Quantitative analysis of pedestrian counterflow in a cellular automaton model

Pedestrian dynamics exhibits various collective phenomena. Here we study bidirectional pedestrian flow in a floor field cellular automaton model. Under certain conditions, lane formation is observed. Although it has often been studied qualitatively, e.g., as a test for the realism of a model, there are almost no quantitative results, neither empirically nor theoretically. As basis for a quantitative analysis we introduce an order parameter which is adopted from the analysis of colloidal suspensions. This allows to determine a phase diagram for the system where four different states (free flow, disorder, lanes, gridlock) can be distinguished. Although the number of lanes formed is fluctuating, lanes are characterized by a typical density. It is found that the basic floor field model overestimates the tendency towards a gridlock compared to experimental bounds. Therefore an anticipation mechanism is introduced which reduces the jamming probability.Comment: 11 pages, 12 figures, accepted for publication in Phys. Rev.

Evaporation of alpha particles from 31^31P nucleus

The energy spectra of alpha particles have been measured in coincidence with the evaporation residues for the decay of the compound nucleus $^31$P produced in the reaction $^19$F (96 MeV) + $^12$C. The data have been compared with the predictions of the statistical model code CASCADE. It has been observed that significant deformation effect in the compound nucleus need to be considered in order to explain the shape of the evaporated alpha particle energy spectra.Comment: 4 pages, 3 figures, revtex, epsf styl

Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer

Many coherence transfer experiments in Nuclear Magnetic Resonance Spectroscopy, involving network of coupled spins, use temporary spin-decoupling to produce desired effective Hamiltonians. In this paper, we show that significant time can be saved in producing an effective Hamiltonian, if spin-decoupling is avoided. We provide time optimal pulse sequences for producing an important class of effective Hamiltonians in three spin networks. These effective Hamiltonians are useful for coherence transfer experiments and implementation of quantum logic gates in NMR quantum computing. It is demonstrated that computing these time optimal pulse sequences can be reduced to geometric problems that involve computing sub-Riemannian geodesics on Homogeneous spaces

Optimal Control of Quantum Dissipative Dynamics: Analytic solution for cooling the three level Λ\Lambda system

We study the problem of optimal control of dissipative quantum dynamics. Although under most circumstances dissipation leads to an increase in entropy (or a decrease in purity) of the system, there is an important class of problems for which dissipation with external control can decrease the entropy (or increase the purity) of the system. An important example is laser cooling. In such systems, there is an interplay of the Hamiltonian part of the dynamics, which is controllable and the dissipative part of the dynamics, which is uncontrollable. The strategy is to control the Hamiltonian portion of the evolution in such a way that the dissipation causes the purity of the system to increase rather than decrease. The goal of this paper is to find the strategy that leads to maximal purity at the final time. Under the assumption that Hamiltonian control is complete and arbitrarily fast, we provide a general framework by which to calculate optimal cooling strategies. These assumptions lead to a great simplification, in which the control problem can be reformulated in terms of the spectrum of eigenvalues of $\rho$, rather than $\rho$ itself. By combining this formulation with the Hamilton-Jacobi-Bellman theorem we are able to obtain an equation for the globaly optimal cooling strategy in terms of the spectrum of the density matrix. For the three-level $\Lambda$ system, we provide a complete analytic solution for the optimal cooling strategy. For this system it is found that the optimal strategy does not exploit system coherences and is a 'greedy' strategy, in which the purity is increased maximally at each instant.Comment: 9 pages, 3 fig

Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system

In this paper, we study time-optimal control problems related to system of two coupled qubits where the time scales involved in performing unitary transformations on each qubit are significantly different. In particular, we address the case where unitary transformations produced by evolutions of the coupling take much longer time as compared to the time required to produce unitary transformations on the first qubit but much shorter time as compared to the time to produce unitary transformations on the second qubit. We present a canonical decomposition of SU(4) in terms of the subgroup SU(2)xSU(2)xU(1), which is natural in understanding the time-optimal control problem of such a coupled qubit system with significantly different time scales. A typical setting involves dynamics of a coupled electron-nuclear spin system in pulsed electron paramagnetic resonance experiments at high fields. Using the proposed canonical decomposition, we give time-optimal control algorithms to synthesize various unitary transformations of interest in coherent spectroscopy and quantum information processing.Comment: 8 pages, 3 figure

