a variety of versions by utilizing computer-aided design, we gain a deep foresight for the structure characteristics of the additive and multiplicative perturbed fuzzy Mandelbric sets. Our novel approach allows us to identify the symmetry states of the Mandelbric set and its perturbations by the membership degrees of complex numbers, unlike the existing methods described in the literature.

Ion core switching during photodissociation dynamics via the Rydberg states of XeAr

The heterodimer, XeAr, is a classic example of a weakly bound van der Waals molecule, which has a variety of accessible bound excited states that exhibit complex interactions. In this study, XeAr has been investigated in the 77,500–81,500 cm−1 region using a combination of Resonance Enhanced Multi-Photon Ionization (REMPI) spectroscopy and Velocity Map Imaging (VMI). By monitoring REMPI and photodissociative product channels across the spectrum, several novel excited states, product channels, excited state symmetries and lifetimes, as well as highly localized perturbations were observed and characterized, including the first VMI study of Ar* dissociating from XeAr Rydberg states accessed by two-photon excitation. In this work we have analyzed 38 vibronic bands representing nine different electronic transitions, and we provide new assignments for two 0+←0+ electronic transitions dissociating to the Xe* 5d [3/2]02 (ca. 80,323 cm−1) and Xe* 5d [7/2]03 (ca. 80,970 cm−1) limits. Several new predissociation product channels were identified at the two- and three-photon levels, including production of Xe* 5p[5/2]3, Xe* 6s'[1/2]o1, Xe* 6p[1/2]1, Ar* 4p[1/2]0, Ar* 4p'[3/2]1, Ar* 4p'[1/2]1, and Ar* 4p[5/2]3. Using the multidimensional analysis offered by VMI, we explore interesting photophysics whereby a resonant state that is reached after absorbing two photons can predissociate to yield Xe*, but which also can absorb a 3rd photon, yielding super-excited Ar*Xe that predissociates to Ar* limits. The ground state dissociation energy for XeAr was determined to be D0 = 114.4 ± 2.7 cm−1, in excellent agreement with previous measurements.

Hybrid-order topological superconductivity in a topological metal 1T’-MoTe2

One key challenge in the field of topological superconductivity (Tsc) has been the rareness of material realization. This is true not only for the first-order Tsc featuring Majorana surface modes, but also for the higher-order Tsc, which host Majorana hinge and corner modes. Here, we propose a four-step strategy that mathematically derives comprehensive guiding principles for the search and design for materials of general higher-order Tsc phases. Specifically, such recipes consist of conditions on the normal state and pairing symmetry that can lead to a given higher-order Tsc state. We demonstrate this strategy by obtaining recipes for achieving three-dimensional higher-order Tsc phases protected by the inversion symmetry. Following our recipe, we predict that the observed superconductivity in centrosymmetric MoTe2 is a hyrbid-order Tsc candidate, which features both surface and corner modes. Our proposed strategy enables systematic materials search and design for higher-order Tsc, which can mobilize the experimental efforts and accelerate the material discovery for higher-order Tsc phases.

Standing waves and global well-posedness for the 2d Hartree equation with a point interaction

We study a class of two-dimensional nonlinear Schrödinger equations with point-like singular perturbation and Hartree non-linearity. The point-like singular perturbation of the free Laplacian induces appropriate perturbed Sobolev spaces that are necessary for the study of ground states and evolution flow. We include in our treatment both mass sub-critical and mass critical Hartree non-linearities. Our analysis is two-fold: we establish existence, symmetry, and regularity of ground states, and we demonstrate the well-posedness of the associated Cauchy problem in the singular perturbed energy space. The first goal, unlike other treatments emerging in parallel with the present work, is achieved by a nontrivial adaptation of the standard properties of Schwartz symmetrization for the modified Weinstein functional. This produces, among others, modified Gagliardo-Nirenberg type inequalities that allow to efficiently control the non-linearity and obtain well-posedness by energy methods. The evolution flow is proved to be global in time in the defocusing case, and in the focusing and mass sub-critical case. It is also global in the focusing and mass critical case, for initial data that are suitably small in terms of the best Gagliardo-Nirenberg constant.

