Semiclassical Study on Tunneling Processes via Complex-Domain Chaos

We investigate the semiclassical mechanism of tunneling process in non-integrable systems. The significant role of complex-phase-space chaos in the description of the tunneling process is elucidated by studying a simple scattering map model. Behaviors of tunneling orbits are encoded into symbolic sequences based on the structure of complex homoclinic tanglement. By means of the symbolic coding, the phase space itineraries of tunneling orbits are related with the amounts of imaginary parts of actions gained by the orbits, so that the systematic search of significant tunneling orbits becomes possible.Comment: 26 pages, 28 figures, submitted to Physical Review

Tunneling Mechanism due to Chaos in a Complex Phase Space

We have revealed that the barrier-tunneling process in non-integrable systems is strongly linked to chaos in complex phase space by investigating a simple scattering map model. The semiclassical wavefunction reproduces complicated features of tunneling perfectly and it enables us to solve all the reasons why those features appear in spite of absence of chaos on the real plane. Multi-generation structure of manifolds, which is the manifestation of complex-domain homoclinic entanglement created by complexified classical dynamics, allows a symbolic coding and it is used as a guiding principle to extract dominant complex trajectories from all the semiclassical candidates.Comment: 4 pages, RevTeX, 6 figures, to appear in Phys. Rev.

Virtual turning points and bifurcation of Stokes curves for higher order ordinary differential equations

For a higher order linear ordinary differential operator P, its Stokes curve bifurcates in general when it hits another turning point of P. This phenomenon is most neatly understandable by taking into account Stokes curves emanating from virtual turning points, together with those from ordinary turning points. This understanding of the bifurcation of a Stokes curve plays an important role in resolving a paradox recently found in the Noumi-Yamada system, a system of linear differential equations associated with the fourth Painleve equation.Comment: 7 pages, 4 figure

Resonance Tunneling in Double-Well Billiards with a Pointlike Scatterer

The coherent tunneling phenomenon is investigated in rectangular billiards divided into two domains by a classically unclimbable potential barrier. We show that by placing a pointlike scatterer inside the billiard, we can control the occurrence and the rate of the resonance tunneling. The key role of the avoided crossing is stressed. Keywords: chaotic tunneling, quantum billiard, delta potential, diabolical degeneracy PACS: 3.65.-w, 4.30.Nk, 5.45.+b, 73.40.GkComment: Five pages ReVTEX, two column format with epsf figure

Level statistics and eigenfunctions of pseudointegrable systems: dependence on energy and genus number

We study the level statistics (second half moment $I_0$ and rigidity $\Delta_3$) and the eigenfunctions of pseudointegrable systems with rough boundaries of different genus numbers $g$. We find that the levels form energy intervals with a characteristic behavior of the level statistics and the eigenfunctions in each interval. At low enough energies, the boundary roughness is not resolved and accordingly, the eigenfunctions are quite regular functions and the level statistics shows Poisson-like behavior. At higher energies, the level statistics of most systems moves from Poisson-like towards Wigner-like behavior with increasing $g$. Investigating the wavefunctions, we find many chaotic functions that can be described as a random superposition of regular wavefunctions. The amplitude distribution $P(\psi)$ of these chaotic functions was found to be Gaussian with the typical value of the localization volume $V_{\rm{loc}}\approx 0.33$. For systems with periodic boundaries we find several additional energy regimes, where $I_0$ is relatively close to the Poisson-limit. In these regimes, the eigenfunctions are either regular or localized functions, where $P(\psi)$ is close to the distribution of a sine or cosine function in the first case and strongly peaked in the second case. Also an interesting intermediate case between chaotic and localized eigenfunctions appears

Quantum Dynamics of Atom-molecule BECs in a Double-Well Potential

We investigate the dynamics of two-component Bose-Josephson junction composed of atom-molecule BECs. Within the semiclassical approximation, the multi-degree of freedom of this system permits chaotic dynamics, which does not occur in single-component Bose-Josephson junctions. By investigating the level statistics of the energy spectra using the exact diagonalization method, we evaluate whether the dynamics of the system is periodic or non-periodic within the semiclassical approximation. Additionally, we compare the semiclassical and full-quantum dynamics.Comment: to appear in JLTP - QFS 200

Scale Anomaly and Quantum Chaos in the Billiards with Pointlike Scatterers

We argue that the random-matrix like energy spectra found in pseudointegrable billiards with pointlike scatterers are related to the quantum violation of scale invariance of classical analogue system. It is shown that the behavior of the running coupling constant explains the key characteristics of the level statistics of pseudointegrable billiards.Comment: 10 pages, RevTex file, uuencode

Semiclassical transmission across transition states

It is shown that the probability of quantum-mechanical transmission across a phase space bottleneck can be compactly approximated using an operator derived from a complex Poincar\'e return map. This result uniformly incorporates tunnelling effects with classically-allowed transmission and generalises a result previously derived for a classically small region of phase space.Comment: To appear in Nonlinearit

Evanescent wave approach to diffractive phenomena in convex billiards with corners

What we are going to call in this paper "diffractive phenomena" in billiards is far from being deeply understood. These are sorts of singularities that, for example, some kind of corners introduce in the energy eigenfunctions. In this paper we use the well-known scaling quantization procedure to study them. We show how the scaling method can be applied to convex billiards with corners, taking into account the strong diffraction at them and the techniques needed to solve their Helmholtz equation. As an example we study a classically pseudointegrable billiard, the truncated triangle. Then we focus our attention on the spectral behavior. A numerical study of the statistical properties of high-lying energy levels is carried out. It is found that all computed statistical quantities are roughly described by the so-called semi-Poisson statistics, but it is not clear whether the semi-Poisson statistics is the correct one in the semiclassical limit.Comment: 7 pages, 8 figure

Slow relaxation to equipartition in spring-chain systems

In this study, one-dimensional systems of masses connected by springs, i.e., spring-chain systems, are investigated numerically. The average kinetic energy of chain-end particles of these systems is larger than that of other particles, which is similar to the behavior observed for systems made of masses connected by rigid links. The energetic motion of the end particles is, however, transient, and the system relaxes to thermal equilibrium after a while, where the average kinetic energy of each particle is the same, that is, equipartition of energy is achieved. This is in contrast to the case of systems made of masses connected by rigid links, where the energetic motion of the end particles is observed in equilibrium. The timescale of relaxation estimated by simulation increases rapidly with increasing spring constant. The timescale is also estimated using the Boltzmann-Jeans theory and is found to be in quite good agreement with that obtained by the simulation