Odd Pair Research Articles

LDOS of electron pair and the role of the Pauli exclusion principle.

The local density of states (LDOS) for a pair of non-relativistic electrons, influenced by repulsive Coulomb forces, is expressed in term of one-dimensional integrals over Whittaker functions. The computation of the electron pair's LDOS relies on a two-particle Green's function (GF), a generalization of the one-particle GF applicable to a charged particle in an attractive Coulomb potential. By incorporating electron spins and considering the Pauli exclusion principle, the resulting LDOS consists of two components: one originating from an exchange-even two-particle GF and the other from an exchange-odd two-particle GF. The calculated LDOS reveals its dependence on both inter-electron distance and energy. The pseudo-LDOS, derived from the two-body contribution to the LDOS, is examined. This term ensures complete LDOS suppression at r = 0, exhibiting a limited spatial extent, and the reasons for its emergence are elucidated. It is shown that for energies exceeding the effective Hartree energy and inter-electron distances beyond the effective Bohr radius, the impact of manybody contributions to the LDOS can be disregarded. The induced LDOS for an electron pair subjected to an attractive contact potential in two dimensions is evaluated. At small distances a from the potential center, a predicted relative difference in LDOS between even and odd state pair reaches approximately 8%. The calculated LDOS is compared with available experimental findings from a two-dimensional electron gas (2DEG). Both exhibit similar oscillation periods; however, the LDOS of the electron pair decays as 1/a3, significantly faster than the 1/a decay observed for free electrons in a 2DEG.&#xD.

Effects of Rashba and Dresselhaus spin-orbit couplings on the critical temperature and paramagnetic limiting field of superconductors with broken inversion symmetry

Transition temperature (Tc) and paramagnetic limiting of a superconductor without spatial inversion symmetry in the presence of both Rashba and Dresselhaus antisymmetric spin-orbit couplings is studied. The critical temperature is derived for anisotropy of the superconducting order parameter, ranging from isotropic s-wave to any pairing state with nonzero angular momentum and mixed parity singlet-triplet states emerge due to spin-orbit coupling (SOC). It will be shown that for unprotected odd parity pairing, pure Rashba and Dresselhaus SOCs have similar effects on the reduction of Tc and for combined effects of the two spin-orbit couplings at fixed SOC, Tc reduced by increasing Dresselhaus component and decreased down to its minimum value in the equal-Rashba-Dresselhaus case. The paramagnetic limiting is also analyzed for spin-singlet pairing and it is shown that the low temperature divergence behavior of paramagnetic limiting is less affected by both Rashba and Dresselhaus SOCs but for fixed SOC strength by increasing Dresselhaus component the paramagnetic limiting field is increased.

Investigating hexagonal closed packed crystal lattice through QSPR modeling via linear regression analysis and Topsis

sThis research work covers three highly dominating reverse degree-based topological descriptors evaluated for the three-dimensional hexagonal close-packed (HCP) crystal structure lattice. HCP crystal lattice has a highly symmetrical and elegant crystal structure, and we have observed that results obtained from symmetrical structures draw symmetry in the numerical formulation obtained from topological descriptors. For this purpose, we will investigate whether the HCP lattice formed by an odd pair of unit cells is the best or an even pair of unit cells forming the lattice and how they behave in a dominating sense when investigated through the conclusions obtained from QSPR modeling. The QSPR model has been proposed to check the efficiency of each specified topological descriptor for five highly commendable physio-chemical properties: melting or boiling point, density, molar heat capacity, and enthalpy. Further, we have discovered the ideology to obtain the best possible structure when investigated and established on a statistically and mathematically strong proving and to what extent we can extract from QSPR to implement MCDM techniques, here considering TOPSIS that provide the best HCP structure lattice rankings. The obtained results may be helpful for researchers to better understand the structure and studying different physical/chemical properties of HCP crystal lattice.

Reimagining language

Abstract What is language and who or what can be said to have it? In this essay we consider this question in the context of interactions with non-humans, specifically: animals and computers. While perhaps an odd pairing at first glance, here we argue that these domains can offer contrasting perspectives through which we can explore and reimagine language. The interactions between humans and animals, as well as between humans and computers, reveal both the essence and the boundaries of language: from examining the role of sequence and contingency in human-animal interaction, to unravelling the challenges of natural interactions with “smart” speakers and language models. By bringing together disparate fields around foundational questions, we push the boundaries of linguistic inquiry and uncover new insights into what language is and how it functions in diverse non-human-exclusive contexts.

Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal

Band topology of materials describes the extent Bloch wavefunctions are twisted in momentum space. Such descriptions rely on a set of topological invariants, generally referred to as topological charges, which form a characteristic class in the mathematical structure of fiber bundles associated with the Bloch wavefunctions. For example, the celebrated Chern number and its variants belong to the Chern class, characterizing topological charges for complex Bloch wavefunctions. Nevertheless, under the space-time inversion symmetry, Bloch wavefunctions can be purely real in the entire momentum space; consequently, their topological classification does not fall into the Chern class, but requires another characteristic class known as the Stiefel-Whitney class. Here, in a three-dimensional acoustic crystal, we demonstrate a topological nodal-line semimetal that is characterized by a doublet of topological charges, the first and second Stiefel-Whitney numbers, simultaneously. Such a doubly charged nodal line gives rise to a doubled bulk-boundary correspondence—while the first Stiefel-Whitney number induces ordinary drumhead states of the nodal line, the second Stiefel-Whitney number supports hinge Fermi arc states at odd inversion-related pairs of hinges. These results experimentally validate the two Stiefel-Whitney topological charges and demonstrate their unique bulk-boundary correspondence in a physical system.

Multiple higher-order topological phases with even and odd pairs of zero-energy corner modes in a C3symmetry broken model

Here we study emergent higher-order topological (HOTI) phases in the extended Haldane model without C 3 symmetry. For the inversion symmetric case, the QSHI and QAHI phases can embed the HOTI phases while the remaining QASHI phase does not yield any HOTI phases. Remarkably, four-fold degeneracy of zero-energy corner states can be reduced to two-fold under the application (withdrawal) of sub-lattice mass (Zeeman field) term. The sub-lattice mass and Zeeman field terms compete with each other to pin down the two mid-gap states at zero-energy. Interestingly, the bulk polarization can topologically characterize the second-order topological insulator phase with the mid-gap corner modes irrespective of their energies as long as inversion symmetry is preserved. Our study indicates that a hybrid symmetry can in principle protect the second-order topological insulator phases, however, spin-spectrum gap has to be essentially finite there.

Design and Analysis of a Three-Speed Wound Bearingless Induction Motor

Aiming at the influence on the actual speed caused by the suspension winding′s rotor induced current of a squirrel-cage bearingless induction motor (SBIM), a novel three-speed wound bearingless induction motor (WBIM) is designed based on establishing the stator–rotor equivalent circuit, deriving the exciting current-suspension slip ratio equation and analyzing the magnetic field distribution with odd pole pairs and dipole pairs. The stator is embedded with a fixed four pole winding and a 2/6 pole-changing winding, while the rotor is wound with series–parallel windings connecting at a slip ratio ring. By changing the connection method of the stator coils, adjusting the three-phase voltage source, and controlling the short circuit of the rotor winding central point, it can realize that the rotor only induces the torque winding′s magnetic field under three speeds. Combining with the finite-element analysis, the induced current, air gap magnetic density, suspension force, and electromagnetic torque of the traditional SBIM and the new WBIM are quantitatively compared. Finally, an experimental platform is built for further verification. The results show that the designed three-speed WBIM can not only effectively suppress the induced current of the suspension winding and reduce its influence on the motor torque and speed, but also makes the motor has a better start-up and steady-state performance.

Acting and Race in Night of the Living Dead (1968)

Acting and Race in <i>Night of the Living Dead</i> (1968)

Universal approach to sending-or-not-sending twin field quantum key distribution

We present a universal approach to sending-or-not-sending (SNS) protocol of twin-field quantum key distribution with the method of actively odd parity pairing. In this improved protocol, the code bits are not limited to heralded events in time windows participated by pulses of intensity μ z and vacuum. All kinds of heralded events can be used for code bits to distill the final keys. The number of intensities (3 or 4) and the kinds of heralded events for code bits are automatically chosen by the key rate optimization itself. Numerical simulation shows that the key rate rises drastically in typical settings, up to 80% improvement compared with the prior results. Also, larger intensity value can be used for decoy pulses. This makes the protocol more robust in practical experiments.

