Wang, Li; Tu, Tao; Gong, Bo; Zhou, Cheng; Guo, Guang-Can
2016-01-07
High fidelity universal gates for quantum bits form an essential ingredient of quantum information processing. In particular, geometric gates have attracted attention because they have a higher intrinsic resistance to certain errors. However, their realization remains a challenge because of the need for complicated quantum control on a multi-level structure as well as meeting the adiabatic condition within a short decoherence time. Here, we demonstrate non-adiabatic quantum operations for a two-level system by applying a well-controlled geometric Landau-Zener-Stückelberg interferometry. By characterizing the gate quality, we also investigate the operation in the presence of realistic dephasing. Furthermore, the result provides an essential model suitable for understanding an interplay of geometric phase and Landau-Zener-Stückelberg process which are well explored separately.
The geometric phase in nonlinear dissipative systems
Ning, C.Z.; Haken, H. )
1992-10-30
In this paper, the authors review the recent progress made in generalizing the concept of the geometric phase to nonlinear dissipative systems. The authors first illustrate the usual form of the parallel transport law with an elementary example of the parallel shift of a line on the complex plane. Important results about the non-adiabatical geometric (Aharonov and Anandan or AA) phase [sup 18] for the Schrodinger equations are reviewed in order to make a comparison with results for dissipative systems. The authors show that a geometric phase can be defined for dissipative systems with the cyclic attractors. Systems undergoing the Hopf bifurcation with a continuous symmetry are shown to possess such cyclic attractors. Examples from laser physics are discussed to exhibit the applicability of our formalism and the widespread existence of the geometric phase in dissipative systems.
Geometric phase in Bohmian mechanics
Chou, Chia-Chun; Wyatt, Robert E.
2010-10-15
Using the quantum kinematic approach of Mukunda and Simon, we propose a geometric phase in Bohmian mechanics. A reparametrization and gauge invariant geometric phase is derived along an arbitrary path in configuration space. The single valuedness of the wave function implies that the geometric phase along a path must be equal to an integer multiple of 2{pi}. The nonzero geometric phase indicates that we go through the branch cut of the action function from one Riemann sheet to another when we locally travel along the path. For stationary states, quantum vortices exhibiting the quantized circulation integral can be regarded as a manifestation of the geometric phase. The bound-state Aharonov-Bohm effect demonstrates that the geometric phase along a closed path contains not only the circulation integral term but also an additional term associated with the magnetic flux. In addition, it is shown that the geometric phase proposed previously from the ensemble theory is not gauge invariant.
Observing the geometric phase of a superconducting harmonic oscillator
NASA Astrophysics Data System (ADS)
Pechal, M.; Berger, S.; Abdumalikov, A. A.; Fink, J. M.; Mlynek, J. A.; Steffen, L.; Wallraff, A.; Filipp, S.
2012-02-01
Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase [1]. However, the linearity of the system precludes its observation without a non-linear quantum probe. We therefore make use of a superconducting qubit serving as an interferometer to measure the adiabatic geometric phase of a harmonic oscillator realized as an on-chip resonant circuit [2]. We study the geometric phase for a variety of trajectories and show that, in agreement with theory, it is proportional to the area enclosed by the trajectory in the space of coherent states. At the transition to the non-adiabatic regime, oscillatory dephasing effects caused by residual qubit-resonator entanglement are observed and analyzed. We also discuss the possibility of using the harmonic oscillator geometric phase to implement two-qubit phase gates. [4pt] [1] S. Chaturvedi, M. S. Sriram, V. Srinivasan, J. Phys. A: Math. Gen. 20, L1071 (1987).[2] M. Pechal et al., arXiv:1109.1157v1 [quant-ph].
Guiding light via geometric phases
NASA Astrophysics Data System (ADS)
Slussarenko, Sergei; Alberucci, Alessandro; Jisha, Chandroth P.; Piccirillo, Bruno; Santamato, Enrico; Assanto, Gaetano; Marrucci, Lorenzo
2016-09-01
All known methods for transverse confinement and guidance of light rely on modification of the refractive index, that is, on the scalar properties of electromagnetic radiation. Here, we disclose the concept of a dielectric waveguide that exploits vectorial spin-orbit interactions of light and the resulting geometric phases. The approach relies on the use of anisotropic media with an optic axis that lies orthogonal to the propagation direction but is spatially modulated, so that the refractive index remains constant everywhere. A spin-controlled cumulative phase distortion is imposed on the beam, balancing diffraction for a specific polarization. As well as theoretical analysis, we present an experimental demonstration of the guidance using a series of discrete geometric-phase lenses made from liquid crystal. Our findings show that geometric phases may determine the optical guiding behaviour well beyond a Rayleigh length, paving the way to a new class of photonic devices. The concept is applicable to the whole electromagnetic spectrum.
Guiding light via geometric phases
NASA Astrophysics Data System (ADS)
Slussarenko, Sergei; Alberucci, Alessandro; Jisha, Chandroth P.; Piccirillo, Bruno; Santamato, Enrico; Assanto, Gaetano; Marrucci, Lorenzo
2016-09-01
All known methods for transverse confinement and guidance of light rely on modification of the refractive index, that is, on the scalar properties of electromagnetic radiation. Here, we disclose the concept of a dielectric waveguide that exploits vectorial spin–orbit interactions of light and the resulting geometric phases. The approach relies on the use of anisotropic media with an optic axis that lies orthogonal to the propagation direction but is spatially modulated, so that the refractive index remains constant everywhere. A spin-controlled cumulative phase distortion is imposed on the beam, balancing diffraction for a specific polarization. As well as theoretical analysis, we present an experimental demonstration of the guidance using a series of discrete geometric-phase lenses made from liquid crystal. Our findings show that geometric phases may determine the optical guiding behaviour well beyond a Rayleigh length, paving the way to a new class of photonic devices. The concept is applicable to the whole electromagnetic spectrum.
Non-adiabatic pulsations in %delta; Scuti stars
NASA Astrophysics Data System (ADS)
Moya, A.; Garrido, R.; Dupret, M. A.
2004-01-01
For δ Scuti stars, phase differences and amplitude ratios between the relative effective temperature variation and the relative radial displacement can be derived from multicolor photometric observations. The same quantities can be also calculated from theoretical non-adiabatic pulsation models. We present here these theoretical results, which indicate that non-adiabatic quantities depend on the mixing length parameter α used to treat the convection in the standard Mixing Length Theory (MLT). This dependence can be used to test and to constrain, through multicolor observations, the way MLT describes convection in the outermost layers of the star. We will use the equilibrium models provided by the CESAM evolutionary code. The pulsational observables are calculated by using a non-adiabatic pulsation code developed by R. Garridon and A. Moya. In the evolutionary and pulsation codes, a complete reconstruction of the non-grey atmosphere (Kurucz models) is included. The interaction between pulsation and atmosphere, as described by Dupret et al. (2002), is also included in the code.
Non-adiabatic dark fluid cosmology
Hipólito-Ricaldi, W.S.; Velten, H.E.S.; Zimdahl, W. E-mail: velten@cce.ufes.br
2009-06-01
We model the dark sector of the cosmic substratum by a viscous fluid with an equation of state p = −ζΘ, where Θ is the fluid-expansion scalar and ζ is the coefficient of bulk viscosity for which we assume a dependence ζ∝ρ{sup ν} on the energy density ρ. The homogeneous and isotropic background dynamics coincides with that of a generalized Chaplygin gas with equation of state p = −A/ρ{sup α}. The perturbation dynamics of the viscous model, however, is intrinsically non-adiabatic and qualitatively different from the Chaplygin-gas case. In particular, it avoids short-scale instabilities and/or oscillations which apparently have ruled out unified models of the Chaplygin-gas type. We calculate the matter power spectrum and demonstrate that the non-adiabatic model is compatible with the data from the 2dFGRS and the SDSS surveys. A χ{sup 2}-analysis shows, that for certain parameter combinations the viscous-dark-fluid (VDF) model is well competitive with the ΛCDM model. These results indicate that non-adiabatic unified models can be seen as potential contenders for a General-Relativity-based description of the cosmic substratum.
Moving walls and geometric phases
NASA Astrophysics Data System (ADS)
Facchi, Paolo; Garnero, Giancarlo; Marmo, Giuseppe; Samuel, Joseph
2016-09-01
We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve unitarity. For these boundary conditions we compute explicitly the geometric phase two-form on the parameter space. The unboundedness of the Hamiltonian describing the system leads to a natural prescription of renormalization for divergent contributions arising from the boundary.
Non-Adiabatic Holonomic Quantum Gates in an atomic system
NASA Astrophysics Data System (ADS)
Azimi Mousolou, Vahid; Canali, Carlo M.; Sjoqvist, Erik
2012-02-01
Quantum computation is essentially the implementation of a universal set of quantum gate operations on a set of qubits, which is reliable in the presence of noise. We propose a scheme to perform robust gates in an atomic four-level system using the idea of non-adiabatic holonomic quantum computation proposed in [1]. The gates are realized by applying sequences of short laser pulses that drive transitions between the four energy levels in such a way that the dynamical phases vanish. [4pt] [1] E. Sjoqvist, D.M. Tong, B. Hessmo, M. Johansson, K. Singh, arXiv:1107.5127v2 [quant-ph
Non-adiabatic perturbations in multi-component perfect fluids
Koshelev, N.A.
2011-04-01
The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models.
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing. PMID:26154384
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach
Arrieta, Jorge; Cartwright, Julyan H. E.; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number— in an inertialess environment—is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the “belly phase,” peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing. PMID:26154384
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.
Second-quantized formulation of geometric phases
Deguchi, Shinichi; Fujikawa, Kazuo
2005-07-15
The level crossing problem and associated geometric terms are neatly formulated by the second-quantized formulation. This formulation exhibits a hidden local gauge symmetry related to the arbitrariness of the phase choice of the complete orthonormal basis set. By using this second-quantized formulation, which does not assume adiabatic approximation, a convenient exact formula for the geometric terms including off-diagonal geometric terms is derived. The analysis of geometric phases is then reduced to a simple diagonalization of the Hamiltonian, and it is analyzed both in the operator and path-integral formulations. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial (and thus no monopole singularity) for arbitrarily large but finite time interval T. The integrability of Schroedinger equation and the appearance of the seemingly nonintegrable phases are thus consistent. The topological proof of the Longuet-Higgins' phase-change rule, for example, fails in the practical Born-Oppenheimer approximation where a large but finite ratio of two time scales is involved and T is identified with the period of the slower system. The difference and similarity between the geometric phases associated with level crossing and the exact topological object such as the Aharonov-Bohm phase become clear in the present formulation. A crucial difference between the quantum anomaly and the geometric phases is also noted.
Coherent control using kinetic energy and the geometric phase of a conical intersection
NASA Astrophysics Data System (ADS)
Liekhus-Schmaltz, Chelsea; McCracken, Gregory A.; Kaldun, Andreas; Cryan, James P.; Bucksbaum, Philip H.
2016-10-01
Conical intersections (CIs) between molecular potential energy surfaces with non-vanishing non-adiabatic couplings generally occur in any molecule consisting of at least three atoms. They play a fundamental role in describing the molecular dynamics beyond the Born-Oppenheimer approximation and have been used to understand a large variety of effects, from photofragmentation and isomerization to more exotic applications such as exciton fission in semiconductors. However, few studies have used the features of a CI as a tool for coherent control. Here we demonstrate two modes of control around a conical intersection. The first uses a continuous light field to control the population on the two intersecting electronic states in the vicinity of a CI. The second uses a pulsed light field to control wavepackets that are subjected to the geometric phase shift in transit around a CI. This second technique is likely to be useful for studying the role of nuclear dynamics in electronic coherence phenomena.
On geometric interpretation of the berry phase
NASA Astrophysics Data System (ADS)
Katanaev, M. O.
2012-03-01
A geometric interpretation of the Berry phase and its Wilczek-Zee non-Abelian generalization are given in terms of connections on principal fiber bundles. It is demonstrated that a principal fiber bundle can be trivial in all cases, while the connection and its holonomy group are nontrivial. Therefore, the main role is played by geometric rather than topological effects.
Geometric phases in discrete dynamical systems
NASA Astrophysics Data System (ADS)
Cartwright, Julyan H. E.; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2016-10-01
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
The Geometric Phase of Stock Trading.
Altafini, Claudio
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote. PMID:27556642
The Geometric Phase of Stock Trading
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote. PMID:27556642
The Geometric Phase of Stock Trading.
Altafini, Claudio
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.
The geometric phase controls ultracold chemistry
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-07-30
In this study, the geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born–Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O + OH → H + O_{2} reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.
The geometric phase controls ultracold chemistry
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-01-01
The geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born–Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O+OH→H+O2 reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity. PMID:26224326
The geometric phase controls ultracold chemistry
NASA Astrophysics Data System (ADS)
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-07-01
The geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born-Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O+OH-->H+O2 reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.
Classical nuclear motion coupled to electronic non-adiabatic transitions
Agostini, Federica; Abedi, Ali; Gross, E. K. U.
2014-12-07
Based on the exact factorization of the electron-nuclear wave function, we have recently proposed a mixed quantum-classical scheme [A. Abedi, F. Agostini, and E. K. U. Gross, Europhys. Lett. 106, 33001 (2014)] to deal with non-adiabatic processes. Here we present a comprehensive description of the formalism, including the full derivation of the equations of motion. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
Local control of non-adiabatic dissociation dynamics
NASA Astrophysics Data System (ADS)
Bomble, L.; Chenel, A.; Meier, C.; Desouter-Lecomte, M.
2011-05-01
We present a theoretical approach which consists of applying the strategy of local control to projectors based on asymptotic scattering states. This allows to optimize final state distributions upon laser excitation in cases where strong non-adiabatic effects are present. The approach, despite being based on a time-local formulation, can take non-adiabatic transitions that appear at later times fully into account and adopt a corresponding control strategy. As an example, we show various dissociation channels of HeH+, a system where the ultrafast dissociation dynamics is determined by strong non-Born-Oppenheimer effects.
Geometric stability of topological lattice phases
Jackson, T. S.; Möller, Gunnar; Roy, Rahul
2015-01-01
The fractional quantum Hall (FQH) effect illustrates the range of novel phenomena which can arise in a topologically ordered state in the presence of strong interactions. The possibility of realizing FQH-like phases in models with strong lattice effects has attracted intense interest as a more experimentally accessible venue for FQH phenomena which calls for more theoretical attention. Here we investigate the physical relevance of previously derived geometric conditions which quantify deviations from the Landau level physics of the FQHE. We conduct extensive numerical many-body simulations on several lattice models, obtaining new theoretical results in the process, and find remarkable correlation between these conditions and the many-body gap. These results indicate which physical factors are most relevant for the stability of FQH-like phases, a paradigm we refer to as the geometric stability hypothesis, and provide easily implementable guidelines for obtaining robust FQH-like phases in numerical or real-world experiments. PMID:26530311
Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics
NASA Astrophysics Data System (ADS)
Albert, Julian; Kaiser, Dustin; Engel, Volker
2016-05-01
Using a model for coupled electronic-nuclear motion we investigate the range from negligible to strong non-adiabatic coupling. In the adiabatic case, the quantum dynamics proceeds in a single electronic state, whereas for strong coupling a complete transition between two adiabatic electronic states takes place. It is shown that in all coupling regimes the short-time wave-packet dynamics can be described using ensembles of classical trajectories in the phase space spanned by electronic and nuclear degrees of freedom. We thus provide an example which documents that the quantum concept of non-adiabatic transitions is not necessarily needed if electronic and nuclear motion is treated on the same footing.
Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics.
Albert, Julian; Kaiser, Dustin; Engel, Volker
2016-05-01
Using a model for coupled electronic-nuclear motion we investigate the range from negligible to strong non-adiabatic coupling. In the adiabatic case, the quantum dynamics proceeds in a single electronic state, whereas for strong coupling a complete transition between two adiabatic electronic states takes place. It is shown that in all coupling regimes the short-time wave-packet dynamics can be described using ensembles of classical trajectories in the phase space spanned by electronic and nuclear degrees of freedom. We thus provide an example which documents that the quantum concept of non-adiabatic transitions is not necessarily needed if electronic and nuclear motion is treated on the same footing.
Non-adiabatic effect in quantum pumping for a spin-boson system
NASA Astrophysics Data System (ADS)
Watanabe, Kota L.; Hayakawa, Hisao
2014-11-01
We clarify the role of non-adiabatic effects in quantum pumping for a spin-boson system. When we sinusoidally control the temperatures of two reservoirs with π /2 phase difference, we find that the pumping current strongly depends on the initial condition, and thus, the current deviates from that predicted by the adiabatic treatment. We also analytically obtain the contribution of non-adiabatic effects in the pumping current proportional to Ω ^3, where Ω is the angular frequency of the temperature control. The validity of the analytic expression is verified by our numerical calculation. Moreover, we extend the steady heat fluctuation theorem to the case for slowly modulated temperatures and large transferred energies.
The geometric phase controls ultracold chemistry
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-07-30
In this study, the geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born–Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O + OH → H + O2more » reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.« less
Geometric phase effects in ultracold chemistry
NASA Astrophysics Data System (ADS)
Hazra, Jisha; Naduvalath, Balakrishnan; Kendrick, Brian K.
2016-05-01
In molecules, the geometric phase, also known as Berry's phase, originates from the adiabatic transport of the electronic wavefunction when the nuclei follow a closed path encircling a conical intersection between two electronic potential energy surfaces. It is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. It arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. Illustrative results are presented for the O+ OH --> H+ O2 reaction and for hydrogen exchange in H+ H2 and D+HD reactions. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. This work was supported in part by NSF Grant PHY-1505557 (N.B.) and ARO MURI Grant No. W911NF-12-1-0476 (N.B.).
Semiclassical Monte Carlo: a first principles approach to non-adiabatic molecular dynamics.
White, Alexander J; Gorshkov, Vyacheslav N; Wang, Ruixi; Tretiak, Sergei; Mozyrsky, Dmitry
2014-11-14
Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.
Semiclassical Monte Carlo: A first principles approach to non-adiabatic molecular dynamics
White, Alexander J.; Gorshkov, Vyacheslav N.; Wang, Ruixi; Tretiak, Sergei; Mozyrsky, Dmitry
2014-11-14
Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.
Semiclassical Monte Carlo: a first principles approach to non-adiabatic molecular dynamics.
White, Alexander J; Gorshkov, Vyacheslav N; Wang, Ruixi; Tretiak, Sergei; Mozyrsky, Dmitry
2014-11-14
Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement. PMID:25399126
Semiclassical Monte Carlo: A first principles approach to non-adiabatic molecular dynamics
NASA Astrophysics Data System (ADS)
White, Alexander J.; Gorshkov, Vyacheslav N.; Wang, Ruixi; Tretiak, Sergei; Mozyrsky, Dmitry
2014-11-01
Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.
Synchronous particle and non-adiabatic capture
Kats, J.M.
