Path-integral solutions of wave equations with dissipation

DeWitt‐Morette, Cécile; Foong, See Kit

doi:10.1103/physrevlett.62.2201

Cited by 66 publications

(32 citation statements)

References 5 publications

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“…[7]. There, the real part can represent the time advance due to the stochastic character of the motion, namely Re t v = (a/v)R 2 , where a is the dissipative parameter entering the telegrapher's equation and v the wavevelocity [13]. Independently of the exact form of the quantity A, we can assert that the spatial advance to be attributed to the forerunner with averaged position M 2 , in Fig.…”

mentioning

confidence: 97%

Diffraction effects in microwave propagation at the origin of superluminal behaviors

Ranfagni

Ricci²,

Ruggeri

et al. 2008

Physics Letters A

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mentioning

confidence: 97%

Diffraction effects in microwave propagation at the origin of superluminal behaviors

Ranfagni

Ricci²,

Ruggeri

et al. 2008

Physics Letters A

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“…This is a new result for the PDF of the random time and has not been derived before, although an expression for the even part of it, viz., h(r; t) = p(r; t) + p(−r; t) without the delta function term is available in [29]. It is also different from the expression given in [13] and [19], because these works assume different initial conditions that do not pertain to the random time ζ(t) that we are considering in the paper.…”

Section: First Order Statistics Of the Random Timementioning

confidence: 99%

“…Equation (40) is also derived in [29], but using the expressions of the Laplace transform of the various moments provided in [18]. However, the approach taken in this paper is more straightforward and as a bonus one can derive expressions for other quantities of interest such as Q(κ; s).…”

Section: First Order Statistics Of the Random Timementioning

confidence: 99%

On random time and on the relation between wave and telegraph equations

Janaswamy

2013

IEEE Trans. Antennas Propagat.

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Abstract-Kac's conjecture relating the solution of wave and telegraph equations in higher dimensions through a Poissonprocess-driven random time is established through the concepts of stochastic calculus. New expression is derived for the probability density function of the random time. We demonstrate how the relationship between the solution of a lossy wave-and that of a lossless wave equation can be exploited to derive some statistical identities. Relevance of the results presented to the study of pulse propagation in a dispersive medium characterized by a Lorentz or Drude model is discussed and new evolution equations for 2D Maxwell's equations are presented for the Drude medium. It is shown that the computational time required for updating the electric field using the stochastic technique is expected to go up as O( √ t).

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“…Next we determine the passage time of photons through the nondispersive and homogeneous medium, where ε, µ and σ are constant. The distribution function g´t τµ of random variable s´tµ was given by DeWitte-Morette and Foong [7]. Mugnai et al proposed to define a passage time in the dissipative wave propagation [8].…”

mentioning

confidence: 99%

Derivation of relativistic wave equation from the Poisson process

Kudo

Ohba

2002

Pramana - J Phys

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A Poisson process is one of the fundamental descriptions for relativistic particles: both fermions and bosons. A generalized linear photon wave equation in dispersive and homogeneous medium with dissipation is derived using the formulation of the Poisson process. This formulation provides a possible interpretation of the passage time of a photon moving in the medium, which never exceeds the speed of light in vacuum. The motion of relativistic particles is represented by the Poisson process. Kac proposed the continuous version of Poisson process in 1956 [1]. Gaveauet al derived the Dirac equation in 1984 using the formulation of Poisson process [2]. McKeon and Old constructed a modified version of the Poisson process in 1992 [3], where the relativistic particles can move both forward and backward in time. These Poisson processes were extended in 2001 [4] to more general frameworks of three-dimensional Dirac equation including an external field. Bialynicki-Birula invented a linear photon wave equation in 1994 [5] as a linearized version of the d'Alembert wave equation. Sipe verified in 1995 [6] that this wave equation identifies the ordinary canonical quantization.We treat the case that a time-dependent external potential V´tµ exists [4]. Let an absorption probability in a time interval δ be I´tµδ , where the path can be absorbed at most once in a time interval δ by the influence of the potential at time t. The conditional expectation is represented aswhere 1 I δ corresponds to a time shift generator in a time interval δ , and the onedimensional space-shift generator is L c∂ ∂ x. The one-dimensional space-shift generator has to be generalized to a three-dimensional generator with minimal coupling, L c σ σ ¡´∇ ∇ ie A´xµ µ in the case that vector field A exists, where σ σ gives the Pauli 413

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Path-integral solutions of wave equations with dissipation

Cited by 66 publications

References 5 publications

Diffraction effects in microwave propagation at the origin of superluminal behaviors

Diffraction effects in microwave propagation at the origin of superluminal behaviors

On random time and on the relation between wave and telegraph equations

Derivation of relativistic wave equation from the Poisson process

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