The transition rates of an isotropic quantum charged oscillator in the presence of external fields

2020 ◽  
Vol 34 (05) ◽  
pp. 2050023
Author(s):  
F. Chegini ◽  
F. Kheirandish ◽  
M. R. Setare
Keyword(s):  
Half Space ◽  
Large Time ◽  
External Source ◽  
Transition Rates ◽  
Classical Source ◽  
Conducting Plate ◽  
External Sources ◽  
The Fourier Transform ◽  
Space Case ◽  
Large Time Limit

In this work, explicit expressions for the transition rates of an isotropic quantum charged harmonic oscillator in the vicinity of a perfectly conducting half-space under the influence of an external classical source are obtained. In the absence of external sources, it is shown that the decay rate of an initially exited state of the oscillator is a periodic function in terms of the normalized distance to the plate. The modified transition rates in the presence of external classical sources are obtained in the large-time limit indicating a contribution proportional to the squared module of the Fourier transform of the external source. In the absence of the conducting plate and external sources, the results are in agreement with the free space case. The problem is generalized to the case of a real conducting half-space.

CAUSAL BULK VISCOUS COSMOLOGIES IN CONFORMALLY FLAT SPACETIME

2000 ◽  
Vol 09 (04) ◽  
pp. 475-493 ◽  
Author(s):  
M. K. MAK ◽  
T. HARKO
Keyword(s):  
Large Time ◽  
Viscosity Coefficient ◽  
Approximate Solutions ◽  
Conformally Flat ◽  
First Order ◽  
Flat Spacetime ◽  
Bulk Viscous ◽  
Type Differential Equation ◽  
Bulk Viscosity Coefficient ◽  
Large Time Limit

The evolution of a causal bulk viscous cosmological fluid filled open conformally flat spacetime is considered. By means of appropriate transformations the equation describing the dynamics and evolution of the very early Universe can be reduced to a first order Abel type differential equation. In the case of a bulk viscosity coefficient proportional to the square root of the density, ξ~ρ1/2, an exact and two particular approximate solutions are obtained. The resulting cosmologies start from a singular state and generally have a noninflationary behavior, the deceleration parameter tending, in the large time limit, to zero. The thermodynamic consistency of the results is also checked.

scholarly journals Large Deviations at Level 2.5 for Markovian Open Quantum Systems: Quantum Jumps and Quantum State Diffusion

2021 ◽  
Vol 184 (1) ◽  
Author(s):  
Federico Carollo ◽  
Juan P. Garrahan ◽  
Robert L. Jack
Keyword(s):  
Quantum State ◽  
Large Time ◽  
Stochastic Dynamics ◽  
Large Deviation ◽  
Open Quantum Systems ◽  
Photon Detection ◽  
State Diffusion ◽  
Quantum State Diffusion ◽  
Quantum Stochastic Processes ◽  
Large Time Limit

AbstractWe consider quantum stochastic processes and discuss a level 2.5 large deviation formalism providing an explicit and complete characterisation of fluctuations of time-averaged quantities, in the large-time limit. We analyse two classes of quantum stochastic dynamics, within this framework. The first class consists of the quantum jump trajectories related to photon detection; the second is quantum state diffusion related to homodyne detection. For both processes, we present the level 2.5 functional starting from the corresponding quantum stochastic Schrödinger equation and we discuss connections of these functionals to optimal control theory.

Electromagnetic Induction in a Stratified Conducting Half-Space by an Arbitrary Periodic Source

1973 ◽  
Vol 51 (10) ◽  
pp. 1064-1074 ◽  
Author(s):  
D. M. Summers ◽  
J. T. Weaver
Keyword(s):  
Half Space ◽  
Recursion Formula ◽  
Electric And Magnetic Fields ◽  
Hertz Potential ◽  
Infinite Line ◽  
The Fourier Transform ◽  
The One ◽  
External Time ◽  
Entire Theory ◽  
Time Periodic

A general theory of induction in a horizontally stratified plane conductor by an external, time-periodic, magnetic source is presented. The analysis is a generalization to the case of an N-layered conductor of a previously published theory for induction in a uniform conducting half-space, in which the electromagnetic field was expressed in terms of electric and magnetic Hertz vectors oriented normally to the surface of the conductor. With the aid of this representation the entire theory is developed in terms of the one scalar component of the magnetic Hertz vector. Solutions for the electric and magnetic fields above and within the conductor are obtained in the form of double integrals whose integrands are related through a recursion formula to the Fourier transform of the magnetic Hertz potential of the source evaluated at the surface of the conductor. Special formulas applicable to 1- and 2-layer conductors are derived and the form of solution for some elementary sources is also discussed. As an illustration of the theory, numerical calculations are given for an infinite line current above a 10-layer conductor whose conductivity increases (i) linearly and (ii) exponentially with depth.

