Covariant jump conditions in electromagnetism

A generally covariant four-dimensional representation of Maxwell’s electrodynamics in a generic material medium can be achieved straightforwardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic phenomena are described by two tensor fields, which satisfy Maxwell’s equations. A generic tensorial constitutive relation between these fields is an independent ingredient of the theory. By use of different constitutive relations (local and non-local, linear and non-linear, etc.), a wide area of applications can be covered. In the current paper, we present the jump conditions for the fields and for the energy–momentum tensor on an arbitrarily moving surface between two media. From the differential and integral Maxwell equations, we derive the covariant boundary conditions, which are independent of any metric and connection. These conditions include the covariantly defined surface current and are applicable to an arbitrarily moving smooth curved boundary surface. As an application of the presented jump formulas, we derive a Lorentzian type metric as a condition for existence of the wave front in isotropic media. This result holds for ordinary materials as well as for metamaterials with negative material constants.     

Hydraulic jump in one-dimensional flow

In the presence of viscosity the hydraulic jump in one dimension is seen to be a first-order transition. A scaling relation for the position of the jump has been determined by applying an averaging technique on the stationary hydrodynamic equations. This gives a linear height profile before the jump, as well as a clear dependence of the magnitude of the jump on the outer boundary condition. The importance of viscosity in the jump formation has been convincingly established, and its physical basis has been understood by a time-dependent analysis of the flow equations. In doing so, a very close correspondence has been revealed between a perturbation equation for the flow rate and the metric of an acoustic white hole. We finally provide experimental support for our heuristically developed theory.     

Specific heat jump in non-Fermi superconductors

We derive the jump in the specific heat at T=T _c for a superconductor in a non-Fermi liquid model. We took into consideration the two possible limits in this problem: the spin-charge separation model for a Fermi liquid and the usual non-Fermi liquid model which satisfies the homogeneity relation for the spectral function , ). We also derive the order parameter behavior for these two cases in the vecinity of the critical temperature. Received: 25 January 1998 / Revised: 25 March 1998 / Accepted: 25 March 1998     

Hydraulic jump as a white hole

In the geometry of the circular hydraulic jump, the velocity of the liquid in the interior region exceeds the speed of the capillary-gravity waves (ripplons), whose spectrum is “relativistic” in the shallow water limit. The velocity flow is radial and outward, and thus the relativistic ripplons cannot propagate into the interior region. In terms of the effective 2 + 1 dimensional Painlevé-Gullstrand metric appropriate for the propagating ripplons, the interior region imitates a white hole. The hydraulic jump represents the physical singularity at the white-hole horizon. The instability of the vacuum in the ergoregion inside the circular hydraulic jump and its observation in recent experiments on superfluid ⁴He by Rolley et al. [3] are discussed.     

Specific heat jump in BCS superconductors

An exact analytical expression for the specific heat jump at the critical temperature T_c has been obtained directly from the BCS gap equation for any shape of the energy dependent electronic density of states (DOS). We consider a model which takes into consideration electron-electron repulsion, formulated in the Hubbard model along with the electron-electron attraction due to electron-phonon interaction in the BCS formalism. We have analyzed this expression for constant as well as for the Lorentzian forms of DOS. It is shown that the constant DOS in the simple BCS theory cannot explain the large values of , found in some superconductors. The specific heat versus temperature curve has been found to have a peak, similar to that of Eliashberg theory of superconductivity. The influence of repulsive interaction is very small and occurs mainly at higher temperatures. Received: 26 January 1998     

N-state Markov jump process

A certain N-state Markov jump process is studied in connection with laser mode hopping and phase switching. We show that the Chapman-Kolmogorov-Smoluchowski equations can be solved exactly to yield a simple expression for the transition probability function. Some properties of such a process and its connection with the related pre-gaussian process are examined. We also study the atomic response to excitation by a laser whose phase or frequency exhibits such jumps, and the non-gaussian property of the line shape is discussed.     

Dynamic pressure jump in barrier-discharge excilamps

Data for the pressure jump are used to study thermodynamic processes in barrier-discharge excilamps under the conditions of a diffuse (uniform) discharge and microdischarges. It is shown that a linear relationship between the pressure jump and excilamp radiation intensity can help to control the radiation power.     

