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We propose an efficient version of ensemble Hartree–Fock/density functional theory to calculate a set of two charge-transfer states for systems with odd-numbers of electrons. The approach does require definitions of donor/acceptor fragments; however, the approach is not very sensitive to such definitions—even in the limit of very strong electronic coupling. The key ansatz is that, by mandating that the vector space spanned by the active orbitals projects equally onto the donor and acceptor fragments, such a constraint eliminates all intra-molecular local excitations and makes it far easier to generate potential energy surfaces that are smooth over a wide region of configuration space. The method is fast, working with only two electron configurations, and should be useful for ab initio non-adiabatic dynamics in the near future. [ABSTRACT FROM AUTHOR]

We demonstrate that, for systems with spin–orbit coupling and an odd number of electrons, the standard fewest switches surface hopping algorithm does not conserve the total linear or angular momentum. This lack of conservation arises not so much from the hopping direction (which is easily adjusted) but more generally from propagating adiabatic dynamics along surfaces that are not time reversible. We show that one solution to this problem is to run along eigenvalues of phase-space electronic Hamiltonians H(R, P) (i.e., electronic Hamiltonians that depend on both nuclear position and momentum) with an electronic–nuclear coupling Γ · P [see Eq. (25)], and we delineate the conditions that must be satisfied by the operator Γ. The present results should be extremely useful as far as developing new semiclassical approaches that can treat systems where the nuclear, electronic orbital, and electronic spin degrees of freedom altogether are all coupled together, hopefully including systems displaying the chiral-induced spin selectivity effect. [ABSTRACT FROM AUTHOR]

Numerical difficulties associated with computing matrix elements of operators between Hartree–Fock–Bogoliubov (HFB) wavefunctions have plagued the development of HFB-based many-body theories for decades. The problem arises from divisions by zero in the standard formulation of the nonorthogonal Wick's theorem in the limit of vanishing HFB overlap. In this Communication, we present a robust formulation of Wick's theorem that stays well-behaved regardless of whether the HFB states are orthogonal or not. This new formulation ensures cancellation between the zeros of the overlap and the poles of the Pfaffian, which appears naturally in fermionic systems. Our formula explicitly eliminates self-interaction, which otherwise causes additional numerical challenges. A computationally efficient version of our formalism enables robust symmetry-projected HFB calculations with the same computational cost as mean-field theories. Moreover, we avoid potentially diverging normalization factors by introducing a robust normalization procedure. The resulting formalism treats even and odd number of particles on equal footing and reduces to Hartree–Fock as a natural limit. As proof of concept, we present a numerically stable and accurate solution to a Jordan–Wigner-transformed Hamiltonian, whose singularities motivated the present work. Our robust formulation of Wick's theorem is a most promising development for methods using quasiparticle vacuum states. [ABSTRACT FROM AUTHOR]

In this work, we have studied, within density functional theory, the interaction of NO with pure and oxidized silver clusters, both anionic and cationic, composed from 11 to 13 Ag atoms. In that size interval, shell closing effects are not expected, and structural and electronic odd–even effects will determine the strength of interaction. First, we obtained that species Ag n ± and AgnO± with odd number of electrons (n = 12) adsorb NO with higher energy than their neighbors (n = 11 and 13). This result is in agreement with the facts observed in recent mass spectroscopy measurements, which were performed, however, at finite temperature. The adsorption energy is about twice for oxidized clusters compared to pure ones and higher for anions than for cations. Second, the adsorption of another NO molecule on AgnNO± forms Ag n (NO) 2 ± , with the dimer (NO)2 in cis configuration, and binding the two N atoms with two neighbor Ag atoms. The n = 12 species show the higher adsorption energy again. Third, in the absence of reaction barriers, all complexes Ag n (NO) 2 ± dissociate spontaneously into AgnO± and N2O, except the n = 12 anion. The maximum high barrier along the dissociation path of Ag 13 (NO) 2 − is about 0.7 eV. Further analysis of projected density of states for Ag 11 − 13 (NO) x ± (x = 0, 1, 2) molecules shows that bonding between NO and Ag clusters mainly occurs in the energy range between −3.0 and 3.0 eV. The overlap between 4d of Ag and 2p of N and O is larger for Ag 12 (NO) 2 ± than for neighbor sizes. For n = 12, the d bands are close to the (NO)2 2π orbital, leading to extra back-donation charge from the 4d of Ag to the closer 2π orbital of (NO)2. [ABSTRACT FROM AUTHOR]

