Constant-cutoff approach to magnetic moments of hyperons

We calculate the magnetic moments of hyperons in the simplified CHK model, with the stabilizing term proportional toe ^–2 omitted, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishna, Sanyuk, Schechter, and Subbaraman, which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. Thus we show that there is qualitative agreement with the experimental values and the accuracy is similar to that obtained with the complete CHK model.     

Alternative generalized master equation approach to the dc phonon-assisted hopping

As the momentum operator has no diagonal elements between localized states, the hopping conduction theory should be formulated in terms of the linear response of the site-off-diagonal elements of the single-electron density matrix to an external field. A theory of this kind, starting from generalized master equations and yielding the dc phonon-assisted hopping conductivity and thermopower is formulated. This is an alternative to the usual approach treating the current conduction via a time-derivative of the electric dipole momentum.Stimulating discussions with Dr. B. Velický turning the present author's attention to his own old ideas about the hopping conduction via off-diagonal elements of the single-electron density matrix are appreciated.     

Another approach to localized magnetic moments in the Hubbard model

By using the band part of the Hubbard Hamiltonian as our starting point, we find that for one electron/atom, with Coulomb repulsion U and bandwidth Δ, there is a single band with sharp Fermi surface and enhanced Pauli paramagnetism for U < Δ, and a splitting into two symmetric bands with local moment formation for U > Δ.     

Reduced dynamics and the master equation of open quantum systems

An exact reduced density operator of a quantum system interacting with a bosonic thermal reservoir is derived by means of the simple algebraic method. The necessary and sufficient condition is found that the time-convolutionless master equation becomes exact up to the second order with respect to the system-reservoir interaction. The result is examined by means of the boson-detector model. The reduced dynamics of a quantum system interacting with a classical reservoir is also discussed.     

Number-resolved master equation approach to quantum transport under the self-consistent Born approximation

We construct a particle-number(n)-resolved master equation(ME) approach under the self-consistent Born approximation(SCBA) for quantum transport through mesoscopic systems.The formulation is essentially non-Markovian and incorporates the interplay of the multi-tunneling processes and many-body correlations.The proposed n-SCBA-ME goes beyond the scope of the BornMarkov master equation,being applicable to transport under small bias voltage,in non-Markovian regime and with strong Coulomb correlations.For steady state,it can recover not only the exact result of noninteracting transport under arbitrary voltages,but also the challenging nonequilibrium Kondo efect.Moreover,the n-SCBA-ME approach is efcient for the study of shot noise.We demonstrate the application by a couple of representative examples,including particularly the nonequilibrium Kondo system.     

The Argyres-Kelley approach to the master equation and an extended theory of superradiance

A discussion of the Argyres-Kelley approach to the Master Equation is set up, and applied to the Bonifacio-Schwendimann-Haake model of Superradiance. Some properties of the approach and its limits are discussed, and an extension of the BSH theory of Superradiance is obtained.     

Unstable state dynamics: A systematic evaluation of the master equation

The master equation for diffusion in a bistable potential is evaluated systematically in terms of the small-noise parameter for the case where the system is initially at the unstable state. The expansion is valid for all times, that is in the initial and intermediate as well as in the final regime. The theory does not involve free fitting parameters and is easily generalized to more complicated processes.     

Measurement master equation

We derive a master equation describing the evolution of a quantum system subjected to a sequence of observations. These measurements occur randomly at a given rate and can be of a very general form. As an example, we analyse the effects of these measurements on the evolution of a two-level atom driven by an electromagnetic field. For the associated quantum trajectories we find Rabi oscillations, Zeno-effect type behaviour and random telegraph evolution spawned by mini quantum jumps as we change the rates and strengths of measurement.     

Force spectroscopy of single multidomain biopolymers: A master equation approach

Experiments using atomic force microscopy for unfolding single multidomain biopolymers cover a broad range of time scales from equilibrium to non-equilibrium. A master equation approach allows to identify and treat coherently three dynamical regimes for increasing linear ramp velocity: i) an equilibrium regime, ii) a transient regime where refolding events still occur, and iii) a saw-tooth regime without any refolding events. For each regime, analytical approximations are derived and compared to numerically investigated examples. We analyze in the framework of this model also a periodic experimental protocol instead of a linear ramp. In this case, a major simplification arises if the dynamics can be restricted to an effectively two-dimensional subspace. For transitions with an intermediate meta-stable state, like Immunoglobulin27, a refined model allows to extract previously unknown molecular parameters related to this meta-stable state.     

Variational approach to configuration interaction

A variational method is developed to determine configuration interaction wave functions. The method is straightforward and is applied to a pairing Hamiltonian with constant matrix elements, for which exact eigenvalues are available. Comparisons are made with the exact results. Calculations can be carried out to any desired degree of accuracy. The method is also applied to a Hamiltonian that has neutron-neutron, proton-proton, and neutron-proton pairing. No difficulties are found in extending the method to this Hamiltonian that has many collective modes. In practice, the method scales linearly with , where is the number of variational basis states.     

The sub master equation

Three postulates are proposed concerning the probabilistic dynamics of chemically reactive systems: the occurrence of the elementary event is a random variable characterized by a Poisson process; the state of the chemical system is a multivariate random variable characterized by a Markov process; the identity of any chemical species in the system is an independent random variable. These postulates when applied to chemically reactive systems in a uniform manner lead to a hierarchy of equations describing in detail how eachk subpopulation varies with time. By summing over all permutations of the equation forf _n ⁽ⁿ⁾ (e ₁, ...,e _n ;t) we obtain the usual master equation. This paper focuses on the simple isomerization reaction.     