Astrophysical S_{17}(0) factor from a measurement of d(7Be,8B)n reaction at E_{c.m.} = 4.5 MeV

Angular distribution measurements of $^2$H($^7$Be,$^7$Be)$^2$H and $^2$H($^7$Be,$^8$B)$n$ reactions at $E_{c.m.}\sim$~4.5 MeV were performed to extract the astrophysical $S_{17}(0)$ factor using the asymptotic normalization coefficient (ANC) method. For this purpose a pure, low emittance $^7$Be beam was separated from the primary $^7$Li beam by a recoil mass spectrometer operated in a novel mode. A beam stopper at 0$^{\circ}$ allowed the use of a higher $^7$Be beam intensity. Measurement of the elastic scattering in the entrance channel using kinematic coincidence, facilitated the determination of the optical model parameters needed for the analysis of the transfer data. The present measurement significantly reduces errors in the extracted $^7$Be(p,$\gamma$) cross section using the ANC method. We get $S_{17}$~(0)~=~20.7~$\pm$~2.4 eV~b.Comment: 15 pages including 3 eps figures, one figure removed and discussions updated. Version to appear in Physical Review

Geodesics for Efficient Creation and Propagation of Order along Ising Spin Chains

Experiments in coherent nuclear and electron magnetic resonance, and optical spectroscopy correspond to control of quantum mechanical ensembles, guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and decoherence and to optimize the sensitivity of the experiments. Here we give efficient syntheses of various unitary transformations on Ising spin chains of arbitrary length. The efficient realization of the unitary transformations presented here is obtained by computing geodesics on a sphere under a special metric. We show that contrary to the conventional belief, it is possible to propagate a spin order along an Ising spin chain with coupling strength J (in units of Hz), significantly faster than 1/(2J) per step. The methods presented here are expected to be useful for immediate and future applications involving control of spin dynamics in coherent spectroscopy and quantum information processing

Time Optimal Control in Spin Systems

In this paper, we study the design of pulse sequences for NMR spectroscopy as a problem of time optimal control of the unitary propagator. Radio frequency pulses are used in coherent spectroscopy to implement a unitary transfer of state. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. We have adopted a general mathematical formulation, and present many of our results in this setting, mindful of the fact that new structures in optimal pulse design are constantly arising. Moreover, the general proofs are no more difficult than the specific problems of current interest. From a general control theory perspective, the problems we want to study have the following character. Suppose we are given a controllable right invariant system on a compact Lie group, what is the minimum time required to steer the system from some initial point to a specified final point? In NMR spectroscopy and quantum computing, this translates to, what is the minimum time required to produce a unitary propagator? We also give an analytical characterization of maximum achievable transfer in a given time for the two spin system.Comment: 20 Pages, 3 figure

The Fundamental Diagram of Pedestrian Movement Revisited

The empirical relation between density and velocity of pedestrian movement is not completely analyzed, particularly with regard to the `microscopic' causes which determine the relation at medium and high densities. The simplest system for the investigation of this dependency is the normal movement of pedestrians along a line (single-file movement). This article presents experimental results for this system under laboratory conditions and discusses the following observations: The data show a linear relation between the velocity and the inverse of the density, which can be regarded as the required length of one pedestrian to move. Furthermore we compare the results for the single-file movement with literature data for the movement in a plane. This comparison shows an unexpected conformance between the fundamental diagrams, indicating that lateral interference has negligible influence on the velocity-density relation at the density domain $1 m^{-2}<\rho<5 m^{-2}$. In addition we test a procedure for automatic recording of pedestrian flow characteristics. We present preliminary results on measurement range and accuracy of this method.Comment: 13 pages, 9 figure