Diagonal representation for a generic matrix valued quantum Hamiltonian

A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a running variable are introduced. This method leads to a formal compact expression for the diagonal Hamiltonian which can be expanded in a power series of the Planck constant. In particular, we provide an explicit expression for the diagonal representation of a generic Hamiltonian to the second order in the Planck constant. This result is applied, as a physical illustration, to Dirac electrons and neutrinos in external fields.     

A molecular dynamics method for simulations in the canonical ensemble

A molecular dynamics simulation method which can generate configurations belonging to the canonical (T, V, N) ensemble or the constant temperature constant pressure (T, P, N) ensemble, is proposed. The physical system of interest consists of N particles (f degrees of freedom), to which an external, macroscopic variable and its conjugate momentum are added. This device allows the total energy of the physical system to fluctuate. The equilibrium distribution of the energy coincides with the canonical distribution both in momentum and in coordinate space. The method is tested for an atomic fluid (Ar) and works well.     

Resonances in the system “piezoelectric emitter-multilayer ultrasonic chamber with losses”

An approach to calculating resonance frequencies and acoustic characteristics of ultrasonic multilayer liquid chambers bordering an air or liquid half-space and loaded to a piezoelectric emitter is proposed. The assumption on the validity of plane motion is accepted. The approach allows for obtaining comprehensive data on physical processes in the chamber. The equation relating electrical admittance of a piezoplate with input impedance of the acoustic load is derived. An unloaded emitter and an emitter loaded to acoustic resistance with constant and frequency-dependent impedances are considered as examples.     

Action principle of Bogoliubov coefficients

It is shown that the Schwinger action principle uniquely determines the Bogoliubov coefficients connecting in- and out-states for an oscillator with a time-dependent spring constant, and hence for a charged particle field in a constant homogeneous electric field. This allows a complete construction of the S-matrix in the external field approximation. Especially it allows an easy calculation of 〈out∥in〉, the vacuum-to-vacuum amplitude, in this approximation. The method is applied to electromagnetism embedded in a non-abelian gauge group.     

Efficient Reconstruction Methods for Nonlinear Elliptic Cauchy Problems with Piecewise Constant Solutions

In this article, a level-set approach for solving nonlinear elliptic Cauchy problems with piecewise constant solutions is proposed, which allows the definition of a Tikhonov functional on a space of level-set functions. We provide convergence analysis for the Tikhonov approach, including stability and convergence results. Moreover, a numerical investigation of the proposed Tikhonov regularization method is presented. Newton-type methods are used for the solution of the optimality systems, which can be interpreted as stabilized versions of algorithms in a previous work and yield a substantial improvement in performance. The whole approach is focused on three dimensional models, better suited for real life applications.     

Phase-field lattice-Boltzmann investigation of dendritic evolution under different flow modes

ABSTRACT

Numerical modelling offers an effective method to investigate the effect of convection on dendritic growth; however, the current numerical approach to modelling convection behaviour is simplified, e.g. only simulating a shear flow by setting a constant inlet velocity and a zero-velocity-gradient outlet boundary condition. In this work, based on a phase-field lattice-Boltzmann approach, the effect of various flow modes on dendritic growth is investigated by introducing an external force term to induce flow. Numerical tests (2-D and 3-D) validate that the results according to the force-induced flow agree well with those by the velocity-imposed flow. Intricate convection effects under complex boundary conditions are discussed in detail. Furthermore, this force-induced flow mode allows additional freedom by eliminating the restriction on the initial position of the nuclei, which provides new ways to the microstructure modelling under complex convection.     

Relativistic motion of a charged particle driven by an ellipticallypolarized electromagnetic wave propagating along a static magnetic field

The relativistic equations of motion of the interaction of a charged particle with an electromagnetic wave of elliptic polarization propagating along the direction of an external and constant magnetic field are solved in exact form. The method of solution is straight forward and allows to recover results previously reported in the literature     

Electron and hole states in a narrow-band semiconductor InSb film in the presence of uniform electrostatic field

The states of charge carriers in a narrow-gap semiconductor InSb film, placed in a uniform electrostatic field, are considered theoretically. We consider the case when the heavy holes are described by the standard dispersion, and Kane’s dispersion law takes place for electrons and for light holes within the framework of two-band mirror model. For a certain range of values of the external field, explicit expressions for the energy spectrum and the envelope wave functions of charge carriers are obtained. Corresponding numerical estimations of allowed range of the external field are derived, for which the proposed approach allows exact analytical solutions.     

On One Possible Generalization of the Regression Theorem

A general approach to derivation of formally exact closed time-local or time-nonlocal evolution equations for non-equilibrium multi-time correlations functions made of observables of an open quantum system interacting simultaneously with external time-dependent classical fields and dissipative environment is discussed. The approach allows for the subsequent treatment of these equations within a perturbative scheme assuming that the system-environment interaction is weak.     

