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991.
Anatoli Polkovnikov 《Annals of Physics》2011,326(2):486-499
We define a diagonal entropy (d-entropy) for an arbitrary Hamiltonian system as Sd=-∑nρnnlnρnn with the sum taken over the basis of instantaneous energy states. In equilibrium this entropy coincides with the conventional von Neumann entropy Sn = −Trρ ln ρ. However, in contrast to Sn, the d-entropy is not conserved in time in closed Hamiltonian systems. If the system is initially in stationary state then in accord with the second law of thermodynamics the d-entropy can only increase or stay the same. We also show that the d-entropy can be expressed through the energy distribution function and thus it is measurable, at least in principle. Under very generic assumptions of the locality of the Hamiltonian and non-integrability the d-entropy becomes a unique function of the average energy in large systems and automatically satisfies the fundamental thermodynamic relation. This relation reduces to the first law of thermodynamics for quasi-static processes. The d-entropy is also automatically conserved for adiabatic processes. We illustrate our results with explicit examples and show that Sd behaves consistently with expectations from thermodynamics. 相似文献
992.
The major purpose of this paper is to clarify the deficiencies identified in the recent paper by Liu et al. (J. Lumin. 130 (2010) 103) as well as to reanalyze the available data and provide corrected results for the orthorhombic crystal field parameters (CFPs) for selected rare-earth ions in garnets. It appears that Liu et al., when utilizing the computer package for standardization of CFPs, have inadvertently confused the properties of CFPs expressed in the Wybourne notation with those in the extended Stevens operator notation. This confusion has led to misinterpretations concerning the orthorhombic standardization transformations and incorrect labeling of the CFP sets as supposedly ‘standardized’ for Yb3+, Pr3+, Nd3+, and Er3+ ions in various garnets. These deficiencies have prompted us to reconsider the CFP sets determined earlier by matching the experimental data, i.e. the orthorhombic spin Hamiltonian parameters (g factors, gi, and hyperfine structure constants, Ai; i=x, y, z) and available optical spectral band positions, with the theoretical data calculated using the complete diagonalization method. To further verify the correctness of the present results the CFPs for orthorhombic Yb3+ centers in Yb3Al5O12 and Yb3Ga5O12 garnets are calculated using the superposition model (SPM), which requires adoption of a well-defined symmetry-adapted axis system (SAAS). Hence, the SPM calculations enable reanalysis of available CFP sets based on the correct standardization procedure and establishing the correspondence between the SAAS and the ‘nominal’ axis systems assigned to fitted CFP sets. Using the proper SAAS and general transformations of the axis systems, the relations between the calculated gi and/or Ai values and the respective principal values determined by EPR experiments can be established. The consistent methodology utilized here may be helpful for proper reanalysis of spectroscopic data for rare-earth and transition-metal ions at orthorhombic symmetry sites in various crystals. 相似文献
993.
R. Milloud S.A. Tashkun 《Journal of Quantitative Spectroscopy & Radiative Transfer》2011,112(3):553-557
The absorption spectrum of nitrous oxide (N2O) has been recorded by Intracavity Laser Absorption Spectroscopy between 12,760 and 12,900 cm−1. The rotational analysis led to an improved determination of rovibrational parameters of the 6ν3 and 6ν3+ν2-ν2 bands of 14N216O. The high J rotational levels of the (0 0 06) and (0 1 16) upper states were found perturbed by an anharmonic interaction. Line intensity values of the 6ν3 band are provided and the main effective dipole moment parameter has been determined. 相似文献
994.
Magnetic and spectroscopic properties of the planar antiferromagnet K2FeF4 are determined by the Fe2+ ions at tetragonal sites. The two-dimensional easy-plane anisotropy exhibited by K2FeF4 is due to the zero field splitting (ZFS) terms arising from the orbital singlet ground state of Fe2+ ions with the spin S=2. To provide insight into the single-ion magnetic anisotropy of K2FeF4, the crystal field theory and the microscopic spin Hamiltonian (MSH) approach based on the tensor method is adopted. Survey of available experimental data on the crystal field energy levels and free-ion parameters for Fe2+ ions in K2FeF4 and related compounds is carried out to provide input for microscopic modeling of the ZFS parameters and the Zeeman electronic ones. The ZFS parameters are expressed in the extended Stevens notation and include contributions up to the fourth-order using as perturbation the spin-orbit and electronic spin-spin couplings within the tetragonal crystal field states of the ground 5D multiplet. Modeling of the ZFS parameters and the Zeeman electronic ones is carried out. Variation of these parameters is studied taking into account reasonable ranges of the microscopic ones, i.e. the spin-orbit and spin-spin coupling constants, and the energy level splittings, suitable for Fe2+ ions in K2FeF4 and Fe2+:K2ZnF4. Conversions between the ZFS parameters in the extended Stevens notation and the conventional ones are considered to enable comparison with the data of others. Comparative analysis of the MSH formulas derived earlier and our more complete ones indicates the importance of terms omitted earlier as well as the fourth-order ZFS parameters and the spin-spin coupling related contributions. The results may be useful also for Fe2+ ions at axial symmetry sites in related systems, i.e. Fe:K2MnF4, Rb2Co1−xFexF4, Fe2+:Rb2CrCl4, and Fe2+:Rb2ZnCl4. 相似文献
995.