The approach to hard-sphere brownian motion: Variational eigenfunctions and evaluation of the Rayleigh-Fokker-Planck equation

We present detailed tabulations of the first few eigenfunctions of the hard-sphere energy scattering kernel for a test-particle in a background heat-bath. Calculations, for a range of heat bath/test particle mass-ratios between $\text{1}\text{8}$ and $\text{1}\text{1024}$, were carried out by a Rayleigh-Ritz method using the exact solutions of the hard-sphere Fokker-Planck equation as a basis set and supplement our previously-published results for the eigenvalues alone. The results, given as expansion coefficients in this representation thus also serve to verify the accuracy of the Fokker-Planck equation itself, the departure from this equation being reflected in the off-diagonal contributions in the Rayleigh-Ritz expansion eigenvectors.As expected, the tendency towards brownian motion behaviour with decrease in the mass-ratio parameter shows itself in a progressive convergence of a larger and larger subset of the true eigenfunctions to the corresponding Fokker-Planck set, beginning with the eigenvalue of lowest index. The class of probability distributions whose evolution is satisfactory predicted by the Fokker-Planck equation is then precisely the class that can be adequately expanded in terms of this incomplete subset. In keeping with the approximations introduced in the derivation of the Fokker-Planck equation and the qualitative nature of the hard-sphere eigenvalue spectrum, the results confirm quantitatively the considerable restrictions which the former imposes upon acceptable solution functions, excluding in particular both short-time behaviour and solutions of insufficient smoothness. A mean-square criterion for accuracy of the Fokker-Planck solutions is suggested and examined in the light of our numerical results.     

New approach to spin dynamics simulation in magnetic system

New approach to spin dynamics simulation in magnetic system is presented. In the approach, we substitute new algorithm for Landau-Lifshitz-Gilbert dynamics, which enable us to achieve the final stable state of magnetic system much faster than traditional spin dynamics simulation. A square-shaped sample with 32×32×4 size under different conditions is calculated. Our results show the new approach can largely reduce the computational time.     

Some approximate solutions to the discrete master equation

Recent mathematical developments on approximate diffusionlike solutions to the master equation are summarized. The technique is applied to two master equations of physical interest-one that describes the phenomenon of superradiance and a second that characterizes generation-recombination noise in semiconductors. For this second case, some previously obtained equilibrium results are found and the extension of these results to finite times is given.     

Some comments on approximations to the master equation

A common strategy for approximating a master equation is to replace it by a diffusion-like equation. Many methods for deriving the form of such an equation have been suggested in the literature. We compare two of these in the light of an example in which the master equation can be solved exactly. One of these is the van KampenΩ-expansion, which generally does not give a useful approximation to the equilibrium solution, and the second is a technique which preserves the noise-free dynamics and gives the correct equilibrium solution. It is shown that the second moment calculated in the latter approximation is not an accurate one at short times. The difficulty is the restriction of the approximating equation to the diffusion form.     

Escape from a fluctuating system: a master equation and trapping approach

We present a general solution for the mean exit time in a system with on-site fluctuations between two configurations described by a master equation. The coupled configurations represent a spatially discretized version of an escape over a fluctuating barrier [C. R. Doering and J. C. Gadoua, Phys. Rev. Lett. 69, 2318 (1992)], and passage through modulating channels. Based on the general properties of the mean exit time, we obtain a simple solution for a coupled "birth" and "death" case that exhibits resonant activation. Within this exactly solvable model we derive analytically the optimal fluctuating rate, which is sensitive to the initial condition and scales as 1/n, where n is the system size. Our approach unifies a number of escape problems and points towards the generality of resonant activation.     

Theory of localized magnetic moments in metals I finite cluster approach

The origin of localized magnetic moments formation in metals is investigated theoretically using a self-consistent local spin density molecular cluster approach. Clusters with up to 55 atoms are employed to describe isolated impurity local moment behavior in the cases of Fe$\text{Ag}$ and Fe$\text{Pd}$. Densities of states and spin magnetic moments were determined and compared with results of spectroscopic (notably photoemission) and magnetization measurements, respectively. In the case of a noble metal host, the spin magnetization density is found to be highly localized around the Fe site; the iron moment is ≈ 3.9μ_B and the polarization of the host Ag atoms is small. In the case of a transition metal host, the iron moment is ≈ 3.2 μ_B but here the strong hybridization of the Fe-3d and Pd-4d states results in a large induced magnetic moment in the host PD metal — in essential agreement with experiment for this giant moment system.     

Variational method for the nonlinear dynamics of an elliptic magnetic stagnation line

The nonlinear evolution of the kink instability of a plasma with an elliptic magnetic stagnation line is studied by means of an amplitude expansion of the ideal magnetohydrodynamic equations. Wahlberg et al. [12] have shown that, near marginal stability, the nonlinear evolution of the stability can be described in terms of a two-dimensional potential U(X,Y), where X and Y represent the amplitudes of the perturbations with positive and negative helical polarization. The potential U(X,Y) is found to be nonlinearly stabilizing for all values of the polarization. In our paper a Lagrangian and an invariant variational principle for two coupled nonlinear ordinal differential equations describing the nonlinear evolution of the stagnation line instability with arbitrary polarization are given. Using a trial function in a rectangular box we find the functional integral. The general case for the two box potential can be obtained on the basis of a different ansatz where we approximate the Jost function by polynomials of order n instead of a piecewise linear function. An example for the second order is given to illustrate the general case. Some considerations concerning solar filaments and filament bands (circular or straight) are indicated as possible applications besides laboratory experiments with cusp geometry corresponding to quadripolar cusp geometries for some clouds and thunderstorms.     

Exchange magnetic moments

Exchange magnetic moments are investigated by adopting a phenomenological approach and a field theoretical model. Their contributions are estimated for nuclei with a particle or hole outside a closed shell. They are expressed in terms of corrections of gyromagnetic factors.