Degenerate Components Research Articles

Floquet Hofstadter butterfly in trilayer graphene with a twisted top layer

The magnetic field generated Hofstadter butterfly in single-twist trilayer graphene (TLG) is investigated using circularly polarized light (CPL) and longitudinal light emanating from a waveguide. We show that single-twist TLG has two distinct chiral limits in the equilibrium state, and the central branch of the butterfly splits into two precisely degenerate components. The Hofstadter butterfly appears to be more discernible. We also discovered that CPL causes a large gap opening at the central branch of the Hofstadter butterfly energy spectrum and between the Landau levels, with a clear asymmetry corresponding to energy E=0. We point out that for right-handed CPL, the central band shifts downward, in stark contrast to left-handed CPL, where the central band shifts upward. Finally, we investigated the effect of longitudinally polarized light, which originates from a waveguide. Interestingly, we observed that the chiral symmetries of the Hofstadter butterfly energy spectrum are broken for small driving strengths and get restored at large ones, contrary to what was observed in twisted bilayer graphene.

Integer and fractionalized vortex lattices and off-diagonal long-range order

We analyze the implication of off-diagonal long-range order (ODLRO) for inhomogeneous periodic field configurations and multi-component order parameters. For single component order parameters we show that the only static, periodic field configuration consistent with ODLRO is a vortex lattice with integer flux in units of the flux quantum in each unit cell. For a superconductor with g degenerate components, fractional vortices are allowed. Depending on the precise order-parameter manifold, they tend to occur in units of 1/g of the flux quantum. These results are well known to emerge from the Ginzburg-Landau or BCS theories of superconductivity. Our results imply that they are valid even if these theories no-longer apply. Integer and fractional vortex lattices are transparently seen to emerge as a consequence of the macroscopic coherence and single valuedness of the condensate.

Tunable terahertz dual-band circularly polarized dielectric resonator antenna

A tunable terahertz (THz) dual-band circularly polarized (CP) dielectric resonator (DR) antenna (DRA) is numerically analysed and implemented. Initially, an aperture coupled dual-band rectangular DRA is designed. This operates with the fundamental mode in the lower band and third order mode in the upper band and provides the linearly polarized response. The diagonal corners of the rectangular DR are truncated for obtaining the orthogonal degenerate components of the operating modes and thus the CP response is achieved. The tunability is achieved in the frequency response by applying a monolayer graphene material coating at the radiating surface of the chamfered DR. The antenna offers 10 dB impedance bandwidth of 18.41% (3.21−3.86 THz) and 4.7% (4.77−5.0 THz) along with 3 dB axial ratio bandwidth of 3.48% (3.38−3.5 THz) and 1.39% (4.98−5.05 THz). Furthermore, the proposed tunable dual-band THz CPDRA provides the gain of more than 6 dBic along with the radiation efficiency of more than 95% in each operating band.

Inference for High-Dimensional Exchangeable Arrays

We consider inference for high-dimensional separately and jointly exchangeable arrays where the dimensions may be much larger than the sample sizes. For both exchangeable arrays, we first derive high-dimensional central limit theorems over the rectangles and subsequently develop novel multiplier bootstraps with theoretical guarantees. These theoretical results rely on new technical tools such as Hoeffding-type decomposition and maximal inequalities for the degenerate components in the Hoeffiding-type decomposition for the exchangeable arrays. We exhibit applications of our methods to uniform confidence bands for density estimation under joint exchangeability and penalty choice for -penalized regression under separate exchangeability. Extensive simulations demonstrate precise uniform coverage rates. We illustrate by constructing uniform confidence bands for international trade network densities.

Circularly Polarized Plasmons in Chiral Gold Nanowires via Quantum-Mechanical Design.

Time-dependent density functional theory (TDDFT) simulations are conducted on a series of chiral gold nanowires to explore whether an enhancement of circular dichroism at the plasmon resonance is possible and identify its quantum-mechanical origin. We find that in linear two-dimensional chiral nanowires the dichroic response is suppressed by destructive interference of nearly degenerate components with opposite signs, pointing to this phenomenon as a common and likely origin of the difficulty encountered so far in achieving a plasmonic CD response in experiment and suggesting nevertheless that these opposite components could be "decoupled" by using multiwall arrangements. In contrast, we predict a giant dichroic response for nanowires with three-dimensional helical coiling. We rationalize this finding via an electronic structure analysis of longitudinal and transversal plasmonic excitations and their coupling into chiral components, and we propose a simple formula for the chiral response as a function of structural parameters (nanowire length and coiling number).

