Competition between crystal field splitting and Hund’s rule coupling in two-orbital magnetic metal-insulator transitions

Competition between crystal field splitting and Hund’s rule coupling in magnetic metal-insulator transitions of half-filled two-orbital Hubbard model is investigated by multi-orbital slave-boson mean field theory. We show that with the increase of Coulomb interaction, the system firstly transits from a paramagnetic (PM) metal to a Néel antiferromagnetic (AFM) Mott insulator, or to a nonmagnetic orbital insulator, depending on the competition of crystal field splitting and the Hund’s rule coupling. The AFM Mott insulating, PM metallic and orbital insulating phases are not, partially and fully orbital polarized, respectively. For a small J _H and a finite crystal field, the orbital insulator is robust. These results demonstrate that large crystal field splitting favors the formation of the orbital insulating phase, while large Hund’s rule coupling tends to destroy it, driving the low-spin to high-spin transition.     

Competition between BCS-pairing and “moth-eaten effect” in BEC–BCS crossover

We study the change in condensation energy from a single pair of fermionic atoms to a large number of pairs interacting via the reduced BCS potential. We find that the energy-saving due to correlations decreases when the pair number increases because the number of empty states available for pairing gets smaller (“moth-eaten effect”). However, this decrease dominates the 3D kinetic energy increase of the same amount of noninteracting atoms only when the pair number is a sizable fraction of the number of states available for pairing. As a result, in BEC–BCS crossover of 3D systems, the condensation energy per pair first increases and then decreases with pair number while in 2D, it always is controlled by the “moth-eaten effect” and thus simply decreases.     

Is the quantum Hall effect influenced by the gravitational field?

Most of the experiments on the quantum Hall effect (QHE) were made at approximately the same height above sea level. A future international comparison will determine whether the gravitational field g(x) influences the QHE. In the realm of (1+2)-dimensional phenomenological macroscopic electrodynamics, the Ohm-Hall law is metric independent ("topological"). This suggests that it does not couple to g(x). We corroborate this result by a microscopic calculation of the Hall conductance in the presence of a post-Newtonian gravitational field.     

Can one derive the Schwartzschild line-element without the field equations?

In 1944 W.Lenz has conceived an ingenious derivation of the Schwartzschild line Element for weak gravitational fields, without using the field equations ofEinstein. The derivation is based only on the Principle of Equivalence and the conservation of energy in the Newtonian approximation. Later M.Köhler raised some doubts how far this derivation is correct. Our aim is to show thatKohler's criticism can be met andLenz's derivation is correct.     

Can an effect precede its cause? A model of a noncausal world

The world appears causal in the sense that the result of a measurement may depend on the past history of the observed system, but not on what the experimenter will do with the system after the measurement. This raises the question whether noncausality at a macroscopic level would necessarily lead to an unreasonable world. The study of a model world with axiomatically well-specified properties shows that noncausal systems can be discussed in a logically consistent manner so that noncausality might well exist in the real world as a weak, but so far overlooked, effect.     

Hexadecapolar Kondo effect in URu2Si2?

We derive the coupling of a localized hexadecapolar mode to conduction electrons in tetragonal symmetry. The derivation can be easily adapted to arbitrary multipoles in an arbitrary environment. We relate our model to the two-channel Kondo (2CK) model and show that for an f(2) configuration a relevant crystal field splitting in addition to the 2CK interaction is intrinsic to tetragonal symmetry. We discuss possible realizations of a hexadecapolar Kondo effect in URu(2)Si(2). Solving our model we find good agreement with susceptibility and specific heat measurements in Th(1-x)U(x)Ru(2)Si(2) (x?1).     

Can gravity distinguish between Dirac and Majorana neutrinos?

We show that spin-gravity interaction can distinguish between Dirac and Majorana neutrino wave packets propagating in a Lense-Thirring background. Using time-independent perturbation theory and the gravitational phase to generate a perturbation Hamiltonian with spin-gravity coupling, we show that the associated matrix element for the Majorana neutrino differs significantly from its Dirac counterpart. This difference can be demonstrated through significant gravitational corrections to the neutrino oscillation length for a two-flavor system, as shown explicitly for SN 1987A.     