《Comptes Rendus Chimie》2014,17(7-8):790-800
Activity and selectivity of bimetallic catalysts for two model reactions, citral hydrogenation in isopropanol and nitrate reduction in water, are reviewed on the basis of results obtained over bimetallic systems prepared in our laboratory, notably by redox techniques. The parent metal is generally a noble metal (Rh, Pd, Pt), while the additive is most often a non-noble metal (Ge, Sn, Cu…) whose oxidation state plays an important role in hydrogenation. Dramatic improvements of the selectivity to unsaturated alcohols are observed in citral hydrogenation with adequate deposition of the additive and pretreatment of the final catalyst. In nitrate reduction, the second metal essentially affects the first step of the process (conversion of nitrate to nitrite) but the global selectivity (limitation of NH3 formation) may be significantly improved by tuning the couple parent metal–additive. Other aspects such as the choice of the support and the optimization of reaction conditions (temperature, pressure, pH effects in water) are also discussed. 相似文献
996.
The longitudinal wave propagating in an elastic rod with a variable cross-section owns wide engineering background, in which the longitudinal wave dissipation determines some important performances of the slender structure. To reproduce the longitudinal wave dissipation effects on an elastic rod with a variable cross-section, a structure-preserving approach is developed based on the dynamic symmetry breaking theory. For the dynamic model controlling the longitudinal wave propagating in the elast... 相似文献
997.
The main objective of this paper is to study the warped product pointwise semi‐slant submanifolds which are isometrically immersed into Sasakian manifolds. First, we prove some characterizations results in terms of the shape operator, under which influence a pointwise semi‐slant submanifold of a Sasakian manifold can be reduced to a warped product submanifold. Then, we determine a geometric inequality for the second fundamental form regarding to intrinsic invariant and extrinsic invariant using the Gauss equation instead of the Codazzi equation. Evenmore, we give some applications of this inequality into Sasakian space forms, and we will investigate the status of equalities in the inequality. As a particular case, we provide numerous applications of the Green lemma, the Laplacian of warped functions and some partial differential equations. Some triviality results for connected, compact warped product pointwise semi‐slant submanifolds of Sasakian space form by means of Hamiltonian and the kinetic energy of warped function involving boundary conditions are established. 相似文献
998.
This paper analyses the properties of the solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. This analysis reveals the presence of a subspace that may provide an appropriate degree of freedom to stabilize the system in the related optimal control problem even in cases where the Riccati equation does not admit a stabilizing solution. 相似文献
999.
This letter studies symmetric and symplectic exponential integrators when applied to numerically computing nonlinear Hamiltonian systems. We first establish the symmetry and symplecticity conditions of exponential integrators and then show that these conditions are extensions of the symmetry and symplecticity conditions of Runge–Kutta methods. Based on these conditions, some symmetric and symplectic exponential integrators up to order four are derived. Two numerical experiments are carried out and the results demonstrate the remarkable numerical behaviour of the new exponential integrators in comparison with some symmetric and symplectic Runge–Kutta methods in the literature. 相似文献
1000.
We establish a general slice theorem for the action of a locally convex Lie group on a locally convex manifold, which generalizes the classical slice theorem of Palais to infinite dimensions. We discuss two important settings under which the assumptions of this theorem are fulfilled. First, using Glöckner's inverse function theorem, we show that the linear action of a compact Lie group on a Fréchet space admits a slice. Second, using the Nash–Moser theorem, we establish a slice theorem for the tame action of a tame Fréchet Lie group on a tame Fréchet manifold. For this purpose, we develop the concept of a graded Riemannian metric, which allows the construction of a path-length metric compatible with the manifold topology and of a local addition. Finally, generalizing a classical result in finite dimensions, we prove that the existence of a slice implies that the decomposition of the manifold into orbit types of the group action is a stratification. 相似文献