On enhanced sensing of chiral molecules in optical cavities

The differential response of chiral molecules to incident left- and right-handed circularly polarized light is used for sensing the handedness of molecules. Currently, significant effort is directed toward enhancing weak differential signals from the molecules, with the goal of extending the capabilities of chiral spectrometers to lower molecular concentrations or small analyte volumes. Previously, optical cavities for enhancing vibrational circular dichroism have been introduced. Their enhancements are mediated by helicity-preserving cavity modes which maintain the handedness of light due to their degenerate TE and TM components. In this article, we simplify the design of the cavity and numerically compare it with the previous one using an improved model for the response of chiral molecules. We use parameters of molecular resonances to show that the cavities are capable of bringing the vibrational circular dichroism signal over the detection threshold of typical spectrometers for concentrations that are one to three orders of magnitude smaller than those needed without the cavities, for a fixed analyte volume. Frequency resolutions of current spectrometers result in enhancements of more than one order (two orders) of magnitude for the new (previous) design. With improved frequency resolution, the new design achieves enhancements of three orders of magnitude. We show that the TE/TM degeneracy in perfectly helicity-preserving modes is lifted by factors that are inherent to the cavities. More surprisingly, this degeneracy is also lifted by the molecules themselves due to their lack of electromagnetic duality symmetry, that is, due to the partial change of helicity during the light-molecule interactions.

Clustering non-linear interactions in factor analysis

Factor analysis is a powerful tool for dimensionality reduction in multivariate studies. This study extends the factor model with non-linear interactions. The main contribution of our work is to present two approaches to cluster the non-linear interactions and thus develop new models that are not restricted to the extreme scenarios where all non-null interactions are different or all are the same. The first strategy to handle the clusters involves a finite mixture of degenerate components. The second option is specified via the Dirichlet process. A comprehensive simulation study is developed to explore the performance of the proposals. A sensitivity analysis is carried out to evaluate advantages of estimating a smoothness parameter defined in a covariance function of the Gaussian process establishing the non-linearity of the interactions. In terms of application, the methodology is illustrated with the analysis of gene expression levels related to four breast cancer data sets. The genes belonging to disjoint genome regions, with copy number alteration, are connected to the main factors and their non-linear interactions are estimated and clustered. The mutual investigation and comparison of these four breast cancer data sets is rarely found in the literature.

Spatial separation of degenerate components of magnon Bose\u2013Einstein condensate by using a local acceleration potential

Bose–Einstein condensation (BEC) of magnons is one of the few macroscopic quantum phenomena observable at room temperature. Due to the competition of the exchange and the magnetic dipole interactions, the minimum-energy magnon state is doubly degenerate and corresponds to two antiparallel non-zero wavevectors. Correspondingly, the room-temperature magnon BEC differs essentially from other condensates, since it takes place simultaneously at ± kmin. The degeneracy of BEC and interaction between its two components have significant impact on condensate properties. Phase locking of the two condensates causes formation of a standing wave of the condensate density and quantized vortices. Additionally, interaction between the two components is believed to be important for stabilization of the condensate with respect to a real-space collapse. Thus, the possibility to create a non-degenerate, single-component condensate is decisive for understanding of underlying physics of magnon BEC. Here, we experimentally demonstrate an approach, which allows one to accomplish this challenging task. We show that this can be achieved by using a separation of the two components of the degenerate condensate in the real space by applying a local pulsed magnetic field, which causes their motion in the opposite directions. Thus, after a certain delay, the two clouds corresponding to different components become well separated in the real space. We find that motion of the clouds can be described well based on the peculiarities of magnon dispersion characteristics. Additionally, we show that, during the motion, the condensate cloud harvests non-condensed magnons, which results in a partial compensation of condensate depletion.

Electronic spectrum of boron dichloride. theoretical study of vibronic levels of the ground and first excited states

As expected by the Walsh diagram of AB2 molecules, the electronic spectrum of BCl2 radical involves bent-linear transitions between the ground and first excited states that form the two degenerate components of the 2Π electronic state of the linear molecule. A high level ab-initio theoretical study on BCl2 radical has been undertaken by constructing potential energy surfaces (PES) using the coupled-cluster singles and doubles with perturbative triples (CCSD(T)) with aug-cc-pVQZ for boron and aug-cc-pV(Q + d)Z for chlorine atoms. Vibronic energy levels were determined variationally, from the obtained PES, up to ~35,000 cm−1 above the relative minima of the ground and excited states. Low-lying vibrational levels of the ground and first excited electronic states were obtained, which showed a very complex structure which is known to be as a result of large Renner-Teller vibronic coupling. For the most abundant isotopologue, 11B35Cl2, the ground state fundamental frequencies are; ω10= 696.0 cm−1, ω20= 281.0 cm−1 and ω30=981.8 cm−1. For the same isotopologue, vibrational fundamentals of the excited state were estimated by fitting Σ vibronic levels to be ω10= 463.2 cm−1, ω20= 281.7 cm−1 and ω30=1245.1 cm−1.