Generator estimation of Markov jump processes

Estimating the generator of a continuous-time Markov jump process based on incomplete data is a problem which arises in various applications ranging from machine learning to molecular dynamics. Several methods have been devised for this purpose: a quadratic programming approach (cf. [D.T. Crommelin, E. Vanden-Eijnden, Fitting timeseries by continuous-time Markov chains: a quadratic programming approach, J. Comp. Phys. 217 (2006) 782–805]), a resolvent method (cf. [T. Müller, Modellierung von Proteinevolution, PhD thesis, Heidelberg, 2001]), and various implementations of an expectation-maximization algorithm ([S. Asmussen, O. Nerman, M. Olsson, Fitting phase-type distributions via the EM algorithm, Scand. J. Stat. 23 (1996) 419–441; I. Holmes, G.M. Rubin, An expectation maximization algorithm for training hidden substitution models, J. Mol. Biol. 317 (2002) 753–764; U. Nodelman, C.R. Shelton, D. Koller, Expectation maximization and complex duration distributions for continuous time Bayesian networks, in: Proceedings of the twenty-first conference on uncertainty in AI (UAI), 2005, pp. 421–430; M. Bladt, M. Sørensen, Statistical inference for discretely observed Markov jump processes, J.R. Statist. Soc. B 67 (2005) 395–410]). Some of these methods, however, seem to be known only in a particular research community, and have later been reinvented in a different context. The purpose of this paper is to compile a catalogue of existing approaches, to compare the strengths and weaknesses, and to test their performance in a series of numerical examples. These examples include carefully chosen model problems and an application to a time series from molecular dynamics.     

The effect of zinc concentration on vacancies jump rate, diffusion coefficient and jump length in Cu-Zn ferrite

Samples with the chemical formula Cu_1−xZn_xFe₂O₄ (x=0.2, 0.4, 0.6, 0.8 and 1) were prepared by the standard ceramic method. The dielectric constant and dielectric loss tangent were studied as a function of vacancy jump rate. The results show that the dielectric constant and dielectric loss tangent decrease with increasing vacancy jump rate. In addition, the electron jump length in the octahedral sites was studied as a function of zinc concentration. The increase in jump length with Zn concentration has been attributed to the substitution of Fe⁺³ for Zn²⁺ at the A-sites, which increases the B-B interaction. The increase of diffusion coefficient with increasing Zn concentration was reinforced by the increase of jump rate.     

Pressure jump across normal ionizing shock waves

The pressure jump across normal ionizing shock waves in hydrogen has been measured using piezoelectric probes. The observed pressure jumps exhibit substantial radial variations with average values higher than those predicted by theory.     

Vibrational coordinates in the electron jump model

The role of quantization of vibrational coordinates in the electron jump model of alkali atom, dimer plus halogen molecule collisions is examined. Despite the bound states of the molecule ions involved, a classical approximation may offer good approximation over a wide collision energy range for the energy distributions of the ions in a single electron jump. Some results are calculated for K + Br₂ and K₂ + Br₂. The theory assumes that the electron jump probability is governed by the electronic matrix element H₁₂ alone. Elementary arguments are offered to suggest that this may be a reasonable approximation.     

From two-state jump to Gaussian stochastic processes

A stochastic process, which bridges the two-state jump Markoff process and the Gaussian process, is introduced and fundamental properties of the process are fully analyzed. The resulting expressions are combined with the “partial cumulant” expansion formula to give an exact power spectrum in the form of a continued fraction. A rigorous expression is also obtained for a relaxation function in an analytic form.     

Backward-to-forward jump rates on a tilted periodic substrate

Driven diffusion of a Brownian particle along a one-dimensional lattice is investigated numerically on decreasing its damping constant. The notions of multiple jumps, jump reversal, and backward-to-forward rates are discussed in detail. In particular, we conclude that in the underdamped limit backward jumps are suppressed relative to forward jumps more effectively than previously assumed. The dependence of such a drive-controlled mechanism on the damping constant and the temperature is interpreted analytically.     

Non-linear jump of wave polarization in a plasma

The hysteresis is pointed out of a non-linear dependence of electromagnetic waves polarization near plasma resonance in magnetoactive plasma due to the wave energy. Stable “low-temperature” and “high-temperature” conditions are found of polarization and critical fields corresponding to transitions between them.     

A generalized microscopic model of quantum jump superoperators

In this paper, we discuss a microscopic model for the detector-field system in the theory of the quantum counting process. The detector-field system is described by a generalized Jaynes-Cummings model, from which we derive an analytic expression of the general quantum jump superoperators. To illustrate the universality and convenience of our method, we consider two specific examples with the help of the analytic expression.     

Quantum mechanical model for two-state jump Markovian process

A quantum mechanical model is given which is equivalent to the stochastic dephasing subject to the two-state jump Markovian process. The stochastic variable corresponds to a Hermitian operator of a spin-1/2 system which is embedded in a thermal reservoir, where the time-evolution of the spin-1/2 system is described by the quantum master equation of the Lindblad form.