Ray and wave chaos in underwater acoustic waveguides

Virovlyansky, A. L.; Макаров, Денис В.; Prants, S. V.

doi:10.3367/ufne.0182.201201b.0019

Cited by 42 publications

(30 citation statements)

References 98 publications

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“…Any type of propagating waves satisfying a linear wave equation, analogous to the Schrödinger equation in quantum theory, has the same property. By wave chaos, one usually means special features of the wave field in the ranges of control parameters and/or initial conditions at which a ray analog of the wave problem is chaotic [35,36]. Thus, the quantum (wave) chaos problem is partly the problem of quantum (wave) -classical (ray) correspondence.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Symmetries, Control, and Chaos with Moving Atoms in High-Quality Cavities

Prants

2015

J Russ Laser Res

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We consider dynamic symmetry, quantum control, and dynamic chaos of atoms moving in high-quality cavities. We review the group-theoretical approach to solve the evolution equations in the cavity quantum electrodynamics and control the quantum evolution in a micromaser device. Taking into account the photon recoil effect, we study nonlinear dynamics of the fundamental interactions between two-level atoms and a quantized cavity field. The strongly coupled atom-field system is treated as a quantum-classical hybrid with dynamically coupled quantum and classical degrees of freedom. Interaction of the purely quantum atom-field system with the classical translational atomic degree of freedom results in emergence of classical dynamic chaos from quantum electrodynamics. That chaos is shown to manifest itself in some ranges of the control parameters in the exponential sensitivity of quantum atomic variables to small variations in the initial conditions and in the appearance of dynamic atomic fractals. We discuss how to observe this effect in real experiments. Our findings establish a quantum-classical correspondence in the cavity quantum electrodynamics.

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Section: Introductionmentioning

confidence: 99%

Dynamic Symmetries, Control, and Chaos with Moving Atoms in High-Quality Cavities

Prants

2015

J Russ Laser Res

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“…A typical chaotic Hamiltonian system has the mixed phase space with regular islands embedded in a chaotic sea. It is a common feature for cold atoms (see, e.g., [22]), sound rays in underwater sound channels in the ocean [27,28], and passive scalars in hydrodynamic flows [29][30][31][32]. A detailed theory of semiclassical Hamiltonian and dissipative chaotic transport of point-like atoms in a laser standing wave has been developed in [23] and [24], respectively.…”

Section: Introductionmentioning

confidence: 99%

Impact of Spontaneous Emission on the form and Dynamics of Atomic Wave Packets in an Optical Lattice

Prants

Kon’kov

2015

J Russ Laser Res

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Using the Monte Carlo wave-function method, we study the influence of spontaneous emission on dynamics of a Gaussian atomic wave packet with two internal states placed initially at a node or antinode of a standing-wave laser field. Without spontaneous emission, the wave packet at a node is known to split both in the position and momentum spaces because of the optical Stern-Gerlach effect. We show that the spontaneous-emission events suppress splitting, causing a strong broadening of the wave packet in both spaces. As for a wave packet placed initially at an antinode, spontaneous emission causes a localization of the atomic wave packet in the first potential well both in the position and momentum spaces as compared to the coherent evolution.

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“…This expectation can fail in the presence of periodic-orbit bifurcations [22,40]. Moreover, analysis of level spacing statistics doesn't provide accurate estimate of the regular phase space area [23].…”

Section: Finite-time Evolution Operatormentioning

confidence: 99%

“…FTEO was firstly utilized in [39] for the problem of noise-driven quantum diffusion. Wave analogue of the FTEO was used in [22,23,[40][41][42].…”

Section: Finite-time Evolution Operatormentioning

confidence: 99%

“…We use the quantum counterpart of the one-step Poincaré map, the so-called finite-time evolution operator, for exploring manifestations of finite-time stability in quantum motion. Mathematically equivalent approach was used for studying sound propagation in a randomly-inhomogeneous oceanic waveguide [22,23]. In the present paper, we use this approach for a purely quantum problem, namely for the quantum nonlinear pendulum subjected to broadband perturbation.…”

Section: Introductionmentioning

confidence: 99%

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Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation

Макаров¹,

Kon’kov²

2015

Phys. Scr.

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Abstract.Motion of randomly-driven quantum nonlinear pendulum is considered. Utilizing one-step Poincaré map, we demonstrate that classical phase space corresponding to a single realization of the random perturbation can involve domains of finite-time stability. Statistical analysis of the finite-time evolution operator (FTEO) is carried out in order to study influence of finite-time stability on quantum dynamics. It is shown that domains of finite-time stability give rise to ordered patterns in distributions of FTEO eigenfunctions. Transition to global chaos is accompanied by smearing of these patterns; however, some of their traces survive on relatively long timescales.

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Ray and wave chaos in underwater acoustic waveguides

Cited by 42 publications

References 98 publications

Dynamic Symmetries, Control, and Chaos with Moving Atoms in High-Quality Cavities

Dynamic Symmetries, Control, and Chaos with Moving Atoms in High-Quality Cavities

Impact of Spontaneous Emission on the form and Dynamics of Atomic Wave Packets in an Optical Lattice

Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation

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