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A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization. Extending the ''probability via expectation'' approach of Whittle to noncommuting quantities, this paper defines quantities, ensembles, and experiments as mathematical concepts and shows how to model complementarity, uncertainty, probability, nonlocality and dynamics in these terms. The approach carries no connotation of unlimited repeatability; hence it can be applied to unique systems such as the universe. Consistent experiments provide an elegant solution to the reality problem, confirming the insistence of the orthodox Copenhagen interpretation on that there is nothing but ensembles, while avoiding its elusive reality picture. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.

We report on the magneto-optical study of spin polarized energetic fine structures for exciton complex in single CdSe quantum dot (QD) by using micro- photoluminescence (micro-PL) spectroscopy. The zero-field splitting of exciton luminescence peak arisen from the anisotropic exchange interaction of carriers in the QDs was observed. The g-factors for exciton and negatively-charged exciton, i.e. trion in a single QD were determined by fitting the magnetic field dependence of the corresponding PL peaks. By exciting the single QD with circularly polarized light of σ- and σ+ polarization, the spin-up and spin-down trions were selectively generated. The ratio, τ/τ_sf, of the exciton lifetime and the time constants for the spin-flipping process of trion in a single QD was estimated to be 0.13, which implies a long spin-lifetime in single CdSe QD.

The superfine structure of Bose-Einstein condensate of alkali atoms due to the spin coupling have been investigated in the mean field approximation. In the limit of large number of atoms, we obtained the analytical solution for the fully condensed states and the states with one-atom excited. It was found that the energy of the one-atom excited state could be smaller than the energy of the fully condensed state, even two states have similar total spin.

This article reviews steady-state spin densities and spin currents in materials with strong spin-orbit interactions. These phenomena are intimately related to spin precession due to spin-orbit coupling, which has no equivalent in the steady state of charge distributions. The focus will initially be on effects originating from the band structure. In this case, spin densities arise in an electric field because a component of each spin is conserved during precession. Spin currents arise because a component of each spin is continually precessing. These two phenomena are due to independent contributions to the steady-state density matrix, and scattering between the conserved and precessing spin distributions has important consequences for spin dynamics and spin-related effects in general. In the latter part of the article, extrinsic effects such as skew scattering and side jump will be discussed, and it will be shown that these effects are also modified considerably by spin precession. Theoretical and experimental progress in all areas will be reviewed.

We show that the electron–positron annihilation process ending with the creation of two gamma photons (with right- and left-hand circular helicity) can be explained in terms of the current loop model. We first show that both electron and positron (which are spin 1/2 particles) carry an intrinsic flux quantum of ±Φ₀/2 even in the absence of an external magnetic field. By using the conservation of the magnetic flux quanta for collisions, we then argue that photon also carries a magnetic flux quantum of ±Φ₀ = ±(hc/e) with itself along the propagation direction, where the (+) sign corresponds to the right-hand helicity and (-) one to the left-hand one.

We present tilted-field experiments on a bilayer electron system at ν_T = 1 with negligible tunneling and demonstrate that the spin degree of freedom plays a decisive role in the ground-state phase diagram of the system. We observe that the phase boundary separating the incompressible quantum Hall state and a compressible state at d/ℓ_B = 1.90 (d: interlayer distance, ℓ_B: magnetic length) in a perpendicular field shifts to higher densities with tilt until it saturates at d/ℓ_B = 2.33. We develop a model describing the energies of the competing phases and show that the observed shift of the phase boundary reflects the spin-polarization dependence of the Coulomb and Zeeman energies of the compressible state. A new phase diagram as a function of d/ℓ_B and the Zeeman energy is established and its implications as to the nature of the phase transition are discussed.

We develop a quantum theory to deal with the coherent magnon excitation in monolayer magnetic nanodots induced by a circularly polarized light. In our theoretical model, the exchange interaction, the magnetic dipole interaction and the light-matter interaction are all taken into account and an effective dynamic equations governing the magnon excitation is derived by a continuum approximation. Our theoretical model shows that the helicity of light and the magnetic dipole interaction govern the magnon excitation and result in the occurrence of various patterns for the spin z-component distribution. We present a scheme to manipulate the single-mode magnon excitation by properly tuning the light frequency.

