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377
Preservation of Adiabatic Invariants under
, 1997
"... Symplectic methods, like the Verlet method, are a standard tool for the long term integration of Hamiltonian systems as they arise, for example, in molecular dynamics. One of the reasons for the popularity of symplectic methods is the conservation of energy over very long periods of time up to smal ..."
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quantities (adiabatic invariants). Using recent results from backward error analysis and normal form theory, we show that a symplectic method, like the Verlet method, preserves those adiabatic invariants. We also discuss stepsize restrictions necessary to maintain adiabatic invariants in practical
BOREL SUMMATION OF ADIABATIC INVARIANTS
"... Abstract. Borel summation techniques are developed to obtain exact invariants from formal adiabatic invariants (given as divergent series in a small parameter) for a class of differential equations, under assumptions of analyticity of the coefficients; the method relies on the study of associated pa ..."
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Cited by 2 (0 self)
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Abstract. Borel summation techniques are developed to obtain exact invariants from formal adiabatic invariants (given as divergent series in a small parameter) for a class of differential equations, under assumptions of analyticity of the coefficients; the method relies on the study of associated
Adiabatic Invariants and Mixmaster Catastrophes
, 1997
"... We present a rigorous analysis of the role and uses of the adiabatic invariant in the Mixmaster dynamical system. We propose a new invariant for the global dynamics which in some respects has an improved behaviour over the commonly used one. We illustrate its behaviour in a number of numerical resul ..."
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We present a rigorous analysis of the role and uses of the adiabatic invariant in the Mixmaster dynamical system. We propose a new invariant for the global dynamics which in some respects has an improved behaviour over the commonly used one. We illustrate its behaviour in a number of numerical
Notes on Adiabatic Invariants
, 1998
"... Introduction Adiabatic invariance, an approximate conservation law, is a general result for any dynamical system that can be described by a Hamiltonian and which follows periodic motion. The problem was first considered by Einstein in 1911 as follows (see Fig. 1): suppose we have a pendulum that is ..."
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Introduction Adiabatic invariance, an approximate conservation law, is a general result for any dynamical system that can be described by a Hamiltonian and which follows periodic motion. The problem was first considered by Einstein in 1911 as follows (see Fig. 1): suppose we have a pendulum
Adiabatic Invariance and the Regularity of Perturbations
 Nonlinearity
, 1994
"... A loss in smoothness of a switching process decreases the accuracy of an adiabatic invariant. Here we show that for classical Hamiltonian systems the degree of smoothness can be observed in the signal. 1 Introduction A parameter dependent family of integrable dynamical systems can be perturbed by m ..."
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Cited by 3 (0 self)
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A loss in smoothness of a switching process decreases the accuracy of an adiabatic invariant. Here we show that for classical Hamiltonian systems the degree of smoothness can be observed in the signal. 1 Introduction A parameter dependent family of integrable dynamical systems can be perturbed
Adiabatic invariance in volumepreserving systems
"... Summary. We consider destruction of adiabatic invariance in volumepreserving systems due to separatrix crossings, scattering on and capture into resonances. These mechanisms result in mixing and transport in large domains of phase space. We consider several examples of systems where these phenomena ..."
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Cited by 1 (0 self)
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Summary. We consider destruction of adiabatic invariance in volumepreserving systems due to separatrix crossings, scattering on and capture into resonances. These mechanisms result in mixing and transport in large domains of phase space. We consider several examples of systems where
ADIABATIC INVARIANTS FOR SPIN–ORBIT MOTION
"... It has been predicted and found experimentally that the polarization direction of particles on the closed orbit can be manipulated, without a noticeable reduction of polarization, by a slow variation of magnetic fields. This feature has been used to avoid imperfection resonances where the spin prec ..."
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precession frequency is close to a multiple of the circulation frequency. We report here on a proof that relates this property to an adiabatic invariant of spin motion. The proof is relatively simple since only two frequencies, the spin rotation frequency and the particle’s rotation frequency on the closed
Preservation of Adiabatic Invariants under Symplectic Discretization
"... Symplectic methods, like the Verlet method, are a standard tool for the long term integration of Hamiltonian systems as they arise, for example, in molecular dynamics. One of the reasons for the popularity of symplectic methods is the conservation of energy over very long periods of time up to small ..."
Abstract
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quantities (adiabatic invariants). Using recent results from backward error analysis and normal form theory, we show that a symplectic method, like the Verlet method, preserves those adiabatic invariants. We also discuss stepsize restrictions necessary to maintain adiabatic invariants in practical
Resonances and adiabatic invariance in classical and quantum scattering theory
, 2004
"... We discover that the energyintegral of timedelay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances, explaining a series of results recently found in nonrelativistic ..."
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We discover that the energyintegral of timedelay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances, explaining a series of results recently found in non
Results 1  10
of
377