Phase Transition of the Isotropic Kondo Hamiltonian:A "Luttinger-Liquid" Description

Analysis of the bosonized Kondo Hamiltonian at zero temperature shows that the interaction between the conduction electrons via a magnetic impurity scattering induces nonlinear couplings between its elementary excitations, which may be described by an effective "Luttinger-liquid". With the Bogoliubov transformation, the corresponding ground-state wave function is obtained. In particular, we are able to treat infrared divergencea led by the strong effective interactions between the conduction electrons for the long wavelength part directly and investigate the nontrivial ferromagnetic-antiferromagnetic transition of the impurity spin. Comparison with the previous studies is also given.     

A simplified linked cluster expansion in the Kondo problem

It is shown that the conduction electron propagator is the average of the propagators evaluated by means of a linked cluster expansion in systems with fixed impurity spin projections. A simple limiting procedure for obtaining these is defined.     

New universal scaling laws of diffusion and Kolmogorov-Sinai entropy in simple liquids

A new universal scaling law relating the self-diffusivities of the components of a binary fluid mixture to their excess entropies is derived using mode coupling theory. These scaling laws yield numerical results, for a hard sphere as well as Lennard-Jones fluid mixtures, in excellent agreement with simulation results even at a low density region, where the empirical scaling laws of Dzugutov [Nature (London) 381, 137 (1996)]] and Hoyt, Asta, and Sadigh [Phys. Rev. Lett. 85, 594 (2001)]] fail completely. A new scaling law relating the Kolmogorov-Sinai entropy to the excess entropy is also obtained.     

Singlet-triplet Hamiltonian for spin excitations in a Kondo insulator

In the nonsymmetric version of the periodic Anderson model for a Kondo insulator, an effective singlet-triplet Hamiltonian Ĥ _s−t with indirect antiferromagnetic f-f exchange is constructed, which makes it possible to analyze the dynamic magnetic susceptibility χ _f (k, ω) of f electrons. Hamiltonian Ĥ _s−t is used to describe the experimentally observed dispersion of the three-level spin excitation spectrum in YbB₁₂. A distinguishing feature of this analysis is the introduction of small-radius singlet and triplet collective f-d excitations that form low- and high-lying spin bands during motion over the lattice.     

A simple derivation of the overlap Dirac operator

We derive the vector-like four-dimensional overlap Dirac operator starting from a five-dimensional Dirac action in the presence of a delta-function space–time defect. The effective operator is obtained by first integrating out all the fermionic modes in the fixed gauge background, and then identifying the contribution from the localized modes as the determinant of an operator in one dimension less. We define physically relevant degrees of freedom on the defect by introducing an auxiliary defect-bound fermion field and integrating out the original five-dimensional bulk fields.     

A simple derivation of the equation of motion for classical electrodynamics

The equation of motion recently obtained by the author is derived by an elementary method. In addition, this paper contains a careful analysis of three well-known derivations of the (incorrect) Lorentz-Dirac equation, identifying their flaws. The fundamental error in each case is a failure to appreciate that the rate of change of field momentum affects the particle differently according to whether it is an applied field or the self-field. This fundamental physical error can be understood with the aid of a simple analogy.     

Confinement scaling laws for the conventional reversed-field pinch

Mechanical behavior of the Si(111)/Si(3)N4(0001) interface is studied using million atom molecular dynamics simulations. At a critical value of applied strain parallel to the interface, a crack forms on the silicon nitride surface and moves toward the interface. The crack does not propagate into the silicon substrate; instead, dislocations are emitted when the crack reaches the interface. The dislocation loop propagates in the (1; 1;1) plane of the silicon substrate with a speed of 500 (+/-100) m/s. Time evolution of the dislocation emission and nature of defects is studied.     

A simple classical derivation of spin-orbit couplings

A general derivation of spin-orbit couplings for arbitrary velocities is given which is based only on the definition of spin as the angular momentum in a rest frame of the particle and on the equation of motion in a non-inertial frame of reference.     

Mobility in a periodic potential: A simple derivation

A simple derivation is given for the mobility of Brownian particles in a periodic potential in the overdamped regime. The method makes use of the fact that the steady state current density, in response to a uniform external force, is uniform in space and can be expressed as a product of the particle density and mean velocity field. To lowest order in the external force, the particle density is given by the equilibrium density in the absence of the external force.     