Coherent influence of RF field on the gamma-optical properties of a medium upon crossing-anticrossing of nuclear levels

A new approach to the observation of electromagnetic-induced transparency in gamma optics is proposed. For this purpose, the propagation of a resonant gamma photon in a ⁵⁷Fe magnetic medium affected by an external radiofrequency (RF) field is considered. It is demonstrated that, in the case of crossing-anticrossing, a resonant RF field significantly transforms gamma-optical properties of the medium that become dependent on its parameters. This allows coherent control of the group velocity of gamma photons and controlled filtering of unpolarized gamma radiation in the sample to be realized.     

Analytical evaluation of chromatic dispersion in photonic crystal fibers

We present a two-dimensional modal approach for the evaluation, in an analytical manner, of chromatic dispersion in any kind of optical fiber. It combines an iterative Fourier technique to compute the propagation constant at any fixed wavelength and an analytical procedure to calculate its derivatives. The proposed formulation takes into account the effective anisotropy of the interfaces and allows us to deal with microstructured fibers, in general, and specifically with realistic photonic crystal fibers (PCFs), including arbitrary spatial refractive-index distributions of dispersive and absorbing materials. This fast and accurate numerical technique is extremely useful for both analysis and design. We show some results of analysis of PCFs with high anisotropy, and we also describe PCFs with new dispersive properties.     

A measure of conductivity for lattice fermions at finite density

We study the linear response to an external electric field of a system of fermions in a lattice at zero temperature. This allows to measure numerically the Euclidean conductivity which turns out to be compatible with an analytical calculation for free fermions. The numerical method is generalizable to systems with dynamical interactions where no analytical approach is possible.     

Asymptotically covariantly constant spinor hair on black holes

It is demonstrated, in a straightforward approach, that a static black hole has no spinor hair if we assume that the fields vanish at infinity. We extend this to the case of asymptotically covariantly constant spinors (Witten spinors) which approach a constant value at spatial infinity. We show that with the dominant energy condition and in absence of external spinor sources, Witten spinors must vanish everywhere in the region exterior to a stationary black hole with an horizon in an asymptotically flat space-time.     

Acoustic field induced in spheres with inhomogeneous density by external sources

Acoustic or electromagnetic fields induced in the interior of inhomogeneous penetrable bodies by external sources can be evaluated via well-known volume integral equations. For bodies of arbitrary shape and/or composition, for which separation of variables fails, a direct attack for the solution of these integral equations is the only available approach. In a previous paper by the same authors the scalar (acoustic) field in inhomogeneous spheres of arbitrary compressibility, but with constant density, was considered. In the present one the direct hybrid (analytical-numerical) method applied to the much simpler integral equation for spheres with constant density is generalized to densities that vary with r, theta, or even psi. This extension is by no means trivial, owing to the appearance of the derivatives of both the density and the unknown function in the volume integral, a fact necessitating a more subtle and accuracy-sensitive approach. Again, the spherical shape allows use of the orthogonal spherical harmonics and of Dini's expansions of a general type for the radial functions. The convergence of the latter, shown to be superior to other possible sets of orthogonal expansions, can be further optimized by the proper selection of a crucial parameter in their eigenvalue equation.     

Cell model calculations of dynamic drag parameters in packings of spheres

An external flow approach is used to predict the viscous drag due to oscillating flow in an air-filled stack of fixed identical rigid spheres. Analytical expressions for dynamic and direct current (dc) permeability, high-frequency limit of tortuosity, and the characteristic viscous dimension are derived using a cell model with an adjustable cell radius which allows for hydrodynamic interactions between the spherical particles. The resulting theory requires knowledge of two fixed parameters: the volume porosity and the particle radius. The theory also requires a value for the cell radius. Use of the cell radius corresponding to that of the sphere circumscribing a unit cell of a cubic lattice arrangement is proposed. This is found to enable good agreement between predictions of the new theory and both published data and numerical results for simple cubic and random spherical packings.     

Properties of an adiabatically cooled SK spin glass

Some physical properties of an SK spin glass subject to slow cooling are investigated. Among those are Edwards-Anderson order parameter, energy, field cooled and zero field cooled susceptibilities. The results are compared with predictions from Parisi's solution. Different values are obtained for the field cooled susceptibility whereas other quantities are identical in both calculations. Ultrametricity results in a natural way if adiabatic temperature changes involving cooling and heating periods are considered. Some results are also given for adiabatic cooling in a finite external field and for adiabatic changes of the field at constant temperature. The present setup allows to investigate explicitly the dependence on history at least for adiabatic changes of temperature and external field.     

On the two-loop divergences of supersymmetric gravitation

Using an essentially dispersive approach to renormalization that allows us to consider subdivergences on-shell, we show that in supergravitational 2-loop amplitudes with external gravitons all non-local, non-renormalizable divergences cancel on-shell.     

Model description of the degree of polarization of nonstationary light waves

A theoretical approach is developed that provides the possibility of representing partially polarized radiation in the form of a sum of mutually orthogonal polarized and incoherent components and in the form of a model device with a time-dependent circular birefringence. This approach allows one to apply the vectormatrix Jones method in calculations. The possibility of theoretically determining the degree of polarization of the light passed through a corresponding device placed in an external magnetic field is shown as an illustration.