Anderson localization of a Rydberg electron along a classical orbit

The connection between the wavefunctions and the classical periodic orbits in a 2D harmonic oscillator is analytically constructed by using the representation of SU(2) coherent states. It is found that the constructed wavefunction generally corresponds to an ensemble of classical trajectories and its localization is extremely efficient. With the constructed wavefunction, we also analyse the property of the probability current density associated with the classical periodic orbit. The appearance of vortex structure in the quantum flow is clearly found to arise from the wave interference.

It is possible to measure in the laboratory the periods Tk or the classical actions Sk of classical periodic orbits of an atomic electron. (We discuss highly excited states of the atom, in which the electron behaves much like a classical particle, and classical orbits become observable.) We will examine situations in which classical dynamics of the electron makes a transition from orderly to chaotic. In this circumstance, periodic orbits proliferate—existing orbits bifurcate, sending out new ones, and new periodic orbits appear ‘‘out of nowhere.’’ In this paper we briefly review experimental measurements carried out by various groups that display these recurrences, and we review the theory that gives a quantitative description of these recurrences and their bifurcations.

The spectrum of a particle in a rotating two-dimensional harmonic oscillator is studied as a function of the cranking frequency. The occurrence of energy gaps is linked to classical periodic orbits. Special attention is paid to the Farey fan pattern generated beyond the Landau limit.

An oscillatory pattern in the smoothed quantum spectrum, which is unique to single-particle motions in a reflection-asymmetric superdeformed oscillator potential, is investigated by means of the semiclassical theory of shell structure. Clear correspondence between the oscillating components of the smoothed level density and the classical periodic orbits is found. It is shown that an interference effect between two families of the short periodic orbits, called supershell effect, becomes more significant with increasing reflection-asymmetric deformations. Possible origins of this enhancement phenomena as well as quantum signatures of period-multipling bifurcations are discussed in connection with stabilities of the classical periodic orbits.

Path integration over closed loops and Gutzwiller's trace formula

We first give a short outline of the semiclassical periodic orbit theory that allows one to relate quantum shell fluctuations in a mean-field system to the periodic orbits of the corresponding classical system. Earlier applications to gross-shell effects in nuclei (ground-state deformations), metal clusters (ground-state deformations and supershells), and quantum dots (conductance oscillations in weak magnetic fields) are briefly summarized. We then report on a recent simple and transparent semiclassical interpretation of the origin of the mass asymmetry in the fission of heavy nuclei. Using only a few classical periodic orbits and a cavity model for the nuclear mean field, we explain the onset of left-right asymmetric shapes at the fission isomer minimum by the principle of constant action of the shortest orbits.

The localization of eigenfunctions around classical periodic orbits is studied numerically for the H-atom in a strong magnetic field by calculating their Husimi distribution in phase space. In contrast to the configuration space representation, the phase space distributions are simply structured: about 90% of eigenstates may be unambigously related to fixed points and invariant manifolds of periodic orbits, indicating that scars are the rule rather than the exception. In order to measure the influence of one particular orbit, we calculate the integrals of the energetically lowest 500 Husimi distributions along the orbit. Their incoherent superposition defines the scar strength distribution for the particular periodic orbit which is analyzed by Fourier transformation. The Husimi distribution at (q, p) in phase space may be represented as a scalar product of the wavefunction with a coherent state of the unperturbed system, i.e., a radial Gaussian wave packet located at (q, p) in the (regularized) Coulomb system. This simplifies the actual calculation of the Husimi distribution and allows to treat their incoherent superposition within Gutzwillers theory extended to matrix elements of an operator A, if we choose A to be the projector on a coherent state.

We consider the problem of optimal boundary control of string vibrations with given initial and final conditions and a given value of the string deflection function at some intermediate time moment and with a quality criterion given over the entire time interval. It is controlled by the displacement of one end while the other end is fixed. A constructive approach to constructing the optimal boundary control action is proposed. A computational experiment was carried out with the construction of the corresponding graphs and their comparative analysis, which confirm the results obtained.

In the course of mathematical modeling, correlations have been established between the parameters of the input and output holes of the pneumatic chamber and the speed of its filling and deflation at a preset temperature. Mathematical relationships, which describe the pneumatic chamber filled with air at the preset initial conditions at a certain moment of time, have been obtained. The experimental data match with the theoretical ones with the specified degree of accuracy.