In this study, we employ the Sachs graph theory to formulate the conduction properties of a single-molecular junction consisting of a molecule in which one carbon atom of an alternant hydrocarbon is replaced with a heteroatom. The derived formula includes odd and even powers of the adjacency matrix, unlike the graph of the parental structure. These powers correspond to odd- and even-length walks. Furthermore, because the heteroatom is represented as a self-loop of unit length in the graph, an odd number of passes of the self-loop will change the parity of the length of the walk. To confirm the aforementioned effects of heteroatoms on conduction in an actual sample, the conduction behavior of meta-connected molecular junctions consisting of a heterocyclic six-membered ring, whose conductive properties have already been experimentally determined, was analyzed based on the enumerated number of walks. [ABSTRACT FROM AUTHOR]

Non-Hermiticity extends the topological phase beyond the given Hermitian structure. Whereas the phases of non-Hermitian topological systems derived from Hermitian components have been extensively explored, the topological properties of an acoustic crystal that occur purely due to non-Hermiticity require further investigation. In this letter, we describe the development of an acoustic crystal with an adjustable loss that is composed of a chain of one-dimensional, coupled acoustic resonators. Each unit cell can contain three or six resonators, which are equivalent to 3 × 3 or 6 × 6 non-Hermitian Hamiltonian matrices, respectively. The topological properties of the crystal were verified by calculating the defined topological invariant, and the states of the edge and interface of the acoustic crystal were obtained by using a practical model. We obtained the states of the edges and the interface for both odd and even numbers of resonators in each unit cell and found that the location of the inductive loss had an important effect on the topological properties. This results here can guide research on advanced wave control for sensing and communication applications. [ABSTRACT FROM AUTHOR]

10.1119/5.0121937.1 We show that a two-dimensional square lattice of magnets can be studied by placing small cylindrical neodymium magnets inside plastic spherical shells and floating them on water, leaving their magnetic moments free to re-orient within the plane. Experimentally, anti-correlated dipole orientations between nearest neighbors appear to be favored energetically. This motivates the construction of a simplified single-variable energy function for a 2D square lattice of magnetic dipoles. For odd numbers of spheres, this ansatz yields a continuum of dipole configurations with the same energies, matching the observed behavior that the orientation of the dipoles in these lattices can be rotated freely. The behavior of square lattices with even numbers of spheres is strikingly different, showing strongly preferred orientations. While the energy calculated in this simplified model is larger than that of the actual ground state for finite size clusters, its asymptotic value in the limit where the number of spheres goes to infinity is in good agreement with the literature value. Additionally, rectangular arrangements of magnetic spheres with and without a defect are analyzed within the class of the single variable energy function. Simple experimental demonstrations qualitatively reproduce several interesting results obtained from all these analyses. [ABSTRACT FROM AUTHOR]

