Parametric Evolution for a Deformed Cavity

Abstract

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>. We describe how the parametric kernel P(n|m) = <n(x)|m(x0)>, also known as the local density of states, evolves as a function of x-x0. We illuminate the non-unitary nature of this parametric evolution, the emergence of non-perturbative features, the final non-universal saturation, and the limitations of random-wave considerations. The parametric evolution is demonstrated numerically for two distinct representative deformation processes.

13 pages, 8 figures, improved introduction, to be published in Phys. Rev. E

References in corpus (5)

• Chaos and energy spreading for time-Dependent Hamiltonians, and the various Regimes in the theory of Quantum Dissipation
• Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle
• Quantum-Classical Correspondence in Energy Space: Two Interacting Spin-Particles
• Unification of perturbation theory, RMT and semiclassical considerations in the study of parametrically-dependent eigenstates
• Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions

Cited by in corpus (19)

• Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states
• Short time decay of the Loschmidt echo
• Parametric dependent Hamiltonians, wavefunctions, random-matrix-theory, and quantal-classical correspondence
• Revivals of Coherence in Chaotic Atom-Optics Billiards
• Uniform Semiclassical Approach to Fidelity Decay: from Weak to Strong Perturbation
• Loschmidt Echo and the Local Density of States
• Displacement Echoes: Classical Decay and Quantum Freeze
• Estimation of the Local Density of States on a Quantum Computer
• Stadium Billiard with Moving Walls
• Hyperfine Spectroscopy of Optically Trapped Atoms
• Failure of random matrix theory to correctly describe quantum dynamics
• Dephasing due to the interaction with chaotic degrees of freedom
• Parametric spin excitations in lateral quantum dots
• The Loschmidt echo in classically chaotic systems: Quantum chaos, irreversibility and decoherence
• Quantum response of weakly chaotic systems
• Diffractive energy spreading and its semiclassical limit
• "Weak Quantum Chaos" and its resistor network modeling
• Echo spectroscopy and Atom Optics Billiards
• Extending the Concept of Probability Flux