Symmetry-selective quasiparticle scattering and electric field tunability of the ZrSiS surface electronic structure

Three-dimensional Dirac semimetals with square-net non-symmorphic symmetry, such as ternary ZrXY (X = Si, Ge; Y = S, Se, Te) compounds, have attracted significant attention owing to the presence of topological nodal lines, loops, or networks in their bulk. Orbital symmetry plays a profound role in such materials as the different branches of the nodal dispersion can be distinguished by their distinct orbital symmetry eigenvalues. The presence of different eigenvalues suggests that scattering between states of different orbital symmetry may be strongly suppressed. Indeed, in ZrSiS, there has been no clear experimental evidence of quasiparticle scattering reported between states of different symmetry eigenvalues at small wave vector q⃗. Here we show, using quasiparticle interference, that atomic step-edges in the ZrSiS surface facilitate quasiparticle scattering between states of different symmetry eigenvalues. This symmetry eigenvalue mixing quasiparticle scattering is the first to be reported for ZrSiS and contrasts quasiparticle scattering with no mixing of symmetry eigenvalues, where the latter occurs with scatterers preserving the glide mirror symmetry of the crystal lattice, e.g. native point defects in ZrSiS. Finally, we show that the electronic structure of the ZrSiS surface, including its unique floating band surface state, can be tuned by a vertical electric field locally applied by the tip of a scanning tunneling microscope (STM), enabling control of a spin–orbit induced avoided crossing near the Fermi level by as much as 300%.

Photoionization cross sections of Ethylene oxide

Abstract In this work a theoretical study for photoionization of Ethylene oxide is presented. The photoionization cross section (PICS) for each of the nine valence orbitals and also the summed cross sections are presented. Electronic structure calculations are done to obtain the required molecular properties and the Variational Schwinger method with Padé approximants is used to calculate the PICS. The results are shown in four different approaches: dipole-length/velocity form, static-exchange and static-exchange-polarization levels. The partial PICS for each orbital shows which symmetries of continuum states are responsible for resonance features and how the polarization effects affect the cross sections magnitudes near the threshold. PICS calculations indicate which parent ion state is generated according to the corresponding ionization energies. A correlation is proposed suggesting that the different ionic fragments can be preferentially produced by different electronic states of the parent ion, based on their ionic fragment appearance energies. The summed cross section of all valence orbitals of Ethylene oxide is compared with the results of Acetaldehyde and the analysis suggests that the PICSs, in a given energy range, can be used to identify these isomers. A comparison of our results for EtO and Acetaldehyde with available experimental results for Acetaldehyde and Ethenol demonstrated the the results of three isomers are similar in magnitude in the energy range from 9 to 12 eV. Furthermore, for acetaldehyde, we observed quantitative agreement with the experiment, indicating the reliability of our calculations.

Preference of C2v Symmetry in Low-Spin Hexacarbonyls of Rare-Earth and f Elements

The structures and bonding of selected neutral M(CO)6 complexes (M = Sc, Y, La, Lu, Ac and U) have been studied by density functional theory calculations. The calculations revealed the preference for C2v symmetry and low-spin electronic state for most of these complexes. The relative stability of the low-symmetry species increases gradually with the size of the metal atom. While the characteristic Oh hexa-coordinated structure is favored in the high-spin electronic state of the smaller metals, for heavier metals, important advantages of the C2v vs. Oh structures include larger charge transfer interactions in terms of transferred electrons as well as better steric conditions. Our joint experimental–theoretical analysis detected and confirmed the Oh structure of the Sc(CO)6 complex in cryogenic CO/Ar matrices.

Pseudospin symmetry in resonant states in deformed nucleus 154Dy

It is known that pseudospin symmetry plays a crucial role in formation of many physical phenomena. By combining the relativistic mean field theory with the complex momentum representation method, the pseudospin symmetry in the single particle resonant states in the deformed nucleus [Formula: see text]Dy is investigated through the energy and width splittings, the quadrupole deformation parameter, the radial density distributions and occupation probabilities of the pseudospin doublets. Near the continuum threshold, the pseudospin symmetry is well reserved in both bound and resonant states. The energy and width splittings of pseudospin doublets in resonant states exhibit correlations with the deformation and quantum numbers. The good pseudospin symmetry is expected with lower pseudo-orbital angular momentum projection [Formula: see text] and the main quantum number N. In general, an increase in deformation tends to weaken the quality of the pseudospin symmetry. The understanding of the evolution of the pseudospin doublets in the resonant states has been deepened by studying the pseudospin symmetry in the deformed nuclei.