Irrigation water management

Non-Peer Reviewe

Geometrically Consistent Approach to Stochastic DBI Inflation

Stochastic effects during inflation can be addressed by averaging the quantum inflaton field over Hubble-patch sized domains. The averaged field then obeys a Langevin-type equation into which short-scale fluctuations enter as a noise term. We solve the Langevin equation for a inflaton field with Dirac Born Infeld (DBI) kinetic term perturbatively in the noise and use the result to determine the field value's Probability Density Function (PDF). In this calculation, both the shape of the potential and the warp factor are arbitrary functions, and the PDF is obtained with and without volume effects due to the finite size of the averaging domain. DBI kinetic terms typically arise in string-inspired inflationary scenarios in which the scalar field is associated with some distance within the (compact) extra dimensions. The inflaton's accessible range of field values therefore is limited because of the extra dimensions' finite size. We argue that in a consistent stochastic approach the distance-inflaton's PDF must vanish for geometrically forbidden field values. We propose to implement these extra-dimensional spatial restrictions into the PDF by installing absorbing (or reflecting) walls at the respective boundaries in field space. As a toy model, we consider a DBI inflaton between two absorbing walls and use the method of images to determine its most general PDF. The resulting PDF is studied in detail for the example of a quartic warp factor and a chaotic inflaton potential. The presence of the walls is shown to affect the inflaton trajectory for a given set of parameters.Comment: 20 pages, 3 figure

Radiative damping: a case study

We are interested in the motion of a classical charge coupled to the Maxwell self-field and subject to a uniform external magnetic field, B. This is a physically relevant, but difficult dynamical problem, to which contributions range over more than one hundred years. Specifically, we will study the Sommerfeld-Page approximation which assumes an extended charge distribution at small velocities. The memory equation is then linear and many details become available. We discuss how the friction equation arises in the limit of "small" B and contrast this result with the standard Taylor expansion resulting in a second order equation for the velocity of the charge.Comment: 4 figure

Diffractive orbits in isospectral billiards

Isospectral domains are non-isometric regions of space for which the spectra of the Laplace-Beltrami operator coincide. In the two-dimensional Euclidean space, instances of such domains have been given. It has been proved for these examples that the length spectrum, that is the set of the lengths of all periodic trajectories, coincides as well. However there is no one-to-one correspondence between the diffractive trajectories. It will be shown here how the diffractive contributions to the Green functions match nevertheless in a ''one-to-three'' correspondence.Comment: 20 pages, 6 figure

Angular distributions of atomic photoelectrons produced in the UV and XUV regimes

We present angular distributions of photoelectrons of atomic model systems excited by intense linearly polarized laser pulses in the VUV- and XUV-regime. We solve the multi-dimensional time-dependent Schr\"odinger equation for one particle on large spatial grids and investigate the direction dependence of the ionized electrons for isotropic s-states as well as p-states. Although the ponderomotive potential is small compared to the binding energy of the initially bound electron and the photon energy of the exciting laser field, richly structured photoelectron angular distributions are found which sensitively depend on the laser frequency and intensity as well as on the number of absorbed photons. The occuring shapes are explained in terms of scattering mechanisms

The language of Einstein spoken by optical instruments

Einstein had to learn the mathematics of Lorentz transformations in order to complete his covariant formulation of Maxwell's equations. The mathematics of Lorentz transformations, called the Lorentz group, continues playing its important role in optical sciences. It is the basic mathematical language for coherent and squeezed states. It is noted that the six-parameter Lorentz group can be represented by two-by-two matrices. Since the beam transfer matrices in ray optics is largely based on two-by-two matrices or $ABCD$ matrices, the Lorentz group is bound to be the basic language for ray optics, including polarization optics, interferometers, lens optics, multilayer optics, and the Poincar\'e sphere. Because the group of Lorentz transformations and ray optics are based on the same two-by-two matrix formalism, ray optics can perform mathematical operations which correspond to transformations in special relativity. It is shown, in particular, that one-lens optics provides a mathematical basis for unifying the internal space-time symmetries of massive and massless particles in the Lorentz-covariant world.Comment: LaTex 8 pages, presented at the 10th International Conference on Quantum Optics (Minsk, Belarus, May-June 2004), to be published in the proceeding

Transient terahertz spectroscopy of excitons and unbound carriers in quasi two-dimensional electron-hole gases

We report a comprehensive experimental study and detailed model analysis of the terahertz dielectric response and density kinetics of excitons and unbound electron-hole pairs in GaAs quantum wells. A compact expression is given, in absolute units, for the complex-valued terahertz dielectric function of intra-excitonic transitions between the 1s and higher-energy exciton and continuum levels. It closely describes the terahertz spectra of resonantly generated excitons. Exciton ionization and formation are further explored, where the terahertz response exhibits both intra-excitonic and Drude features. Utilizing a two-component dielectric function, we derive the underlying exciton and unbound pair densities. In the ionized state, excellent agreement is found with the Saha thermodynamic equilibrium, which provides experimental verification of the two-component analysis and density scaling. During exciton formation, in turn, the pair kinetics is quantitatively described by a Saha equilibrium that follows the carrier cooling dynamics. The terahertz-derived kinetics is, moreover, consistent with time-resolved luminescence measured for comparison. Our study establishes a basis for tracking pair densities via transient terahertz spectroscopy of photoexcited quasi-two-dimensional electron-hole gases.Comment: 14 pages, 8 figures, final versio

Recovery of chaotic tunneling due to destruction of dynamical localization by external noise

Quantum tunneling in the presence of chaos is analyzed, focusing especially on the interplay between quantum tunneling and dynamical localization. We observed flooding of potentially existing tunneling amplitude by adding noise to the chaotic sea to attenuate the destructive interference generating dynamical localization. This phenomenon is related to the nature of complex orbits describing tunneling between torus and chaotic regions. The tunneling rate is found to obey a perturbative scaling with noise intensity when the noise intensity is sufficiently small and then saturate in a large noise intensity regime. A relation between the tunneling rate and the localization length of the chaotic states is also demonstrated. It is shown that due to the competition between dynamical tunneling and dynamical localization, the tunneling rate is not a monotonically increasing function of Planck's constant. The above results are obtained for a system with a sharp border between torus and chaotic regions. The validity of the results for a system with a smoothed border is also explained.Comment: 14 pages, 15 figure

Mathematical structure of unit systems

We investigate the mathematical structure of unit systems and the relations between them. Looking over the entire set of unit systems, we can find a mathematical structure that is called preorder (or quasi-order). For some pair of unit systems, there exists a relation of preorder such that one unit system is transferable to the other unit system. The transfer (or conversion) is possible only when all of the quantities distinguishable in the latter system are always distinguishable in the former system. By utilizing this structure, we can systematically compare the representations in different unit systems. Especially, the equivalence class of unit systems (EUS) plays an important role because the representations of physical quantities and equations are of the same form in unit systems belonging to an EUS. The dimension of quantities is uniquely defined in each EUS. The EUS's form a partially ordered set. Using these mathematical structures, unit systems and EUS's are systematically classified and organized as a hierarchical tree.Comment: 27 pages, 3 figure

On the regular-geometric-figure solution to the N-body problem

The regular-geometric-figure solution to the $N$-body problem is presented in a very simple way. The Newtonian formalism is used without resorting to a more involved rotating coordinate system. Those configurations occur for other kinds of interactions beyond the gravitational ones for some special values of the parameters of the forces. For the harmonic oscillator, in particular, it is shown that the $N$-body problem is reduced to $N$ one-body problems.Comment: To appear in Eur. J. Phys. (5 pages