Odd frequency pairing in a quantum critical metal

We analyze a possibility for odd-frequency pairing near a quantum critical point(QCP) in a metal. We consider a model with dynamical pairing interaction $V(\Omega_n)\sim 1/|\Omega_n|^\gamma$ (the $\gamma$-model). This interaction gives rise to a non-Fermi liquid in the normal state and is attractive for pairing. The two trends compete with each other. We search for odd-frequency solutions for the pairing gap $\Delta (\omega_m)= -\Delta(\omega_m)$. We show that for $\gamma <1$, odd-frequency superconductivity looses the competition with a non-Fermi liquid and does not develop. We show that the pairing does develop in the extended model in which interaction in the pairing channel is larger than the one in the particle-hole channel. For $\gamma >1$, we argue that the original model is at the boundary towards odd-frequency pairing and analyze in detail how superconductivity is triggered by a small external perturbation. In addition, we show that for $\gamma >2$, the system gets frozen at the critical point towards pairing in a finite range in the parameter space. This give rise to highly unconventional phase diagrams with flat regions.

Gestational Filmmaking with Art: An Odd Pair

Gestational Filmmaking <i>with</i> Art: An Odd Pair

The Child's Philosopher ed. by Maughn Rollins Gregory and Megan Jane Laverty

Reviewed by: The Child's Philosopher ed. by Maughn Rollins Gregory and Megan Jane Laverty Claudia Mills (bio) Gareth B. Matthews, The Child's Philosopher. Edited by Maughn Rollins Gregory and Megan Jane Laverty. Routledge, 2022. Throughout my career as a philosophy professor who is also a children's book author, and a children's book author who is also a philosophy professor, I have often been asked about what seemed to many an odd pairing of professions. I'd answer that philosophers were just the grownups who kept on asking the childlike questions that the other grownups had long ago abandoned. Gareth B. Matthews (1929-2011) was a highly respected philosopher specializing in Aristotelian metaphysics who forged a pioneering path by responding to children's philosophical questions with extraordinary respect and deep seriousness. In books such as Philosophy and the Young Child (1980), Dialogues with Children (1984), and The Philosophy of Childhood (1994), he analyzed conversations with his own children and grandchildren as well as schoolchildren in both American and international settings, arguing that even young children are capable of conceptual reasoning and their philosophical speculations are worthy of adult attention. His work as a visionary leader in the Philosophy for Children movement is given appreciative (but also critical) examination in this title in Routledge's new series on Philosophy for Children Founders. Following the series format, the volume on Matthews is organized into sections featuring different aspects of his work, each with a substantial introduction by a prominent scholar who situates his writings in a wider context and provides an extensive bibliography of relevant literature, followed by a selection of Matthews's essays curated by that scholar. The introductions are uniformly well researched and thoughtful, striking a tone that is both celebratory of Matthews's work and willing to note its limitations, among these that his evidence for the "naturalness" of children's philosophizing is a product of specific culture factors that he ignores. But it is Matthews's own words that are rightly the star of this excellent collection. His clarity of thought, droll but provocative examples of the children's insights he recorded, and bold positions advanced with disarming charm make for delightful reading. Part I, on philosophy and children's literature, reflects Matthews's view that "authors of children's books are more likely than psychologists, educational theorists, or even philosophers to be sensitive to philosophical thought in young children" (44). In his seminal 1976 article "Philosophy and Children's Literature" which, according to section editor Karin Murris, "inaugurated the study of philosophy in children's literature" (47), he highlights children's books that raise philosophical questions in a style he calls "philosophical whimsy." The Bear That Wasn't by Frank Tashlin engages [End Page 337] themes of "dreaming and skepticism," "being and non-being," "appearance and reality," and "the foundations of knowledge" (61). Rich philosophical insights abound in Baum's Tin Woodman (personal identity), Thurber's Many Moons (perception and illusion), and the Roo-capturing scene in Winnie-the-Pooh when Pooh ponders the "Aha!" that he's supposed to say to Kanga and wonders whether he can make it mean all the elaborate things Rabbit has told him it needs to mean; Matthews likens Pooh's speculations to questions about meaning posed by Wittgenstein in his Philosophical Investigations. A second essay in this section contrasts the condescension toward children of "Questions" in Jean Van Leeuwen's More Tales of Oliver the Pig, which offers a "phony contrast between naïve ignorance in children and patient wisdom in adults" (69), with Arnold Lobel's invitation for readers of all ages to join together in exploring puzzles about the nature of causation posed by Toad's mistaken reasoning in "The Garden" in Frog and Toad Are Friends, where Toad thinks his "hard work" of singing and reading to his seeds has caused them to grow. Matthew's essay "Children, Irony and Philosophy" (reprinted in the section on developmental psychology) employs this same story to refute theorists who argue that preschoolers cannot understand irony. Part II, on children's philosophical thinking, is replete with children's philosophical questions and comments that demonstrate remarkable imagination and insight...

