Degenerate Levels Research Articles

Restricting sterile neutrinos by neutrinoless double beta decay

The bounds on parameters of the eV and higher scale Majorana sterile neutrinos from the 0νββ decay have been refined and updated. We present a simple and compact analytic expression for the bound in the Δm412−sin22θ14 plane, which includes all relevant parameters. Dependencies of the bound on unknown CP phases and the type of mass spectrum of light neutrinos (mass ordering and level of degeneracy) are studied in detail. We have computed the bounds using the latest and most stringent data from KamLAND-Zen. The projected constraints from future experiments are estimated. The obtained bounds are confronted with positive indications of the presence of sterile neutrinos as well as with the other existing bounds. The 0νββ decay results exclude the regions of parameters implied by BEST and Neutrino-4, and the regions indicated by LSND and MiniBooNE are in conflict with 0νββ decay results combined with νμ-disappearance bounds. Published by the American Physical Society 2025

Exploring structural, magnetic, and catalytic diversity in tetranuclear {Cu4O4} cubane cores and a dinuclear complex derived from closely related ligand systems.

The coordination compounds featuring a {Cu4O4} core, typically bridged by hydroxo or alkoxo groups, are particularly intriguing due to their notable magnetic properties and catalytic activity. In this study, we explored the synthesis and characterization of four new Schiff base ligands and their subsequent complexation with CuII salts, which resulted in the formation of three tetranuclear complexes: [Cu4(L1)4]·2H2O (1), [Cu4(L2)2(HL2)2](Cl)(NO3)·5H2O (2), and [Cu4(L3)4] (3), as well as one dinuclear complex: [Cu2(L4)2] (4). These tetranuclear complexes all feature a {Cu4O4} core, but with differing coordination environments around the CuII centers. For instance, complex 1 exhibits μ3-phenoxido bridges and a distorted octahedral geometry, while complex 3 features μ3-alkoxido bridges and a square pyramidal geometry. Complex 2 displays an open cubane core with mixed μ2-phenoxido and μ3-alkoxido bridges, with both square planar (CuNO4) and octahedral (CuNO5) geometries. In addition, dinuclear complex 4 was synthesized, featuring square planar CuII centers linked by μ2-alkoxido bridges. The magnetic studies revealed that 1 and 2 exhibit strong antiferromagnetic coupling, which is attributed to their larger Cu-O-Cu bond angles, while complex 3 demonstrates moderate ferromagnetic behavior, associated with smaller bond angles. Literature reports indicate that {Cu4O4} cubane cores generally show ferromagnetic interactions at bond angles near 104°, but in complex 3, we observed moderate ferromagnetic interactions with a Cu-O-Cu bridging angle of 108.41(9)°, making it one of the highest bond angles observed for ferromagnetic interactions in a {Cu4O4} cubane-like system. The planar dinuclear complex 4 exhibits extremely strong antiferromagnetic coupling, which is attributed to the ideal Cu-O-Cu bridging angles and the planar Cu-O-O-Cu core. Additionally, EPR measurements of complex 3 at 4 K reveal a well-isolated S = 2 ground state, separated by a gap of 65.8 cm-1 from the three closest degenerate spin levels (S = 0, 1, and 1). Finally, all four complexes were used as catalysts for the aerobic oxidation of 2-aminophenol, and the mechanism of the oxidation process was elucidated by EPR spectroscopy.

THE INTERSUBBAND OPTICAL ABSORPTION COEFFICIENT OF THE QD WITH ACCEPTOR IMPURITY UNDER APPLIED ELECTRIC FIELD

In this work, a spherical quantum dot (QD) under the influence of an external electric field is investigated. A multi-band model of the valence band is applied. The influence of off-center acceptor impurity, electric field and QD size dispersion on the absorption coefficient during intersubband transitions between hole states has been analyzed. The results show that an electric field combined with an off-center impurity induces the appearance of two distinct absorption bands corresponding to different magnetic quantum numbers. The intensity of absorption bands depends on the direction and strength of the electric field, and significant differences are observed between fields of opposite polarity. It is important to note that there is a critical field strength that restores the degeneracy of the energy levels, narrowing the broadband absorption tail for systems with small or large dispersion sizes. This research aims to improve the understanding and optimization of the optical properties of nanomaterials.