To the theory of semilinear equations in the plane

In two dimensions, we present a new approach to the study of the semilinear equations of the form div[A(z)∇u] = f(u), the diffusion term of which is the divergence uniform elliptic operator with measurable matrix functions A(z), whereas its reaction term f(u) is a continuous non-linear function. Assuming that f(t)/t → 0 as t → ∞, we establish a theorem on existence of weak $$ C\left(\overline{D}\right)\cap {W}_{\mathrm{loc}}^{1,2}(D) $$ solutions of the Dirichlet problem with arbitrary continuous boundary data in any bounded domains D without degenerate boundary components. As consequences, we give applications to some concrete model semilinear equations of mathematical physics, arising from modeling processes in anisotropic and inhomogeneous media. With a view to the further development of the theory of boundary-value problems for the semilinear equations, we prove a theorem on the solvability of the Dirichlet problem for the Poisson equation in Jordan domains with arbitrary boundary data that are measurable with respect to the logarithmic capacity.

To the theory of semilinear equations in the plane

In two dimensions, we present a new approach to the study of the semilinear equations of the form \(\mathrm{div}[ A(z) \nabla u] = f(u)\), the diffusion term of which is the divergence uniform elliptic operator with measurable matrix functions \(A(z)\), whereas its reaction term \(f(u)\) is a continuous non-linear function. Assuming that \(f(t)/t\to 0\) as \(t\to\infty\), we establish a theorem on existence of weak \(C(\overline D)\cap W^{1,2}_{\rm loc}(D)\) solutions of the Dirichlet problem with arbitrary continuous boundary data in any bounded domains \(D\) without degenerate boundary components. As consequences, we give applications to some concrete model semilinear equations of mathematical physics, arising from modeling processes in anisotropic and inhomogeneous media. With a view to the further development of the theory of boundary-value problems for the semilinear equations, we prove a theorem on the solvability of the Dirichlet problem for the Poisson equation in Jordan domains with arbitrary boundary data that are measurable with respect to the logarithmic capacity.

Conical intersections and nonadiabatic coupling terms in 1,3,5-C6H3F3 +: A six state beyond Born-Oppenheimer treatment.

In order to circumvent numerical inaccuracy originating from the singularity of nonadiabatic coupling terms (NACTs), we need to perform kinetically coupled adiabatic to potentially coupled diabatic transformation of the nuclear Schrödinger Equation. Such a transformation is difficult to achieve for higher dimensional sub-Hilbert spaces due to inherent complicacy of adiabatic to diabatic transformation (ADT) equations. Nevertheless, detailed expressions of ADT equations are formulated for six coupled electronic states for the first time and their validity is extensively examined for a well-known radical cation, namely, 1,3,5-C6H3F3 + (TFBZ+). While implementing this formulation, we compute ab initio adiabatic potential energy surfaces (PESs) and NACTs within the low-lying six electronic states (X̃2E'', Ã2A2 '', B̃2E', and C̃2A2 '), where several types of nonadiabatic interactions, like Jahn-Teller conical intersections (CI), accidental CIs, accidental seams (series of degenerate points), and pseudo Jahn-Teller interactions can be observed over the Franck-Condon region of nuclear configuration space. Those interactions are depicted by exploring degenerate components of C-C asymmetric stretching, C-C symmetric stretching, and C-C-C scissoring motion (Q9x, Q9y, Q10x, Q10y, Q12x, and Q12y) to compute complete active space self-consistent field level adiabatic PESs and NACTs as implemented in the MOLPRO quantum chemistry package. Subsequently, we perform the ADT using our newly devised fifteen (15) ADT equations to locate the position of CIs, verify the quantization of NACTs, and to construct highly accurate diabatic PESs.