We study the dynamics of multistable coexisting rotating waves that propagate along a unidirectional ring consisting of coupled double-well Duffing oscillators with different numbers of oscillators. By employing time series analysis, phase portraits, bifurcation diagrams, and basins of attraction, we provide evidence of multistability on the route from coexisting stable equilibria to hyperchaos via a sequence of bifurcations, including the Hopf bifurcation, torus bifurcations, and crisis bifurcations, as the coupling strength is increased. The specific bifurcation route depends on whether the ring comprises an even or odd number of oscillators. In the case of an even number of oscillators, we observe the existence of up to 32 coexisting stable fixed points at relatively weak coupling strengths, while a ring with an odd number of oscillators exhibits 20 coexisting stable equilibria. As the coupling strength increases, a hidden amplitude death attractor is born in an inverse supercritical pitchfork bifurcation in the ring with an even number of oscillators, coexisting with various homoclinic and heteroclinic orbits. Additionally, for stronger coupling, amplitude death coexists with chaos. Notably, the rotating wave speed of all coexisting limit cycles remains approximately constant and undergoes an exponential decrease as the coupling strength is increased. At the same time, the wave frequency varies among different coexisting orbits, exhibiting an almost linear growth with the coupling strength. It is worth mentioning that orbits originating from stronger coupling strengths possess higher frequencies. [ABSTRACT FROM AUTHOR]

We propose a graphene nanoribbon pumping device and study its quantum charge and spin pumping properties for both adiabatic and non-adiabatic regimes by using the Keldysh non-equilibrium Green's function and renormalization procedure. We show that the adiabatic regime is suitable for the generation of high charge current, while the non-adiabatic regime is appropriate for the generation of fully spin polarized and pure spin currents. Also, it is shown that the proposed device can act as a perfect and controllable spin filter. Moreover, we investigate the effects of width and edge of graphene nanoribbons and show that the pumped charge current in the zigzag graphene nanoribbon (ZGNR) strongly depends on nanoribbon width so that the maximum pumped current for width with even numbers of carbon chains is about one order of magnitude larger than that with odd numbers. In contrast with ZGNR, in armchair graphene nanoribbon, the pumped currents with even and odd numbers have the same order of magnitude. [ABSTRACT FROM AUTHOR]

The transmission of linearly and circularly polarized waves is studied both theoretically and experimentally for chiral metasurfaces formed by arrays of metallic square helices. The helical particles of the metasurfaces are constructed of rectangular bars manufactured by direct three-dimensional printing in solid metals. The transmittance of the metasurface is found to depend critically on the number of bars forming the square helical particles. In the case of an even number of bars, the chiral metasurface exhibits identical co-polarized transmittance of orthogonal linearly polarized waves, which are characterized by a dual-band asymmetric transmission. For an odd number of bars, the metasurface provides the same cross-polarization conversion for any polarization orientation of the incident field and thus serves as a polarization-independent twist polarizer. Finally, the transmittance of this polarizer is investigated with respect to the dimensions of the square helices. The investigated chiral metasurfaces are characterized by strong broadband circular dichroism regardless of the number of bars in the helical particles. The wide variety of transmission properties observed in the metasurfaces makes them particularly attractive for use in polarization conversion and separation devices. [ABSTRACT FROM AUTHOR]

Although the quantum classical Liouville equation (QCLE) arises by cutting off the exact equation of motion for a coupled nuclear-electronic system at order 1 (1 = ℏ0), we show that the QCLE does include Berry's phase effects and Berry's forces (which are proportional to a higher order, ℏ = ℏ1). Thus, the fundamental equation underlying mixed quantum-classical dynamics does not need a correction for Berry's phase effects and is valid for the case of complex (i.e., not just real) Hamiltonians, where exotic features can arise in the course of electronic relaxation. Furthermore, we also show that, even though Tully's surface hopping model ignores Berry's phase, Berry's phase effects are included automatically within Ehrenfest dynamics. These findings should be of great importance if we seek to model coupled nuclear-electronic dynamics for systems with odd numbers of electrons and spin-orbit coupling, where the complex nature of the Hamiltonian is paramount. [ABSTRACT FROM AUTHOR]

