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Matthias Brack - One of the best experts on this subject based on the ideXlab platform.

  • Periodic orbit theory for the Hénon-Heiles system in the continuum region.
    Physical review. E Statistical nonlinear and soft matter physics, 2004
    Co-Authors: Jörg Kaidel, Peter Winkler, Matthias Brack
    Abstract:

    We investigate the resonance spectrum of the Hénon-Heiles potential up to twice the barrier energy. The quantum spectrum is obtained by the method of complex coordinate rotation. We use periodic orbit theory to approximate the Oscillating Part of the resonance spectrum semiclassically and Strutinsky smoothing to obtain its smooth Part. Although the system in this energy range is almost chaotic, it still contains stable periodic orbits. Using Gutzwiller's trace formula, complemented by a uniform approximation for a co-dimension-two bifurcation scenario, we are able to reproduce the coarse-grained quantum-mechanical density of states very accurately, including only a few stable and unstable orbits.

  • Periodic orbit theory for the Hénon-Heiles system in the continuum region
    Physical Review E, 2004
    Co-Authors: Jörg Kaidel, Peter Winkler, Matthias Brack
    Abstract:

    We investigate the resonance spectrum of the H\'enon-Heiles potential up to twice the barrier energy. The quantum spectrum is obtained by the method of complex coordinate rotation. We use periodic orbit theory to approximate the Oscillating Part of the resonance spectrum semiclassically and Strutinsky smoothing to obtain its smooth Part. Although the system in this energy range is almost chaotic, it still contains stable periodic orbits. Using Gutzwiller's trace formula, complemented by a uniform approximation for a codimension-two bifurcation scenario, we are able to reproduce the coarse-grained quantum-mechanical density of states very accurately, including only a few stable and unstable orbits.

  • Semiclassical analysis of the lowest-order multipole deformations of simple metal clusters
    Physics Letters A, 2002
    Co-Authors: V. V. Pashkevich, Matthias Brack, P. Meier, A. V. Unzhakova
    Abstract:

    Abstract We use a perturbative semiclassical trace formula to calculate the three lowest-order multipole (quadrupole ϵ 2 , octupole ϵ 3 , and hexadecapole ϵ 4 ) deformations of simple metal clusters with 90⩽ N ⩽550 atoms in their ground states. The self-consistent mean field of the valence electrons is modeled by an axially deformed cavity and the Oscillating Part of the total energy is calculated semiclassically using the shortest periodic orbits. The average energy is obtained from a liquid-drop model adjusted to the empirical bulk and surface properties of the sodium metal. We obtain good qualitative agreement with the results of quantum-mechanical calculations using Strutinsky's shell-correction method.

Shinji Maedan - One of the best experts on this subject based on the ideXlab platform.

  • How parametric resonance mechanism follows quench mechanism in disoriented chiral condensate
    Physics Letters B, 2001
    Co-Authors: Shinji Maedan
    Abstract:

    We show how parametric resonance mechanism follows quench mechanism in the classical linear sigma model. The parametric resonance amplifies long wavelength modes of the pion for more than $10 fm/c$. The shifting from the quench mechanism to the parametric resonance mechanism is described by a time dependent quantity. After the quench mechanism is over, that quantity has an Oscillating Part, which causes the parametric resonance. Since its frequency is $2 m_\pi ~(m_\pi$ : pion mass), very long wavelength modes such as k = 40 MeV of the pion are amplified by the parametric resonance.

Zhituo Wang - One of the best experts on this subject based on the ideXlab platform.

  • Quantum Quench dynamics in Non-local Luttinger Model: Rigorous Results
    arXiv: Mathematical Physics, 2017
    Co-Authors: Zhituo Wang
    Abstract:

    We investigate, in the Luttinger model with fixed box potential, the time evolution of an inhomogeneous state prepared as a localized fermion added to the noninteracting ground state. We proved that, if the state is evolved with the interacting Hamiltonian, the averaged density has two peaks moving in opposite directions, with a constant but renormalized velocity. We also proved that a dynamical `Landau quasi-Particle weight' appears in the Oscillating Part of the averaged density, asymptotically vanishing with large time. The results are proved with the Mattis-Lieb diagonalization method. A simpler proof with the exact Bosonization formulas is also provided.

  • Quantum quench for inhomogeneous states in the nonlocal Luttinger model
    Physical Review B, 2015
    Co-Authors: Vieri Mastropietro, Zhituo Wang
    Abstract:

    In the Luttinger model with non-local interaction we investigate, by exact analytical methods, the time evolution of an inhomogeneous state with a localized fermion added to the non interacting ground state. In absence of interaction the averaged density has two peaks moving in opposite directions with constant velocities. If the state is evolved with the interacting Hamiltonian two main effects appear. The first is that the peaks have velocities which are not constant but vary between a minimal and maximal value. The second is that a dynamical `Landau quasi-Particle weight' appears in the Oscillating Part of the averaged density, asymptotically vanishing with time, as consequence of the fact that fermions are not excitations of the interacting Hamiltonian.

Brandon P. Van Zyl - One of the best experts on this subject based on the ideXlab platform.

  • Zeta function zeros, powers of primes, and quantum chaos.
    Physical Review E, 2003
    Co-Authors: Jamal Sakhr, Rajat K. Bhaduri, Brandon P. Van Zyl
    Abstract:

    We present a numerical study of Riemann's formula for the Oscillating Part of the density of the primes and their integer powers. The formula consists of an infinite series of oscillatory terms, one for each zero of the zeta function on the critical line, and was derived by Riemann in his paper on primes, assuming the Riemann hypothesis. We show that high-resolution spectral lines can be generated by the truncated series at all integer powers of primes and demonstrate explicitly that the relative line intensities are correct. We then derive a Gaussian sum rule for Riemann's formula. This is used to analyze the numerical convergence of the truncated series. The connections to quantum chaos and semiclassical physics are discussed.

Dmitry S. Kulyabov - One of the best experts on this subject based on the ideXlab platform.