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Chaos and Energy Spreading for Time-Dependent Hamiltonians, and the Various Regimes in the Theory of Quantum Dissipation
Abstract We make the first steps toward a generic theory for energy spreading and quantum dissipation. The Wall formula for the calculation of friction in nuclear physics and the Drude formula for
Quantum Dissipation due to the Interaction with Chaotic Degrees of Freedom and the Correspondence Principle
Both in atomic physics and in mesoscopic physics it is sometimes interesting to consider the energy time-dependence of a parametrically-driven chaotic system. We assume an Hamiltonian ${\cal
Parametric dependent Hamiltonians, wave functions, random matrix theory, and quantal-classical correspondence.
  • D. Cohen, T. Kottos
  • Physics
    Physical review. E, Statistical, nonlinear, and…
  • 13 January 2000
TLDR
The study addresses the issue of quantum-classical correspondence and analyzes numerically how the parametric kernel P(n/m)=//(2) evolves as a function of delta(x)[triple bond](x-x(0)).
Dephasing due to the interaction with chaotic degrees of freedom.
  • D. Cohen
  • Physics
    Physical review. E, Statistical, nonlinear, and…
  • 13 March 2001
TLDR
This work considers the motion of a particle, taking into account its interaction with environmental degrees of freedom, and obtains results for the dephasing time and compares them with those of the effective-bath approach.
Minimal Fokker-Planck theory for the thermalization of mesoscopic subsystems.
TLDR
A minimal paradigm for thermalization is explored, consisting of two weakly coupled, low dimensional, nonintegrable subsystems, as demonstrated for Bose-Hubbard trimers, which supports the hypothesis that thermalization can be described by a Fokker-Planck equation.
Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states.
TLDR
P perturbation independent decay reflects the Lyapunov instability of the underlying semiclassical dynamics, and it can be distinguished from the Wigner-type decay that holds in the perturbative regime.
Path integral approach to the quantum fidelity amplitude
TLDR
An exact path integral formula for the fidelity amplitude is derived and used to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent.
Quantum reversibility: is there an echo?
TLDR
It is demonstrated that the time t(r) for maximum return probability is in general shorter than the ratio of the error in setting the parameters (fields) for the time-reversed evolution to the perturbation which is involved in the preparation process.
The information entropy of quantum-mechanical states
TLDR
A new definition of entropy is introduced that reflects the inherent uncertainty of quantum-mechanical states and distinguishes between the minimum uncertainty entropy of pure states, and the excess statistical entropy of mixtures.
Thermalization of Bipartite Bose-Hubbard Models.
TLDR
The time evolution of a bipartite Bose-Hubbard model prepared far from equilibrium is studied to observe ergodization of the number distribution and a constant increase of the entanglement entropy between the constituent subsystems until it saturates to thermal equilibrium values.
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