1988-01-01
In the theory of particle longitudinal motion, a classical definition of synchronous particle (synchronous energy, phase, and orbit) assumes that there is a one-to-one correspondence between the guiding magnetic field and the frequency of the accelerating electrical field. In practice, that correspondence may not be sustained because of errors in the magnetic field, in the frequency, or because sometimes one does not want to keep that relationship for some reason. In this paper, a definition of synchronous particle is introduced when the magnetic field and the frequency are independent functions of time. The result is that the size and shape of the bucket (separatrix) depends not only on the field rate of change but also on the frequency rate of change. This means, for example, that one can have a stationary bucket even with a rising field. Having the frequency, in addition to the field and voltage, as parameters controlling the shape and the size of the bucket, it is shown how to decrease particle losses during injection and capture. 2 refs., 2 figs.
Geometric Phase Effect in Heat Transport
NASA Astrophysics Data System (ADS)
Ren, Jie; Hanggi, Petter; Li, Baowen
2011-03-01
Nonlinear molecular heat-pumping devices, which operate via explicitly modulating at least two parameters, are crucial for energy control in low dimensional nano-scale systems. We have applied slow two-parameter modulations on such a molecular junctions and consequently uncovered an intrinsic heat flux contribution, additional to the known, usual dynamical heat flux (from hot to cold). This additional heat flux derives from a nontrivial geometric origin that relates to a non-vanishing, so termed finite Berry phase. It provides a free lunch for the pumped heat and even can direct heat flux against the temperature bias. In addition we are able to show that this so pumped energy exhibits a novel robust fractional quantization phenomenon. Interestingly, this additional geometric heat pump mechanism is also shown to cause a breakdown of the heat-flux fluctuation theorem, which holds true for the non-driving, stationary heat flux transfer. The validity of this theorem is guaranteed whenever (i) the geometric phase contribution vanishes and (ii) the cyclic protocol preserves the detailed balance symmetry.
Analysis of geometric phase effects in the quantum-classical Liouville formalism
Ryabinkin, Ilya G.; Izmaylov, Artur F.; Hsieh, Chang-Yu; Kapral, Raymond
2014-02-28
We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.
Analysis of geometric phase effects in the quantum-classical Liouville formalism.
Ryabinkin, Ilya G; Hsieh, Chang-Yu; Kapral, Raymond; Izmaylov, Artur F
2014-02-28
We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.
Toroidal Precession as a Geometric Phase
J.W. Burby and H. Qin
2012-09-26
Toroidal precession is commonly understood as the orbit-averaged toroidal drift of guiding centers in axisymmetric and quasisymmetric configurations. We give a new, more natural description of precession as a geometric phase effect. In particular, we show that the precession angle arises as the holonomy of a guiding center's poloidal trajectory relative to a principal connection. The fact that this description is physically appropriate is borne out with new, manifestly coordinate-independent expressions for the precession angle that apply to all types of orbits in tokamaks and quasisymmetric stellarators alike. We then describe how these expressions may be fruitfully employed in numerical calculations of precession.
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2015-07-07
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In most cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo.
White, Alexander J; Gorshkov, Vyacheslav N; Tretiak, Sergei; Mozyrsky, Dmitry
2015-07-01
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In most cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems. PMID:26156473
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2015-07-07
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficientmore » as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In many cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.« less
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2015-07-07
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In many cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.
Geometric Phase of a Transported Oscillator
Dittirich, W.
2004-02-25
An oscillator constrained to a plane that is transported along some surface will rotate by an angle dependent only on the path and the surface, not on the speed at which it is transported. This is thus an example of a geometric phase. We analyze this phase using the methods of parallel transport. This concept plays a key role in General Relativity, but it can also be applied in classical mechanics. The Foucault pendulum can be seen as an application of this analysis, where the surface is a sphere and the curve is a line of constant latitude. In view of some considerable confusion and erroneous treatments in the recent literature, we here present a rather simple way for visualizing the motion of the Foucault pendulum using concepts that are based on Frenet's formulae and the methods of parallel displacement.
When do we need to account for the geometric phase in excited state dynamics?
Ryabinkin, Ilya G.; Joubert-Doriol, Loïc; Izmaylov, Artur F.
2014-06-07
We investigate the role of the geometric phase (GP) in an internal conversion process when the system changes its electronic state by passing through a conical intersection (CI). Local analysis of a two-dimensional linear vibronic coupling (LVC) model Hamiltonian near the CI shows that the role of the GP is twofold. First, it compensates for a repulsion created by the so-called diagonal Born–Oppenheimer correction. Second, the GP enhances the non-adiabatic transition probability for a wave-packet part that experiences a central collision with the CI. To assess the significance of both GP contributions we propose two indicators that can be computed from parameters of electronic surfaces and initial conditions. To generalize our analysis to N-dimensional systems we introduce a reduction of a general N-dimensional LVC model to an effective 2D LVC model using a mode transformation that preserves short-time dynamics of the original N-dimensional model. Using examples of the bis(methylene) adamantyl and butatriene cations, and the pyrazine molecule we have demonstrated that their effective 2D models reproduce the short-time dynamics of the corresponding full dimensional models, and the introduced indicators are very reliable in assessing GP effects.
Geometric phase for collinear conical intersections. I. Geometric phase angle and vector potentials
Li Xuan; Brue, Daniel A.; Blandon, Juan D.; Parker, Gregory A.; Kendrick, Brian K.
2011-02-14
We present a method for properly treating collinear conical intersections in triatomic systems. The general vector potential (gauge theory) approach for including the geometric phase effects associated with collinear conical intersections in hyperspherical coordinates is presented. The current study develops an introductory method in the treatment of collinear conical intersections by using the phase angle method. The geometric phase angle, {eta}, in terms of purely internal coordinates is derived using the example of a spin-aligned quartet lithium triatomic system. A numerical fit and thus an analytical form for the associated vector potentials are explicitly derived for this triatomic A{sub 3} system. The application of this methodology to AB{sub 2} and ABC systems is also discussed.
Cao Jun; Liu Lihong; Fang Weihai; Xie Zhizhong; Zhang Yong
2013-04-07
Azobenzene is one of the most widely used photoactive units and recently an ethylene-bridged azobenzene (BAB) was reported to have greatly enhanced conversion efficiency, quantum yield, and other favorable properties. As the first step towards exploring its photo-switchable character in real systems, we report here a systematic study on the photoisomerization dynamics between trans (E) and cis (Z) isomers in the gas phase and the CH{sub 3}OH solution, using ab initio based surface hopping and molecular dynamics, which is the first report of dynamics simulation to reveal the environmental effects on BAB photoreactions. Results show that while the relatively faster S{sub 1} relaxation of the photo-induced E{yields}Z process is only mildly affected by the solvent effect, the relatively slower S{sub 1} relaxation of the reverse reaction becomes even slower in the solution compared to the gas phase. The subsequent S{sub 0} dynamics from the conical intersection between S{sub 1} and S{sub 0} (CI{sub E}) to Z is accelerated in solution compared to the gas phase because of avoided re-crossing to the S{sub 1} state, while the S{sub 0} dynamics from the conical intersection between S{sub 1} and S{sub 0} (CI{sub Z}) to E are basically the same in both phases. Overall, the solvent effect was found to enhance the back-and-forth photo-switch efficiency between the Z and E isomers compared to the gas phase, while the quantum yields are reduced. But the solution yields of both the forward and backward photoreactions are still around 0.4. Therefore, BAB may have good photo-responsive properties if used as a photoactive unit in real systems. These results will facilitate future experimental and theoretical studies in this area to help design new azobenzene derivatives as photoactive units in biological processes, nanoscale devices, and photo-responsive materials.
Non-adiabatic dynamics around a conical intersection with surface-hopping coupled coherent states.
Humeniuk, Alexander; Mitrić, Roland
2016-06-21
A surface-hopping extension of the coupled coherent states-method [D. Shalashilin and M. Child, Chem. Phys. 304, 103-120 (2004)] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schrödinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully's fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronic wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both interference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [A. Ferretti, J. Chem. Phys. 104, 5517 (1996)], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and interferes with itself. These interference effects are absent in classical trajectory-based molecular dynamics but can be fully incorpo rated if trajectories are replaced by surface hopping coupled coherent states. PMID:27334155
Non-adiabatic dynamics around a conical intersection with surface-hopping coupled coherent states
NASA Astrophysics Data System (ADS)
Humeniuk, Alexander; Mitrić, Roland
2016-06-01
A surface-hopping extension of the coupled coherent states-method [D. Shalashilin and M. Child, Chem. Phys. 304, 103-120 (2004)] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schrödinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully's fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronic wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both interference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [A. Ferretti, J. Chem. Phys. 104, 5517 (1996)], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and interferes with itself. These interference effects are absent in classical trajectory-based molecular dynamics but can be fully incorpo rated if trajectories are replaced by surface hopping coupled coherent states.
Turbulent Density Variations in Non-Adiabatic Interstellar Fluids
NASA Astrophysics Data System (ADS)
Higdon, J. C.; Conley, Alex
1998-05-01
Analyses of radio scintillation measurements have demonstrated (e.g., Rickett, ARAA, 28, 561, 1990) the existence of ubiquitous turbulent density fluctuations in the interstellar medium. Higdon (ApJ, 309, 342, 1986) and Goldreich and Sridhar (ApJ, 438, 763 1995) have modeled successfully these density variations as entropy structures distorted by convection in anisotropic magnetohydrodynamic turbulent flows. However, the interstellar medium is a heterogeneous non-adiabatic fluid whose thermal properties result ( Field, ApJ, 142, 531 1965) from a balance of heating and cooling rates. The effect of the non-adiabatic nature of interstellar fluids on the properties of turbulent cascades to small scales has not been considered previously. We find that in thermally stable fluids that the required balance of heating and cooling decreases the amplitudes of entropy structures independently of their spatial scale. Consequently, we show that if the time scale for turbulent flows to cascade to small scales is significantly greater than the cooling time of an interstellar fluid, the generation of turbulent denisty density variations at large wave numbers is greatly suppressed. Such results constrain possible values for the turbulent outer scale in models of interstellar turbulent flows.
Quantum back-reaction from non-adiabatic changes
NASA Astrophysics Data System (ADS)
Asplund, Curtis; Berenstein, David
2011-04-01
Motivated by the problem of thermalization in QFTs and the dual non-equilibrium BH dynamics, we examine a generic and non-trivial aspect of these phenomena, non-adiabatic changes, in a highly simplified setting. We consider a harmonic oscillator whose frequency depends on a second quantum variable x. Beginning with a classical analysis, we show how the system can be described by an improved adiabatic expansion with a velocity dependent force for x. We find an instability at a critical velocity beyond which the adiabatic (Born-Oppenheimer) approximation breaks down. We extend this calculation to the fully quantum system and to field theory and describe how to study fermions with similar techniques. Finally, we set up a model with an abrupt change in the oscillator whose quantum mechanics can be solved exactly so that one can study the effects of back-reaction of a fully non-adiabatic change in a controlled setting. We comment on applications of these general results to the physics of D-branes, inflation, and BHs in AdS/CFT.
Digital polarization holography advancing geometrical phase optics.
De Sio, Luciano; Roberts, David E; Liao, Zhi; Nersisyan, Sarik; Uskova, Olena; Wickboldt, Lloyd; Tabiryan, Nelson; Steeves, Diane M; Kimball, Brian R
2016-08-01
Geometrical phase or the fourth generation (4G) optics enables realization of optical components (lenses, prisms, gratings, spiral phase plates, etc.) by patterning the optical axis orientation in the plane of thin anisotropic films. Such components exhibit near 100% diffraction efficiency over a broadband of wavelengths. The films are obtained by coating liquid crystalline (LC) materials over substrates with patterned alignment conditions. Photo-anisotropic materials are used for producing desired alignment conditions at the substrate surface. We present and discuss here an opportunity of producing the widest variety of "free-form" 4G optical components with arbitrary spatial patterns of the optical anisotropy axis orientation with the aid of a digital spatial light polarization converter (DSLPC). The DSLPC is based on a reflective, high resolution spatial light modulator (SLM) combined with an "ad hoc" optical setup. The most attractive feature of the use of a DSLPC for photoalignment of nanometer thin photo-anisotropic coatings is that the orientation of the alignment layer, and therefore of the fabricated LC or LC polymer (LCP) components can be specified on a pixel-by-pixel basis with high spatial resolution. By varying the optical magnification or de-magnification the spatial resolution of the photoaligned layer can be adjusted to an optimum for each application. With a simple "click" it is possible to record different optical components as well as arbitrary patterns ranging from lenses to invisible labels and other transparent labels that reveal different images depending on the side from which they are viewed. PMID:27505793
Flapping current sheet motions in magnetotail excited by non-adiabatic ions: case study
NASA Astrophysics Data System (ADS)
Wei, X., Jr.
2015-12-01
The current sheet is a crucial region of the magnetotail, where energy reserve and release take place. The origin of the up-down motions of the current sheet, referred to as flapping motions, is among the most fundamental issues of magnetotail dynamics. Observational evidences suggest that the flapping motion is a kind of internal excited kink-like waves, but its particular propagating features such as the low phase speeds and the propagating direction from the tail center toward flanks do not match any local generation mechanisms previously established so far. Here we report observations of the current sheet flapping motions induced by non-adiabatic ions in the magnetic field configurations with a finite guiding component, whose population present periodic hemispherical asymmetries. Three type of current sheet flapping event in this paper will be discussed. This current sheet flapping phenomenon implies that the excitation mechanism of the current sheet flapping motions is a self-circulation process between the non-adiabatic ion population and the current sheet equilibrium itself.
The current sheet tiled and non-adiabatic ions effect on the flapping motion in magnetotail
NASA Astrophysics Data System (ADS)
Wei, XinHua
2016-04-01
The current sheet is a crucial region of the magnetotail, where energy reserve and release take place. The origin of the up-down motions of the current sheet, referred to as flapping motions, is among the most fundamental issues of magnetotail dynamics. Observational evidences suggest that the flapping motion is a kind of internal excited kink-like waves, but its particular propagating features such as the low phase speeds and the propagating direction from the tail center toward flanks do not match any local generation mechanisms previously established so far. Here we report observations of the current sheet flapping motions induced by non-adiabatic ions in the magnetic field configurations with a finite guiding component, whose population present periodic hemispherical asymmetries. These flapping motion current sheet cases often observed tiled. The current sheet flapping phenomenon implies that the excitation mechanism of the current sheet flapping motions is a self-circulation process between the non-adiabatic ion population and the current sheet equilibrium itself.
Entanglement dynamics via geometric phases in quantum spin chains
Castro, C. S.; Sarandy, M. S.
2011-04-15
We introduce a connection between entanglement induced by interaction and geometric phases acquired by a composite quantum spin system. We begin by analyzing the evaluation of cyclic (Aharonov-Anandan) and noncyclic (Mukunda-Simon) geometric phases for general spin chains evolving in the presence of time-independent magnetic fields. Then, by considering Heisenberg chains, we show that the interaction geometric phase, namely, the total geometric phase with subtraction of free spin contributions, is directly related to the global (Meyer-Wallach) entanglement exhibited by an initially separable state during its evolution in Hilbert space. This is analytically shown for N=2 spins and numerically illustrated for larger chains. This relationship promotes the interaction geometric phase to an indicator of global entanglement in the system, which may constitute a useful tool for quantum tasks based on entanglement as a resource to their performance.
Geometric Phase for Adiabatic Evolutions of General Quantum States
Wu, Biao; Liu, Jie; Niu, Qian; Singh, David J
2005-01-01
The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.
Observational tests of non-adiabatic Chaplygin gas
Carneiro, S.; Pigozzo, C. E-mail: cpigozzo@ufba.br
2014-10-01
In a previous paper [1] it was shown that any dark sector model can be mapped into a non-adiabatic fluid formed by two interacting components, one with zero pressure and the other with equation-of-state parameter ω = -1. It was also shown that the latter does not cluster and, hence, the former is identified as the observed clustering matter. This guarantees that the dark matter power spectrum does not suffer from oscillations or instabilities. It applies in particular to the generalised Chaplygin gas, which was shown to be equivalent to interacting models at both background and perturbation levels. In the present paper we test the non-adiabatic Chaplygin gas against the Hubble diagram of type Ia supernovae, the position of the first acoustic peak in the anisotropy spectrum of the cosmic microwave background and the linear power spectrum of large scale structures. We consider two different compilations of SNe Ia, namely the Constitution and SDSS samples, both calibrated with the MLCS2k2 fitter, and for the power spectrum we use the 2dFGRS catalogue. The model parameters to be adjusted are the present Hubble parameter, the present matter density and the Chaplygin gas parameter α. The joint analysis best fit gives α ≈ - 0.5, which corresponds to a constant-rate energy flux from dark energy to dark matter, with the dark energy density decaying linearly with the Hubble parameter. The ΛCDM model, equivalent to α = 0, stands outside the 3σ confidence interval.
Measurement of a vacuum-induced geometric phase.
Gasparinetti, Simone; Berger, Simon; Abdumalikov, Abdufarrukh A; Pechal, Marek; Filipp, Stefan; Wallraff, Andreas J
2016-05-01
Berry's geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a geometric phase, even when the field is in the vacuum state or any other Fock state. We demonstrate the appearance of a vacuum-induced Berry phase in an artificial atom, a superconducting transmon, interacting with a single mode of a microwave cavity. As we vary the phase of the interaction, the artificial atom acquires a geometric phase determined by the path traced out in the combined Hilbert space of the atom and the quantum field. Our ability to control this phase opens new possibilities for the geometric manipulation of atom-cavity systems also in the context of quantum information processing. PMID:27386533
Measurement of a vacuum-induced geometric phase
Gasparinetti, Simone; Berger, Simon; Abdumalikov, Abdufarrukh A.; Pechal, Marek; Filipp, Stefan; Wallraff, Andreas J.
2016-01-01
Berry’s geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a geometric phase, even when the field is in the vacuum state or any other Fock state. We demonstrate the appearance of a vacuum-induced Berry phase in an artificial atom, a superconducting transmon, interacting with a single mode of a microwave cavity. As we vary the phase of the interaction, the artificial atom acquires a geometric phase determined by the path traced out in the combined Hilbert space of the atom and the quantum field. Our ability to control this phase opens new possibilities for the geometric manipulation of atom-cavity systems also in the context of quantum information processing. PMID:27386533
Geometric phase for open quantum systems and stochastic unravelings
Bassi, Angelo; Ippoliti, Emiliano
2006-06-15
We analyze the geometric phase for an open quantum system when computed by resorting to a stochastic unraveling of the reduced density matrix (quantum jump approach or stochastic Schroedinger equations). We show that the resulting phase strongly depends on the type of unraveling used for the calculations: as such, this phase is not a geometric object since it depends on nonphysical parameters, which are not related to the path followed by the density matrix during the evolution of the system.
Geometric phase and its applications to fundamental physics
NASA Astrophysics Data System (ADS)
Capolupo, A.; Vitiello, G.