The configurations, electronic and spin of the FeO–HCNO clusters are calculated at the PW91 level. The results show that the Fe atom of FeO molecule prefers to interact with the O and N atoms of HCNO molecule and the corresponding FeO–HCNO cluster possesses highest kinetic stability. For this lowest-energy FeO–HCNO clusters, the 2p3d orbitals of O and N atoms obtain more electrons than the 2s orbital of the two atoms loss. In the isomer (6) which O atoms occur at the same ends of the FeO and HCNO fragments, it leads to increase the dipole moment. As for the axisymmetric isomer (1), the total spin is zero due to upward spin is perfectly offset by the downward spin.

In this review, we present the recent discovery and confirmation of a new negative molecular ion, the ${\text{CH}}_4^{-}$ anion. The experimental identification of this high-spin exciplex was difficult because it overlaps with the negative oxygen ion commonly present as a contaminant in vacuum systems and with the same mass-spectrometric signature. Born–Oppenheimer molecular dynamics (BOMD) simulations finally reveal that this anion is a quartet ($S=3/2$) metastable species, which leads to the formation of a molecular (${\text{CH}}_2:H_2{)}^{-}$ excited complex.

Flexible solar cells have drawn wide attention because of their high photoelectric conversion efficiency, convenient preparation, excellent bendability and lower cost advantages. This paper introduces the effect of mesoporous layer on the morphology of CH₃NH₃PbI₃ films. The uniformity and optical transmittance of the different films were also studied in detail. By adjusting the ratio of TiO₂ and ZrO₂, mesoporous structure of CH₃NH₃PbI₃ perovskite solar cells were prepared by two-step spin coating. The fabricated films were investigated by XRD, SEM and spectrophotometer. The results indicate that perovskite layers have good surface morphology, density and coverage with TiO₂ and ZrO₂ composition ratio of 1:1. These well-structured thin films lay a good foundation for the preparation of high performance flexible perovskite solar cells.

The configurations, electronic and spin of the FeN–HNCO clusters are calculated at PW91 basis set. The results indicate that a chain structure of H–N–N–Fe–C–O possesses the highest structural and kinetic stability. The FeN–HNCO cluster which possesses an Fe–N–C–N quadrangular ring displays the highest adsorption capacity between FeN and HNCO. The isomer (16) which possesses the chain configuration has higher kinetic activity. The $2p3d$ orbitals of C and N atoms of the FeN–HNCO clusters gain electrons and the $2s$ orbital of C and N atoms of the FeN–HNCO clusters loss electrons. The chain structure of the isomer (17) has the largest total spin (2.955 ${\mu }_B$/atom) than the others.

The configurations, electronic and spin of the FeO–HNCO clusters are investigated at PW91 method. The calculated results show that the Fe–O–C–N four-member ring preferred to form the FeO–HNCO cluster and it has higher kinetic stability. The isomer which possesses an Fe–O–C triangle ring has higher kinetic activity. The hybridization of sp orbital of C and N atoms of the FeO–HNCO clusters is stronger. For the lowest-energy FeO–HNCO cluster, the Fe and O atoms have the opposite spin direction.

More and more studies indicate that the effects of quantum size and energy level statistics play a crucial role in the thermodynamic properties of ultrasmall metallic grains. This paper aims to investigate how they affect the specific heat of ultrasmall metallic grains in magnetic field. As the particle size decreases, fluctuation effects and the impact of energy level separation are becoming more and more important. The method of static path approximation (SPA) is adopted to handle the fluctuation effect. Random matrix theory (RMT) is adopted due to its successful description of the energy level of metal nanoparticles. The normalized specific heat of several typical temperatures and electron spins were taken in the calculation, and the results were analyzed. It was found that spin and the spin-orbit coupling affect the specific heat very obviously, and the suppressed high spin weakens the contribution of electrons to the heat capacity.

In this paper, molecular dynamics simulations are performed on a [10, 10]/[5, 5] carbon nanotube-based oscillator. In our work, we observed a spin phenomenon of the inner tube when it oscillated in an isolated oscillator system. If there exist a rocking motion when the inner tube started to oscillate, an axial torque would be observed, and it would drive the inner tube to spin. When the oscillation became stable, the torque almost vanished, and the spin was stabilized with a constant frequency of 21.78 GHz. Such a spin phenomenon was also observed when the oscillator system was at a room temperature of 300 K. However, both magnitude and direction of the spin angular velocity varied from time to time, even after the oscillation of the inner tube stopped due to the energy dissipation.

