Kinetic theory of long-range interacting systems with angle–action variables and collective effects

We develop a kinetic theory of systems with long-range interactions taking collective effects and spatial inhomogeneity into account. Starting from the Klimontovich equation and using a quasilinear approximation, we derive a Lenard–Balescu-type kinetic equation written in angle–action variables. We confirm the result obtained by Heyvaerts [Heyvaerts, Mon. Not. R. Astron. Soc. 407, 355 (2010)] who started from the Liouville equation and used the BBGKY hierarchy truncated at the level of the two-body distribution function (i.e., neglecting three-body correlations). When collective effects are ignored, we recover the Landau-type kinetic equation obtained in our previous papers [P.H. Chavanis, Physica A 377, 469 (2007); J. Stat. Mech., P05019 (2010)]. We also consider the relaxation of a test particle in a bath of field particles. Its stochastic motion is described by a Fokker–Planck equation written in angle–action variables. We determine the diffusion tensor and the friction force by explicitly calculating the first and second order moments of the increment of action of the test particle from its equations of motion, taking collective effects into account. This generalizes the expressions obtained in our previous works. We discuss the scaling with N$N$ of the relaxation time for the system as a whole and for a test particle in a bath.     

Killing spinors for the bosonic string and Kaluza–Klein theory with scalar potentials

The paper consists mainly of two parts. In the first part, we obtain well-defined Killing spinor equations for the low-energy effective action of the bosonic string with the conformal anomaly term. We show that the conformal anomaly term is the only scalar potential that one can add into the action that is consistent with the Killing spinor equations. In the second part, we demonstrate that Kaluza–Klein theory can be gauged so that the Killing spinors are charged under the Kaluza–Klein vector. This gauging process generates a scalar potential with a maximum that gives rise to an AdS spacetime. We also construct solutions of these theories.     

Topological phase transition in anisotropic square-octagon lattice with spin–orbit coupling and exchange field

We investigate the topological phase transitions in an anisotropic square-octagon lattice in the presence of spin–orbit coupling and exchange field. On the basis of the Chern number and spin Chern number, we find a number of topologically distinct phases with tuning the exchange field, including time-reversal-symmetry-broken quantum spin Hall phases, quantum anomalous Hall phases and a topologically trivial phase. Particularly, we observe a coexistent state of both the quantum spin Hall effect and quantum anomalous Hall effect. Besides, by adjusting the exchange filed, we find the phase transition from time-reversal-symmetry-broken quantum spin Hall phase to spin-imbalanced and spin-polarized quantum anomalous Hall phases, providing an opportunity for quantum spin manipulation. The bulk band gap closes when topological phase transitions occur between different topological phases. Furthermore, the energy and spin spectra of the edge states corresponding to different topological phases are consistent with the topological characterization based on the Chern and spin Chern numbers.     

Electromagnetic field quantization and input–output relation for anisotropic magnetodielectric metamaterial

A phenomenological quantization of electromagnetic field is introduced in the presence of the anisotropic magnetodielectric metamaterial.For a single layer structure with the anisotropic metamaterial,input–output relations of quantized radiation are derived using the Green-function approach.Based on these relations,the reflectance of the linearly polarized wave through this structure is calculated.The results show that different resonant peaks of reflectance appear for different polarized waves and indicate the use of the anisotropic metamaterial as a reflector for a certain polarized wave.Furthermore it is found that such a structure can realize the resonant gap with the increase of the thickness.Finally the effects of the absorption are considered and we find that the above properties do not change with the introduction of the absorption.     

Critical behavior and phase diagrams of a spin-1 Blume–Capel model with random crystal field interactions: An effective field theory analysis

A spin-1 Blume–Capel model with dilute and random crystal fields is examined for honeycomb and square lattices by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. For dilute crystal fields, we have given a detailed exploration of the global phase diagrams of the system in _kBTc/J−D/J$k_B{T}_c/J-D/J$ plane with the second and first order transitions, as well as tricritical points. We have also investigated the effect of the random crystal field distribution characterized by two crystal field parameters D/J$D/J$ and △/J$△/J$ on the phase diagrams of the system. The system exhibits clear distinctions in a qualitative manner with coordination number q$q$ for random crystal fields with △/J,D/J≠0$△/J,D/J\ne 0$. We have also found that, under certain conditions, the system may exhibit a number of interesting and unusual phenomena, such as reentrant behavior of first and second order, as well as a double reentrance with three successive phase transitions.     

Constant volume exponential solutions in Einstein–Gauss–Bonnet flat anisotropic cosmology with a perfect fluid

In this paper we investigate the constant volume exponential solutions (i.e. the solutions with the scale factors change exponentially over time so that the comoving volume remains the same) in the Einstein–Gauss–Bonnet gravity. We find conditions for these solutions to exist and show that they are compatible with any perfect fluid with the equation of state parameter \(\upomega <1/3\) if the matter density of the Universe exceeds some critical value. We write down some exact solutions which generalize ones found in our previous paper for models with a cosmological constant.     