2016-09-01
We report on recent results showing that the geometric phase can be used as a tool in the analysis of many different physical systems, as mixed boson systems, CPT and CP violations, Unruh effects, and thermal states. We show that the geometric phases appearing in the time evolution of mixed meson systems like Bs0- bar{{B}}_{{s}}^{{0}} and the K0- bar{{K}}^{{0}}_{} are linked to the parameter z describing the CPT violation. A non-zero phase difference between particle and antiparticle arises only in the presence of CPT symmetry breaking. Then the geometric phase can represent a completely new test for the CPT invariance. Moreover, we study the geometric phase of systems represented by mixed state and undergoing a nonunitary evolution and propose the realization of interferometers which can prove the existence of the Unruh effect and can allow very precise measurements of temperature.
NASA Astrophysics Data System (ADS)
Wu, Wei; Xu, Jing-Bo
2016-09-01
We investigate the quantum phase transition of an atomic ensemble trapped in a single-mode optical cavity via the geometric phase and quantum Fisher information of an extra probe atom which is injected into the optical cavity and interacts with the cavity field. We also find that the geometric quantum correlation between two probe atoms exhibits a double sudden transition phenomenon and show this double sudden transition phenomenon is closely associated with the quantum phase transition of the atomic ensemble. Furthermore, we propose a theoretical scheme to prolong the frozen time during which the geometric quantum correlation remains constant by applying time-dependent electromagnetic field.
Geometric phases in astigmatic optical modes of arbitrary order
Habraken, Steven J. M.; Nienhuis, Gerard
2010-08-15
The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different orders, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of nonastigmatic optical modes with orbital angular momentum in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights into the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schroedinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.
Geometrical phase imprinted on eigenfunctions near an exceptional point
Lee, Soo-Young
2010-12-15
We illustrate how to get the geometric phase from eigenfunctions in the vicinity of an exceptional point in a dielectric microcavity whose non-Hermitian character comes from the outgoing-wave boundary condition. It is shown that the geometrical phase {+-}{pi} can be obtained either from total variation of the inner product of eigenfunctions or from a continuous change of phase plot, not of intensity plot, during a double cyclic parameter variation encircling the exceptional point. One can use either of the two ways by properly choosing the arbitrary phase of the calculated eigenfunctions.
Geometric phase of atoms in a magnetic storage ring
Zhang, P.; You, L.
2006-12-15
A magnetically trapped atom experiences an adiabatic geometric (Berry's) phase due to changing field direction. We investigate theoretically such an Aharonov-Bohm-like geometric phase for atoms adiabatically moving inside a storage ring as demonstrated in several recent experiments. Our result shows that this phase shift is easily observable in a closed-loop interference experiment, and thus the shift has to be accounted for in the proposed inertial sensing applications. The spread in phase shift due to the atom transverse distribution is quantified through numerical simulations.
Geometric phases and cyclic isotropic cosmologies
NASA Astrophysics Data System (ADS)
Banchi, Leonardo; Caravelli, Francesco
2016-05-01
In the present paper we study the evolution of the modes of a scalar field in a cyclic cosmology. In order to keep the discussion clear, we study the features of a scalar field in a toy model, a Friedman-Robertson-Walker Universe with a periodic scale factor, in which the Universe expands, contracts and bounces infinite times, in the approximation in which the dynamic features of this Universe are driven by some external factor, without the backreaction of the scalar field under study. In particular, we show that particle production exhibits features of the cyclic cosmology. Also, by studying the Berry phase of the scalar field, we show that contrary to what is commonly believed, the scalar field carries information from one bounce to another in the form of a global phase which occurs as generically non-zero. The Berry phase is then evaluated numerically in the case of the effective loop quantum cosmology closed Universe. We observe that Berry’s phase is non-zero, but that in the quantum regime the particle content is non-negligible.
Optical Mode Control by Geometric Phase in Quasicrystal Metasurface
NASA Astrophysics Data System (ADS)
Yulevich, Igor; Maguid, Elhanan; Shitrit, Nir; Veksler, Dekel; Kleiner, Vladimir; Hasman, Erez
2015-11-01
We report on the observation of optical spin-controlled modes from a quasicrystalline metasurface as a result of an aperiodic geometric phase induced by anisotropic subwavelength structure. When geometric phase defects are introduced in the aperiodic structured surface, the modes exhibit polarization helicity dependence resulting in the optical spin-Hall effect. The radiative thermal dispersion bands from a quasicrystal structure are studied where the observed bands arise from the optical spin-orbit interaction induced by the aperiodic space-variant orientations of anisotropic antennas. The optical spin-flip behavior of the revealed modes that arise from the geometric phase pickup is experimentally observed within the visible spectrum by measuring the spin-projected diffraction patterns. The introduced ability to manipulate the light-matter interaction of quasicrystals in a spin-dependent manner provides the route for molding light via spin-optical aperiodic artificial planar surfaces.
Optical Mode Control by Geometric Phase in Quasicrystal Metasurface.
Yulevich, Igor; Maguid, Elhanan; Shitrit, Nir; Veksler, Dekel; Kleiner, Vladimir; Hasman, Erez
2015-11-13
We report on the observation of optical spin-controlled modes from a quasicrystalline metasurface as a result of an aperiodic geometric phase induced by anisotropic subwavelength structure. When geometric phase defects are introduced in the aperiodic structured surface, the modes exhibit polarization helicity dependence resulting in the optical spin-Hall effect. The radiative thermal dispersion bands from a quasicrystal structure are studied where the observed bands arise from the optical spin-orbit interaction induced by the aperiodic space-variant orientations of anisotropic antennas. The optical spin-flip behavior of the revealed modes that arise from the geometric phase pickup is experimentally observed within the visible spectrum by measuring the spin-projected diffraction patterns. The introduced ability to manipulate the light-matter interaction of quasicrystals in a spin-dependent manner provides the route for molding light via spin-optical aperiodic artificial planar surfaces.
Phase-space networks of geometrically frustrated systems.
Han, Yilong
2009-11-01
We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.
Phase-space networks of geometrically frustrated systems
NASA Astrophysics Data System (ADS)
Han, Yilong
2009-11-01
We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.
Exploring percolative landscapes: Infinite cascades of geometric phase transitions
NASA Astrophysics Data System (ADS)
Timonin, P. N.; Chitov, Gennady Y.
2016-01-01
The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2 D directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process we show from the Monte Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometric transitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions are a generic feature of percolation as well as of many other transitions with nonlocal order parameters.
Importance of geometric phase effects in ultracold chemistry
Hazra, Jisha; Kendrick, Brian K.; Balakrishnan, Naduvalath
2015-08-28
Here, it is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. The effect arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. It is magnified when the two scattering amplitudes have comparable magnitude and they scatter into the same angular region which occurs in the isotropic scatteringmore » characteristic of the ultracold regime (s-wave scattering). Results are presented for the O + OH → H + O2 reaction for total angular momentum quantum number J = 0–5. Large geometric phase effects occur for collision energies below 0.1 K, but the effect vanishes at higher energies when contributions from different partial waves are included. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. In this case, the geometric phase plays the role of a “quantum switch” which can turn the reaction “on” or “off”.« less
Importance of geometric phase effects in ultracold chemistry
Hazra, Jisha; Kendrick, Brian K.; Balakrishnan, Naduvalath
2015-08-28
Here, it is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. The effect arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. It is magnified when the two scattering amplitudes have comparable magnitude and they scatter into the same angular region which occurs in the isotropic scattering characteristic of the ultracold regime (s-wave scattering). Results are presented for the O + OH → H + O_{2} reaction for total angular momentum quantum number J = 0–5. Large geometric phase effects occur for collision energies below 0.1 K, but the effect vanishes at higher energies when contributions from different partial waves are included. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. In this case, the geometric phase plays the role of a “quantum switch” which can turn the reaction “on” or “off”.
Geometrical Series and Phase Space in a Finite Oscillatory Motion
ERIC Educational Resources Information Center
Mareco, H. R. Olmedo
2006-01-01
This article discusses some interesting physical properties of oscillatory motion of a particle on two joined inclined planes. The geometrical series demonstrates that the particle will oscillate during a finite time. Another detail is the converging path to the origin of the phase space. Due to its simplicity, this motion may be used as a…
A mechanical device to study geometric phases and curvatures
NASA Astrophysics Data System (ADS)
Gil, Salvador
2010-04-01
A simple mechanical device is introduced that can be used to illustrate the parallel transport of a vector along a curved surface and the geometric phase shift that occurs when a vector is carried along a loop on a curved surface. Its connection with the Foucault pendulum and Berry phases is discussed. The experimental results are in close agreement with the theoretical expectations. The experiment is inexpensive and conceptually easy to understand and perform.
Artefacts in geometric phase analysis of compound materials.
Peters, Jonathan J P; Beanland, Richard; Alexe, Marin; Cockburn, John W; Revin, Dmitry G; Zhang, Shiyong Y; Sanchez, Ana M
2015-10-01
The geometric phase analysis (GPA) algorithm is known as a robust and straightforward technique that can be used to measure lattice strains in high resolution transmission electron microscope (TEM) images. It is also attractive for analysis of aberration-corrected scanning TEM (ac-STEM) images that resolve every atom column, since it uses Fourier transforms and does not require real-space peak detection and assignment to appropriate sublattices. Here it is demonstrated that, in ac-STEM images of compound materials with compositionally distinct atom columns, an additional geometric phase is present in the Fourier transform. If the structure changes from one area to another in the image (e.g. across an interface), the change in this additional phase will appear as a strain in conventional GPA, even if there is no lattice strain. Strategies to avoid this pitfall are outlined.
Geometric Phase of Phase Space Trajectories:Mobius Strip and Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Balakrishnan, Radha; Satija, Indubala
2005-03-01
We present a gauge invariant formulation of associating a geometric phase with classical phase space trajectories. This geometric phase which depends upon the integrated torsion of the trajectory, bears a close analogy to the generalized Berry phase associated with the time evolution of the quantum wave functions. This topological quantity serves as an order parameter signalling phase transitions including novel geometrical transitions. One of the interesting aspects seen in Duffing and other nonlinear oscillators is the sudden jumps in the geometric phase which is accompanied by the divergence of the local torsion and the vanishing of the local curvature. Intriguingly, the analogous phenomenon was seen in a mobius strip when the ratio of the width to the length of the strip exceeds beyound a critical value.
BOOK REVIEW: The Geometric Phase in Quantum Systems
NASA Astrophysics Data System (ADS)
Pascazio, S.
2003-12-01
The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke `after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is
Non-adiabatic holonomic quantum computation in linear system-bath coupling.
Sun, Chunfang; Wang, Gangcheng; Wu, Chunfeng; Liu, Haodi; Feng, Xun-Li; Chen, Jing-Ling; Xue, Kang
2016-02-05
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of (N - 2)/N. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.
Non-adiabatic holonomic quantum computation in linear system-bath coupling
Sun, Chunfang; Wang, Gangcheng; Wu, Chunfeng; Liu, Haodi; Feng, Xun-Li; Chen, Jing-Ling; Xue, Kang
2016-01-01
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of . The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities. PMID:26846444
Non-adiabatic holonomic quantum computation in linear system-bath coupling
NASA Astrophysics Data System (ADS)
Sun, Chunfang; Wang, Gangcheng; Wu, Chunfeng; Liu, Haodi; Feng, Xun-Li; Chen, Jing-Ling; Xue, Kang
2016-02-01
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of . The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.
Geometric Phase Of The Faraday Rotation Of Electromagnetic Waves In Magnetized Plasma
Jian Liu and Hong Qin
2011-11-07
The geometric phase of circularly polarized electromagnetic waves in nonuniform magnetized plasmas is studied theoretically. The variation of the propagation direction of circularly polarized waves results in a geometric phase, which also contributes to the Faraday rotation, in addition to the standard dynamical phase. The origin and properties of the geometric phase is investigated. The in uence of the geometric phase to plasma diagnostics using Faraday rotation is also discussed as an application of the theory.
Geometric phases of the Faraday rotation of electromagnetic waves in magnetized plasmas
Liu Jian; Qin Hong
2012-10-15
Geometric phases of circularly polarized electromagnetic waves in nonuniform magnetized plasmas is studied theoretically. The variation of the propagation direction of circularly polarized waves results in a geometric phase, which also contributes to the Faraday rotation, in addition to the standard dynamical phase. The origin and properties of the geometric phase are investigated. The influence of the geometric phase to plasma diagnostics using the Faraday rotation is discussed as an application of the theory.
Non Abelian structures and the geometric phase of entangled qudits
Oxman, L.E. Khoury, A.Z.
2014-12-15
In this work, we address some important topological and algebraic aspects of two-qudit states evolving under local unitary operations. The projective invariant subspaces and evolutions are connected with the common elements characterizing the su(d) Lie algebra and their representations. In particular, the roots and weights turn out to be natural quantities to parametrize cyclic evolutions and fractional phases. This framework is then used to recast the coset contribution to the geometric phase in a form that generalizes the usual monopole-like formula for a single qubit.
Towards disentangling coupled electronic-vibrational dynamics in ultrafast non-adiabatic processes
Blanchet; Lochbrunner; Schmitt; Shaffer; Larsen; Zgierski; Seideman; Stolow
2000-01-01
Femtosecond time-resolved photoelectron spectroscopy is emerging as a new technique for investigating polyatomic excited state dynamics. Due to the sensitivity of photoelectron spectroscopy to both electronic configurations and vibrational dynamics, it is well suited to the study of non-adiabatic processes such as internal conversion, which often occur on sub-picosecond time scales. We discuss the technical requirements for such experiments, including lasers systems, energy- and angle-resolved photoelectron spectrometers and new detectors for coincidence experiments. We present a few examples of these methods applied to problems in diatomic wavepacket dynamics and ultrafast non-adiabatic processes in polyatomic molecules.
Geometric phases causing lifetime modifications of metastable states of hydrogen
NASA Astrophysics Data System (ADS)
Trappe, Martin-Isbjörn; Augenstein, Peter; DeKieviet, Maarten; Gasenzer, Thomas; Nachtmann, Otto
2016-04-01
Externally applied electromagnetic fields in general have an influence on the width of atomic spectral lines. The decay rates of atomic states can also be affected by the geometry of an applied field configuration giving rise to an imaginary geometric phase. A specific chiral electromagnetic field configuration is presented which geometrically modifies the lifetimes of metastable states of hydrogen. We propose to extract the relevant observables in a realistic longitudinal atomic beam spin-echo apparatus which allows the initial and final fluxes of the metastable atoms to be compared with each other interferometrically. A geometry-induced change in lifetimes at the 5%-level is found, an effect large enough to be observed in an available experiment.
A study of geometric phase topology using Fourier transform method
NASA Astrophysics Data System (ADS)
Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-07-01
Topological aspect of the geometric phase (GP) due to pure polarization projection is studied using the 2D Fourier transform (2D-FT) method. Projection of orthogonal polarization state results in a phase singularity in the 2D parameter space of ellipticity and orientation of polarization ellipse. Projection of its surrounding states results in an accumulation of GP in different amount that form a spiral structure. A half wave plate-quarter wave plate combination is used to generate different polarization states which are projected using a polarizer. The accumulated phase for each orientation of the wave plate is extracted from 2D-FT of the interferogram, obtained by interfering it with a reference beam in a Mach-Zehnder like interferometer.
Geometric phase and gauge connection in polyatomic molecules.
Wittig, Curt
2012-05-14
Geometric phase is an interesting topic that is germane to numerous and varied research areas: molecules, optics, quantum computing, quantum Hall effect, graphene, and so on. It exists only when the system of interest interacts with something it perceives as exterior. An isolated system cannot display geometric phase. This article addresses geometric phase in polyatomic molecules from a gauge field theory perspective. Gauge field theory was introduced in electrodynamics by Fock and examined assiduously by Weyl. It yields the gauge field A(μ), particle-field couplings, and the Aharonov-Bohm phase, while Yang-Mills theory, the cornerstone of the standard model of physics, is a template for non-Abelian gauge symmetries. Electronic structure theory, including nonadiabaticity, is a non-Abelian gauge field theory with matrix-valued covariant derivative. Because the wave function of an isolated molecule must be single-valued, its global U(1) symmetry cannot be gauged, i.e., products of nuclear and electron functions such as χ(n)ψ(n) are forbidden from undergoing local phase transformation on R, where R denotes nuclear degrees of freedom. On the other hand, the synchronous transformations (first noted by Mead and Truhlar): ψ(n)→ψ(n)e(iζ) and simultaneously χ(n)→χ(n)e(-iζ), preserve single-valuedness and enable wave functions in each subspace to undergo phase transformation on R. Thus, each subspace is compatible with a U(1) gauge field theory. The central mathematical object is Berry's adiabatic connection i
Geometrically-frustrated pseudogap phase of Coulomb liquids
NASA Astrophysics Data System (ADS)
Pramudya, Y.; Terletska, H.; Pankov, S.; Manousakis, E.; Dobrosavljević, V.
2012-06-01
We study a class of models with long-range repulsive interactions of the generalized Coulomb form V(r)∼1/rα. We show that decreasing the interaction exponent in the regime α
Non-adiabatic pumping in an oscillating-piston model
NASA Astrophysics Data System (ADS)
Chuchem, Maya; Dittrich, Thomas; Cohen, Doron
2012-05-01
We consider the prototypical "piston pump" operating on a ring, where a circulating current is induced by means of an AC driving. This can be regarded as a generalized Fermi-Ulam model, incorporating a finite-height moving wall (piston) and non-trivial topology (ring). The amount of particles transported per cycle is determined by a layered structure of phase space. Each layer is characterized by a different drift velocity. We discuss the differences compared with the adiabatic and Boltzmann pictures, and highlight the significance of the "diabatic" contribution that might lead to a counter-stirring effect.
Martínez-Mesa, Aliezer; Saalfrank, Peter
2015-05-21
Femtosecond-laser pulse driven non-adiabatic spectroscopy and dynamics in molecular and condensed phase systems continue to be a challenge for theoretical modelling. One of the main obstacles is the “curse of dimensionality” encountered in non-adiabatic, exact wavepacket propagation. A possible route towards treating complex molecular systems is via semiclassical surface-hopping schemes, in particular if they account not only for non-adiabatic post-excitation dynamics but also for the initial optical excitation. One such approach, based on initial condition filtering, will be put forward in what follows. As a simple test case which can be compared with exact wavepacket dynamics, we investigate the influence of the different parameters determining the shape of a laser pulse (e.g., its finite width and a possible chirp) on the predissociation dynamics of a NaI molecule, upon photoexcitation of the A(0{sup +}) state. The finite-pulse effects are mapped into the initial conditions for semiclassical surface-hopping simulations. The simulated surface-hopping diabatic populations are in qualitative agreement with the quantum mechanical results, especially concerning the subpicosend photoinduced dynamics, the main deviations being the relative delay of the non-adiabatic transitions in the semiclassical picture. Likewise, these differences in the time-dependent electronic populations calculated via the semiclassical and the quantum methods are found to have a mild influence on the overall probability density distribution. As a result, the branching ratios between the bound and the dissociative reaction channels and the time-evolution of the molecular wavepacket predicted by the semiclassical method agree with those computed using quantum wavepacket propagation. Implications for more challenging molecular systems are given.
Geometric phase effects in ultracold hydrogen exchange reaction
NASA Astrophysics Data System (ADS)
Hazra, Jisha; Kendrick, Brian K.; Balakrishnan, N.