Takagi Topological Insulator on the Honeycomb Lattice

Recently, real topological phases protected by PT symmetry have been actively investigated. In two dimensions, the corresponding topological invariant is the Stiefel-Whitney number. A recent theoretical advance is that in the presence of the sublattice symmetry, the Stiefel-Whitney number can be equivalently formulated in terms of Takagi’s factorization. The topological invariant gives rise to a novel second-order topological insulator with odd PT-related pairs of corner zero modes. In this article, we review the elements of this novel second-order topological insulator, and demonstrate the essential physics by a simple model on the honeycomb lattice. Novelly, the higher-order topological boundary modes can not only be tuned by the parameters but also the geometric shape of the sample.

Spectral properties of confining superexponential potentials

We explore the spectral properties and behaviour of confining superexponential potentials. Several prototypes of these highly nonlinear potentials are analysed in terms of the eigenvalues and eigenstates of the underlying stationary Schrödinger equation up to several hundreds of excited states. A generalization of the superexponential self-interacting oscillator shows a scaling behaviour of the spacing of the eigenvalues which turns into an alternating behaviour for the power law modified oscillator. Superexponential potentials with an oscillating power show a very rich spectral structure with varying amplitudes and wave vectors. In the parity symmetric case doublets of near degenerate energy eigenvalues emerge in the spectrum. The corresponding eigenstates are strongly localized in the outer wells of the potential and occur as even–odd pairs which are interspersed into the spectrum of delocalized states. We provide an outlook on future perspectives including the possibility to use these features for applications in e.g. cold atom physics.

Inverse design couplers for the excitation of odd plasmonic pairs in thin semiconducting films

A set of grating couplers that converts plane waves into odd pairs of plasmons supported by extremely thin layers of doped indium tin oxide is designed. The inverse design approach is implemented to improve the efficiency of ordinary periodical couplers significantly. The optimization code based on the gradient descent method and direct Maxwell solver is designed in Matlab. Three models with different optimization levels are compared and discussed. The results of calculations are prepared for subsequent experimental verification. Considered odd plasmonic pairs represent an example of high quality modes tunable using a field effect. They are potentially applicable for the implementation in various active electro-optical devices and lead the way to fully semiconductor based plasmonics.

Multiplicity, Parity and Angular Momentum of a Cooper Pair in Unconventional Superconductors of D4h Symmetry: Sr2RuO4 and Fe-Pnictide Materials

Sr2RuO4 and Fe-pnictide superconductors belong to the same point group symmetry D4h. Many experimental data confirm odd pairs in Sr2RuO4 and even pairs in Fe-pnictides, but opposite conclusions also exist. Recent NMR results of Pustogow et al., which revealed even Cooper pairs in Sr2RuO4, require reconsideration of symmetry treatment of its SOP (superconducting order parameter). In the present work making use of the Mackey–Bradley theorem on symmetrized squares, a group theoretical investigation of possible pairing states in D4h symmetry is performed. It is obtained for I4/mmm , i.e., space group of Sr2RuO4, that triplet pairs with even spatial parts are possible in kz direction and in points M and Y. For the two latter cases pairing of equivalent electrons with nonzero total momentum is proposed. In P4/nmm space group of Fe- pnictides in point M, even and odd pairs are possible for singlet and triplet cases. It it shown that even and odd chiral states with angular momentum projection m=±1 have nodes in vertical planes, but Eg is nodal , whereas Eu is nodeless in the basal plane. It is also shown that the widely accepted assertion that the parity of angular momentum value is directly connected with the spatial parity of a pair is not valid in a space-group approach to the wavefunction of a Cooper pair.

Field Test of Twin-Field Quantum Key Distribution through Sending-or-Not-Sending over 428km.