Bleustein-Gulyaev Waves in an Inhomogeneous Layered Piezoelectric Half-Space

2006 ◽  
Vol 306-308 ◽  
pp. 1223-1228
Author(s):  
Fei Peng ◽  
Hua Rui Liu
Keyword(s):  
Fourier Transform ◽  
Phase Velocity ◽  
Half Space ◽  
Electric Potential ◽  
Piezoelectric Layer ◽  
Field Equations ◽  
Transform Method ◽  
Coupled Field ◽  
Coupled Field Equations ◽  
The Fourier Transform

The propagation of Bleustein-Gulyaev (BG) waves in an inhomogeneous layered piezoelectric half-space is investigated in this paper. Application of the Fourier transform method and by solving the electromechanically coupled field equations, solutions to the mechanical displacement and electric potential are obtained for the piezoelectric layer and substrate, respectively. The phase velocity equations for BG waves are obtained for the surface electrically shorted case. When the layer and the substrate are homogenous, the dispersion equations are in agreement with the corresponding results. Numerical calculations are performed for the case that the layer and the substrate are identical LiNbO3 except that they are polarized in opposite directions. Effects of the inhomogeneities induced by either the layer or substrate are discussed in detail.

Poisson’s integral formula via heat kernels

Analysis ◽  
2019 ◽  
Vol 39 (2) ◽  
pp. 59-64
Author(s):  
Yoichi Miyazaki
Keyword(s):  
Fourier Transform ◽  
Heat Kernel ◽  
Half Space ◽  
Unbounded Domain ◽  
Harmonic Functions ◽  
Integral Formula ◽  
Heat Kernels ◽  
Transform Method ◽  
Fourier Transform Method ◽  
The Fourier Transform

Abstract We give another proof of Poisson’s integral formula for harmonic functions in a ball or a half space by using heat kernels with Green’s formula. We wish to emphasize that this method works well even for a half space, which is an unbounded domain; the functions involved are integrable, since the heat kernel decays rapidly. This method needs no trick such as the subordination identity, which is indispensable when applying the Fourier transform method for a half space.

Stimulation of the acoustico-lateralis system of clupeid fish by external sources and their own movements

1993 ◽  
Vol 341 (1296) ◽  
pp. 113-127 ◽  
Keyword(s):  
Lateral Line ◽  
External Source ◽  
Clupea Harengus ◽  
Pressure Gradients ◽  
Surrounding Water ◽  
Low Frequencies ◽  
Lateral Recess ◽  
Lateral Lines ◽  
External Sources ◽  
Net Pressure

1. The receptor organs of the acoustico-lateralis system in fish respond in various ways to pressures and pressure gradients and provide the fish with information about external sources of vibration. 2. A fish’s movements will set up pressures and pressure gradients and this poses three questions, (i) Can a fish obtain useful information from self-generated pressures and pressure gradients? (ii) To what extent do self-generated pressures mask signals from external sources? (iii) Can interactions between external and self-generated pressures and gradients in the acoustico-lateralis system give patterns of activity from the receptor organs which have special significance? 3. In herring ( Clupea harengus L. ) and sprat ( Spratus sprattus (L.)) measurements have been made of dimensions of various parts of the acoustico-lateralis system particularly of the subcerebral perilymph canal which crosses the head between the lateral lines. 4. Self-generated pressures produced by lateral movements of the head are antisymmetric, i.e. equal and opposite in sign on the left and right sides of the head. They oppose the accelerations of the head that produce them. In contrast, external sources give pressures that are largely symmetric. Any pressure gradients they give will accelerate the fish and the surrounding water together and any net pressure gradients will be small and so will any flows through the subcerebral perilymph canal. 5. Flows of liquid between the lateral lines across the lateral-recess membranes have been measured at various frequencies for pressure gradients applied across the head. Between 5 and 200 Hz the velocity of flow per unit pressure does not vary by more than than a factor of 2. At low frequencies the absolute values of flow are very much larger (more than 50 times) than those found for equally large symmetrically applied pressures (as from an external source) due to flow into the elastic gas containing bullae. 6. It is calculated that a net pressure difference (at optimum frequency) across the head of only 0.008 Pa will reach threshold for the lateral line neuromast nearest the lateral recess and one of 0.02 Pa for that under the eye. The responses of these neuromasts are expected to saturate and provide little information when the pressure differences across the head exceed 6 to 18 Pa. The pressures given by the swimming fish are discussed in the light of a theory advanced by Lighthill in the paper that follows this paper. With such antisymmetric pressures the direction of flow in the lateral-line canals will be towards the lateral recess on one side of the fish and away on the other and so differ from the situation found with an external source when flow at any instant will be either towards or away from the lateral recess on both sides of the head. 7. Antisymmetric pressures can produce large flows past the utricular maculae. However, at low frequencies flows across the maculae, on which their stimulation depends, will be small. We do not know the direction of these latter flows though they will be in opposite sense on the two sides of the head, again unlike the situation with an external source. 8. Calculations of impedances below 30 Hz show that the observed flows across the head are consistent with the dimensions and properties of the known structures. 9. There are major and systematic differences in the patterns of receptor organ stimulation between those expected from external sources and from a fish’s own movements. 10. Experiments on the red mullet ( Mullus surmuletus L.) showed that it too has a transverse channel connecting the right and left lateral-line systems. At low frequencies its properties resemble those of the subcerebral perilymph canal of the clupeid.