Flexural-gravity wave scattering due to an array of polynyas is investigated from the perspective of the blocking dynamics. The canonical eigenfunction expansion method is generalized to account for multiple propagating wave modes within blocking frequencies. Bragg scattering occurs due to the presence of multiple gaps in the floating ice sheet, and the number of sub-harmonic peaks in wave reflection becomes one/two less than the number of gaps as the reflection coefficient varies with a change in gap/ice-sheet length. In addition, the amplitudes of harmonic peaks in wave reflection increase with an increase in the number of gaps. The variation of wave reflection with an increase in wavenumber/length of the ice sheet depicts that common zero minima occur for an even number of gaps, while common sub-harmonic maxima occur for an odd number of gaps. The scattering coefficients vary between zero and unity within the blocking frequencies, despite the individual amplitudes of the scattered waves becoming more than unity for certain frequencies. Noticeably, higher amplitudes of the scattered waves are associated with lower energy transfer rates and vice versa. Extrema in wave reflection occur for higher values of frequency within the primary and secondary blocking points. In addition, removable discontinuities are found in the scattering coefficient at the blocking frequencies, whereas a jump discontinuity is observed for certain frequencies within the blocking limits due to the incident wave mode conversion. Moreover, irregularities in the ice sheet's deflection are observed for any frequency within the blocking limit due to the superposition of three propagating wave modes. [ABSTRACT FROM AUTHOR]

Understanding the stress patterns produced by microbubbles (MB) in blood vessels is important in enhancing the efficacy and safety of ultrasound-assisted therapy, diagnosis, and drug delivery. In this study, the wall stress produced by the non-spherical oscillation of MBs within the lumen of micro-vessels was numerically analyzed using a three-dimensional finite element method. We systematically simulated configurations containing an odd number of bubbles from three to nine, equally spaced along the long axis of the vessel, insonated at an acoustic pressure of 200 kPa. We observed that 3 MBs were sufficient to simulate the stress state of an infinite number of bubbles. As the bubble spacing increased, the interaction between them weakened to the point that they could be considered to act independently. In the relationship between stress and acoustic frequency, there were differences between the single and 3 MB cases. The stress induced by 3 MBs was greater than the single bubble case. When the bubbles were near the wall, the shear stress peak was largely independent of vessel radius, but the circumferential stress peak increased with the radius. This study offers further insight into our understanding of the magnitude and distribution of stresses produced by multiple ultrasonically excited MBs inside capillaries. [ABSTRACT FROM AUTHOR]

A numerical study based on detached eddy simulations is conducted to investigate the effects of the odd and even number of rotor/stator blades, that is, nr/ns, on the hydrodynamic performance of a pre-swirl pumpjet propulsor (PJP). In this paper, six PJPs, the PJP 6-4 (ns–nr), 8-6, 10-8, 7-5, 9-7, and 11-9, are created. The hydrodynamic performance, the unsteady force of blades, and the wake structure of the PJPs are compared. The results show that the frequency of the fluctuating force of the whole rotor highly depends on the number or, more specifically, the parity of nr. When the parameter nr is the even number, it can be found that the total unsteady force of the rotor blades will be strengthened at the k-order stator-blades-passing frequency (k = 1 / 2 n r ). Moreover, it indicates that the superposition-enhancement coefficient (is defined as A * ) at k = 1 / 2 n r equals to nr, at least from the present tests. In terms of both the rotor and stator numbers are even, a phenomenon of the rotor–stator resonance occurs at f = 1 / 2 n s n r f n , where fn represents the hub rotational frequency. This work is expected to give some insight in the design of a PJP. [ABSTRACT FROM AUTHOR]