The nature of singularity in multidimensional anisotropic Gauss–Bonnet cosmology with a perfect fluid

We investigate dynamics of (4 + 1) and (5 + 1) dimensional flat anisotropic Universe filled with a perfect fluid in the Gauss–Bonnet gravity. An analytical solutions valid for particular values of the equation of state parameter w = 1/3 have been found. For other values of w structure of cosmological singularity have been studied numerically. We found that for w > 1/3 the singularity is isotropic. Several important differences between (4 + 1) and (5 + 1) dimensional cases are discussed.     

Hubbard model on an anisotropic checkerboard lattice at finite temperatures: Magnetic and metal–insulator transitions

We study magnetic and Mott transitions of the Hubbard model on the geometrically frustrated anisotropic checkerboard lattice at half filling using cellular dynamical mean-field theory. Phase diagrams over a wide area of the parameter space are obtained by varying the interparticle interaction strength, geometric frustration strength, and temperature. Our results show that frustration and thermal fluctuations play a competing role against the interactions and in general favor a metallic phase without antiferromagnetic order. Due to their interplay, the system exhibits competition between antiferromagnetic insulator, antiferromagnetic metal, paramagnetic insulator, and paramagnetic metal phases in the intermediateinteraction regime. In the strong-interaction limit, which reduces to the Heisenberg model, our result is consistent with previous studies.     

Quantum-invariant theory and the evolution of a Dirac field in Friedmann–Robertson–Walker flat space-times

On the basis of the generalized invariant formulation, the invariant-related unitary transformation method is used to study the evolution of a quantum Dirac field in Friedmann–Robertson–Walker spatially flat space-times. We first solve the functional Schr?dinger equation for a free Dirac field and obtain the exact solutions. We then investigate the way of extending the method to treat the case in which there is an interaction between the Dirac field and a scalar field. Received: 17 July 1999 / Published online: 6 March 2000     

Comment on ＇The scale-transformation of electromagnetic theory and its applications＇, ＇Distribution characteristic of scattering field for an ellipsoidal target irradiated by an electromagnetic wave from an arbitrary direction＇ and ＇Electric fields inside and outside an anisotropic dielectric sphere＇

It is shown that the ＇scale-transformation＇ method proposed by Li Ying-Le et al. is not applicable to the Maxwell theory.     

Dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model in an oscillating field: the effective-field theory based on the Glauber-type stochastic dynamics

Using the effective-field theory based on the Glauber-type stochastic dynamics (DEFT), we investigate dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model under an oscillating magnetic field. We presented the dynamic phase diagrams in (T/J, h₀/J), (D/J, T/J) and (K/J, T/J) planes, where T, h₀, D, K and z are the temperature, magnetic field amplitude, crystal–field interaction, biquadratic interaction and the coordination number. The dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and special critical points, as well as re-entrant behavior depending on interaction parameters. We also compare and discuss the results with the results of the same system within the mean-field theory based on the Glauber-type stochastic dynamics and find that some of the dynamic first-order phase lines and special dynamic critical points disappeared in the DEFT calculation.     

Spectral and scattering theory for a Schrödinger operator with a class of momentum-dependent long-range potentials

Let be the selfadjoint operator for the static electromagnetic field where W _j for 0, 1, 2, ..., n is a sum of (i) a short-range potential and (ii) a smooth long-range potential decreasing at as |x|^- with in (0, 1]. Then for >1/2, asymptotic completeness holds for the scattering system (H, H ₀).     

Multiplet splittings and other properties from density functional theory: an assessment in iron–porphyrin systems

In transition metal compounds with spin states close in energy, the magnitude and sign of the energy splitting calculated with density functional theory depends strongly on the functional used. Therefore we must turn to additional criteria to assess the level of accuracy and reliability of predictions based on this level of theory. We report optimized geometries, total energies, and Mössbauer quadrupole splitting values for low-spin and high-spin, ferric and ferrous model hemes using a variety of gradient-corrected and hybrid functionals. In one model, the iron–porphyrin is axially ligated by two strong-field imidazole ligands [FeP(Im)₂] and has a low-spin ground state. In the other model complex the axial ligands are two weak-field, water molecules [FeP(H₂O)₂], and have a high-spin ground state. Among all the functionals used (UHF, B3LYP, B3LYP*, BLYP, half-and-half, LSDA), the B3LYP hybrid functional most consistently reproduced the experimental geometry, Mössbauer, and spin state data for the two model hemes. Simply gradient-corrected functionals exhibit strong biases towards low spin states, while Hartree–Fock favours strongly high spin states. These findings suggest that for systems with similar characteristics of several accessible electronic spin configurations, it is imperative to include properties other than just the energy in the assessment of the DFT predictions.