A new search for the variation of fundamental constants using the rovibrational levels and isotope effects of the magnesium fluoride molecule

Abstract The recently demonstrated methods for cooling and trapping diatomic molecules offer new possibilities for precision searches in fundamental physical theories. Here, we propose to study the variations of the fine-structure constant (α=e 2/ħc) and the proton-to-electron mass ratio (μ = mp/me) with time - by taking advantage of the nearly degenerate rovibrational levels in the electronic states of the magnesium fluoride (MgF) molecule. Specifically, due to the cancellation between the fine structure splitting and the rovibrational intervals in the different MgF natural isotopes, a degeneracy occurs for the A 2Π(3/2) (v'=0,J'=18.5,-) and the A2Π(1/2) (v''=0,J''=20.5,-). We find that using the nearly degenerate energy level of such states can be 104 times more sensitive than using a pure rotational transition to measure the variations of α and μ. To quantify the small gap between the A2Π(3/2) (v'=0,J'=18.5,-) and the A2Π(1/2) (v''=0,J''=20.5,-), the special transitions of choice are feasible: the X 2Σ(1/2) + (v=0,J=19.5,+) to the A2Π(3/2) (v'=0,J'=18.5,-) and the X 2Σ(1/2) + (v=0,J=19.5,+) to the A 2Π(1/2) (v''=0,J''=20.5,-). In addition, we estimate the frequency uncertainties caused by the narrow linewidth, Zeeman shift, the Stark shift, Doppler boarding and the Blackbody radiation.

On the degeneracy of the energy levels of Schrödinger and Klein-Gordon equations on Riemannian coverings

Abstract We study the degeneracy of the energy levels of the Schrödinger equation with Kepler-Coulomb potential and of the Klein-Gordon equation on Riemannian coverings of the Euclidean space and of the Schwarzschild space-time respectively. Degeneracy of energy levels is a consequence of the superintegrability of the system. We see how the degree of degeneracy changes depending on the covering parameter k, the parameter that in space-times can be related with a cosmic string, and show examples of lower degeneracy in correspondence of non integer values of k.

Benchmark computations of nearly degenerate singlet and triplet states of N-heterocyclic chromophores. I. Wavefunction-based methods.

In this paper, we investigate the role of electron correlation in predicting the S1-S0 and T1-S0 excitation energies and, hence, the singlet-triplet gap (ΔEST) in a set of cyclazines, which act as templates for potential candidates for fifth generation organic light emitting diode materials. This issue has recently garnered much interest with the focus being on the inversion of the ΔEST, although experiments have indicated near degenerate levels with both positive and negative being within the experimental error bar [J. Am. Chem. Soc. 102, 6068 (1980), J. Am. Chem. Soc. 108, 17(1986)]. We have carried out a systematic and exhaustive study of various excited state electronic structure methodologies and identified the strengths and shortcomings of the various approaches and approximations in view of this challenging case. We have found that near degeneracy can be achieved either with a proper balance of static and dynamic correlation in multireference theories or with state-specific orbital corrections, including its coupling with correlation. The role of spin contamination is also discussed. Eventually, this paper seeks to produce benchmark numbers for establishing cost-effective theories, which can then be used for screening derivatives of these templates with desirable optical and structural properties. Additionally, we would like to point out that the use of domain-based local pair natural orbital-similarity transformed EOM-coupled cluster singles and doubles as the benchmark for ΔEST [as used in J. Phys. Chem. A 126(8), 1378 (2022), Chem. Phys. Lett. 779, 138827 (2021)] is not a suitable benchmark for these classes of molecules.

Slowing down the hot electron cooling to activate near-infrared photocatalytic activity in potassium/carbon co-doped polymeric carbon nitride

The research on hot electron cooling in photocatalysis has been neglected. Here, taking polymeric carbon nitride as an example, a potassium/carbon (K/C) co-doping strategy is proposed to slow down hot electron cooling. The K/C co-doping reduces the specific arrangement and overlap of electronic band structures, and decreases the degeneracy of conduction band energy levels, thus exciting phonon bottleneck effect to effectively suppress the relaxation of hot electrons by reducing the interaction between hot electrons and phonons. Our work benefits to improve the efficiency of photocatalytic energy conversion.