We demonstrate flux-bias locking and operation of a gradiometric fluxonium artificial atom using two symmetric granular aluminum (grAl) loops to implement the superinductor. The gradiometric fluxonium shows two orders of magnitude suppression of sensitivity to homogeneous magnetic fields, which can be an asset for hybrid quantum systems requiring strong magnetic field biasing. By cooling down the device in an external magnetic field while crossing the metal-to-superconductor transition, the gradiometric fluxonium can be locked either at 0 or Φ 0 / 2 effective flux bias, corresponding to an even or odd number of trapped fluxons, respectively. At mK temperatures, the fluxon parity prepared during initialization survives to magnetic field bias exceeding 100 Φ 0 . However, even for states biased in the vicinity of 1 Φ 0 , we observe unexpectedly short fluxon lifetimes of a few hours, which cannot be explained by thermal or quantum phase slips. When operating in a deep-underground cryostat of the Gran Sasso laboratory, the fluxon lifetimes increase to days, indicating that ionizing events activate phase slips in the grAl superinductor. [ABSTRACT FROM AUTHOR]

Natural convection resulting from discrete reactive heat sources on the bottom wall of an enclosure is investigated. The rest of the bottom wall apart from the heat sources, the top wall, and the vertical walls are kept at the surrounding temperature. The remarkable findings, which have not been reported in any study, are that the flow field and temperature distribution are quite distinct depending on the odd and even number of reactive heat sources on the bottom wall. For odd numbers of heat sources, the vortices have a quite sharp corner near the center of the middle source and the base of the thermal plume is in the middle heat source. Contrary to this, for even numbers of reactive heat sources, the vortices have a blunt corner near the middle two heat sources and it seems that the thermal plume evolves from the coalescence of the middle two heat sources. Whatever the number of heat sources, for increasing the Rayleigh number, the maximum value of the stream function increases and the maximum temperature decreases. However, both of them are increased for higher values of the Frank–Kamenetskii number. It is also observed that the heat loss to the environment through the walls of the enclosure is stronger with the increase in the Rayleigh number and Frank–Kamenetskii number. [ABSTRACT FROM AUTHOR]

A class of frustrated one-dimensional periodic Heisenberg spin systems formed either by triangular unit cells with spin 1/2 or by composite unit cells formed by two different structural units, triangles and small linear segments formed by an odd number of spin-1/2 is investigated. Based on perturbative processing and numerical calculations of the density matrix renormalization group method, the gapless character of the exact energy spectrum of excitation for these systems was found. Their instability with respect to regular (Peierls) oscillations of interactions between structural units is demonstrated. The corresponding critical exponents for the energies of the ground state are estimated numerically. For some frustrated systems, a quantum phase transition associated with the spin symmetry of the ground state, caused by frustration, has been discovered. [ABSTRACT FROM AUTHOR]

To realize spin wave logic gates, programable phase inverters are essential. We image using phase-resolved Brillouin light scattering microscopy propagating spin waves in a one-dimensional magnonic crystal consisting of dipolarly coupled magnetic nanostripes. We demonstrate phase shifts upon a single nanostripe of opposed magnetization. Using micromagnetic simulations, we model our experimental finding in a wide parameter space of biasfields and wave vectors. We find that low-loss phase inversion is achieved, when the internal field of the oppositely magnetized nanostripe is tuned such that the latter supports a resonant standing spin wave mode with an odd quantization number at the given frequency. Our results are key for the realization of phase inverters with optimized signal transmission. [ABSTRACT FROM AUTHOR]