Quantum key distribution endows people with information-theoretical security in communications. Twin-field quantum key distribution (TF-QKD) has attracted considerable attention because of its outstanding key rates over long distances. Recently, several demonstrations of TF-QKD have been realized. Nevertheless, those experiments are implemented in the laboratory, and therefore a critical question remains about whether the TF-QKD is feasible in real-world circumstances. Here, by adopting the sending-or-not-sending twin-field QKD (SNS-TF-QKD) with the method of actively odd parity pairing (AOPP), we demonstrate a field-test QKD over 428km of deployed commercial fiber and two users are physically separated by about 300km in a straight line. To this end, we explicitly measure the relevant properties of the deployed fiber and develop a carefully designed system with high stability. The secure key rate we achieved breaks the absolute key rate limit of repeaterless QKD. The result provides a new distance record for the field test of both TF-QKD and all types of fiber-based QKD systems. Our work bridges the gap of QKD between laboratory demonstrations and practical applications and paves the way for an intercity QKD network with measurement-device-independent security.

Separating the aa-index into Solar and Hale Cycle Related Components Using Principal Component Analysis

We decompose the monthly aa-index of Cycles 10 to 23 using principal component analysis (PCA). We show that the first component (PC1) is related to the 11-year solar cycle, and accounts for 41.5% of the variance of the data. The second component (PC2) is related to 22-year Hale cycle, and explains 23.6% of the variance of the data. The PC1 time series of the aa-index for Cycles 10 – 23 has only one peak in its power spectrum at the period 10.95 years, which is the average solar cycle (SC) period for the interval SC10 – SC23. The PC2 time series of the same cycles has a clear peak at period 21.90 (Hale cycle) and a smaller peak at 3/4 of that period. We also study the principal components of the sunspot number (SSN) for Cycles 10 – 23, and compare the mutual behavior of the PC2 components of the aa-index and SSN PCA analyses. We note that they are in the same phase in all other cycles but Solar Cycles 15 and 20. The aa-index of Cycle 20 also differs from other even aa-index cycles in its shape, especially in anomalously high peaks during its descending phase. Even though there is a coherence in the PC2 time series phases of the aa-index and sunspot number, this effect is too small to be the origin of all the differences between the shape of even and odd aa cycles. We estimate that 30% of the shape of the PC2 component of the aa-index is due to the shape of the PC2 of the sunspot number and the rest to other recurrent events in the Sun and solar wind. The first maximum of the aa-index (typical to odd cycles), during sunspot maximum, has been shown to be related to coronal mass ejections (CME), while the second maximum (typical to even cycles) in the cycle descending phase, is probably related to high-speed streams (HSS). The last events increase the activity level such that the minimum between even and odd cycle pairs is always higher than the minimum between succeeding odd and even cycle pairs.

Dynamical torque from Shiba states ins-wave superconductors

Magnetic impurities inserted in a $s$-wave superconductor give rise to spin-polarized in-gap states called Shiba states. We study the back-action of these induced states on the dynamics of the classical moments. We show that the Shiba state pertains to both reactive and dissipative torques acting on the precessing classical spin that can be detected through ferromagnetic resonance measurements. Moreover, we highlight the influence of the bulk states as well as the effect of the finite linewidth of the Shiba state on the magnetization dynamics. Finally, we demonstrate that the torques are a direct measure of the even and odd frequency triplet pairings generated by the dynamics of the magnetic impurity. Our approach offers non-invasive alternative to the STM techniques used to probe the Shiba states.

Fine-tuning of the electro-optical switching behavior in indium tin oxide

Indium tin oxide is often used as an active material in photonics. Strong correlation between its optical response and a state of conduction electrons, as well as an intermediate density of charges typical for semiconductors, makes it highly tunable using an external electric field. This property is extensively used in various types of electro-optical modulators. Usually for infrared switching the charge concentration is manipulated in order to reach the epsilon-near-zero regime, where the real part of permittivity is small and losses are high. This allows one to switch between an optically transparent state and a highly absorbing state. In this paper we investigate the possibility of a different switching mechanism, namely, between the state where the propagation of surface plasmons is possible and another state where surface waves are forbidden. To obtain modes with high quality factors, which is challenging in indium tin oxide, we suggest using odd pairs of surface plasmons supported by thin films. The accumulation layer, formed at the boundary between indium tin oxide and the insulator under the influence of an external voltage, is considered as a tunable plasmonic waveguide. Both analytical and numerical analysis is used, first, to localize the regime where such modes are possible and, second, to compute the characteristics of corresponding plasmons in realistic conditions. Drift-diffusion equations and Maxwell equations are solved numerically in a self-consistent way to handle electronic and optical aspects of the problem. High tunability of plasmonic modes is demonstrated in infrared. The obtained results can be implemented in the new generation of plasmonic modulators and electro-optical circuits.