2016-10-01
The role of the geometric phase effect on chemical reaction dynamics is explored by examining the hydrogen exchange process in the fundamental H+HD reaction. Results are presented for vibrationally excited HD molecules in the v = 4 vibrational level and for collision energies ranging from 1 μK to 100 K. It is found that, for collision energies below 3 K, inclusion of the geometric phase leads to dramatic enhancement or suppression of the reaction rates depending on the final quantum state of the HD molecule. The effect was found to be the most prominent for rotationally resolved integral and differential cross sections but it persists to a lesser extent in the vibrationally resolved and total reaction rate coefficients. However, no significant GP effect is present in the reactive channel leading to the D+H2 product or in the D+H2 (v=4,j=0) \\to HD+H reaction. A simple interference mechanism involving inelastic (nonreactive) and exchange scattering amplitudes is invoked to account for the observed GP effects. The computed results also reveal a shape resonance in the H+HD reaction near 1 K and the GP effect is found to influence the magnitude of the resonant part of the cross section. Experimental detection of the resonance may allow a sensitive probe of the GP effect in the H+HD reaction.
Macroscopic polarization in crystalline dielectrics: the geometric phase approach
NASA Astrophysics Data System (ADS)
Resta, Raffaele
1994-07-01
The macroscopic electric polarization of a crystal is often defined as the dipole of a unit cell. In fact, such a dipole moment is ill defined, and the above definition is incorrect. Looking more closely, the quantity generally measured is differential polarization, defined with respect to a "reference state" of the same material. Such differential polarizations include either derivatives of the polarization (dielectric permittivity, Born effective charges, piezoelectricity, pyroelectricity) or finite differences (ferroelectricity). On the theoretical side, the differential concept is basic as well. Owing to continuity, a polarization difference is equivalent to a macroscopic current, which is directly accessible to the theory as a bulk property. Polarization is a quantum phenomenon and cannot be treated with a classical model, particularly whenever delocalized valence electrons are present in the dielectric. In a quantum picture, the current is basically a property of the phase of the wave functions, as opposed to the charge, which is a property of their modulus. An elegant and complete theory has recently been developed by King-Smith and Vanderbilt, in which the polarization difference between any two crystal states-in a null electric field-takes the form of a geometric quantum phase. The author gives a comprehensive account of this theory, which is relevant for dealing with transverse-optic phonons, piezoelectricity, and ferroelectricity. Its relation to the established concepts of linear-response theory is also discussed. Within the geometric phase approach, the relevant polarization difference occurs as the circuit integral of a Berry connection (or "vector potential"), while the corresponding curvature (or "magnetic field") provides the macroscopic linear response.
Non-adiabatic dynamics close to conical intersections and the surface hopping perspective
Malhado, João Pedro; Bearpark, Michael J.; Hynes, James T.
2014-01-01
Conical intersections play a major role in the current understanding of electronic de-excitation in polyatomic molecules, and thus in the description of photochemistry and photophysics of molecular systems. This article reviews aspects of the basic theory underlying the description of non-adiabatic transitions at conical intersections, with particular emphasis on the important case when the dynamics of the nuclei are treated classically. Within this classical nuclear motion framework, the main aspects of the surface hopping methodology in the conical intersection context are presented. The emerging picture from this treatment is that of electronic transitions around conical intersections dominated by the interplay of the nuclear velocity and the derivative non-adiabatic coupling vector field. PMID:25485263
Multi-qubit non-adiabatic holonomic controlled quantum gates in decoherence-free subspaces
NASA Astrophysics Data System (ADS)
Hu, Shi; Cui, Wen-Xue; Guo, Qi; Wang, Hong-Fu; Zhu, Ai-Dong; Zhang, Shou
2016-09-01
Non-adiabatic holonomic quantum gate in decoherence-free subspaces is of greatly practical importance due to its built-in fault tolerance, coherence stabilization virtues, and short run-time. Here, we propose some compact schemes to implement two- and three-qubit controlled unitary quantum gates and Fredkin gate. For the controlled unitary quantum gates, the unitary operator acting on the target qubit is an arbitrary single-qubit gate operation. The controlled quantum gates can be directly implemented by utilizing non-adiabatic holonomy in decoherence-free subspaces and the required resource for the decoherence-free subspace encoding is minimal by using only two neighboring physical qubits undergoing collective dephasing to encode a logical qubit.
NASA Astrophysics Data System (ADS)
Hofmann, C.; Zimmermann, T.; Zielinski, A.; Landsman, A. S.
2016-04-01
The validity of the adiabatic approximation in strong field ionization under typical experimental conditions has recently become a topic of great interest. Experimental results have been inconclusive, in part, due to the uncertainty in experimental calibration of intensity. Here we turn to the time-dependent Schrödinger equation, where all the laser parameters are known exactly. We find that the centre of the electron momentum distribution (typically used for calibration of elliptically and circularly polarized light) is sensitive to non-adiabatic effects, leading to intensity shifts in experimental data that can significantly affect the interpretation of results. On the other hand, the transverse momentum spread in the plane of polarization is relatively insensitive to such effects, even in the Keldysh parameter regime approaching γ ≈ 3. This suggests the transverse momentum spread in the plane of polarization as a good alternative to the usual calibration method, particularly for experimental investigation of non-adiabatic effects using circularly polarized light.
Semiclassical Monte-Carlo approach for modelling non-adiabatic dynamics in extended molecules
Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2013-01-01
Modelling of non-adiabatic dynamics in extended molecular systems and solids is a next frontier of atomistic electronic structure theory. The underlying numerical algorithms should operate only with a few quantities (that can be efficiently obtained from quantum chemistry), provide a controlled approximation (which can be systematically improved) and capture important phenomena such as branching (multiple products), detailed balance and evolution of electronic coherences. Here we propose a new algorithm based on Monte-Carlo sampling of classical trajectories, which satisfies the above requirements and provides a general framework for existing surface hopping methods for non-adiabatic dynamics simulations. In particular, our algorithm can be viewed as a post-processing technique for analysing numerical results obtained from the conventional surface hopping approaches. Presented numerical tests for several model problems demonstrate efficiency and accuracy of the new method. PMID:23864100
Semiclassical Monte-Carlo approach for modelling non-adiabatic dynamics in extended molecules.
Gorshkov, Vyacheslav N; Tretiak, Sergei; Mozyrsky, Dmitry
2013-01-01
Modelling of non-adiabatic dynamics in extended molecular systems and solids is a next frontier of atomistic electronic structure theory. The underlying numerical algorithms should operate only with a few quantities (that can be efficiently obtained from quantum chemistry), provide a controlled approximation (which can be systematically improved) and capture important phenomena such as branching (multiple products), detailed balance and evolution of electronic coherences. Here we propose a new algorithm based on Monte-Carlo sampling of classical trajectories, which satisfies the above requirements and provides a general framework for existing surface hopping methods for non-adiabatic dynamics simulations. In particular, our algorithm can be viewed as a post-processing technique for analysing numerical results obtained from the conventional surface hopping approaches. Presented numerical tests for several model problems demonstrate efficiency and accuracy of the new method. PMID:23864100
Multi-qubit non-adiabatic holonomic controlled quantum gates in decoherence-free subspaces
NASA Astrophysics Data System (ADS)
Hu, Shi; Cui, Wen-Xue; Guo, Qi; Wang, Hong-Fu; Zhu, Ai-Dong; Zhang, Shou
2016-06-01
Non-adiabatic holonomic quantum gate in decoherence-free subspaces is of greatly practical importance due to its built-in fault tolerance, coherence stabilization virtues, and short run-time. Here, we propose some compact schemes to implement two- and three-qubit controlled unitary quantum gates and Fredkin gate. For the controlled unitary quantum gates, the unitary operator acting on the target qubit is an arbitrary single-qubit gate operation. The controlled quantum gates can be directly implemented by utilizing non-adiabatic holonomy in decoherence-free subspaces and the required resource for the decoherence-free subspace encoding is minimal by using only two neighboring physical qubits undergoing collective dephasing to encode a logical qubit.
Non-adiabatic molecular dynamics with complex quantum trajectories. I. The diabatic representation.
Zamstein, Noa; Tannor, David J
2012-12-14
We extend a recently developed quantum trajectory method [Y. Goldfarb, I. Degani, and D. J. Tannor, J. Chem. Phys. 125, 231103 (2006)] to treat non-adiabatic transitions. Each trajectory evolves on a single surface according to Newton's laws with complex positions and momenta. The transfer of amplitude between surfaces stems naturally from the equations of motion, without the need for surface hopping. In this paper we derive the equations of motion and show results in the diabatic representation, which is rarely used in trajectory methods for calculating non-adiabatic dynamics. We apply our method to the first two benchmark models introduced by Tully [J. Chem. Phys. 93, 1061 (1990)]. Besides giving the probability branching ratios between the surfaces, the method also allows the reconstruction of the time-dependent wavepacket. Our results are in quantitative agreement with converged quantum mechanical calculations.
Determination of the spin torque non-adiabaticity in perpendicularly magnetized nanowires.
Heinen, J; Hinzke, D; Boulle, O; Malinowski, G; Swagten, H J M; Koopmans, B; Ulysse, C; Faini, G; Ocker, B; Wrona, J; Kläui, M
2012-01-18
Novel nanofabrication methods and the discovery of an efficient manipulation of local magnetization based on spin polarized currents has generated a tremendous interest in the field of spintronics. The search for materials allowing for fast domain wall dynamics requires fundamental research into the effects involved (Oersted fields, adiabatic and non-adiabatic spin torque, Joule heating) and possibilities for a quantitative comparison. Theoretical descriptions reveal a material and geometry dependence of the non-adiabaticity factor β, which governs the domain wall velocity. Here, we present two independent approaches for determining β: (i) measuring the dependence of the dwell times for which a domain wall stays in a metastable pinning state on the injected current and (ii) the current-field equivalence approach. The comparison of the deduced β values highlights the problems of using one-dimensional models to describe two-dimensional dynamics and allows us to ascertain the reliability, robustness and limits of the approaches used. PMID:22172802
Coverage dependent non-adiabaticity of CO on a copper surface
Omiya, Takuma; Arnolds, Heike
2014-12-07
We have studied the coverage-dependent energy transfer dynamics between hot electrons and CO on Cu(110) with femtosecond visible pump, sum frequency probe spectroscopy. We find that transients of the C–O stretch frequency display a red shift, which increases from 3 cm{sup −1} at 0.1 ML to 9 cm{sup −1} at 0.77 ML. Analysis of the transients reveals that the non-adiabatic coupling between the adsorbate vibrational motion and the electrons becomes stronger with increasing coverage. This trend requires the frustrated rotational mode to be the cause of the non-adiabatic behavior, even for relatively weak laser excitation of the adsorbate. We attribute the coverage dependence to both an increase in the adsorbate electronic density of states and an increasingly anharmonic potential energy surface caused by repulsive interactions between neighboring CO adsorbates. This work thus reveals adsorbate-adsorbate interactions as a new way to control adsorbate non-adiabaticity.
Adiabatic geometric phase for a Bose-Einstein condensate coupled to a cavity
Li Shengchang; Fu Libin; Liu Jie
2011-11-15
We investigate the geometric phase in a model of a Bose-Einstein condensate coupled to an optical cavity in which both the condensate and the cavity are described with coherent states. When the argument of the atom-cavity coupling term varies in time slowly from zero to 2{pi}, we calculate the geometric phase accumulated by the ground state and obtain its analytic expression in explicit form. We find that the adiabatic geometric phase jumps from zero to nontrivial {pi} at a critical value that corresponds to the normal-superradiant phase-transition point. The magneticlike flux interpretation of the geometric phase is also discussed.
Geometric phase of a qubit driven by a phase noise laser under non-Markovian dynamics
Berrada, K.
2014-01-15
Robustness of the geometric phase (GP) with respect to the environmental effects is a basic condition for an effective quantum computation. Here, we study quantitatively the GP of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system. We find that with the change of the damping coupling, the GP is very sensitive to its properties exhibiting long collapse and revival phenomena, which play a significant role in enhancing the stabilization and control of the system dynamics. Moreover, we show that the GP can be considered as a tool for testing and characterizing the nature of the qubit–environment coupling. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement dynamics between the qubit with its environment under external classical noise is evaluated and investigated during the time evolution. -- Highlights: •Geometric phase under noise phase laser. •Dynamics of the geometric phase under non-Markovian dynamics in the presence of classical noise. •Solution of master equation of the system in terms atomic inversion. •Nonlocal correlation between the system and its environment under non-Markovianity.
Geometric-phase theory of coherent transport in insulators
NASA Astrophysics Data System (ADS)
Souza, Ivo; Íñiguez, Jorge; Vanderbilt, David
2003-03-01
We consider the macroscopic polarization current J=dP/dt induced, in the absence of scattering, by a homogeneous electric field l E(t) or some other time-varying parameter in the Hamiltonian of an insulating solid. We find that, even under nonadiabatic conditions, the integrated current Δ P=int_0^T J(t) dt is still given by the King-Smith-Vanderbilt geometric-phase formula,(R. D. King-Smith and D. Vanderbilt, Phys. Rev. B 47), 1651 (1993). originally derived assuming adiabaticity. This leads to a computationally convenient form for the time-dependent Schrödinger equation in an electric field. The recently proposed minimization of an energy functional for an insulator in a static field(I. Souza, J. Íñiguez, and D. Vanderbilt, Phys. Rev. Lett. 89), 117602 (2002). is recovered as a stationary solution. The formalism is used to compute the Franz-Keldysh effect in the context of a tight-binding model.
Geometric phase of mixed states for three-level open systems
Jiang Yanyan; Ji, Y. H.; Wang, Z. S.; Xu Hualan; Hu Liyun; Chen, Z. Q.; Guo, L. P.
2010-12-15
Geometric phase of mixed state for three-level open system is defined by establishing in connecting density matrix with nonunit vector ray in a three-dimensional complex Hilbert space. Because the geometric phase depends only on the smooth curve on this space, it is formulated entirely in terms of geometric structures. Under the limiting of pure state, our approach is in agreement with the Berry phase, Pantcharatnam phase, and Aharonov and Anandan phase. We find that, furthermore, the Berry phase of mixed state correlated to population inversions of three-level open system.
Manifestation of the geometric phase in neutron spin-echo experiments
NASA Astrophysics Data System (ADS)
Kraan, W. H.; Grigoriev, S. V.; Rekveldt, M. T.
2010-07-01
We show how the geometric (Berry’s) phase becomes manifest on adiabatic rotation of the polarization vector in the magnetic field configuration in the arms in a neutron spin echo (NSE) experiment. When the neutron beam used is monochromatic, a geometric phase collected in one spin-echo arm can be exactly compensated in the other arm either by an opposite geometrical rotation or by adding/subtracting a dynamic (Larmor) phase. This is not possible in a white beam, because, contrary to the dynamic phase, the geometric phase is independent of wavelength. Therefore, the NSE pattern can be disturbed. We demonstrate that adiabatic resonant spin flippers inherently produce a geometric phase which can influence the performance of NSE setups based on such flippers. This effect can be avoided by a proper mutual symmetry of the gradient fields in these flippers.
Density matrix treatment of non-adiabatic photoinduced electron transfer at a semiconductor surface.
Micha, David A
2012-12-14
Photoinduced electron transfer at a nanostructured surface leads to localized transitions and involves three different types of non-adiabatic couplings: vertical electronic transitions induced by light absorption emission, coupling of electronic states by the momentum of atomic motions, and their coupling due to interactions with electronic density fluctuations and vibrational motions in the substrate. These phenomena are described in a unified way by a reduced density matrix (RDM) satisfying an equation of motion that contains dissipative rates. The RDM treatment is used here to distinguish non-adiabatic phenomena that are localized from those due to interaction with a medium. The fast decay of localized state populations due to electronic density fluctuations in the medium has been treated within the Lindblad formulation of rates. The formulation is developed introducing vibronic states constructed from electron orbitals available from density functional calculations, and from vibrational states describing local atomic displacements. Related ab initio molecular dynamics calculations have provided diabatic momentum couplings between excited electronic states. This has been done in detail for an indirect photoexcitation mechanism of the surface Ag(3)Si(111):H, which leads to long lasting electronic charge separation. The resulting coupled density matrix equations are solved numerically to obtain the population of the final charge-separated state as it changes over time, for several values of the diabatic momentum coupling. New insight and unexpected results are presented here which can be understood in terms of photoinduced non-adiabatic transitions involving many vibronic states. It is found that the population of long lasting charge separation states is larger for smaller momentum coupling, and that their population grows faster for smaller coupling.
Non-adiabatic effects on the optical response of driven systems
NASA Astrophysics Data System (ADS)
Fregoso, Benjamin M.; Kolodrubetz, Michael; Moore, Joel
Periodically driven systems have received renewed interest due to their capacity to engineer non-trivial effective Hamiltonians. A characteristic of such systems is how they respond to weak periodicity-breaking drive, as for example when a laser is pulsed instead of continuous wave. We develop semi-classical equations of motion of a wave packet in the presence of electric and magnetic fields which are turned on non-adiabatically. We then show the emergence of significant corrections to electronic collective excitations and optical responses of topological insulator surface states, Weyl metals and semiconductor mono-chalcogenides.
Taple-top imaging of the non-adiabatically driven isomerization in the acetylene cation
NASA Astrophysics Data System (ADS)
Beaulieu, Samuel; Ibrahim, Heide; Wales, Benji; Schmidt, Bruno E.; Thiré, Nicolas; Bisson, Éric; Hebeisen, Christoph T.; Wanie, Vincent; Giguere, Mathieu; Kieffer, Jean-Claude; Sanderson, Joe; Schuurman, Michael S.; Légaré, François
2014-05-01
One of the primary goals of modern ultrafast science is to follow nuclear and electronic evolution of molecules as they undergo a photo-chemical reaction. Most of the interesting dynamics phenomena in molecules occur when an electronically excited state is populated. When the energy difference between electronic ground and excited states is large, Free Electron Laser (FEL) and HHG-based VUV sources were, up to date, the only light sources able to efficiently initiate those non-adiabatic dynamics. We have developed a simple table-top approach to initiate those rich dynamics via multiphoton absorption. As a proof of principle, we studied the ultrafast isomerization of the acetylene cation. We have chosen this model system for isomerization since the internal conversion mechanism which leads to proton migration is still under debate since decades. Using 266 nm multiphoton absorption as a pump and 800 nm induced Coulomb Explosion as a probe, we have shoot the first high-resolution molecular movie of the non-adiabatically driven proton migration in the acetylene cation. The experimental results are in excellent agreement with high level ab initio trajectory simulations.
Deviation from Berry's adiabatic geometric phase in a [sup 131]Xe nuclear gyroscope
Appelt, S.; Waeckerle, G.; Mehring, M. )
1994-06-20
The concept of geometric phase is demonstrated in a nuclear gyroscope using [sup 131]Xe nuclear spins ([ital I]=3/2) as sensors for quantum-phase accumulation. By spatial rotation sub-Hertz splittings due to geometric phases are resolved in nuclear-quadrupole spectra. Deviations from Berry's adiabatic geometric phase appear in the regime of nonadiabatic rotation. The observed frequency splittings are no longer linear in the rotational frequency, as expected from adiabatic rotations, and all possible transitions, namely, six in this partially degenerate spin-3/3 system, are observed experimentally.