Cryptographic protocols for exchange of key information in a computer network containing a trusted center (server) and a number of users sharing individual keys of a symmetric encryption system with the server are studied. There are sets of privileged user groups and sets of alienated user coalitions. Preliminary keys are computed on the server according to a certain preliminary key distribution scheme, from which the users of any privileged group can determine a common working key that is not accessible to the users of any alienated coalition that does not overlap with this privileged user group. A general structure of protocols is proposed, in which the preliminary keys delivered to the users and used by them to obtain the working keys are computed using the updated system key information. The studied protocols inherit the structure and functionality of the protocol with time stamps and extend them for the stage of delivering to users the preliminary keys and data from which the users can compute a common working key for communications within the group. Such protocols ensure mutual authentication of users in each privileged group at a certain moment of time and resistance to attacks from the members of alienated groups, that is, impossibility to behave as a privileged group member or to impose an outdated or compromised key.

In recent years more and more emphasis was placed on the idea of autonomous mobile robots, researches being constantly rising. Mobile robots have a large scale use in industry, military operations, exploration and other applications where human intervention is risky. The accurate estimation of the position is a key component for the successful operation for most of autonomous mobile robots. The localization of an autonomous robot system refers mainly to the precise determination of the coordinates where the system is present at a certain moment of time. In many applications, the orientation and an initial estimation of the robot position are known, being supplied directly or indirectly by the user or the supervisor. During the execution of the tasks, the robot must update this estimation using measurements from its sensors. This is known as local localization. Using only sensors that measure relative movements, the error in the pose estimation increases over time as errors are accumulated. Localization is a fundamental operation for navigating mobile robots

The paper describes the SPH modeling of a plane problem of fluid flow around a rigid circular cylinder. In the model considered, the cylinder is placed in a rectangular fluid domain at a certain distance from a horizontal plane boundary, and it is subjected to fluid flow forces. The fluid motion is induced by a piston type generator. The generator - fluid system starts to move from rest at a certain moment of time. The work aims at a discrete description of the fluid flow around the cylinder and, at the same time, calculation of the pressure distribution along the circumference of the cylinder and the resultant of the pressure on the cylinder. In order to solve the initial value problem considered, a new SPH formulation of boundary conditions on the cylinder surface is proposed which match the physical condition for the fluid velocity at this boundary. For a viscous fluid, an approximate description of the stress tensor is formulated which allows to reduce the differentiation of field functions to the first order in calculating the shear forces in the SPH approach.

The article studies specific features of assessing the development project efficiency by using technologies of information modeling (TIM) in view of principle stakeholders. It showed what kind of impact TIM exercises on each of concerned parties and on their relations with the developer, what advantages and drawbacks depend on the degree of information model integration in company business-processes. By results of the analysis and on the basis of the classic system of project appraisal a new multifactor assessment of the development project efficiency was elaborated and put forward, which demonstrates interest of stakeholders in participation in the project using TIM. This appraisal uses the matrix that shows cash flows of each stakeholder in the project and allows them to find in advance the way of interaction with concerned parties of the project and to choose the most appropriate companies for further partnership. On the basis of the matrix it is possible to forecast expectations of the project on the part of all stakeholders at different stages of its implementation. It could help the developer work out the optimum strategy of interaction at a certain moment of time. The author came to a practical conclusion about efficiency of using and opportunity of introduction of such appraisal system in construction.

The evolution of a counterstream quasimonochromatic surface wave on a localized two-dimensional inhomogeneous perturbation of a current is investigated theoretically and experimentally. The model equation describing the surface wave field transformation has been derived and solved numerically. The time evolution of the initially homogeneous wave field when the flow perturbation arises at a certain moment of time is investigated. It is shown that in the case when the group velocity of surface waves is nearly equal and opposite to current velocity the even weak perturbations of current velocity modify appreciably the surface wave field. The dependence of the two-dimensional quasistationary pattern of the surface wave field in the vicinity of the inhomogeneous flow domain on the wavelength of the surface wave and the angle between the surface wave vector and the current velocity is investigated. It is found that there are definite directions (at angle /spl sim/55 degrees to the current velocity) where the main variations of the surface wave field occur. The space dimensions of the domain, where the wave field transformation is essential, greatly exceed the space dimensions of the localized flow perturbation. The growth rate of the wave field perturbation decreases as the group velocity of surface waves tends to the current velocity. Qualitative interpretation of results of the numerical calculation is given. The theoretical results has been checked experimentally in laboratory tank.

In analogy with the usual Anderson localization taking place in time-independent disordered quantum systems where the disorder acts in configuration space, systems exposed to temporally disordered potentials can display Anderson localization in the time domain. We demonstrate this phenomenon with one-dimensional examples where a temporally disordered potential induces localization during the quantum evolution of wave packets, in contrast with a fully delocalized classical dynamics. This is an example of a time crystal phenomenon, i.e., a crystalline behavior in the time domain.