A theoretical study on cyclacenes: Analytical tight‐binding approach

AbstractWe present a theoretical study of cyclacene molecules performed at tight‐binding level. The orbital energies and eigenvectors have been analytically computed, and exact expressions for the axial component of the total position spread and polarizability tensors have been obtained. In absence of dimerization, the system has a Dnh symmetry, where n is the number of hexagonal units. The energy bands present no gap at the Fermi level, and to this fact it corresponds a diverging (per‐electron) polarizability for in the direction of the system symmetry axis. The two (degenerate) components of the polarizability on the σh symmetry plane, conversely, remain finite for . The total position spread tensor presents a qualitatively different behavior, since all the three components of the position spread per electron remain finite for . The results are analyzed and discussed for both axial and planar components separately as these are affected differently with respect to the increasing system size. Both dipole polarizability and total position spread have been computed using an ab initio approach for the smallest systems, to compare the analytical tight‐binding expressions with a higher‐level theory.

Nonexistence of degenerate horizons in static vacua and black hole uniqueness

We show that in any spacetime dimension D≥4, degenerate components of the event horizon do not exist in static vacuum configurations with positive cosmological constant. We also show that without a cosmological constant asymptotically flat solutions cannot possess a degenerate horizon component. Several independent proofs are presented. One proof follows easily from differential geometry in the near-horizon limit, while others use Bakry–Émery–Ricci bounds for static Einstein manifolds.

Bose–Einstein condensation of heteronuclear bound states formed in a Fermi gas of two atomic species: a microscopic approach

We study a many-body system of interacting fermionic atoms of two species that are in thermodynamic equilibrium with their condensed heteronuclear bound states (molecules). In order to describe such an equilibrium state, we use a microscopic approach that involves the Bogoliubov model for a weakly interacting Bose gas and approximate formulation of the second quantization method in the presence of bound states of particles elaborated earlier by the authors. This microscopic approach is valid at low temperatures, when the average kinetic energy of all the components in the system is small in comparison with the bound state energy. The coupled equations, which relate the chemical potentials of fermionic components and molecular condensate density, are obtained within the proposed theory. At zero temperature, these equations are analyzed both analytically and numerically, attracting the relevant experimental data. We find the conditions at which a condensate of heteronuclear molecules coexists in equilibrium with degenerate components of a Fermi gas. The ground state energy and single-particle excitation spectrum are found. The boundaries of the applicability of the developed microscopic approach are analyzed.

Decay structure of two hyperbolic relaxation models with regularity loss

The paper aims at investigating two types of decay structure for linear symmetric hyperbolic systems with non-symmetric relaxation. Precisely, the system is of the type $(p,q)$ if the real part of all eigenvalues admits an upper bound $-c|\xi|^{2p}/(1+|\xi|^2)^{q}$, where $c$ is a generic positive constant and $\xi$ is the frequency variable, and the system enjoys the regularity-loss property if $p<q$. It is well known that the standard type $(1,1)$ can be assured by the classical Kawashima-Shizuta condition. A new structural condition was introduced in \cite{UDK} to analyze the regularity-loss type $(1,2)$ system with non-symmetric relaxation. In the paper, we construct two more complex models of the regularity-loss type corresponding to $p=m-3$, $q=m-2$ and $p=(3m-10)/2$, $q=2(m-3)$, respectively, where $m$ denotes phase dimensions. The proof is based on the delicate Fourier energy method as well as the suitable linear combination of series of energy inequalities. Due to arbitrary higher dimensions, it is not obvious to capture the energy dissipation rate with respect to the degenerate components. Thus, for each model, the analysis always starts from the case of low phase dimensions in order to understand the basic dissipative structure in the general case, and in the mean time, we also give the explicit construction of the compensating symmetric matrix $K$ and skew-symmetric matrix $S$.

Krylov implicit integration factor WENO method for SIR model with directed diffusion

SIR models with directed diffusions are important in describing the population movement. However, efficient numerical simulations of such systems of fully nonlinear second order partial differential equations (PDEs) are challenging. They are often mixed type PDEs with ill-posed or degenerate components. The solutions may develop singularities along with time evolution. Stiffness due to nonlinear diffusions in the system gives strict constraints in time step sizes for numerical methods. In this paper, we design efficient Krylov implicit integration factor (IIF) Weighted Essentially Non-Oscillatory (WENO) method to solve SIR models with directed diffusions. Numerical experiments are performed to show the good accuracy and stability of the method. Singularities in the solutions are resolved stably and sharply by the WENO approximations in the scheme. Unlike a usual implicit method for solving stiff nonlinear PDEs, the Krylov IIF WENO method avoids solving large coupled nonlinear algebraic systems at every time step. Large time step size computations are achieved for solving the fully nonlinear second-order PDEs, namely, the time step size is proportional to the spatial grid size as that for solving a pure hyperbolic PDE. Two biologically interesting cases are simulated by the developed scheme to study the finite-time blow-up time and location or discontinuity locations in the solution of the SIR model.

