scholarly journals TIME DELAY AND CALABI INVARIANT IN CLASSICAL SCATTERING THEORY

2012 ◽  
Vol 24 (09) ◽  
pp. 1250023
Author(s):  
A. GOURNAY ◽  
R. TIEDRA DE ALDECOA
Keyword(s):  
Quantum Mechanics ◽  
Time Delay ◽  
Explicit Expression ◽  
Scattering Theory ◽  
Scattering Matrix ◽  
Classical Particle ◽  
Hamiltonian Mechanics ◽  
Classical Version ◽  
Calabi Invariant ◽  
Scattering Map

We define, prove the existence and obtain explicit expressions for classical time delay defined in terms of sojourn times for abstract scattering pairs (H0, H) on a symplectic manifold. As a by-product, we establish a classical version of the Eisenbud–Wigner formula of quantum mechanics. Using recent results of Buslaev and Pushnitski on the scattering matrix in Hamiltonian mechanics, we also obtain an explicit expression for the derivative of the Calabi invariant of the Poincaré scattering map. Our results are applied to dispersive Hamiltonians, to a classical particle in a tube and to Hamiltonians on the Poincaré ball.

scholarly journals On the Lax-Phillips scattering theory

1981 ◽  
Vol 87 (3-4) ◽  
pp. 219-230 ◽  
Author(s):  
W. O. Amrein ◽  
M. Wollenberg
Keyword(s):  
Time Delay ◽  
Scattering Theory ◽  
Scattering Matrix ◽  
Scattering Operator ◽  
Simple Description ◽  
Wave Operators ◽  
Scattering Systems ◽  
Delay Operator

SynopsisWe give a simple description of the wave operators appearing in the Lax-Phillips scattering theory. This is used to derive a relation between the scattering matrix and a kind of time delay operator and to characterize all scattering systems having the same scattering operator.

Simulation and Calculation of 10.6μm Laser Time Broadening and Space Broadening Characteristics in Near-Earth Dust

2013 ◽  
Vol 401-403 ◽  
pp. 437-440 ◽  
Author(s):  
Ni Chen Yang ◽  
Hong Xia Wang ◽  
You Zhang Zhu
Keyword(s):  
Monte Carlo ◽  
Time Delay ◽  
Size Distribution ◽  
Scattering Theory ◽  
Mie Scattering ◽  
Dust Particles ◽  
Distribution Model ◽  
Laser Scattering ◽  
Transmission Distance ◽  
Mie Scattering Theory

Based on the Mie scattering theory and the gamma size distribution model, 10.6μm laser scattering characteristics in dust particles are calculated and analyzed.On this basis,the time broadening and space broadening characteristics of the laser are analyzed by using Monte Carlo method.Transmittance change with the transmission distance are quantitative calculated and the time detention and space broadening characteristics of the laser passed through dust for different transmission distances are calculated and analyzed. The results show that the transmittance decreases with increasing transmission distance, and the transmittance is close to 0 when transmission distance is close to 200m; The time delay of 10.6μm laser is more significant with the increaseing transmission distance; The space broadening of 10.6μm laser is more obvious and the energy is more dispersed with the increaseing transmission distance.

TIME DELAY IN SEMICLASSICAL SCATTERING THEORY

1995 ◽  
Vol 10 (33) ◽  
pp. 2509-2517
Author(s):  
M.P. PATO ◽  
M.S. HUSSEIN
Keyword(s):  
Time Delay ◽  
Effective Potential ◽  
Scattering Theory ◽  
Semiclassical Approximation ◽  
Asymptotic Series ◽  
Complex Potentials ◽  
Nuclear Scattering ◽  
Asymptotic Evaluation ◽  
Repulsive Potentials ◽  
Semiclassical Scattering

An asymptotic evaluation of the time delay in the context of the semiclassical approximation is performed. It is shown that it is related to Stokes’s discontinuities of the asymptotic series caused by singularities determined by the turning points and points of equilibrium of the effective potential in the complex r-plane. The theory is applied to the repulsive potentials inversely proportional to the fourth and the sixth power of the distance. The case of complex potentials, usually considered in nuclear scattering is also discussed.