Infrared optical spectra of a silicene quantum dot modulated by spin-orbit coupling and uniaxial strain

Abstract We theoretically study the electronic structure and light absorption spectra of a triangular silicene quantum dot (TZSQD) modulated by spin-orbit coupling (SOC) and the uniaxial strain from a symmetry point of view. After considering the SOC, the symmetry of the system decreases and the degenerate energy level split, creating the absorption peaks in the far infrared region and some multimodal structures in the near-infrared region and visible region. In addition, the intensity of the SOC also affects the degree of splitting of the energy levels, which makes the absorption peaks in the far infrared region are blueshifted to the mid-infrared region, and absorption edge in the near infrared region is redshifted to the mid-infrared region. We also find that when a uniaxial strain and SOC coexist at the same time, the symmetry of the system is further reduced, and the number of absorption peaks is increased. Moreover, the uniaxial strain intensity can efficiently regulate the frequency position of the absorption edge in the near-infrared region, and make its spectral range greatly expanded.

Observation of Pairwise Level Degeneracies and the Quantum Regime of the Arrhenius Law in a Double-Well Parametric Oscillator

By applying a microwave drive to a specially designed Josephson circuit, we have realized a double-well model system: a Kerr oscillator submitted to a squeezing force. We have observed, for the first time, the spectroscopic fingerprint of a quantum double-well Hamiltonian when its barrier height is increased: a pairwise level kissing (coalescence) corresponding to the exponential reduction of tunnel splitting in the excited states as they sink under the barrier. The discrete levels in the wells also manifest themselves in the activation time across the barrier which, instead of increasing smoothly as a function of the barrier height, presents steps each time a pair of excited states is captured by the wells. This experiment illustrates the quantum regime of Arrhenius’s law, whose observation is made possible here by the unprecedented combination of low dissipation, time-resolved state control, 98.5% quantum nondemolition single shot measurement fidelity, and complete microwave control over all Hamiltonian parameters in the quantum regime. Direct applications to quantum computation and simulation are discussed. Published by the American Physical Society 2024

Local aromatic ring cleaves the global aromatic ring in hexaphyrin(2.1.2.1.2.1)

Novel benzo-bridged hexaphyrin(2.1.2.1.2.1) and its copper complex were synthesized. Single-crystal structures showed typical figure-of-eight Hückel topologies. NMR, NICS, HOMA, ACID, and EDDB analysis supported their non-aromatic properties owning to the strong local aromatic benzo rings cutting the global aromatic ring of the benzo-bridged figure-of-eight hexaphyrin(2.1.2.1.2.1). The redox properties and degenerate HOMOs and LUMOs levels indicate multielectron donating and accepting abilities.

Two atoms in a harmonic trap with spin-orbital-angular-momentum coupling

We study the problem of two harmonically trapped atoms in the presence of spin-orbital-angular-momentum (SOAM) coupling. The two-body energy spectrum is numerically calculated by utilizing the exact diagonalization method. We analyze how the degeneracy of energy levels is lifted under the interplay between the interatomic interaction and SOAM coupling. The exact numerical results show excellent agreement with that of perturbation theory in the weak-interaction limit as well as that in the absence of SOAM coupling. The properties of correlations between the two atoms are also discussed with respect to the interaction strength. The findings in this paper may provide valuable insights into few-body physics subjected to SOAM coupling and the possible experimental detection of spectrum functions in many-body systems, such as radiofrequency spectroscopy. Published by the American Physical Society 2024

Valley landau level crossings in weakly coupled bilayer WSe2

Abstract WSe2 is a p-type 2D-semiconductor that can be mechanically exfoliated down to atomic layers. Unlike the Bernal stacked bilayer graphene, the two layers in a bilayer WSe2 flake are weakly coupled. The electric displacement field can easily break the layer degeneracy of the bilayer WSe2. Together with the strong spin–orbit coupling, it exhibits many novel quantum physical properties. In this work, we fabricate high quality dual-gated bilayer WSe2 devices and observe twofold degenerate Landau levels(LLs) and density-dependent quantum Hall states which show transitions between even and odd filling. When introducing carriers into the system from the valence band edge by gating, two WSe2 layers are filled independently and the bottom layer WSe2 shows negative compressibility at the crossover point. Above 9 T, we observe the degeneracy of LLs is completely broken and there are two sets of LL crossings in the top WSe2 layer at Zeeman-to-cyclotron energy ratio E Z / E N ≈ 4 and E Z / E N ≈ 5. The interplay between two LLs from the two WSe2 layers confirms the weak coupling between them. Our results show that the bilayer WSe2 behave like two closely packed independent electronic systems under electric displacement fields.