NASA Astrophysics Data System (ADS)
Mandal, Anirban; Hunt, Katharine L. C.
2015-07-01
The energy of a molecule subject to a time-dependent perturbation separates completely into adiabatic and non-adiabatic terms, where the adiabatic term reflects the adjustment of the ground state to the perturbation, while the non-adiabatic term accounts for the transition energy [A. Mandal and K. L. C. Hunt, J. Chem. Phys. 137, 164109 (2012)]. For a molecule perturbed by a time-dependent electromagnetic field, in this work, we show that the expectation value of the power absorbed by the molecule is equal to the time rate of change of the non-adiabatic term in the energy. The non-adiabatic term is given by the transition probability to an excited state k, multiplied by the transition energy from the ground state to k, and then summed over the excited states. The expectation value of the power absorbed by the molecule is derived from the integral over space of the scalar product of the applied electric field and the non-adiabatic current density induced in the molecule by the field. No net power is absorbed due to the action of the applied electric field on the adiabatic current density. The work done on the molecule by the applied field is the time integral of the power absorbed. The result established here shows that work done on the molecule by the applied field changes the populations of the molecular states.
Asymptotic geometric phase and purity for phase qubit dispersively coupled to lossy LC circuit
Mohamed, A.-B.A.; Obada, A.-S.F.
2011-09-15
Analytical descriptions of the geometric phases (GPs) for the total system and subsystems are studied for a current biased Josephson phase qubit strongly coupled to a lossy LC circuit in the dispersive limit. It is found that, the GP and purity depend on the damping parameter which leads to the phenomenon of GP death. Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP. The asymptotic behavior of the GP and the purity for the qubit-LC resonator state closely follow that for the qubit state, but however, for the LC circuit these asymptotic values are equal to zero. - Highlights: > The model of a current biased Josephson phase qubit, strongly coupled to loss LC circuit, is considered. > Analytical descriptions of the geometric phase (GP) of this model, in the dispersive limit, are studied. > The GP and purity depend on the dissipation which leads to the GP death phenomenon. > Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP.
Non-Abelian geometric phase and long-range atomic forces
NASA Technical Reports Server (NTRS)
Zygelman, B.
1990-01-01
It is shown how gauge fields, or geometric phases, manifest as observable effects in both bound and free diatom systems. It is shown that, in addition to altering energy splittings in bound systems, geometric phases induce transitions in levels separated by a finite-energy gap. An example is given where the non-Abelian gauge field couples nondegenerate electronic levels in a diatom. This gauge-field coupling gives rise to an observable effect. It is shown that when the diatom is 'pulled apart', the non-Abelian geometric phase manifests as a long-range atomic force.
Reflective Spin-Orbit Geometric Phase from Chiral Anisotropic Optical Media.
Rafayelyan, Mushegh; Tkachenko, Georgiy; Brasselet, Etienne
2016-06-24
We report on highly reflective spin-orbit geometric phase optical elements based on a helicity-preserving circular Bragg-reflection phenomenon. First, we present a dynamical geometric phase experiment using a flat chiral Bragg mirror. Then, we show that shaping such a geometric phase allows the efficient spin-orbit tailoring of light fields without the need to fulfill any condition on birefringent phase retardation, in contrast to the case of transmission spin-orbit optical elements. This is illustrated by optical vortex generation from chiral liquid crystal droplets in the Bragg regime that unveils spin-orbit consequences of the droplet's curvature. Our results thus introduce a novel class of geometric phase elements-"Bragg-Berry" optical elements. PMID:27391723
Inflationary perturbation theory is geometrical optics in phase space
Seery, David; Frazer, Jonathan; Mulryne, David J.; Ribeiro, Raquel H. E-mail: D.Mulryne@qmul.ac.uk E-mail: R.Ribeiro@damtp.cam.ac.uk
2012-09-01
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ({sup t}ransport equations{sup )}, analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar 'δN' Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, ζ, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of f{sub NL} in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.
Numerical solution of non-isothermal non-adiabatic flow of real gases in pipelines
NASA Astrophysics Data System (ADS)
Bermúdez, Alfredo; López, Xián; Vázquez-Cendón, M. Elena
2016-10-01
A finite volume scheme for the numerical solution of a mathematical model for non-isothermal non-adiabatic compressible flow of a real gas in a pipeline is introduced. In order to make an upwind discretization of the flux, the Q-scheme of van Leer is used. Unlike standard Euler equations, the model takes into account wall friction, variable height and heat transfer between the pipe and the environment. Since all these terms are sources, in order to get a well-balanced scheme they are discretized by making a similar upwinding to the one in the flux term. The performance of the overall method has been shown for some usual numerical tests. The final goal, which is beyond the scope of this paper, is to consider a network including several pipelines connected at junctions, as those employed for natural gas transport.
Fernandez-Alberti, Sebastian; Makhov, Dmitry V; Tretiak, Sergei; Shalashilin, Dmitrii V
2016-04-21
Photoinduced dynamics of electronic and vibrational unidirectional energy transfer between meta-linked building blocks in a phenylene ethynylene dendrimer is simulated using a multiconfigurational Ehrenfest in time-dependent diabatic basis (MCE-TDDB) method, a new variant of the MCE approach developed by us for dynamics involving multiple electronic states with numerous abrupt crossings. Excited-state energies, gradients and non-adiabatic coupling terms needed for dynamics simulation are calculated on-the-fly using the Collective Electron Oscillator (CEO) approach. A comparative analysis of our results obtained using MCE-TDDB, the conventional Ehrenfest method and the surface-hopping approach with and without decoherence corrections is presented. PMID:27004611
NASA Astrophysics Data System (ADS)
Coïsson, M.; Barrera, G.; Celegato, F.; Martino, L.; Vinai, F.; Martino, P.; Ferraro, G.; Tiberto, P.
2016-10-01
An experimental setup for magnetic hyperthermia operating in non-adiabatic conditions is described. A thermodynamic model that takes into account the heat exchanged by the sample with the surrounding environment is developed. A suitable calibration procedure is proposed that allows the experimental validation of the model. Specific absorption rate can then be accurately determined just from the measurement of the sample temperature at the equilibrium steady state. The setup and the measurement procedure represent a simplification with respect to other systems requiring calorimeters or crucial corrections for heat flow. Two families of magnetic nanoparticles, one superparamagnetic and one characterised by larger sizes and static hysteresis, have been characterised as a function of field intensity, and specific absorption rate and intrinsic loss power have been obtained.
The exact forces on classical nuclei in non-adiabatic charge transfer.
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Maitra, Neepa T; Gross, E K U
2015-02-28
The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect.
Non-adiabatic generation of NOON states in a Tonks-Girardeau gas
NASA Astrophysics Data System (ADS)
Schloss, James; Benseny, Albert; Gillet, Jérémie; Swain, Jacob; Busch, Thomas
2016-03-01
Adiabatic techniques can be used to control quantum states with high fidelity while exercising limited control over the parameters of a system. However, because these techniques are slow compared to other timescales in the system, they are usually not suitable for creating highly unstable states or performing time-critical processes. Both of these situations arise in quantum information processing, where entangled states may be isolated from the environment only for a short time and where quantum computers require high-fidelity operations to be performed quickly. Recently it has been shown that techniques like optimal control and shortcuts to adiabaticity can be used to prepare quantum states non-adiabatically with high fidelity. Here we present two examples of how these techniques can be used to create maximally entangled many-body NOON states in one-dimensional Tonks-Girardeau gases. Dedicated to the memory of Marvin D Girardeau.
The exact forces on classical nuclei in non-adiabatic charge transfer.
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Maitra, Neepa T; Gross, E K U
2015-02-28
The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect. PMID:25725727
The exact forces on classical nuclei in non-adiabatic charge transfer
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Gross, E. K. U.; Maitra, Neepa T.
2015-02-28
The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect.
Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation
Zamstein, Noa; Tannor, David J.
2012-12-14
We present a complex quantum trajectory method for treating non-adiabatic dynamics. Each trajectory evolves classically on a single electronic surface but with complex position and momentum. The equations of motion are derived directly from the time-dependent Schroedinger equation, and the population exchange arises naturally from amplitude-transfer terms. In this paper the equations of motion are derived in the adiabatic representation to complement our work in the diabatic representation [N. Zamstein and D. J. Tannor, J. Chem. Phys. 137, 22A517 (2012)]. We apply our method to two benchmark models introduced by John Tully [J. Chem. Phys. 93, 1061 (1990)], and get very good agreement with converged quantum-mechanical calculations. Specifically, we show that decoherence (spatial separation of wavepackets on different surfaces) is already contained in the equations of motion and does not require ad hoc augmentation.
NASA Astrophysics Data System (ADS)
Drolias, B.; Quenby, J. J.; Witcombe, A.; Korth, A.; Keppler, E.; Blake, J. B.
1996-02-01
The Ulysses encounter with Jupiter gave a unique opportunity for the study of ions in the Jovian day side in the range 0.3 < ( E/nuc) < 6 MeV. The EPAC experiment has already provided a wealth of interesting results concerning the composition and the anisotropies in the magnetosphere (Krupp et al., Planet. Space Sci.41, 953, 1993), however a more complete understanding of the observations is still lacking from the scientific literature. This paper contributes to the field with the analysis of numerical simulations of non-adiabatic trajectories in Jupiter's current sheet and the calculation of the appropriate anisotropies. The results presented here differ from the existing numerical results in that they seem to be in good agreement with the observations of both the Ulysses and Voyager encounters.
Non-adiabatic molecular dynamic simulations of opening reaction of molecular junctions
NASA Astrophysics Data System (ADS)
Zobač, Vladmír; Lewis, James P.; Jelínek, Pavel
2016-07-01
We report non-adiabatic molecular dynamic simulations of the ring opening reaction of diarylethene (DAE) derivative molecules, both free standing and embedded between gold electrodes. Simulations are performed by the surface hopping method employing density functional theory. Typically, the free-standing molecules exhibit large quantum yields to open and close; however the process is quenched for the molecules embedded between electrodes. Our simulations reveal the importance of the DAE side chemical groups, which explain the efficiency of the quenching process. Namely, delocalization of the LUMO state contributes to electronic coupling between the molecule and electrodes, suppressing or enhancing the reaction process. The simulations indicate that a proper choice of the chemical side group, which provides the strong localization of the LUMO state, can substantially diminish the quenching mechanism. Additionally, we analyze a strong dependency of the quantum yield of the opening reaction coming from the mechanical strength of the molecules.
Non-adiabatic effects in near-adiabatic mixed-field orientation and alignment
NASA Astrophysics Data System (ADS)
Maan, Anjali; Ahlawat, Dharamvir Singh; Prasad, Vinod
2016-11-01
We present a theoretical study of the impact of a pair of moderate electric fields tilted an angle with respect to one another on a molecule. As a prototype, we consider a molecule with large rotational constant (with corresponding small rotational period) and moderate dipole moment. Within rigid-rotor approximation, the time-dependent Schrodinger equation is solved using fourth-order Runge-Kutta method. We have analysed that lower rotational states are significantly influenced by variation in pulse durations, the tilt angle between the fields and also on the electric field strengths. We also suggest a control scheme of how the rotational dynamics, orientation and alignment of a molecule can be enhanced by a combination of near-adiabatic pulses in comparision to non-adiabatic or adiabatic pulses.
Non-adiabatic molecular dynamic simulations of opening reaction of molecular junctions.
Zobač, Vladmír; Lewis, James P; Jelínek, Pavel
2016-07-15
We report non-adiabatic molecular dynamic simulations of the ring opening reaction of diarylethene (DAE) derivative molecules, both free standing and embedded between gold electrodes. Simulations are performed by the surface hopping method employing density functional theory. Typically, the free-standing molecules exhibit large quantum yields to open and close; however the process is quenched for the molecules embedded between electrodes. Our simulations reveal the importance of the DAE side chemical groups, which explain the efficiency of the quenching process. Namely, delocalization of the LUMO state contributes to electronic coupling between the molecule and electrodes, suppressing or enhancing the reaction process. The simulations indicate that a proper choice of the chemical side group, which provides the strong localization of the LUMO state, can substantially diminish the quenching mechanism. Additionally, we analyze a strong dependency of the quantum yield of the opening reaction coming from the mechanical strength of the molecules. PMID:27255903
Wiebeler, Christian; Bader, Christina A; Meier, Cedrik; Schumacher, Stefan
2014-07-28
Photochromism allows for reversible light-induced conversion of a molecular species into a different form with significantly altered optical properties. One promising compound that excels with high fatigue resistance and shows its photochromic functionality both in solution and in molecular solid films is the diarylethene derivative CMTE. Here we present a comprehensive study of its photophysical properties with density-functional theory based methods and benchmark the results against higher-level quantum-chemical approaches and experiments. In addition to static properties such as optical absorption, perceived color, and refractive index, we also investigate reaction dynamics based on non-adiabatic ab initio molecular dynamics. This gives detailed insight into the molecules' ultrafast reaction dynamics and enables us to extract reaction time scales and quantum yields for the observed electrocyclic reaction following photoexcitation.
Geometric Phase of the Gyromotion for Charged Particles in a Time-dependent Magnetic Field
Jian Liu and Hong Qin
2011-07-18
We study the dynamics of the gyrophase of a charged particle in a magnetic field which is uniform in space but changes slowly with time. As the magnetic field evolves slowly with time, the changing of the gyrophase is composed of two parts. The rst part is the dynamical phase, which is the time integral of the instantaneous gyrofrequency. The second part, called geometric gyrophase, is more interesting, and it is an example of the geometric phase which has found many important applications in different branches of physics. If the magnetic field returns to the initial value after a loop in the parameter space, then the geometric gyrophase equals the solid angle spanned by the loop in the parameter space. This classical geometric gyrophase is compared with the geometric phase (the Berry phase) of the spin wave function of an electron placed in the same adiabatically changing magnetic field. Even though gyromotion is not the classical counterpart of the quantum spin, the similarities between the geometric phases of the two cases nevertheless reveal the similar geometric nature of the different physics laws governing these two physics phenomena.
Pixel-wise absolute phase unwrapping using geometric constraints of structured light system.
An, Yatong; Hyun, Jae-Sang; Zhang, Song
2016-08-01
This paper presents a method to unwrap phase pixel by pixel by solely using geometric constraints of the structured light system without requiring additional image acquisition or another camera. Specifically, an artificial absolute phase map, Φmin, at a given virtual depth plane z = zmin, is created from geometric constraints of the calibrated structured light system; the wrapped phase is pixel-by-pixel unwrapped by referring to Φmin. Since Φmin is defined in the projector space, the unwrapped phase obtained from this method is absolute for each pixel. Experimental results demonstrate the success of this proposed novel absolute phase unwrapping method. PMID:27505808
Stochastic pump effect and geometric phases in dissipative and stochastic systems
Sinitsyn, Nikolai
2008-01-01
The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).
Geometric phase and quantum correlations for a bipartite two-level system
NASA Astrophysics Data System (ADS)
Lombardo, Fernando C.; Villar, Paula I.
2015-07-01
We calculate the geometric phase of a bipartite two-level system coupled to an external environment. We compute the correction to the unitary geometric phase through a kinematic approach. To this end, we analyse the reduced density matrix of the bipartite system after tracing over the environmental degrees of freedom, for arbitrary initial states of the composite system. In all cases considered, the correction to the unitary phase has a similar structure as a function of the degree of the entanglement of the initial state. In the case of a maximally entangled state (MES), the survival phase is only the topological phase, and there is no correction induced by the environments. Further, we compute the quantum discord and concurrence of the bipartite state and analyse possible relations among these quantities and the geometric phase acquired during the non-unitary system's evolution.
Spatially varying geometric phase in classically entangled vector beams of light
NASA Astrophysics Data System (ADS)
King-Smith, Andrew; Leary, Cody
We present theoretical results describing a spatially varying geometric (Pancharatnam) phase present in vector modes of light, in which the polarization and transverse spatial mode degrees of freedom exhibit classical entanglement. We propose an experimental setup capable of characterizing this effect, in which a vector mode propagates through a Mach-Zehnder interferometer with a birefringent phase retarder present in one arm. Since the polarization state of a classically entangled light beam exhibits spatial variation across the transverse mode profile, the phase retarder gives rise to a spatially varying geometric phase in the beam propagating through it. When recombined with the reference beam from the other interferometer arm, the presence of the geometric phase is exhibited in the resulting interference pattern. We acknowledge funding from the Research Corporation for Science Advancement by means of a Cottrell College Science Award.
Bruno, Patrick
2012-06-15
The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined. PMID:23004240
Bruno, Patrick
2012-06-15
The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined.
On the accuracy of surface hopping dynamics in condensed phase non-adiabatic problems
NASA Astrophysics Data System (ADS)
Chen, Hsing-Ta; Reichman, David R.
2016-03-01
We perform extensive benchmark comparisons of surface hopping dynamics with numerically exact calculations for the spin-boson model over a wide range of energetic and coupling parameters as well as temperature. We find that deviations from golden-rule scaling in the Marcus regime are generally small and depend sensitively on the energetic bias between electronic states. Fewest switches surface hopping (FSSH) is found to be surprisingly accurate over a large swath of parameter space. The inclusion of decoherence corrections via the augmented FSSH algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic, at least for the case of an environment modeled with the commonly used Debye spectral density.
Geometric relativistic phase from Lorentz symmetry breaking effects in the cosmic string spacetime
NASA Astrophysics Data System (ADS)
Belich, H.; Bakke, K.
2016-04-01
In this paper, we have investigated the arising of geometric quantum phases in a relativistic quantum dynamics of a Dirac neutral particle from the spontaneous Lorentz symmetry violation effects in the cosmic string spacetime. We started by the Dirac equation in an effective metric, and we have observed a relativistic geometric phase which stems from the topology of the cosmic string spacetime and an intrinsic Lorentz symmetry breaking effects. It is shown that both Lorentz symmetry breaking effects and the topology of the defect yields a phase shift in the wave function of the nonrelativistic spin-1/2 particle.
Geometric phases for laser-induced aligned pendular states of linear molecules
Aleynikov, Dmitriy V.
2006-02-15
Geometric phases may arise in a linear molecule interacting via its anisotropic polarizability with a strong nonresonant laser field. When the polarization vector of laser radiation undergoes cyclic evolution, the molecule returns to its original state but may acquire a Berry or Aharonov-Anandan phase factor.
Geometric phase in entangled systems: A single-neutron interferometer experiment
Sponar, S.; Klepp, J.; Loidl, R.; Durstberger-Rennhofer, K.; Badurek, G.; Hasegawa, Y.; Filipp, S.; Bertlmann, R. A.; Rauch, H.
2010-04-15
The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. [Phys. Rev. A 69, 032112 (2004)] and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path-entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time-dependent interaction with a radiofrequency field. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme yields a sinusoidal oscillation of the correlation function S, dependent on the geometric phase, such that it varies in the range between 2 and 2{radical}(2) and therefore always exceeds the boundary value 2 between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like CHSH inequality, where S remains 2{radical}(2) for all settings of the geometric phase.