The flux integral for axisymmetric perturbations of static space-times

1990 ◽  
Vol 428 (1875) ◽  
pp. 325-349 ◽  
Keyword(s):  
Black Holes ◽  
Perfect Fluid ◽  
Gravitational Radiation ◽  
Scattering Theory ◽  
Scattering Matrix ◽  
Conservation Of Energy ◽  
Fluid Source ◽  
Maxwell Space ◽  
Static Space ◽  
Axisymmetric Perturbations

The axisymmetric perturbations of static space-times with prevailing sources (a Maxwell field or a perfect fluid) are considered; and it is shown how a flux integral can be derived directly from the relevant linearized equations. The flux integral ensures the conservation of energy in the attendant scattering of radiation and the sometimes accompanying transformation of one kind of radiation into another. The flux integral derived for perturbed Einstein-Maxwell space-times will be particularly useful in this latter context (as in the scattering of radiation by two extreme Reissner-Nordström black-holes) and in the setting up of a scattering matrix. And the flux integral derived for a space-time with a perfect-fluid source will be directly applicable to the problem of the non-radial oscillations of a star with accompanying emission of gravitational radiation and enable its reformulation as a problem in scattering theory.

scholarly journals Stability Problem of Wave Variable Based Bilateral Control: Influence of the Force Source Design

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Dapeng Tian ◽  
Bao Zhang ◽  
Honghai Shen ◽  
Jiaquan Li
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Time Delay ◽  
Robust Stability ◽  
Scattering Theory ◽  
Stability Problem ◽  
Bilateral Control ◽  
Wave Variable ◽  
Small Gain ◽  
The Stability

The wave variable has been proposed to achieve robust stability against the time delay in bilateral control system. However, the influence of the force source on the overall system is still not clear. This paper analyzes this problem and proposes a supplement to the stability analysis for wave variable based bilateral control. Based on the scattering theory, it is pointed out that the design of force source decides the passivity of the two-port network of slave robot. This passivity influences the stability of overall system. Based on the characteristic equation and small gain theorem, it is clear that inappropriate designed force source in encoding the wave variable destroys the stability in the presence of time delay. A wave domain filter makes up for the broken stability. The principle of this reparation is explained in this paper. A reference is also provided by the analysis to design the parameter of the wave domain filter. Experiments prove the correctness and validity.

scholarly journals WAVE PROPAGATION AND SCATTERING FOR THE RS2 BRANE COSMOLOGY MODEL

2009 ◽  
Vol 06 (04) ◽  
pp. 809-861 ◽  
Author(s):  
ALAIN BACHELOT
Keyword(s):  
Cauchy Problem ◽  
Scattering Theory ◽  
Scattering Matrix ◽  
Asymptotic Completeness ◽  
Decay Estimates ◽  
Brane Cosmology ◽  
Dispersive Waves ◽  
Wave Operators ◽  
Global Cauchy Problem

We study the wave equation for the gravitational fluctuations in the Randall–Sundrum brane cosmology model. We solve the global Cauchy problem and we establish that the solutions are the sum of a slowly decaying massless wave localized near the brane, and a superposition of massive dispersive waves. We compute the kernel of the truncated resolvent. We prove some L1-L∞, L2-L∞ decay estimates and global Lp Strichartz type inequalities. We develop the complete scattering theory: existence and asymptotic completeness of the wave operators, computation of the scattering matrix, determination of the resonances on the logarithmic Riemann surface.

scholarly journals Classical-quantum versus exact quantum results for a particle in a box

2012 ◽  
Vol 34 (2) ◽  
Author(s):  
Salvatore De Vincenzo
Keyword(s):  
Quantum Mechanics ◽  
Fourier Series ◽  
Classical Particle ◽  
Quantization Rule ◽  
One Dimensional ◽  
Exact Quantum ◽  
Classical Quantum

The problems of a free classical particle inside a one-dimensional box: (i) with impenetrable walls and (ii) with penetrable walls, were considered. For each problem, the classical amplitude and mechanical frequency of the T -th harmonic of the motion of the particle were identified from the Fourier series of the position function. After using the Bohr-Sommerfeld-Wilson quantization rule, the respective quantized amplitudes and frequencies (i.e., as a function of the quantum label n ) were obtained. Finally, the classical-quantum results were compared to those obtained from modern quantum mechanics, and a clear correspondence was observed in the limit of n » τ.

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