Magnetic ordering and the Kondo effect in the alloys,Ce2Co1−xPdxSi3

The compound Ce₂CoSi₃, crystallizing in a AlB₂-derived hexagonal structure, has been recently identified as a Kondo lattice with a non-magnetic ground state. Here, we report the influence of gradual replacement of Co by Pd on the magnetic behaviour in the pseudo-ternary solid solution, Ce₂Co_1−xPd_xSi_3, by magnetization (2–300 K), electrical resistivity (2–300 K) and heat-capacity (0.7–30 K) measurements to bring out a transformation from non-magnetic to magnetic ordering. Distinct features attributable to the existence of a competition between the Kondo effect and magnetic ordering with varying x and temperature are observed in the electrical resistivity data. The results reveal that small substitutions of Pd (x=0.2–0.3) are sufficient to induce magnetic ordering of the Ce ions at low temperatures. The strength of the Kondo interaction as indicated by the paramagnetic Curie temperature decreases monotonically with increasing Pd content. A notable finding is that there are qualitative changes in the isothermal magnetization data in the magnetically ordered state, as if there are modifications in the magnetic structure with changes in the Co/Pd composition. The importance of electronic structure relative to unit-cell volume in deciding magnetic characteristics of this class of compounds is brought out taking into account the trends in the magnetic behaviour of isostructural Ce compounds.     

Can the spin-orbit interaction break the channel degeneracy (conservation) of the two-channel orbital Kondo problem?

Two-level systems (TLS) interacting with conduction electrons are possibly described by the two-channel Kondo Hamiltonian. In this case the channel degeneracy is due to the real spin of the electrons. The possibility of breaking that degeneracy (conservation) has interest on his own. In fact, we show that the interaction of the conduction electrons with a spin-orbit scatterer nearby the TLS leads to the breaking of the channel degeneracy (conservation) only in the case of electron-hole symmetry breaking. The generated channel symmetry breaking TLS-electron couplings are, however, too weak to result in any observable effects.Received: 21 October 2003, Published online: 8 December 2003PACS: 72.15.Cz Electrical and thermal conduction in amorphous and liquid metals and alloys - 72.10.Fk Scattering by point defects, dislocations, surfaces, and other imperfections (including Kondo effect) - 71.55.-i Impurity and defect levels     

Competition, efficiency and collective behavior in the “El Farol” bar model

The El Farol bar model, proposed to study the dynamics of competition of agents in a variety of contexts (W.B. Arthur, Amer. Econ. Assoc. Pap. Proc. 84, 406 (1994)) is studied. We characterize in detail the three regions of the phase diagram (efficient, better than random and inefficient) of the simplest version of the model (D. Challet, Y.-C. Zhang, Physica A 246, 407 (1997)). The efficient region is shown to have a rich structure, which is investigated in some detail. Changes in the payoff function enhance further the tendency of the model towards a wasteful distribution of resources. Received 13 November 1998     

Periodic behavior of collapse–revival phenomenon in the full nonlinear interaction between a three-level atom and a single-mode field

In this paper based on a generalization of the Jaynes–Cummings model we solve the dynamical Hamiltonian describing the interaction between a (Λ$\Lambda$ or V-type) three-level atom and a single-mode field in the “full nonlinear regime” and then the analytical form of state vector of the system is explicitly obtained. In this manner, we encountered with “intensity-dependent detuning” as well as “intensity-dependent atom–field coupling” in our two models. Via choosing an appropriate deformation function (which imposes nonlinearity to the system) we consider the influence of Kerr-like medium from which the resonance condition for a selected number of quanta is achieved (selective transition is occurred). Furthermore, by these considerations, we may find the optimum values for atom–field coupling constants which provide a regular periodic behavior of probability amplitudes for the two considered atomic systems. Moreover, to show this periodic time behavior, the temporal evolution of the probability of the allowed atomic transitions as well as the Mandel parameter (as a non-classical sign) is depicted for various circumstances. As is observed, complete revivals may appear in some particular situations.     