Dirac fermions in a spinning conical Gödel-type spacetime

AbstractIn this paper, we determine the relativistic and nonrelativistic energy levels for Dirac fermions in a spinning conical Gödel-type spacetime in(2+1)-dimensions, where we work with the curved Dirac equation in polar coordinates and we use the tetrads formalism. Solving a second-order differential equation for the two components of the Dirac spinor, we obtain a generalized Laguerre equation, and the relativistic energy levels of the fermion and antifermion, where such levels are quantized in terms of the radial and total magnetic quantum numbersnandmj, and explicitly depends on the spin parameters(describes the ‘spin’), spinorial parameteru(describes the two components of the spinor), curvature and rotation parametersαandβ(describes the conical curvature and the angular momentum of the spinning cosmic string), and on the vorticity parameter Ω (describes the Gödel-type spacetime). In particular, the quantization is a direct result of the existence of Ω (i.e. such quantity acts as a kind of ‘external field or potential’). We see that formj>0, the energy levels do not depend onsandu; however, depend onn,mj,α, andβ. In this case,αbreaks the degeneracy of the energy levels and such levels can increase infinitely in the limit4Ωβα→1. Already formj<0, we see that the energy levels depends ons,uandn; however, it no longer depends onmj,αandβ. In this case, it is as if the fermion/antifermion ‘lives only in a flat Gödel-type spacetime’. Besides, we also study the low-energy or nonrelativistic limit of the system. In both cases (relativistic and nonrelativistic), we graphically analyze the behavior of energy levels as a function of Ω,α, andβfor three different values ofn(ground state and the first two excited states).

Non-Abelian Holonomy in Degenerate Non-Hermitian Systems.

Non-Abelian holonomy, a noncommutative process that measures the parallel transport of non-Abelian gauge fields, has so far been realized in degenerate Hermitian systems with degenerate eigenstates or nondegenerate non-Hermitian systems with exceptional points. Here, we introduce non-Abelian holonomy into degenerate non-Hermitian systems possessing degenerate exceptional points and degenerate energy topologies. The interplay between energy degeneracy and energy topology around exceptional points leads to a non-Abelian holonomy with multiple energy levels and multiple degenerate levels simultaneously, going beyond that in degenerate Hermitian systems with a single energy level, or in nondegenerate non-Hermitian systems with a single degenerate level. We exploit an on-chip photonic platform to experimentally demonstrate the holonomy induced non-Abelian phenomenon, including the switching of eigenstates associated with different degenerate exceptional points and sequence-dependent holonomic outcomes. Our work shifts the paradigm of non-Abelian holonomy and adds new degrees of freedom for non-Abelian applications.

Understanding multiple timescales in quantum dissipative dynamics: Insights from quantum trajectories

Open quantum systems with nearly degenerate energy levels have been shown to exhibit long-lived metastable states in the approach to equilibrium, even when modelled with certain Lindblad-form quantum master equations. This is a result of dramatic separation of timescales due to differences between Liouvillian eigenvalues. These metastable states often have nonzero coherences that die off only in the long-time limit once the system reaches thermal equilibrium. We examine two distinct situations that give rise to this effect: one in which dissipative dynamics couple together states only within a nearly degenerate subspace, and one in which they give rise to jumps over finite-energy splittings, between nearly degenerate subspaces. We find, in each case, that a change of basis can often lead to a representation that more naturally captures the impact of the system-bath interaction than does the energy eigenbasis, revealing that separate timescales are associated with separate processes (e.g., decoherence into a nonenergy eigenbasis, decay of population correlations to the initial state). This approach is paired with the inspection of quantum trajectories, which further provide intuition as to how open system evolution is characterized when coherent oscillations, thermal relaxation, and decoherence all occur simultaneously. Published by the American Physical Society 2024

Majorana-Free Bound State in the Continuum in the Double-Channel Fano–Anderson Structure