Nonadiabatic Renner-Teller quantum dynamics of OH(X2Π) + H+ reactive collisions.

Following previous studies on the O(3P) + H2+(X2Σg+) collisions, we present the nonadiabatic quantum dynamics of the reactions OH(X2Π) + H'+ → OH'(X2Π) + H+, exchange (e), → OH+(X3Σ-) + H'(2S), quenching (q), and → OH'+ (X3Σ-) + H(2S), exchange-quenching (eq). The reactants and products correlate via the ground X[combining tilde]2A'' and first excited Ã2A' electronic states of OH2+, which are the degenerate components of linear 2Π species. Therefore, they are strongly perturbed by nonadiabatic Renner-Teller (RT) effects, opening the (q) and (eq) channels that are closed in the Born-Oppenheimer approximation. Using accurate potential energy surfaces (PESs) and RT matrix elements, initial-state-resolved reaction probabilities, real-time dynamics, cross sections, and rate constants of the product channels are obtained through the time-dependent real wavepacket (WP) method and full coupled-channel calculations. Owing to the nonadiabatic couplings, the WP jumps from the excited Ã2A' surface to the X[combining tilde]2A'' ground PES, avoiding any barrier, opening the quenching channels, and giving many collision complexes into the deep minima of both PESs, as it is clearly shown by the oscillations of the reaction probabilities and by the time-dependent WP dynamics. All the results show that the nonadiabatic-RT channels (q) and (eq) are highly reactive, much more than the adiabatic one (e), pointing out large RT effects. The reactivity of the quenching channels is similar, accounting for 97% of the overall reactivity. In fact, the maximum values of the (q) and (eq) cross sections σq and σeq are equal to 31.6 Å2, whereas the maximum σe value equals 1.34 Å2, and the maximum values of the rate constants kq, keq, and ke are 2.07 × 10-10, 2.45 × 10-10, and 0.23 × 10-10 cm3 s-1. Some calculations show that the centrifugal-sudden and the truncated coupled-channel approximations cannot be employed for the (q) channel. After a sharp increase at the threshold, σq and σeq decrease at larger collision energies while σe and the rate constants depend slightly on the collision energy and temperature, respectively. These findings are consistent with the barrierless nature of both PESs and the exoergicity of the quenching products, with the small role played by the centrifugal and RT barriers in the reactant channel, and with the large RT couplings in the OH2+ intermediates. Finally, we contrast the present results with those for the opposite reactions O + H2+ and for the nonadiabatic-induced quenchings NH + H' and OH + H'.

Spin-valley splitting of electron beam in graphene

We study spatial separation of the four degenerate spin-valley components of an electron beam in a EuO-induced and top-gated ferromagnetic/pristine/strained graphene structure. We show that, in a full resonant tunneling regime for all beam components, the formation of standing waves can lead sudden phase jumps ∼−π and giant lateral Goos-Hänchen shifts as large as the transverse beam width, while the interplay of the spin and valley imaginary wave vectors in the modulated regions can lead differences of resonant angles for the four spin-valley flavors, manifesting a spin-valley beam splitting effect. The splitting effect is found to be controllable by the gating and strain.

Role of commensurate and incommensurate low-energy excitations in the paramagnetic to hidden-order transition ofURu2Si2

We report low-energy inelastic neutron scattering data of the paramagnetic (PM) to hidden-order (HO) phase transition at $T_0=17.5\,{\rm K}$ in URu$_2$Si$_2$. While confirming previous results for the HO and PM phases, our data reveal a pronounced wavevector dependence of low-energy excitations across the phase transition. To analyze the energy scans we employ a damped harmonic oscillator model containing a fit parameter $1/\Gamma$ which is expected to diverge at a second-order phase transition. Counter to expectations the excitations at $\vec{Q}_1=(1.44,0,0)$ show an abrupt step-like suppression of $1/\Gamma$ below $T_0$, whereas excitations at $\vec{Q}_0=(1,0,0)$, associated with large-moment antiferromagnetism (LMAF) under pressure, show an enhancement and a pronounced peak of $1/\Gamma$ at $T_0$. Therefore, at the critical HO temperature $T_0$, LMAF fluctuations become nearly critical as well. This is the behavior expected of a super-vector order parameter with nearly degenerate components for the HO and LMAF leading to nearly isotropic fluctuations in the combined order-parameter space.