Competition between Jahn-Teller effect and spin-orbit coupling in Td Au20 ±γ, γ = 1,2,3

In this work we explored the competition between spin-orbit and Jahn-Teller effects as decisive influences in the ground states of the T_d Au₂₀ ^±γ (γ=1,2,3). All our electronic calculations were based in the relativistic density functional theory in the zeroth-order regular approximation (ZORA) to the Dirac equation. Calculations were done in both versions of ZORA: scalar relativistic and full-relativistic including the spin-orbit interaction. We concluded that for the Au₂₀ ^-3 ion is necessary to use a full-relativistic theory in order to predict a symmetry-lowering from tetrahedral. We predict a trigonal C_3v isomeric form for this trianion due to a Jahn-Teller distortion of its parent T_d. For the rest of ions we found a tendency to conserve their pristine tetrahedral configurations. In these cases we found one of both possibilities: a quenching of the vibronic interaction by spin-orbit coupling or simply a weak Jahn-Teller effect which is not enough to distort appreciably the cluster.     

Network correlation between investor’s herding behavior and overconfidence behavior

It is generally accepted that herding behavior and overconfidence behavior are unrelated or even mutually exclusive.However,these behaviors can both lead to some similar market anomalies,such as excessive trading volume and volatility in the stock market.Due to the limitation of traditional time series analysis,we try to study whether there exists network relevance between the investor’s herding behavior and overconfidence behavior based on the complex network method.Since the investor’s herding behavior is based on market trends and overconfidence behavior is based on past performance,we convert the time series data of market trends into a market network and the time series data of the investor’s past judgments into an investor network.Then,we update these networks as new information arrives at the market and show the weighted in-degrees of the nodes in the market network and the investor network can represent the herding degree and the confidence degree of the investor,respectively.Using stock transaction data of Microsoft,US S&P 500 stock index,and China Hushen 300 stock index,we update the two networks and find that there exists a high similarity of network topological properties and a significant correlation of node parameter sequences between the market network and the investor network.Finally,we theoretically derive and conclude that the investor’s herding degree and confidence degree are highly related to each other when there is a clear market trend.     

Can D'yakonov–Perel' effect cause spin dephasing in GaAs(110) quantum wells?

Current theory [Fiz. Tekh. Popluprovodn. 20 (1986) 178; Sov. Phys. Semicond. 20 (1986) 110] indicates that the D'yakonov–Perel' (DP) mechanism is unable to cause spin dephasing in quantum well (QW) with [110] growth direction. We point out that this is no longer true when the many-body inhomogeneous broadening effect of the DP term is taken into account. Based on our many-body theory [J. Supercond. 14 (2001) 245], by solving the kinetic Bloch equations, we show that the DP term contributes to the spin dephasing in (110) QW. The spin dephasing is also compared with that in (100) QW.     

Competition between aggregation and migration processes of a multi-species system

We propose a solvable multi-species aggregation--migration model, in which irreversible aggregations occur between any two aggregates of the same species and reversible migrations occur between any two different species. The kinetic behaviour of an aggregation--migration system is then studied by means of the mean-field rate equation. The results show that the kinetics of the system depends crucially on the details of reaction events such as initial concentration distributions and ratios of aggregation rates to migration rate. In general, the aggregate mass distribution of each species always obeys a conventional or a generalized scaling law, and for most cases at least one species is scaled according to a conventional form with universal constants. Moreover, there is at least one species that can survive finally.     

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.     

Competition between α-decay and β-decay for heavy and superheavy nuclei

In this work, the β-stable region for Z 90 is proposed based on a successful binding energy formula.The calculated β-stable nuclei in the β-stable region are in good agreement with the ones obtained by Mo¨ller et al. The half-lives of the nuclei close to the β-stable region are calculated and the competition between α-decay andβ-decay is systematically investigated. The calculated half-lives and the suggested decay modes are well in line with the experimental results. The decay modes are mostly β--decay above the β-stable region. Especially for Z 111,all the decay modes are β--decay. Regarding the nuclei above the β-stable region, α-decay and β--decay(α+β-)can occur simultaneously when Z 112. This is a very interesting phenomenon. The competition between α-decay and β-decay is very complex and drastic below the β-stable region. The predictions for half-lives and decay modes of the nuclei with Z =107–110 are presented in detail.