The model of weak localization in 2D semiconductor structures in the whole range of classically weak magnetic fields in the presence of the Elliot–Yafet spin relaxation has been developed. It was shown that the spin–orbit interaction influences the value of magnetoresistance in small magnetic fields (within diffusion approximation) and when diffusion approximation is no longer valid.

For a massive spin 1/2 field, we present the reduced spin and helicity density matrix, respectively, for the same pure one particle state. Their relation has also been developed. Furthermore, we calculate and compare the corresponding entanglement entropy for spin and helicity within the same inertial reference frame. Due to the distinct dependence on momentum degree of freedom between spin and helicity states, the resultant helicity entropy is different from that of spin in general. In particular, we find that both helicity entanglement for a spin eigenstate and spin entanglement for a right handed or left handed helicity state do not vanish, and their Von Neumann entropy has no dependence on the specific form of momentum distribution, as long as it is isotropic.

Heisenberg’s uncertainty principle in a formulation of uncertainties, intrinsic to any quantum system, is rigorously proven and demonstrated in various quantum systems. Nevertheless, Heisenberg’s original formulation of the uncertainty principle was given in terms of a reciprocal relation between the error of a position measurement and the thereby induced disturbance on a subsequent momentum measurement. However, a naive generalization of a Heisenberg-type error-disturbance relation for arbitrary observables is not valid. An alternative universally valid relation was derived by Ozawa in 2003. Though universally valid, Ozawa’s relation is not optimal. Recently, Branciard has derived a tight error-disturbance uncertainty relation (EDUR), describing the optimal trade-off between error and disturbance under certain conditions. Here, we report a neutron-optical experiment that records the error of a spin-component measurement, as well as the disturbance caused on another spin-component to test EDURs. We demonstrate that Heisenberg’s original EDUR is violated, and Ozawa’s and Branciard’s EDURs are valid in a wide range of experimental parameters, as well as the tightness of Branciard’s relation.

This paper aims at reproducing quantum mechanical (QM) spin and spin entanglement results using a realist, stochastic, and local approach, without the standard QM mathematical formulation. The concrete model proposed includes the description of Stern–Gerlach apparatuses and of Bell test experiments. Single particle trajectories are explicitly evaluated as a function of a few stochastic variables that they assumedly carry on. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. Notably, it is shown that the proposed model, despite being both local and realist, is able to violate the Bell–CHSH inequalities by exploiting the coincidence loophole and thus intrinsically renouncing to one of the Bell’s assumptions.

We review the formulation of gauge fields in terms of the frame of reference as well as the space in which the frame is defined. We highlighted some recent applications of gauge physics in the momentum space — in the modern fields of the spin Hall effect, the magnon Hall, the optical Magnus and the graphene valley Hall. General procedures of gauge transformation which lead to the construction of the gauge curvature and the equations of motion (EOM) are outlined. Central to this review is our intention to illustrate the impact of gauge physics on the past and future development of many new research fields emerging out of condensed matter physics, particularly in quantum nanosciences and nanoelectronics.

The molecular approach of a spin model is constructed on the Bethe lattice (BL), and then it is examined in terms of exact recursion relations. Rather than assuming that each BL site is inhabited by a single spin, each site is occupied by two spin-1/2 atoms A and B, forming a molecule. Each molecule is considered to contain two spin-1/2 atoms, as well as $q=3,4,$ or 6 nearest-neighbor molecules. In addition to the internal interactions between the atoms of each molecule, the molecules interact via their atoms in terms of bilinear interaction parameters J. Atoms of a molecule interact with $J_{A^i{B}^i}$, while the molecules interact via their atoms in terms of $J_{A^i{B}^{i+1}}=J_{B^i{A}^{i+1}}$ and $J_{A^i{A}^{i+1}}=J_{B^i{B}^{i+1}}$. After obtaining the magnetizations of each atom in the central molecule of the BL, the average magnetization of the molecule is determined. It is found that the model presents first-and second-order and random phase transitions. The model also displays tricritical, bicritical and end points, in addition to reentrant behavior for appropriate J values.