Abstract We investigate the electron transport through a double-channel Fano–Anderson structure, by considering the side-coupling of Majorana bound states (MBSs). It is found that the bound state in the continuum (BIC) phenomenon can be induced when interchannel dot–lead couplings are identical to the intrachannel dot–lead couplings, whose signature is manifested as a halved quantum transmission ability. If the balance between the dot–lead couplings is broken, the BIC phenomenon will also be destroyed, leading to further suppression of the transmission ability. Next, when MBSs are introduced to this system, the BIC phenomenon can be modified efficiently. For the case of two MBSs side-coupled to the quantum dots in a symmetric way, level degeneracy causes a new BIC phenomenon. As only one MBS is incorporated, it suppresses the electron transmission by inducing new transmission dips. When the interdot Coulomb interaction is considered, the BIC phenomena are still robust despite the complicated changes of the transmission ability spectra. One can then understand the realization of BICs in coupled quantum dots and their variation due to the presence of side-coupled MBSs.

Crystalline electric field and large anomalous Hall effect in NdGaGe single crystals

We grew NdGaGe single crystals and investigated their magnetic and electrical transport properties. The magnetic susceptibility data revealed that NdGaGe orders magnetically at Tm≈ 8.8 K; also confirmed by heat capacity and electrical resistivity data. In ordered state, the heat capacity and electrical resistivity data exhibit a gapped-magnon behavior with an energy gap of ∼ 4.7 K. Our detailed crystalline electric field analysis of magnetic susceptibility, magnetization, and heat capacity data indicates that the (2J+1) degenerate energy levels of Nd3+ ion split into five doublets with an overall splitting of ∼ 123 K. We observe a large anomalous Hall conductivity (AHC) ∼ 530 Ω−1 cm−1 at 2 K, which is close to the theoretical expected value due to intrinsic Berry-curvature. Moreover, the scaling parameter between anomalous Hall resistivity and magnetoresistivity together with the linear relationship between AHC and saturation magnetization suggests that the origin of large AHC in NdGaGe is due to the intrinsic Berry curvature.

The effects of common reservoirs on the performance of a quantum refrigerator

In this work, we study and find that the performance of an autonomous refrigerator can be improved by means of collective dissipations of common reservoirs. The refrigerator is based on a four-level system with two degenerate levels, coupled to three thermal reservoirs with different temperatures. Our study reveals that utilizing only one common reservoir can not significantly enhance the refrigerator’s performance. However, when two reservoirs are shared simultaneously, the performance improvement becomes more evident. Furthermore, we find that the refrigerator’s performance can be further enhanced by operating in a regime where the decoherence-free subspace is present. Our results indicate that careful engineering is essential to maximize the benefits of common reservoirs in enhancing the performance of quantum thermal machines.

A note on degeneracy of excited energy levels in massless Dirac fermions

We propose a mechanism to construct the eigenvalues and eigenfunctions of the massless Dirac-Weyl equation in the presences of magnetic flux Φ localized in a restricted region of the plane. Using this mechanism we analyze the degeneracy of the existed energy levels. We find that the zero and first energy level has the same N+1 degeneracy, where N is the integer part of Φ2π. In addition, and contrary to what is described in the literature regarding graphene, we show that higher energy levels are N+m degenerate, being m the level of energy. In other words, this implies an indefinite growth of degenerate states as the energy level grows.

Fermion self-energy and damping rate in a hot magnetized plasma

We derive a general expression for the fermion self-energy in a hot magnetized plasma by using the Landau-level representation. In the one-loop approximation, the Dirac structure of the self-energy is characterized by five different functions that depend on the Landau-level index n and the longitudinal momentum pz. We derive general expressions for all five functions and obtain closed-form expressions for their imaginary parts. The latter receive contributions from three types of on shell processes, which are interpreted in terms of Landau-level transitions, accompanied by a single photon (gluon) emission or absorption. By making use of the imaginary parts of the self-energy functions, we also derive the Landau-level dependent fermion damping rates Γn(pz) and study them numerically in a wide range of model parameters. We also demonstrate that the two-spin degeneracy of the Landau levels is lifted by the one-loop self-energy corrections. While the spin splitting of the damping rates is small, it may be important for some spin and chiral effects. We argue that the general method and the numerical results for the rates can have interesting applications in heavy-ion physics, astrophysics, and cosmology, where strongly magnetized QED or QCD plasmas are ubiquitous. Published by the American Physical Society 2024