Geochemical Evidence of Saharan Dust Parent Material for Soils Developed on Quaternary Limestones of Caribbean and Western Atlantic Islands

1990 ◽  
Vol 33 (2) ◽  
pp. 157-177 ◽  
Author(s):  
Daniel R. Muhs ◽  
Charles A. Bush ◽  
Kathleen C. Stewart ◽  
Tracy R. Rowland ◽  
Russell C. Crittenden
Keyword(s):  
Volcanic Ash ◽  
Florida Keys ◽  
External Source ◽  
Parent Material ◽  
Saharan Dust ◽  
Caribbean Island ◽  
Trade Winds ◽  
Western Atlantic ◽  
Parent Materials ◽  
External Sources

AbstractMost previous workers have regarded the insoluble residues of high-purity Quaternary limestones (coral reefs and oolites) as the most important parent material for well-developed, clay-rich soils on Caribbean and western Atlantic islands, but this genetic mechanism requires unreasonable amounts of limestone solution in Quaternary time. Other possible parent materials from external sources are volcanic ash from the Lesser Antilles island arc and Saharan dust carried across the Atlantic Ocean on the northeast trade winds. Soils on Quaternary coral terraces and carbonate eolianites on Barbados, Jamaica, the Florida Keys (United States), and New Providence Island (Bahamas) were studied to determine which, if either, external source was important. Caribbean volcanic ashes and Saharan dust can be clearly distinguished using ratios of relatively immobile elements (Al2O3/TiO2, Ti/Y, Ti/Zr, and Ti/Th). Comparison of these ratios in 25 soils, where estimated ages range from 125,000 to about 870,000 yr, shows that Saharan dust is the most important parent material for soils on all islands. These results indicate that the northeast trade winds have been an important component of the regional climatology for much of the Quaterary. Saharan dust may also be an important parent material for Caribbean island bauxites of much greater age.

scholarly journals Energetics of Poisson–Kac Stochastic Processes Possessing Finite Propagation Velocity

2016 ◽  
Vol 41 (2) ◽  
Author(s):  
Antonio Brasiello ◽  
Massimiliano Giona ◽  
Silvestro Crescitelli
Keyword(s):  
Large Time ◽  
Coarse Grained ◽  
Langevin Equations ◽  
Stochastic Forcing ◽  
Stochastic Perturbations ◽  
Wiener Processes ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Almost Everywhere ◽  
Large Time Limit

AbstractA local fluctuation–dissipation theorem for the power delivered by a stochastic forcing is derived for Ornstein–Uhlenbeck processes driven by smooth, i. e. almost everywhere (a. e.)-differentiable stochastic perturbations (Poisson–Kac processes). An analytic expression for the probability density function of the fluctuational power is obtained in the large time limit. As these processes converge, in the Kac limit, toward classical Langevin equations driven by Wiener processes, a coarse-grained analysis of the statistical properties of the fluctuational work is developed.

scholarly journals Large-time limit of the quantum Zeno effect

2017 ◽  
Vol 58 (3) ◽  
pp. 032103 ◽  
Author(s):  
Paolo Facchi ◽  
Marilena Ligabò
Keyword(s):  
Large Time ◽  
Time Limit ◽  
Quantum Zeno Effect ◽  
Zeno Effect ◽  
Large Time Limit

scholarly journals A model building framework for answer set programming with external computations

2015 ◽  
Vol 16 (4) ◽  
pp. 418-464 ◽  
Author(s):  
THOMAS EITER ◽  
MICHAEL FINK ◽  
GIOVAMBATTISTA IANNI ◽  
THOMAS KRENNWALLNER ◽  
CHRISTOPH REDL ◽  
...  
Keyword(s):  
Model Building ◽  
External Source ◽  
Software Systems ◽  
Logic Programs ◽  
New Approach ◽  
Evaluation Approach ◽  
Real World Application ◽  
External Sources ◽  
Model Graph ◽  
Answer Set

AbstractAs software systems are getting increasingly connected, there is a need for equipping nonmonotonic logic programs with access to external sources that are possibly remote and may contain information in heterogeneous formats. To cater for this need,hexprograms were designed as a generalization of answer set programs with an API style interface that allows to access arbitrary external sources, providing great flexibility. Efficient evaluation of such programs however is challenging, and it requires to interleave external computation and model building; to decide when to switch between these tasks is difficult, and existing approaches have limited scalability in many real-world application scenarios. We present a new approach for the evaluation of logic programs with external source access, which is based on a configurable framework for dividing the non-ground program into possibly overlapping smaller parts called evaluation units. The latter will be processed by interleaving external evaluation and model building using an evaluation graph and a model graph, respectively, and by combining intermediate results. Experiments with our prototype implementation show a significant improvement compared to previous approaches. While designed forhex-programs, the new evaluation approach may be deployed to related rule-based formalisms as well.

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