Resonance- and Chaos-Assisted Tunneling

We consider dynamical tunneling between two symmetry-related regular islands that are separated in phase space by a chaotic sea. Such tunneling processes are dominantly governed by nonlinear resonances, which induce a coupling mechanism between ``regular'' quantum states within and ``chaotic'' states outside the islands. By means of a random matrix ansatz for the chaotic part of the Hamiltonian, one can show that the corresponding coupling matrix element directly determines the level splitting between the symmetric and the antisymmetric eigenstates of the pair of islands. We show in detail how this matrix element can be expressed in terms of elementary classical quantities that are associated with the resonance. The validity of this theory is demonstrated with the kicked Harper model.Comment: 25 pages, 5 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

Resonance-assisted tunneling in near-integrable systems

Dynamical tunneling between symmetry related invariant tori is studied in the near-integrable regime. Using the kicked Harper model as an illustration, we show that the exponential decay of the wave functions in the classically forbidden region is modified due to coupling processes that are mediated by classical resonances. This mechanism leads to a substantial deviation of the splitting between quasi-degenerate eigenvalues from the purely exponential decrease with 1 / hbar obtained for the integrable system. A simple semiclassical framework, which takes into account the effect of the resonance substructure on the KAM tori, allows to quantitatively reproduce the behavior of the eigenvalue splittings.Comment: 4 pages, 2 figures, gzipped tar file, to appear in Phys. Rev. Lett, text slightly condensed compared to first versio

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

Stress Responses in Tropical Sparrows: Comparing Tropical and Temperate Zonotrichia

Seasonal modulation of the adrenocortical response appears to be ubiquitous in mid- to high- latitude vertebrates but has not been investigated in tropical vertebrates. Previous studies demonstrate that temperate passerines show seasonality in corticosterone secretion and corticosteroid binding globulin capacities. We examined seasonal and sex differences in the stress response in an equatorial population of Zonotrichia capensis, the only Zonotrichia that breeds in the tropics, and compared the results with those of northern Zonotrichia. Seasonal differences in tropical Zonotrichia would presumably be independent of photoperiod and thus directly related to such activities as reproduction and feather molt. In addition, we investigated the possible role of binding globulin as a sex steroid binding globulin, as suggested for temperate passerines. Similar to northern congeners, Z. capensis show seasonal modulation in total corticosterone and binding globulin capacity with higher levels during breeding than molt. However, unlike many temperate passerines, there are no sex differences in corticosterone secretion or binding globulin capacity. Furthermore, the seasonal differences in total corticosterone diminish when the free levels are calculated. The contrast between equatorial and northern congeners indicates factors such as breeding environment and life-history strategy may play important roles in shaping stress response in these species

Scarring Effects on Tunneling in Chaotic Double-Well Potentials

The connection between scarring and tunneling in chaotic double-well potentials is studied in detail through the distribution of level splittings. The mean level splitting is found to have oscillations as a function of energy, as expected if scarring plays a role in determining the size of the splittings, and the spacing between peaks is observed to be periodic of period {$2\pi\hbar$} in action. Moreover, the size of the oscillations is directly correlated with the strength of scarring. These results are interpreted within the theoretical framework of Creagh and Whelan. The semiclassical limit and finite-{$\hbar$} effects are discussed, and connections are made with reaction rates and resonance widths in metastable wells.Comment: 22 pages, including 11 figure

Semiclassical Trace Formulas for Noninteracting Identical Particles

We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur in continuous families. The identical nature of the particles also introduces discrete permutational symmetries. We exploit the formalism of Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied semiclassical dynamics in the presence of continuous symmetries, to derive many-body trace formulas for the full and symmetry-reduced densities of states. Numerical studies of the three-particle cardioid billiard are used to explicitly illustrate and test the results of the theory.Comment: 29 pages, 11 figures, submitted to PR

Semiclassical theory of spin-orbit interaction in the extended phase space

We consider the semiclassical theory in a joint phase space of spin and orbital degrees of freedom. The method is developed from the path integrals using the spin-coherent-state representation, and yields the trace formula for the density of states. We discuss special cases, such as weak and strong spin-orbit coupling, and relate the present theory to the earlier approaches.Comment: 36 pages, 8 figures. Version 2: revised Sec. 4.4 and Appendix B; minor corrections elsewher

Near-field MIMO communication links

A procedure to achieve near-field multiple input multiple output (MIMO) communication with equally strong channels is demonstrated in this paper. This has applications in near-field wireless communications, such as Chip-to-Chip (C2C) communication or wireless links between printed circuit boards. Designing the architecture of these wireless C2C networks is, however, based on standard engineering design tools. To attain this goal, a network optimization procedure is proposed, which introduces decoupling and matching networks. As a demonstration, this optimization procedure is applied to a 2-by-2 MIMO with dipole antennas. The potential benefits and design trade-offs are discussed for implementation of wireless radio-frequency interconnects in chip-to-chip or device-to-device communication such as in an Internet-of-Things scenario

Instantons revisited: dynamical tunnelling and resonant tunnelling

Starting from trace formulae for the tunnelling splittings (or decay rates) analytically continued in the complex time domain, we obtain explicit semiclassical expansions in terms of complex trajectories that are selected with appropriate complex-time paths. We show how this instanton-like approach, which takes advantage of an incomplete Wick rotation, accurately reproduces tunnelling effects not only in the usual double-well potential but also in situations where a pure Wick rotation is insufficient, for instance dynamical tunnelling or resonant tunnelling. Even though only one-dimensional autonomous Hamiltonian systems are quantitatively studied, we discuss the relevance of our method for multidimensional and/or chaotic tunnelling