Non-Adiabatic, Multi-State Ring-Polymer Molecular Dynamics
NASA Astrophysics Data System (ADS)
Bell, Franziska; Menzeleev, Artur; Miller, Thomas, III
2014-03-01
Ring-polymer molecular dynamics (RPMD) has been shown to be a promising method for studying mechanisms and rates in large systems which require the inclusion of quantum effects, such as zero-point energies and tunneling. Examples involve electron and/or proton transfer reactions in enzymes and artificial catalysts. However, the traditional formulation of RPMD has several shortcomings: (i) it is restricted to migrations of only one distinguishable electron, (ii) it cannot describe photophysical processes, and (iii) it cannot be used in conjunction with potential energy surfaces obtained from electronic structure methods. Here I present a parameter-free extension of the RPMD method that addresses these issues and allows for the direct simulation of non-adiabatic processes involving many-electron wavefunctions without prior assumptions of the reaction mechanism. The new approach is demonstrated to provide a quantitative description of electron-transfer reaction rates and mechanisms throughout (i) the normal and inverted regimes and (ii) the weak- and strong-coupling regimes. I would like to thank the APS for financial support in form of a New Investigator Travel Award.
Vibrational coherences in charge-transfer dyes: A non-adiabatic picture
Sissa, Cristina; Delchiaro, Francesca; Di Maiolo, Francesco
2014-10-28
Essential-state models efficiently describe linear and nonlinear spectral properties of different families of charge-transfer chromophores. Here, the essential-state machinery is applied to the calculation of the early-stage dynamics after ultrafast (coherent) excitation of polar and quadrupolar chromophores. The fully non-adiabatic treatment of coupled electronic and vibrational motion allows for a reliable description of the dynamics of these intriguing systems. In particular, the proposed approach is reliable even when the adiabatic and harmonic approximations do not apply, such as for quadrupolar dyes that show a multistable, broken-symmetry excited state. Our approach quite naturally leads to a clear picture for a dynamical Jahn-Teller effect in these systems. The recovery of symmetry due to dynamical effects is however disrupted in polar solvents where a static symmetry lowering is observed. More generally, thermal disorder in polar solvents is responsible for dephasing phenomena, damping the coherent oscillations with particularly important effects in the case of polar dyes.
Two-level system in spin baths: Non-adiabatic dynamics and heat transport
Segal, Dvira
2014-04-28
We study the non-adiabatic dynamics of a two-state subsystem in a bath of independent spins using the non-interacting blip approximation, and derive an exact analytic expression for the relevant memory kernel. We show that in the thermodynamic limit, when the subsystem-bath coupling is diluted (uniformly) over many (infinite) degrees of freedom, our expression reduces to known results, corresponding to the harmonic bath with an effective, temperature-dependent, spectral density function. We then proceed and study the heat current characteristics in the out-of-equilibrium spin-spin-bath model, with a two-state subsystem bridging two thermal spin-baths of different temperatures. We compare the behavior of this model to the case of a spin connecting boson baths, and demonstrate pronounced qualitative differences between the two models. Specifically, we focus on the development of the thermal diode effect, and show that the spin-spin-bath model cannot support it at weak (subsystem-bath) coupling, while in the intermediate-strong coupling regime its rectifying performance outplays the spin-boson model.
Moving difference (MDIFF) non-adiabatic rapid sweep (NARS) EPR of copper(II).
Hyde, James S; Bennett, Brian; Kittell, Aaron W; Kowalski, Jason M; Sidabras, Jason W
2013-11-01
Non-adiabatic rapid sweep (NARS) EPR spectroscopy has been introduced for application to nitroxide-labeled biological samples (Kittell et al., 2011). Displays are pure absorption, and are built up by acquiring data in spectral segments that are concatenated. In this paper we extend the method to frozen solutions of copper-imidazole, a square planar copper complex with four in-plane nitrogen ligands. Pure absorption spectra are created from concatenation of 170 5-gauss segments spanning 850 G at 1.9 GHz. These spectra, however, are not directly useful since nitrogen superhyperfine couplings are barely visible. Application of the moving difference (MDIFF) algorithm to the digitized NARS pure absorption spectrum is used to produce spectra that are analogous to the first harmonic EPR. The signal intensity is about four times higher than when using conventional 100 kHz field modulation, depending on line shape. MDIFF not only filters the spectrum, but also the noise, resulting in further improvement of the SNR for the same signal acquisition time. The MDIFF amplitude can be optimized retrospectively, different spectral regions can be examined at different amplitudes, and an amplitude can be used that is substantially greater than the upper limit of the field modulation amplitude of a conventional EPR spectrometer, which improves the signal-to-noise ratio of broad lines.
NASA Astrophysics Data System (ADS)
Heaps, Charles W.; Mazziotti, David A.
2016-08-01
Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, we employ pseudospectral sampling of time-dependent Gaussian basis functions for the simulation of non-adiabatic dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics tests the Schrödinger equation with N Dirac delta functions located at the centers of the Gaussian functions reducing the scaling of potential energy evaluations from O ( N 2 ) to O ( N ) . By projecting the Gaussian basis onto discrete points in space, the method is capable of efficiently and quantitatively describing the nonadiabatic population transfer and intra-surface quantum coherence. We investigate three model systems: the photodissociation of three coupled Morse oscillators, the bound state dynamics of two coupled Morse oscillators, and a two-dimensional model for collinear triatomic vibrational dynamics. In all cases, the pseudospectral Gaussian method is in quantitative agreement with numerically exact calculations. The results are promising for nonadiabatic molecular dynamics in molecular systems where strongly correlated ground or excited states require expensive electronic structure calculations.
Periodic pseudo-Hermitian Hamiltonian: Nonadiabatic geometric phase
NASA Astrophysics Data System (ADS)
Maamache, M.
2015-09-01
It is well known that Hermitian operators have real eigenvalues while non-Hermitian ones may have complex eigenvalues. Recently, numerical and analytical results indicated that the spectra of many non-Hermitians Hamiltonians H are indeed real if they are invariant under the combined action of self-adjoint parity P and time reversal T . The concept of a pseudo-Hermitian operator showed that the remarkable spectral properties of the P T -symmetric Hamiltonians follow from their pseudo-Hermiticity. It is possible to explain these observations by the concept of pseudo-Hermitian operators and to formulate completeness and orthonormality relations. Most of the effort has been devoted to study time-independent non-Hermitian systems. In this paper, we study the exactly solvable time-dependent periodic pseudo-Hermitian Hamiltonians. The method introduced, to make the reality of eigenvalues and phases, is based on a Floquet decomposition of the evolution operator UH(t ) =ZH(t ) exp(i MHt ) associated with the periodic pseudo-hermitian Hamiltonian H (t )=H (t +T ) . One of the results found in this paper concerns a calculation of Berry's phase for periodic, but not necessarily adiabatic, pseudo-Hermitian Hamiltonians. A two-level pseudo-Hermitian system is discussed as an illustrative example.
Geometric phases and quantum correlations dynamics in spin-boson model
Wu, Wei; Xu, Jing-Bo
2014-01-28
We explore the dynamics of spin-boson model for the Ohmic bath by employing the master equation approach and obtain an explicit expression of reduced density matrix. We also calculate the geometric phases of the spin-boson model by making use of the analytical results and discuss how the dissipative bosonic environment affects geometric phases. Furthermore, we investigate the dynamics of quantum discord and entanglement of two qubits each locally interacting with its own independent bosonic environments. It is found that the decay properties of quantum discord and entanglement are sensitive to the choice of initial state's parameter and coupling strength between system and bath.
An angular frequency dependence on the Aharonov–Casher geometric phase
Barboza, P.M.T.; Bakke, K.
2015-10-15
A quantum effect characterized by a dependence of the angular frequency associated with the confinement of a neutral particle to a quantum ring on the quantum numbers of the system and the Aharonov–Casher geometric phase is discussed. Then, it is shown that persistent spin currents can arise in a two-dimensional quantum ring in the presence of a Coulomb-type potential. A particular contribution to the persistent spin currents arises from the dependence of the angular frequency on the geometric quantum phase.
NASA Astrophysics Data System (ADS)
Acharya, Shree Ram; Baral, Nisha; Turkowski, Volodymyr; Rahman, Talat S.
2015-03-01
We apply Dynamical Mean-Field Theory (DMFT) to calculate the non-adiabatic (frequency-dependent) exchange-correlation kernel for the three-dimensional Hubbard model. We analyze the dependence of the kernel on the electron doping, local Coulomb repulsion and frequency by using three different impurity solvers: Hubbard-I, Iterative Perturbation Theory (IPT) and Continuous-Time Quantum Monte Carlo (CT-QMC). From the calculated data, we obtain approximate analytical expressions for the kernel. We apply the exact numerical and analytical kernels to study the non-equilibrium response of the system for applied ultrafast laser pulse. We demonstrate that the non-adiabaticity of the kernel plays an important role in the system response; in particular, leading to new excited-states involved in the system dynamics. Work supported in part by DOE Grant No. DOE-DE-FG02-07ER46354.
Geometric phase in the Hopf bundle and the stability of non-linear waves
NASA Astrophysics Data System (ADS)
Grudzien, Colin J.; Bridges, Thomas J.; Jones, Christopher K. R. T.
2016-11-01
We develop a stability index for the traveling waves of non-linear reaction-diffusion equations using the geometric phase induced on the Hopf bundle S 2 n - 1 ⊂Cn. This can be viewed as an alternative formulation of the winding number calculation of the Evans function, whose zeros correspond to the eigenvalues of the linearization of reaction-diffusion operators about the wave. The stability of a traveling wave can be determined by the existence of eigenvalues of positive real part for the linear operator. Our method of geometric phase for locating and counting eigenvalues is inspired by the numerical results in Way's Dynamics in the Hopf bundle, the geometric phase and implications for dynamical systems Way (2009). We provide a detailed proof of the relationship between the phase and eigenvalues for dynamical systems defined on C2 and sketch the proof of the method of geometric phase for Cn and its generalization to boundary-value problems. Implementing the numerical method, modified from Way (2009), we conclude with open questions inspired from the results.
Optimization of the Geometric Phase Sensitivity of an Array of Atom Ring Interferometers
NASA Astrophysics Data System (ADS)
Sandoval-Sanchez, Karina; Campo, Christian; Rivera, Tabitha; Toland, John
2015-05-01
Sagnac, and Aharonov-Bohm phase shifts are important geometric phase shifts in atom interferometry. These phase shifts characterize rotational and magnetic field interference effects respectively. Theoretical explorations have shown that a series of ring interferometers can be connected in series to increase the sensitivity of the overall device while keeping the maximum path separation less than the coherence length of the atoms. It has also been shown that the application of an area chirp to the rings will further enhance the sensitivity of the array of rings to geometric phase shifts. Area chirp refers to characterizing all of the rings in the array to a fixed percentage of a reference ring, this allows for the phase shifts in each ring to be characterized by one ring. The goal of this project is to determine a set of parameters namely kL, the product of the ring circumference and the wave number and γ, the chirp factor for the area chirp, that optimize the geometric phase sensitivity for an array of N rings. We model the transmission coefficient of a quantum matter wave through an area chirped array of interferometers as a function of phase, using transfer matrices to represent the transmission and reflection of individual rings in the array. Isolated transmission resonances represent the domain of interest, these are regions of high phase sensitivity. After optimizing a ring array without loss we apply velocity broadening to the input matter waves to investigate a more realistic output.
Li, Chunhe; Wang, Jin
2013-01-01
Cellular differentiation, reprogramming and transdifferentiation are determined by underlying gene regulatory networks. Non-adiabatic regulation via slow binding/unbinding to the gene can be important in these cell fate decision-making processes. Based on a stem cell core gene network, we uncovered the stem cell developmental landscape. As the binding/unbinding speed decreases, the landscape topography changes from bistable attractors of stem and differentiated states to more attractors of stem and other different cell states as well as substates. Non-adiabaticity leads to more differentiated cell types and provides a natural explanation for the heterogeneity observed in the experiments. We quantified Waddington landscapes with two possible cell fate decision mechanisms by changing the regulation strength or regulation timescale (non-adiabaticity). Transition rates correlate with landscape topography through barrier heights between different states and quantitatively determine global stability. We found the optimal speeds of these cell fate decision-making processes. We quantified biological paths and predict that differentiation and reprogramming go through an intermediate state (IM1), whereas transdifferentiation goes through another intermediate state (IM2). Some predictions are confirmed by recent experimental studies. PMID:24132204
Geometric phase of an atom inside an adiabatic radio-frequency potential
Zhang, P.; You, L.
2007-09-15
We investigate the geometric phase of an atom inside an adiabatic radio-frequency (rf) potential created from a static magnetic field (B field) and a time-dependent rf field. The spatial motion of the atomic center of mass is shown to give rise to a geometric phase, or Berry's phase, in the adiabatically evolving atomic hyperfine spin along the local B field. This phase is found to depend on both the static B field along the semiclassical trajectory of the atomic center of mass and an effective magnetic field consisting of the total B field, including the oscillating rf field. Specific calculations are provided for several recent atom interferometry experiments and proposals utilizing adiabatic rf potentials.
Emergent excitation in the paramagnetic phase of geometrically frustrated GdMn2O5
NASA Astrophysics Data System (ADS)
Bukhari, Syed Hamad; Ahmad, Javed
2016-07-01
We have measured dielectric constant (ε) as well as magnetic susceptibility (χ) of GdMn2O5 in order to elucidate magnetoelectric phase transitions slightly above and below Néel temperature (TN). Our measurements clearly show that above TN there are short range magnetic correlations arising from geometrically frustrated Mn moments, which fluctuate with respect to field and frequency. These well-defined magnetoelectric phase transitions, together with other transitions below TN, have been observed and discussed in the light of the χ. Magnetoelectric phase diagram is drawn which corresponds well to polarization flip phenomenon as induced by 90° rotation of Gd moments in low temperature phase.
Fast non-Abelian geometric gates via transitionless quantum driving
Zhang, J.; Kyaw, Thi Ha; Tong, D. M.; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-01-01
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer. PMID:26687580
Fast non-Abelian geometric gates via transitionless quantum driving.
Zhang, J; Kyaw, Thi Ha; Tong, D M; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-12-21
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.
NASA Astrophysics Data System (ADS)
Liu, Bao; Zhang, Feng-Yang; Song, Jie; Song, He-Shan
2015-06-01
We propose a direct measurement scheme to read out the geometric phase of a coupled double quantum dot system via a quantum point contact(QPC) device. An effective expression of the geometric phase has been derived, which relates the geometric phase of the double quantum dot qubit to the current through QPC device. All the parameters in our expression are measurable or tunable in experiment. Moreover, since the measurement process affects the state of the qubit slightly, the geometric phase can be protected. The feasibility of the scheme has been analyzed. Further, as an example, we simulate the geometrical phase of a qubit when the QPC device is replaced by a single electron transistor(SET).
NASA Astrophysics Data System (ADS)
Xue, Liyuan; Yu, Yanxia; Cai, Xiaoya; Pan, Hui; Wang, Zisheng
2016-01-01
We investigate time-dependent Pancharatnam phases and the relations between such geometric phases and quantum correlations, i.e., quantum discord and concurrence, of superconducting two-qubit coupling system in dissipative environment with the mixture effects of four different eigenstates of density matrix. We find that the time-dependent Pancharatnam phases not only keep the motion memory of such a two-qubit system, but also include the information of quantum correlations. We show that the sudden died and alive phenomena of quantum entanglement are intrinsic in the transition of Pancharatnam phase in the X-state and the complex oscillations of Pancharatnam phase in the Y-state. The faster the Pancharatnam phases change, the slower the quantum correlations decay. In particular, we find that a subspace of quantum entanglement can exist in the Y-state by choosing suitable coupling parameters between two-qubit system and its environment, or initial conditions.
NASA Astrophysics Data System (ADS)
Zhang, Kai; Nusran, N. M.; Slezak, B. R.; Gurudev Dutt, M. V.
2016-05-01
While it is often thought that the geometric phase is less sensitive to fluctuations in the control fields, a very general feature of adiabatic Hamiltonians is the unavoidable dynamic phase that accompanies the geometric phase. The effect of control field noise during adiabatic geometric quantum gate operations has not been probed experimentally, especially in the canonical spin qubit system that is of interest for quantum information. We present measurement of the Berry phase and carry out adiabatic geometric phase gate in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. We manipulate the spin qubit geometrically by careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting Berry phase signal via spin echo interferometry. Our results show that control field noise at frequencies higher than the spin echo clock frequency causes decay of the quantum phase, and degrades the fidelity of the geometric phase gate to the classical threshold after a few (∼10) operations. This occurs inspite of the geometric nature of the state preparation, due to unavoidable dynamic contributions. We have carried out systematic analysis and numerical simulations to study the effects of the control field noise and imperfect driving waveforms on the quantum phase gate.
Krix, David; Nienhaus, Hermann
2014-08-21
Thin potassium films grown on Si(001) substrates are used to measure internal chemicurrents and the external emission of exoelectrons simultaneously during adsorption of molecular oxygen on K surfaces at 120 K. The experiments clarify the dynamics of electronic excitations at a simple metal with a narrow valence band. X-ray photoemission reveals that for exposures below 5 L almost exclusively peroxide K{sub 2}O{sub 2} is formed, i.e., no dissociation of the molecule occurs during interaction. Still a significant chemicurrent and a delayed exoelectron emission are detected due to a rapid injection of unoccupied molecular levels below the Fermi level. Since the valence band width of potassium is approximately equal to the potassium work function (2.4 eV) the underlying mechanism of exoemission is an Auger relaxation whereas chemicurrents are detected after resonant charge transfer from the metal valence band into the injected level. The change of the chemicurrent and exoemission efficiencies with oxygen coverage can be deduced from the kinetics of the reaction and the recorded internal and external emission currents traces. It is shown that the non-adiabaticity of the reaction increases with coverage due to a reduction of the electronic density of states at the surface while the work function does not vary significantly. Therefore, the peroxide formation is one of the first reaction systems which exhibits varying non-adiabaticity and efficiencies during the reaction. Non-adiabatic calculations based on model Hamiltonians and density functional theory support the picture of chemicurrent generation and explain the rapid injection of hot hole states by an intramolecular motion, i.e., the expansion of the oxygen molecule on the timescale of a quarter of a vibrational period.
Cotton, Stephen J.; Miller, William H.
2013-12-21
A recently described symmetrical windowing methodology [S. J. Cotton and W. H. Miller, J. Phys. Chem. A 117, 7190 (2013)] for quasi-classical trajectory simulations is applied here to the Meyer-Miller [H.-D. Meyer and W. H. Miller, J. Chem. Phys. 70, 3214 (1979)] model for the electronic degrees of freedom in electronically non-adiabatic dynamics. Results generated using this classical approach are observed to be in very good agreement with accurate quantum mechanical results for a variety of test applications, including problems where coherence effects are significant such as the challenging asymmetric spin-boson system.