Revisiting scaling laws for the diffusion coefficients in simple melts based on the structural deviation from hard-sphere-like case

Molecular simulations of a series of simple melts, including Al, Cu, Ni, Pt, Ti, Si and Ge, are used to study the scaling laws of diffusion coefficients proposed by Rosenfeld and Dzugutov. Our simulation results give strong support to the result that the scaling laws of diffusion coefficients hold true for simple liquids with isotropic many-body interactions but fail for systems with anisotropic interatomic interaction. The failure of the scaling laws in application liquid Si (l-Si) and liquid Ge (l-Ge) is connected to the fact that the excess entropy of them cannot be calculated approximately in terms of the two-body contribution and the original reduction parameters are no longer appropriate. In particular, since the ratio between the positions of the second and first peaks in structure factor ($Q_2/Q_1$) is a direct measure of the structural deviation from the hard-sphere-like case, the temperature dependence of $Q_2/Q_1$ was analyzed. Moreover, in comparison with 1.86, the value of $Q_2/Q_1$ for the hard-sphere-like case, we modified the scaling laws of diffusion coefficients proposed by Rosenfeld and Dzugutov. The modified scaling relations are appropriate not only for simple liquid metals, but also for l-Si and l-Ge with anisotropic interatomic interaction.     

n模二次型哈密顿量对角化的一种简单方法

利用线性量子变换理论，对ｎ模Ｂｏｓｅ（Ｆｅｒｍｉ）体系给出了一种简单的对角化方法。     

Reprint of : The Boltzmann--Langevin approach: A simple quantum-mechanical derivation

We present a simple quantum-mechanical derivation of correlation function of Langevin sources in the semiclassical Boltzmann–Langevin equation. The specific case of electron–phonon scattering is considered. It is shown that the assumption of weak scattering leads to the Poisson nature of the scattering fluxes.     

A novel strong coupling expansion of the QCD Hamiltonian

Introducing an infinite spatial lattice with box length a, a systematic expansion of the physical QCD Hamiltonian in λ = g ^?2/3 can be obtained, with the free part being the sum of the Hamiltonians of the quantum mechanics of spatially constant fields for each box, and interaction terms proportional to λ ⁿ with n spatial derivatives connecting different boxes. As an example, the energy of the vacuum and the lowest scalar glueball is calculated up to order λ ² for the case of SU(2) Yang-Mills theory.     

Polarized coincidence electroproduction scaling laws for the final state

We study the inclusive electroproduction of single hadrons off a polarized target. Bjorken scaling laws and the hadron azimuthal distribution are derived from the quark parton model.The polarization asymmetries scale when the target spin is along the direction of the virtual photon, and (apart from one significant exception) vanish for transverse spin. These results have a simple explanation; emphasis is given both to the general mathematical formalism and to intuitive physical reasoning.Through this framework we consider other cases: quarks with anomalous magnetic moment; renormalization group effects and asymptotic freedom; production of vector mesons (whose spin state is analysed by their decay); relation to large transverse momentum hadron production; and a covariant parton model calculation. We also look into spin-0 partons and Regge singularities.All of these cases (apart from the last two) modify the pattern of conclusions. Vector meson production shows polarization enhancements in the density matrix element ?₀₊; the renormalization group approach does not lead to any significant suppressions. They are also less severe in parton models for large p_T hadrons, and are not supported by the covariantly formulated calculation. The origins of these differences are isolated and used to exemplify the sensitivity that polarized hadron electroproduction has to delicate detail that is otherwise concealed.     

On the derivation of the incompressible Mavier-Stokes equation for Hamiltonian particle systems

We consider a Hamiltonian paticle system interacting by means of a pair potetial. We look at the behavior of the system on a space scale of order ^-1, times of order ^-2 and mean velocities of order , with a scale parameter. Assuming that the phase space density of the particles is give by a series in (the analog of the Chapman-Enskog expansion), the behavior of the system under this rescaling is described, to the lowest order in , by the incompressible Navier-Stokes equations. The viscosity is given in terms of microscopic correlations, and its expression agrees with the Green-Kubo formula.     

High-order connected moments expansion for the Rabi Hamiltonian

We analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large-order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.     

Dynamics of complex systems: scaling laws for the period of boolean networks

Boolean networks serve as models for complex systems, such as social or genetic networks, where each vertex, based on inputs received from selected vertices, makes its own decision about its state. Despite their simplicity, little is known about the dynamical properties of these systems. Here we propose a method to calculate the period of a finite Boolean system, by identifying the mechanisms determining its value. The proposed method can be applied to systems of arbitrary topology, and can serve as a roadmap for understanding the dynamics of large interacting systems in general.