Long-Time Coherence in Echo Spectroscopy with π/2\pi/2--π\pi--π/2\pi/2 Pulse Sequence

Motivated by atom optics experiments, we investigate a new class of fidelity functions describing the reconstruction of quantum states by time-reversal operations as $M_{\mathrm{Da}}(t) = | <\psi | e^{i H_2 t / 2} e^{i H_1 t / 2} e^{-i H_2 t / 2} e^{-i H_1 t / 2} | \psi >|^2$. We show that the decay of $M_{\mathrm{Da}}$ is quartic in time at short times, and that it freezes well above the ergodic value at long times, when $H_2-H_1$ is not too large. The long-time saturation value of $M_{\mathrm{Da}}$ contains easily extractable information on the strength of decoherence in these systems.Comment: 5 pages, 3 figure

Unbounded quantum backflow in two dimensions

Quantum backflow refers to the counterintuitive fact that the probability can flow in the direction opposite to the momentum of a quantum particle. This phenomenon has been seen to be small and fragile for one-dimensional systems, in which the maximal amount of backflow has been found to be bounded. Quantum backflow exhibits dramatically different features in two-dimensional systems that, contrary to the one-dimensional case, allow for degenerate energy eigenstates. Here we investigate the case of a charged particle that is confined to move on a finite disk punctured at the center and that is pierced through the center, and normally to the disk, by a magnetic flux line. We demonstrate that quantum backflow can be unbounded (in a certain sense), which makes this system a promising physical platform regarding the yet-to-be-performed experimental observation of this fundamental quantum phenomenon.Comment: 11 pages, 1 figur

Scattering of quantum wave packets by shallow potential islands: a quantum lens

We consider the problem of quantum scattering of a localized wave packet by a weak Gaussian potential in two spatial dimensions. We show that, under certain conditions, this problem bears close analogy with that of focusing (or defocusing) of light rays by a thin optical lens: Quantum interference between straight paths yields the same lens equation as for refracted rays in classical optics

Long-time saturation of the Loschmidt echo in quantum chaotic billiards

The Loschmidt echo (LE) (or fidelity) quantifies the sensitivity of the time evolution of a quantum system with respect to a perturbation of the Hamiltonian. In a typical chaotic system the LE has been previously argued to exhibit a long-time saturation at a value inversely proportional to the effective size of the Hilbert space of the system. However, until now no quantitative results have been known and, in particular, no explicit expression for the proportionality constant has been proposed. In this paper we perform a quantitative analysis of the phenomenon of the LE saturation and provide the analytical expression for its long-time saturation value for a semiclassical particle in a two-dimensional chaotic billiard. We further perform extensive (fully quantum mechanical) numerical calculations of the LE saturation value and find the numerical results to support the semiclassical theory.Comment: 5 pages, 2 figure

Wave packet autocorrelation functions for quantum hard-disk and hard-sphere billiards in the high-energy, diffraction regime

We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision expansions we provide a first-principle analytical calculation of the time-dependent autocorrelation function for the wave packet in the high-energy diffraction regime, in which the particle's de Broglie wave length, while being small compared to the size of the scatterers, is large enough to prevent the formation of geometric shadow over distances of the order of the particle's free flight path. The hard-disk or hard-sphere scattering system must be sufficiently dilute in order for this high-energy diffraction regime to be achievable. Apart from the overall exponential decay, the autocorrelation function exhibits a generally complicated sequence of relatively strong peaks corresponding to partial revivals of the wave packet. Both the exponential decay (or escape) rate and the revival peak structure are predominantly determined by the underlying classical dynamics. A relation between the escape rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the counterpart classical system, previously known for hard-disk billiards, is strengthened by generalization to three spatial dimensions. The results of the quantum mechanical calculation of the time-dependent autocorrelation function agree with predictions of the semiclassical periodic orbit theory.Comment: 24 pages, 13 figure

Secretory structures in plants: lessons from the Plumbaginaceae on their origin, evolution and roles in stress tolerance

Special IssueThe Plumbaginaceae (non-core Caryophyllales) is a family well known for species adapted to a wide range of arid and saline habitats. Of its salt-tolerant species, at least 45 are in the genus Limonium; two in each of Aegialitis, Limoniastrum and Myriolimon, and one each in Psylliostachys, Armeria, Ceratostigma, Goniolimon and Plumbago. All the halophytic members of the family have salt glands, which are also common in the closely related Tamaricaceae and Frankeniaceae. The halophytic species of the three families can secrete a range of ions (Na+, K+, Ca2+, Mg2+, Cl−, HCO3 −, SO4 2-) and other elements (As, Cd, Cr, Cu, Fe, Mn, Ni, Pb and Zn). Salt glands are, however, absent in salt-tolerant members of the sister family Polygonaceae. We describe the structure of the salt glands in the three families and consider whether glands might have arisen as a means to avoid the toxicity of Na+ and/or Cl− or to regulate Ca2+ concentrations within the leaves. We conclude that the establishment of lineages with salt glands took place after the split between the Polygonaceae and its sister group the Plumbaginaceaeinfo:eu-repo/semantics/publishedVersio