NASA Astrophysics Data System (ADS)
Segel, S. L.; Creel, R. B.; Torgeson, D. R.
1983-12-01
We describe the theory, practice and experimental results of a continuous wave (CW) resonance technique which we call non-adiabatic superfast passage (NASP). NASP signal to noise per unit time (SNT) is better than pulsed Fourier transform spectrometers (PFTS) and far better than the conventional CW slow passage NMR using field modulation, lock-in amplifiers and signal averaging techniques. It is most useful in situations of long spin-lattice relaxation time and particularly those cases where the line shape is composed of narrow and broad components, as in a typical second-order quadrupolar perturbed magnetic resonance line shape.
Measurement of the Aharonov-Casher geometric phase with a separated-arm atom interferometer
NASA Astrophysics Data System (ADS)
Gillot, Jonathan; Lepoutre, Steven; Gauguet, Alexandre; Vigué, Jacques; Büchner, Matthias
2014-06-01
In this letter, we report a measurement of the Aharonov-Casher (AC) geometric phase with our lithium atom interferometer. The AC phase appears when a particle carrying a magnetic dipole propagates in a transverse electric field. The first measurement of the AC phase was done with a neutron interferometer in 1989 by Cimmino et al. [Phys. Rev. Lett. 63, 380 (1989)] and all the following experiments were done with Ramsey or Ramsey-Bordé interferometers with molecules or atoms. In our experiment, we use lithium atoms pumped in a single hyperfine-Zeeman sublevel and we measure the AC-phase by applying opposite electric fields on the two interferometer arms. Our measurements are in good agreement with the expected theoretical values and they also provide a further test of the independence of the AC phase with the atom velocity.
Coriolis effect in optics: unified geometric phase and spin-Hall effect.
Bliokh, Konstantin Y; Gorodetski, Yuri; Kleiner, Vladimir; Hasman, Erez
2008-07-18
We examine the spin-orbit coupling effects that appear when a wave carrying intrinsic angular momentum interacts with a medium. The Berry phase is shown to be a manifestation of the Coriolis effect in a noninertial reference frame attached to the wave. In the most general case, when both the direction of propagation and the state of the wave are varied, the phase is given by a simple expression that unifies the spin redirection Berry phase and the Pancharatnam-Berry phase. The theory is supported by the experiment demonstrating the spin-orbit coupling of electromagnetic waves via a surface plasmon nanostructure. The measurements verify the unified geometric phase, demonstrated by the observed polarization-dependent shift (spin-Hall effect) of the waves.
NASA Astrophysics Data System (ADS)
Acharya, Shree Ram; Turkowski, Volodymyr; Rahman, Talat S.
We study the ultrafast response of electrons in the one-band Hubbard model to an external laser-pulse perturbation by using the Non-adiabatic Time-Dependent Density Functional Theory + Dynamical Mean-Field Theory (TDDFT +DMFT) approach. The corresponding exchange-correlation kernel (XC) is obtained from the DMFT charge susceptibility by using the Quantum Monte Carlo solver for the impurity problem. Detailed analysis of the time-dependent excited charge density, the Fermi distribution function, and the spatially nonhomogeneous response (metallic domain growth), is performed for different values for the carrier density and local Coulomb repulsion. We compare the results with the corresponding non-equilibrium DMFT solutions, and demonstrate that non-adiabaticity (frequency-dependence) of the XC kernel is important in order to reproduce the non-equilibrium DMFT solution. Also, from the numerical results for the charge susceptibility, we obtain an approximate analytical expression for the XC kernel. Using this kernel, we reveal possible types of ''elementary'' excitations and the dynamics of metallic domain growth in the case of the one-band Hubbard model. Possible generalization of the approach to the multi-orbital case is discussed. Work supported in part by DOE Grant No. DOE-DE-FG02-07ER46354.
A non-adiabatic dynamics study of octatetraene: the radiationless conversion from S2 to S1.
Qu, Zexing; Liu, Chungen
2013-12-28
Simulation of the excited state dynamics of all-trans-1,3,5,7-octatetraene has been performed to investigate the ultrafast radiationless S2 → S1 internal conversion process. Multireference configuration interaction with single excitation method has been employed to optimize the equilibrium structure of the excited states, as well as the S2/S1 conical intersection, and to investigate the non-adiabatic molecular dynamics of the S2/S1 state transition. At the conical intersection, the molecule is found to be distorted from the original planar trans structure to a nearly perpendicular conformation around C3-C4 bond, with the torsion angle being about 107°. Such structural change can result in mutual approaching of states S2 and S1 in energy, and drastically increase the nonadiabatic coupling between the two states by destroying the inter-state symmetry prohibition in the electronic wavefunctions. Surface-hopping molecular dynamics simulations are performed to describe the non-adiabatic process. Upon the Franck-Condon excitation to the S2 state, the molecule quickly twists its C3-C4 bond and approaches the conical intersection region, where it can undergo efficient internal conversion to S1. The decay time constant (τ) of S2 state is estimated to be around 251 fs by fitting the occupation number of average fraction of trajectories using an exponential damping function. This value is reasonably consistent with previous experimental measurements of around 300-400 fs.
NASA Astrophysics Data System (ADS)
Dai, Xianglu; Xie, Huimin; Wang, Qinghua
2014-06-01
The geometric phase analysis (GPA), an important image-based deformation measurement method, has been used at both micro- and nano-scale. However, when a deformed image has apparent distortion, non-ignorable error in the obtained deformation field could occur by using this method. In this paper, the geometric phase analysis based on the windowed Fourier transform (WFT) is proposed to solve the above-mentioned issue, defined as the WFT-GPA method. In WFT-GPA, instead of the Fourier transform (FT), the WFT is utilized to extract the phase field block by block, and therefore more accurate local phase information can be acquired. The simulation tests, which include detailed discussion of influence factors for measurement accuracy such as window size and image noise, are conducted with digital deformed grids. The results verify that the WFT-GPA method not only keeps all advantages of traditional GPA method, but also owns a better accuracy for deformation measurement. Finally, the WFT-GPA method is applied to measure the machining distortion incurred in soft ultraviolet nanoimprint lithography (UV-NIL) process. The successful measurement shows the feasibility of this method and offers a full-field way for characterizing the replication quality of UV-NIL process.
Multi-target-qubit unconventional geometric phase gate in a multi-cavity system.
Liu, Tong; Cao, Xiao-Zhi; Su, Qi-Ping; Xiong, Shao-Jie; Yang, Chui-Ping
2016-01-01
Cavity-based large scale quantum information processing (QIP) may involve multiple cavities and require performing various quantum logic operations on qubits distributed in different cavities. Geometric-phase-based quantum computing has drawn much attention recently, which offers advantages against inaccuracies and local fluctuations. In addition, multiqubit gates are particularly appealing and play important roles in QIP. We here present a simple and efficient scheme for realizing a multi-target-qubit unconventional geometric phase gate in a multi-cavity system. This multiqubit phase gate has a common control qubit but different target qubits distributed in different cavities, which can be achieved using a single-step operation. The gate operation time is independent of the number of qubits and only two levels for each qubit are needed. This multiqubit gate is generic, e.g., by performing single-qubit operations, it can be converted into two types of significant multi-target-qubit phase gates useful in QIP. The proposal is quite general, which can be used to accomplish the same task for a general type of qubits such as atoms, NV centers, quantum dots, and superconducting qubits. PMID:26898176
Kittell, Aaron W.; Camenisch, Theodore G.; Ratke, Joseph J.; Sidabras, Jason W.; Hyde, James S.
2011-01-01
A continuous wave (CW) electron paramagnetic resonance (EPR) spectrum is typically displayed as the first harmonic response to the application of 100 kHz magnetic field modulation, which is used to enhance sensitivity by reducing the level of 1/f noise. However, magnetic field modulation of any amplitude causes spectral broadening and sacrifices EPR spectral intensity by at least a factor of two. In the work presented here, a CW rapid-scan spectroscopic technique that avoids these compromises and also provides a means of avoiding 1/f noise is developed. This technique, termed non-adiabatic rapid sweep (NARS) EPR, consists of repetitively sweeping the polarizing magnetic field in a linear manner over a spectral fragment with a small coil at a repetition rate that is sufficiently high that receiver noise, microwave phase noise, and environmental microphonics, each of which has 1/f characteristics, are overcome. Nevertheless, the rate of sweep is sufficiently slow that adiabatic responses are avoided and the spin system is always close to thermal equilibrium. The repetitively acquired spectra from the spectral fragment are averaged. Under these conditions, undistorted pure absorption spectra are obtained without broadening or loss of signal intensity. A digital filter such as a moving average is applied to remove high frequency noise, which is approximately equivalent in bandwidth to use of an integrating time constant in conventional field modulation with lock-in detection. Nitroxide spectra at L- and X-band are presented. PMID:21741868
Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
NASA Astrophysics Data System (ADS)
Shi, Qian-Qian; Wang, Hong-Lei; Li, Sheng-Hao; Cho, Sam Young; Batchelor, Murray T.; Zhou, Huan-Qiang
2016-06-01
Geometric entanglement (GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. In this paper we outline a systematic method to compute GE for two-dimensional (2D) quantum many-body lattice models based on the translational invariant structure of infinite projected entangled pair state (iPEPS) representations. By employing this method, the q -state quantum Potts model on the square lattice with q ∈{2 ,3 ,4 ,5 } is investigated as a prototypical example. Further, we have explored three 2D Heisenberg models: the antiferromagnetic spin-1/2 X X X and anisotropic X Y X models in an external magnetic field, and the antiferromagnetic spin-1 X X Z model. We find that continuous GE does not guarantee a continuous phase transition across a phase transition point. We observe and thus classify three different types of continuous GE across a phase transition point: (i) GE is continuous with maximum value at the transition point and the phase transition is continuous, (ii) GE is continuous with maximum value at the transition point but the phase transition is discontinuous, and (iii) GE is continuous with nonmaximum value at the transition point and the phase transition is continuous. For the models under consideration, we find that the second and the third types are related to a point of dual symmetry and a fully polarized phase, respectively.
Analytical calculation of spectral phase of grism pairs by the geometrical ray tracing method
NASA Astrophysics Data System (ADS)
Rahimi, L.; Askari, A. A.; Saghafifar, H.
2016-07-01
The most optimum operation of a grism pair is practically approachable when an analytical expression of its spectral phase is in hand. In this paper, we have employed the accurate geometrical ray tracing method to calculate the analytical phase shift of a grism pair, at transmission and reflection configurations. As shown by the results, for a great variety of complicated configurations, the spectral phase of a grism pair is in the same form of that of a prism pair. The only exception is when the light enters into and exits from different facets of a reflection grism. The analytical result has been used to calculate the second-order dispersions of several examples of grism pairs in various possible configurations. All results are in complete agreement with those from ray tracing method. The result of this work can be very helpful in the optimal design and application of grism pairs at various configurations.
Geometric phase of a central spin coupled to an antiferromagnetic environment
Yuan Xiaozhong; Zhu Kadi; Goan, H.-S.
2010-03-15
Using the spin-wave approximation, we study the geometric phase (GP) of a central spin (signal qubit) coupled to an antiferromagnetic (AF) environment under the application of an external global magnetic field. The external magnetic field affects the GP of the qubit directly and also indirectly through its effect on the AF environment. We find that when the applied magnetic field is increased to the critical magnetic field point, the AF environment undergoes a spin-flop transition, a first-order phase transition, and at the same time the GP of the qubit changes abruptly to zero. This sensitive change of the GP of a signal qubit to the parameter change of a many-body environment near its critical point may serve as another efficient tool or witness to study the many-body phase transition. The influences of the AF environment temperature and crystal anisotropy field on the GP are also investigated.
Absorption and impedance boundary conditions for phased geometrical-acoustics methods.
Jeong, Cheol-Ho
2012-10-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials.
Reimers, Jeffrey R; McKemmish, Laura K; McKenzie, Ross H; Hush, Noel S
2015-10-14
Using a simple model Hamiltonian, the three correction terms for Born-Oppenheimer (BO) breakdown, the adiabatic diagonal correction (DC), the first-derivative momentum non-adiabatic correction (FD), and the second-derivative kinetic-energy non-adiabatic correction (SD), are shown to all contribute to thermodynamic and spectroscopic properties as well as to thermal non-diabatic chemical reaction rates. While DC often accounts for >80% of thermodynamic and spectroscopic property changes, the commonly used practice of including only the FD correction in kinetics calculations is rarely found to be adequate. For electron-transfer reactions not in the inverted region, the common physical picture that diabatic processes occur because of surface hopping at the transition state is proven inadequate as the DC acts first to block access, increasing the transition state energy by (ℏω)(2)λ/16J(2) (where λ is the reorganization energy, J the electronic coupling and ω the vibration frequency). However, the rate constant in the weakly-coupled Golden-Rule limit is identified as being only inversely proportional to this change rather than exponentially damped, owing to the effects of tunneling and surface hopping. Such weakly-coupled long-range electron-transfer processes should therefore not be described as "non-adiabatic" processes as they are easily described by Born-Huang ground-state adiabatic surfaces made by adding the DC to the BO surfaces; instead, they should be called just "non-Born-Oppenheimer" processes. The model system studied consists of two diabatic harmonic potential-energy surfaces coupled linearly through a single vibration, the "two-site Holstein model". Analytical expressions are derived for the BO breakdown terms, and the model is solved over a large parameter space focusing on both the lowest-energy spectroscopic transitions and the quantum dynamics of coherent-state wavepackets. BO breakdown is investigated pertinent to: ammonia inversion, aromaticity
Reimers, Jeffrey R; McKemmish, Laura K; McKenzie, Ross H; Hush, Noel S
2015-10-14
Using a simple model Hamiltonian, the three correction terms for Born-Oppenheimer (BO) breakdown, the adiabatic diagonal correction (DC), the first-derivative momentum non-adiabatic correction (FD), and the second-derivative kinetic-energy non-adiabatic correction (SD), are shown to all contribute to thermodynamic and spectroscopic properties as well as to thermal non-diabatic chemical reaction rates. While DC often accounts for >80% of thermodynamic and spectroscopic property changes, the commonly used practice of including only the FD correction in kinetics calculations is rarely found to be adequate. For electron-transfer reactions not in the inverted region, the common physical picture that diabatic processes occur because of surface hopping at the transition state is proven inadequate as the DC acts first to block access, increasing the transition state energy by (ℏω)(2)λ/16J(2) (where λ is the reorganization energy, J the electronic coupling and ω the vibration frequency). However, the rate constant in the weakly-coupled Golden-Rule limit is identified as being only inversely proportional to this change rather than exponentially damped, owing to the effects of tunneling and surface hopping. Such weakly-coupled long-range electron-transfer processes should therefore not be described as "non-adiabatic" processes as they are easily described by Born-Huang ground-state adiabatic surfaces made by adding the DC to the BO surfaces; instead, they should be called just "non-Born-Oppenheimer" processes. The model system studied consists of two diabatic harmonic potential-energy surfaces coupled linearly through a single vibration, the "two-site Holstein model". Analytical expressions are derived for the BO breakdown terms, and the model is solved over a large parameter space focusing on both the lowest-energy spectroscopic transitions and the quantum dynamics of coherent-state wavepackets. BO breakdown is investigated pertinent to: ammonia inversion, aromaticity
Generation of equal-intensity coherent optical beams by binary geometrical phase on metasurface
NASA Astrophysics Data System (ADS)
Wang, Zheng-Han; Jiang, Shang-Chi; Xiong, Xiang; Peng, Ru-Wen; Wang, Mu
2016-06-01
We report here the design and realization of a broadband, equal-intensity optical beam splitter with a dispersion-free binary geometric phase on a metasurface with unit cell consisting of two mirror-symmetric elements. We demonstrate experimentally that two identical beams can be efficiently generated with incidence of any polarization. The efficiency of the device reaches 80% at 1120 nm and keeps larger than 70% in the range of 1000-1400 nm. We suggest that this approach for generating identical, coherent beams have wide applications in diffraction optics and in entangled photon light source for quantum communication.
Geometric phase for a neutral particle in the presence of a topological defect
Bakke, K.; Nascimento, J. R.; Furtado, C.
2008-09-15
In this paper we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved space-time. The nonrelativistic quantum dynamics are investigated using the Foldy-Wouthuysen expansion. The gravitational Aharonov-Casher and He-McKellar-Wilkens effects are investigated for a series of electric and magnetic field configurations.
NASA Astrophysics Data System (ADS)
Miller, William H.; Cotton, Stephen J.
2015-04-01
It is noted that the recently developed symmetrical quasi-classical (SQC) treatment of the Meyer-Miller (MM) model for the simulation of electronically non-adiabatic dynamics provides a good description of detailed balance, even though the dynamics which results from the classical MM Hamiltonian is "Ehrenfest dynamics" (i.e., the force on the nuclei is an instantaneous coherent average over all electronic states). This is seen to be a consequence of the SQC windowing methodology for "processing" the results of the trajectory calculation. For a particularly simple model discussed here, this is shown to be true regardless of the choice of windowing function employed in the SQC model, and for a more realistic full classical molecular dynamics simulation, it is seen to be maintained correctly for very long time.
Miller, William H. Cotton, Stephen J.
2015-04-07
It is noted that the recently developed symmetrical quasi-classical (SQC) treatment of the Meyer-Miller (MM) model for the simulation of electronically non-adiabatic dynamics provides a good description of detailed balance, even though the dynamics which results from the classical MM Hamiltonian is “Ehrenfest dynamics” (i.e., the force on the nuclei is an instantaneous coherent average over all electronic states). This is seen to be a consequence of the SQC windowing methodology for “processing” the results of the trajectory calculation. For a particularly simple model discussed here, this is shown to be true regardless of the choice of windowing function employed in the SQC model, and for a more realistic full classical molecular dynamics simulation, it is seen to be maintained correctly for very long time.
Mendive-Tapia, David; Lasorne, Benjamin; Worth, Graham A; Robb, Michael A; Bearpark, Michael J
2012-12-14
In this article, we investigate the convergence of quantum dynamics calculations with coupled variationally optimized gaussian product basis functions, describing wavepacket motion on regions of molecular potential energy surfaces calculated on the fly. As a benchmark system, we model the radiationless decay of fulvene from its first electronic excited state through an extended S(1)∕S(0) conical intersection seam and monitor two associated properties: the spatial extent to which the conical intersection seam is sampled and the timescale and stepwise nature of the population transfer. We suggest that the fully variational description reviewed here (direct dynamics-variational multi-configuration gaussian) provides a way to balance accuracy against computational cost for molecules of comparable sizes by choosing the number of coupled gaussian product basis functions and a middle way forward between grid based and trajectory surface hopping approaches to non-adiabatic molecular quantum dynamics calculations.
Phase transition of charged Black Holes in Brans-Dicke theory through geometrical thermodynamics
NASA Astrophysics Data System (ADS)
Hendi, S. H.; Panahiyan, S.; Panah, B. Eslam; Armanfard, Z.