Bragg scattering of long gravity waves by an array of floating elastic plates in the presence of a series of rectangular trenches is studied under the assumption of linearized water wave theory and small amplitude structural response. Bragg reflection occurs in the case of an array of multiple floating flexible plates and trenches in isolation or combination, and the number of sub-harmonic peaks between two consecutive peaks is two less than the number of plates/trenches. In the case of long-wave scattering by an array of trenches in the absence of floating plates, wave reflection becomes zero minimum for a certain fixed wavenumber at the end of the first cycle (as referred to 0 < k1h1 < 0.32), irrespective of the even/odd number of trenches. Furthermore, the Bragg resonant reflection pattern of the second cycle is a mirror image of the reflection occurring in the first cycle. Conversely, the symmetric pattern of Bragg reflection exhibited in the case of an array of trenches does not occur for an array of plates in isolation or for plates and trenches in combination. Between consecutive harmonic peaks, the minima/maxima in the wave reflection occur in the case of the even/odd number of trenches/plates in isolation. In contrast, it occurs within the first cycle in the case of trenches and plates in combination. Between consecutive harmonic peaks, maxima/minima of wave reflection coincide for a certain wavenumber, irrespective of the even/odd number of trenches/plates in isolation. In addition, these maxima attained for a certain wavenumber for the even number of trenches/plates are 180° out of phase to that of minima for an odd number of trenches/plates. However, similar phenomena occur within the first cycle of Bragg resonance in the case of trenches and plates in combination. Moreover, the amplitude of oscillation in the wave reflection increases with an increase in plate rigidity. Time-dependent motion due to Bragg scattering by trenches and plates is demonstrated in different cases. [ABSTRACT FROM AUTHOR]

Using general rigid bead–rod theory, we explore the effect of twisting a macromolecule on its rheological properties in suspensions. We thus focus on macromolecules having the form of Möbius bands so that the number of twists can be incremented. We call these Möbius macromolecules. When represented in general rigid bead–rod theory, these macromolecules comprise beads whose centers all fall on a Möbius band. From first principles, we calculate the complex viscosity of twisted rings with zero to seven twists. We find that the zero-shear values of the viscosity and first normal stress coefficient increase with twisting. Furthermore, we find that the real part of the complex viscosity descends more rapidly, with frequency, with extent of twist. For the imaginary part of the complex viscosity, the more twisted, the higher the peak. For each part of the dimensionless complex viscosity and the first normal stress coefficient, the results fall on one of just three curves corresponding to zero, even, or odd numbers of twists. We also explore the effects of the length and the aspect ratio of twisted macromolecular suspensions. We close with a worked example for a suspension of triply twisted Möbius annulene. [ABSTRACT FROM AUTHOR]

A familiar anomaly affects SU(2) gauge theory in four dimensions: a theory with an odd number of fermion multiplets in the spin 1/2 representation of the gauge group, and more generally in representations of spin 2r + 1/2, is inconsistent. We describe here a more subtle anomaly that can affect SU(2) gauge theory in four dimensions under the condition that fermions transform with half-integer spin under SU(2) and bosons transform with integer spin. Such a theory, formulated in a way that requires no choice of spin structure, and with an odd number of fermion multiplets in representations of spin 4r + 3/2, is inconsistent. The theory is consistent if one picks a spin or spinc structure. Under Higgsing to U(1), the new SU(2) anomaly reduces to a known anomaly of "all-fermion electrodynamics." Like that theory, an SU(2) theory with an odd number of fermion multiplets in representations of spin 4r + 3/2 can provide a boundary state for a five-dimensional gapped theory whose partition function on a closed five-manifold Y is (− 1) ∫ Y w 2 w 3 . All statements have analogs with SU(2) replaced by Sp(2N). There is also an analog in five dimensions. [ABSTRACT FROM AUTHOR]

Multipactor is a vacuum discharge driven by secondary electron emission. Multiple period multipactors have long been known to exist but have been studied less extensively. In a period-n multipactor, electrons undergo multiple impacts in one rf period, with the synchronous phase alternating periodically between multiple values. A novel resonant form is proposed that combines one- and two-surface impacts within a single period, provided the total transit time is an odd number of rf half-periods and the product of secondary yields exceeds unity. For low fD products, the simplest such mode is shown to significantly increase the upper electric field boundary of the multipacting region and lead to overlap of higher-order bands. The results agree nicely with 3-D particle-in-cell code simulations. An alternative, map-based method is introduced for analyzing higher-periodicity multipactor. Practical implications of the findings are discussed, including consequences for multipactor suppression strategies using a dc magnetic field. [ABSTRACT FROM AUTHOR]