2016-07-01
In this paper, we take into account black hole solutions of Brans-Dicke-Maxwell theory and investigate their stability and phase transition points. We apply the concept of geometry in thermodynamics to obtain phase transition points and compare its results with those, calculated in the canonical ensemble through heat capacity. We show that these black holes enjoy second order phase transitions. We also show that there is a lower bound for the horizon radius of physical charged black holes in Brans-Dicke theory, which originates from restrictions of positivity of temperature. In addition, we find that employing a specific thermodynamical metric in the context of geometrical thermodynamics yields divergencies for the thermodynamical Ricci scalar in places of the phase transitions. It will be pointed out that due to the characteristic behavior of the thermodynamical Ricci scalar around its divergence points, one is able to distinguish the physical limitation point from the phase transitions. In addition, the free energy of these black holes will be obtained and its behavior will be investigated. It will be shown that the behavior of the free energy in the place where the heat capacity diverges demonstrates second order phase transition characteristics.
NASA Astrophysics Data System (ADS)
Tiwari, Vivek
2015-05-01
Understanding the fundamental physics of light-harvesting in both, natural and artificial systems is key for the development of efficient light-harvesting technologies. My thesis addresses the following topics, i.) the mechanism underlying the remarkably efficient electronic energy transfer in natural light harvesting antennas, ii.) a femtosecond time-resolved photonumeric technique to quantitatively characterize transient chemical species. This talk will concentrate on the first project, while briefly touching the key ideas of the second project. Light harvesting antennas use a set of closely spaced pigment molecules held in a controlled relative geometry by a protein. It is shown that in certain antenna proteins the excited state electronic energy gaps between the pigments are resonant with a quantum of pigment vibrational energy. With such a vibrational-electronic resonance, anti-correlated motions between the pigments lead to a strong coupling between the electronic and nuclear motions, that is, breakdown of the Born-Oppenheimer approximation, over a wide range of pigment vibrational motions. It is shown that the 2D spectroscopic signatures of the resulting unavoidable nested non-adiabatic energy funnel on the excited states of photosynthetic antennas are consistent with all the reported 2D signatures of long-lived coherent oscillations, including the ones that are not explained by prior models of excited state electronic energy transfer. Extensions that account for both resonant and near-resonant pigment vibrations suggest that photosynthetic energy transfer presents a novel design in which electronic energy transfer proceeds non-adiabatically through clusters of vibrations with frequencies distributed around electronic energy gaps. I will also briefly talk about our experiments demonstrating quantitative time-resolved measurement of absolute number of excited state molecules. Based on these measurements, an all-optical technique that simultaneously determines
Trugenberger, Carlo A
2015-12-01
Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension d(H)=4. The model has a geometric quantum phase transition with disorder parameter (d(H)-d(s)), where d(s) is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions. PMID:26764755
Critical space-time networks and geometric phase transitions from frustrated edge antiferromagnetism
NASA Astrophysics Data System (ADS)
Trugenberger, Carlo A.
2015-12-01
Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension dH=4 . The model has a geometric quantum phase transition with disorder parameter (dH-ds) , where ds is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions.
Application of geometric phase to wavefront sensing for astronomical adaptive optics
NASA Astrophysics Data System (ADS)
Bloemhof, E. E.
2014-02-01
Modern adaptive optics systems give high performance, both in terms of Strehl ratio (degree of correction) and corrected field of view. Arguably the most important subsystem is the wavefront sensor, which measures the deviation from flatness of the incident wavefront that has been perturbed by the turbulent atmosphere, and commands an actuated mirror to compensate. An aspect of the wavefront sensor essential to achieving high sensitivity is that it perform over a broad spectral bandwidth; operation without correction for guide star color is also desirable. With this in mind, wavefront sensors are considered that make use of the geometric (or topological) phase, which has the property that the value of the phase is independent of wavelength. Conceptual system designs and advantages are discussed.
Geometrical aspects of the frustration in the cubic phases of lyotropic liquid crystals.
Anderson, D M; Gruner, S M; Leibler, S
1988-01-01
Bicontinuous cubic phases, composed of bilayers arranged in the geometries of periodic minimal surfaces, are found in a variety of different lipid/water systems. It has been suggested recently that these cubic structures arrive as the result of competition between two free-energy terms: the curvature energy of each monolayer and the stretching energy of the lipid chains. This scenario, closely analogous to the one that explains the origin of the hexagonal phases, is investigated here by means of simple geometrical calculations. It is first assumed that the lipid bilayer is of constant thickness and the distribution of the (local) mean curvature of the phospholipid-water interfaces is calculated. Then, assuming the mean curvature of these interfaces is constant, the distribution of the bilayer's thickness is calculated. Both calculations quantify the fact that the two energy terms are frustrated and cannot be satisfied simultaneously. However, the amount of the frustration can be smaller for the cubic phase than for the lamellar and hexagonal structures. Therefore, this phase can appear in the phase diagram between the other two, as observed in many recent experiments. PMID:3399497
NASA Astrophysics Data System (ADS)
Wójcik, P.; Zegrodnik, M.; Rzeszotarski, B.; Adamowski, J.
2016-09-01
The tunneling conductance through the half-metal/conical magnet/superconductor (HM/CM/SC) junctions is investigated with the use of the Bogoliubov-de Gennes equations in the framework of Blonder-Tinkham-Klapwijk formalism. Due to the spin band separation in the HM, the conductance in the subgap region is mainly determined by the anomalous Andreev reflection, the probability of which strongly depends on the spin transmission in the CM layer. We show that the spins of electrons injected from the HM can be transmitted through the CM to the SC either adiabatically or non-adiabatically depending on the period of the spatial modulation of the exchange field. We find that the conductance in the subgap region oscillates as a function of the CM layer thickness wherein the oscillations transform from the irregular pattern in the non-adiabatic regime to the regular one in the adiabatic regime. For both adiabatic and non-adiabatic transport regimes the conductance is studied over a broad range of parameters determining the spiral magnetization in the CM. We find that in the non-adiabatic regime, the decrease of the exchange field amplitude in the CM leads to the emergence of the conductance peak for the particular CM thickness in agreement with recent experiments.
Geometric-Phase approach to macroscopic polarization in lattice fermion models
NASA Astrophysics Data System (ADS)
Ortiz, Gerardo; Martin, Richard M.; Ordejón, Pablo
1996-03-01
The Geometric-Phase approach is a convenient way to calculate changes in the macroscopic polarization of an insulating system, based on the concept that the integrated current is connected to the phase of the wavefunction of interacting electrons. The method has provided a powerful mathematical scheme to study dielectric phenomena in correlated systems. We have applied these ideas to a variety of strongly correlated lattice fermion models in one and two dimensions; in particular, the 3-band Hubbard model in Cu-O planes in the parent compounds of High-Temperature superconductors. We analyze the information contained in the phase when a quantum transition takes place as one parameter of the hamiltonian is adiabatically changed. Previous results assume a correlated insulator in zero macroscopic electric field. In presence of such a singular perturbation there is no stable ground state. We present a way to overcome this problem, the main idea of which consists in constraining the manifold where the electrons move, i.e., the configuration space of the N identical particles.
Geometric phase of a spin-1 2 particle coupled to a quantum vector operator
NASA Astrophysics Data System (ADS)
Aguilar, Pedro; Chryssomalakos, Chryssomalis; Guzmán, Edgar
2016-05-01
We calculate Berry’s phase when the driving field, to which a spin-1 2 is coupled adiabatically, rather than the familiar classical magnetic field, is a quantum vector operator, of noncommuting, in general, components, e.g. the angular momentum of another particle, or another spin. The geometric phase of the entire system, spin plus “quantum driving field”, is first computed, and is then subdivided into the two subsystems, using the Schmidt decomposition of the total wave function — the resulting expression shows a marked, purely quantum effect, involving the commutator of the field components. We also compute the corresponding mean “classical” phase, involving a precessing magnetic field in the presence of noise, up to terms quadratic in the noise amplitude — the results are shown to be in excellent agreement with numerical simulations in the literature. Subtleties in the relation between the quantum and classical case are pointed out, while three concrete examples illustrate the scope and internal consistency of our treatment.
Non-adiabatic effects in the pseudorotational motion of triatomic molecules
NASA Astrophysics Data System (ADS)
Hagelberg, Frank; Deumens, Erik
2002-03-01
Electron-Nuclear Dynamics (END) theory simulations have been performed with the aim to understand the dynamic aspects of triatomic molecules in pseudorotational motion. More specifically, the units H_3^+ and Li_3^+ are investigated close to the threshold of dissociation. For both species, the dynamic response of the electronic system to the nuclear motion is examined by the computation of electronic angular momentum expectation values. The respective results differ markedly for alpha and beta spin orientations, reflecting the emergence of rapid spin oscillations. This phenomenon is investigated by a detailed analysis of the electronic excitation content in both molecules. This is achieved by projection of the dynamic wavefunction on adiabatic electronic states which are evaluated along the nuclear trajectories. From an inspection of the phase relations between the expansion coefficients for electronic excitations with alpha and beta spin orientation, we conclude that the systems maximize the observed spin polarization effects.
NASA Astrophysics Data System (ADS)
Tang, Yihao; Hassanaly, Malik; Raman, Venkat
2015-11-01
In the development of highly efficient gas turbine combustion system, using high-hydrogen-content fuels is a new solution that limits pollutant emissions but also triggers flame stabilization issues. One promising concept to handle such instabilities within a large range of operating conditions is the FLOX® burner. A noticeable feature of the FLOX® burner is that it discharges high momentum jets without swirl, and flame stabilization is achieved in the shear layer around the jets. Experimental investigations have concluded that low velocity zones were absent and the flashback propensity was effectively decreased. It is proposed to study the stabilization mechanism to understand what physical phenomena are decisive in the process. In a preliminary numerical study, an adiabatic flamelet table was used along with LES simulations. Although the flow field's main features were captured, the simulation had issues in accurately predicting some important thermochemical quantities, including near wall quenching effects and OH mass fraction distribution. This work focuses on the effect of the adiabatic hypothesis on the flame stabilization mechanism. A non-adiabatic flamelet model is implemented and the impact on the stabilization mechanism is being quantified.
Shi Yu
2010-06-15
We consider how to obtain a nontrivial two-qubit unitary transformation purely based on geometric phases of two spin-1/2 's with Ising-like interaction in a magnetic field with a static z-component and a rotating xy-component. This is an interesting problem both for the purpose of measuring the geometric phases and in quantum computing applications. In previous approach, coupling of one of the qubit with the rotating component of field is ignored. By considering the exact two-spin geometric phases, we find that a nontrivial two-spin unitary transformation purely based on Berry phases can be obtained by using two consecutive cycles with opposite directions of the magnetic field and opposite signs of the interaction constant. In the nonadiabatic case, starting with a certain initial state, a cycle in the projected space of rays and thus Aharonov-Anandan phase can be achieved. The two-cycle scheme cancels the total phases, hence any unknown initial state evolves back to itself without a phase factor.
Chen, Ke; Feng, Yijun; Yang, Zhongjie; Cui, Li; Zhao, Junming; Zhu, Bo; Jiang, Tian
2016-01-01
Ultrathin metasurface compromising various sub-wavelength meta-particles offers promising advantages in controlling electromagnetic wave by spatially manipulating the wavefront characteristics across the interface. The recently proposed digital coding metasurface could even simplify the design and optimization procedures due to the digitalization of the meta-particle geometry. However, current attempts to implement the digital metasurface still utilize several structural meta-particles to obtain certain electromagnetic responses, and requiring time-consuming optimization especially in multi-bits coding designs. In this regard, we present herein utilizing geometric phase based single structured meta-particle with various orientations to achieve either 1-bit or multi-bits digital metasurface. Particular electromagnetic wave scattering patterns dependent on the incident polarizations can be tailored by the encoded metasurfaces with regular sequences. On the contrast, polarization insensitive diffusion-like scattering can also been successfully achieved by digital metasurface encoded with randomly distributed coding sequences leading to substantial suppression of backward scattering in a broadband microwave frequency. The proposed digital metasurfaces provide simple designs and reveal new opportunities for controlling electromagnetic wave scattering with or without polarization dependence. PMID:27775064
Geometric phase and entanglement of Raman photon pairs in the presence of photonic band gap
Berrada, K.; Ooi, C. H. Raymond; Abdel-Khalek, S.
2015-03-28
Robustness of the geometric phase (GP) with respect to different noise effects is a basic condition for an effective quantum computation. Here, we propose a useful quantum system with real physical parameters by studying the GP of a pair of Stokes and anti-Stokes photons, involving Raman emission processes with and without photonic band gap (PBG) effect. We show that the properties of GP are very sensitive to the change of the Rabi frequency and time, exhibiting collapse phenomenon as the time becomes significantly large. The system allows us to obtain a state which remains with zero GP for longer times. This result plays a significant role to enhance the stabilization and control of the system dynamics. Finally, we investigate the nonlocal correlation (entanglement) between the pair photons by taking into account the effect of different parameters. An interesting correlation between the GP and entanglement is observed showing that the PBG stabilizes the fluctuations in the system and makes the entanglement more robust against the change of time and frequency.
NASA Astrophysics Data System (ADS)
Hellman, A.
2009-01-01
The initial adsorption of O2 on Si(1 0 0) is investigated by density-functional theory calculations. The potential energy surface shows strong corrugations which can be interpreted as precursor states, however, there are also large areas where adsorption proceeds without a barrier. Furthermore, the initial sticking probability as a function of translational energy using first-principles molecular dynamics is calculated. The result is in disagreement with measurements of sticking probability which vary from high-low-high values as the translational energy of the oxygen molecules increase. A simple non-adiabatic model is put-forth that explains not only the measured sticking probability, but also have a novel interpretation of the increased sticking probability owing to tensile stress. The model deals with non-adiabatic effects originating both from a discrete and continuous set of electronic excitations. The implications are general and can be applied to other systems.
NASA Astrophysics Data System (ADS)
Zibaii, M. I.; Latifi, H.; Karami, M.; Gholami, M.; Hosseini, S. M.; Ghezelayagh, M. H.
2010-10-01
A single-mode non-adiabatic tapered optical fiber (NATOF) sensor was utilized for sensing the variation in refractive index (RI) with concentration of d-glucose in deionized water and measurement of the RI of amino acids (AAs) in carbohydrate solutions. This method showed a rewarding ability in understanding the basis of biomolecular interactions in biological systems. Due to high sensitivity, ease of application, low cost and real-time measurement, this method is more efficient in comparison with other techniques, such as calorimetric titration, NMR, UV absorption spectroscopy, x-ray crystallography, computer calculations, kinetic studies and chromatography data. The NATOF is fabricated by the heat pulling method, utilizing a CO2 laser. The limit of detection of the NATOF was 55 ppm for a d-glucose concentration ranging from 0 to 80 mg ml-1, and the limit of detection of the RI measurement corresponding to these concentrations in the range from 1.3330 to 1.3447 was 8.2 × 10-6 as a refractometer sensor. The response of the NATOF shows that different kinds of interactions of various groups of AAs, such as l-alanine, l-leucine and l-cysteine with d-glucose, sucrose and water molecules, depend on functional groups in AAs such as OH, SH, CH2, NH+3 and COO-. These results can be interpreted in terms of solute-solute and solute-solvent interactions and the structure making/breaking ability of solutes in the given solution. Such a study helps in the better understanding of the interactions occurring between AA molecules and entities present in biological matrices.
Kubař, Tomáš; Elstner, Marcus
2013-04-28
In this work, a fragment-orbital density functional theory-based method is combined with two different non-adiabatic schemes for the propagation of the electronic degrees of freedom. This allows us to perform unbiased simulations of electron transfer processes in complex media, and the computational scheme is applied to the transfer of a hole in solvated DNA. It turns out that the mean-field approach, where the wave function of the hole is driven into a superposition of adiabatic states, leads to over-delocalization of the hole charge. This problem is avoided using a surface hopping scheme, resulting in a smaller rate of hole transfer. The method is highly efficient due to the on-the-fly computation of the coarse-grained DFT Hamiltonian for the nucleobases, which is coupled to the environment using a QM/MM approach. The computational efficiency and partial parallel character of the methodology make it possible to simulate electron transfer in systems of relevant biochemical size on a nanosecond time scale. Since standard non-polarizable force fields are applied in the molecular-mechanics part of the calculation, a simple scaling scheme was introduced into the electrostatic potential in order to simulate the effect of electronic polarization. It is shown that electronic polarization has an important effect on the features of charge transfer. The methodology is applied to two kinds of DNA sequences, illustrating the features of transfer along a flat energy landscape as well as over an energy barrier. The performance and relative merit of the mean-field scheme and the surface hopping for this application are discussed. PMID:23493847
Sanz-Sanz, Cristina; Aguado, Alfredo; Roncero, Octavio; Naumkin, Fedor
2016-01-01
Analytical derivatives and non-adiabatic coupling matrix elements are derived for Hn+ systems (n=3, 4 and 5). The method uses a generalized Hellmann-Feynman theorem applied to a multi-state description based on diatomics-in-molecules (for H3+) or triatomics-in-molecules (for H4+ and H5+) formalisms, corrected with a permutationally invariant many-body term to get high accuracy. The analytical non-adiabatic coupling matrix elements are compared with ab initio calculations performed at multi-reference configuration interaction level. These magnitudes are used to calculate H2(v′=0,j′=0)+H2+(v,j=0) collisions, to determine the effect of electronic transitions using a molecular dynamics method with electronic transitions. Cross sections for several initial vibrational states of H2+ are calculated and compared with the available experimental data, yielding an excellent agreement. The effect of vibrational excitation of H2+ reactant, and its relation with non-adiabatic processes are discussed. Also, the behavior at low collisional energies, in the 1 meV-0.1 eV interval, of interest in astrophysical environments, are discussed in terms of the long range behaviour of the interaction potential which is properly described within the TRIM formalism. PMID:26696058
Sanz-Sanz, Cristina; Aguado, Alfredo; Roncero, Octavio; Naumkin, Fedor
2015-12-21
Analytical derivatives and non-adiabatic coupling matrix elements are derived for Hn (+) systems (n = 3-5). The method uses a generalized Hellmann-Feynman theorem applied to a multi-state description based on diatomics-in-molecules (for H3 (+)) or triatomics-in-molecules (for H4 (+) and H5 (+)) formalisms, corrected with a permutationally invariant many-body term to get high accuracy. The analytical non-adiabatic coupling matrix elements are compared with ab initio calculations performed at multi-reference configuration interaction level. These magnitudes are used to calculate H2(v(')=0,j(')=0)+H2 (+)(v,j=0) collisions, to determine the effect of electronic transitions using a molecular dynamics method with electronic transitions. Cross sections for several initial vibrational states of H2 (+) are calculated and compared with the available experimental data, yielding an excellent agreement. The effect of vibrational excitation of H2 (+) reactant and its relation with non-adiabatic processes are discussed. Also, the behavior at low collisional energies, in the 1 meV-0.1 eV interval, of interest in astrophysical environments, is discussed in terms of the long range behaviour of the interaction potential which is properly described within the triatomics-in-molecules formalism. PMID:26696058
Takano, Yoshihide; Liou, Kuo-Nan
2010-07-10
We have developed a hit-and-miss Monte Carlo geometric ray-tracing program to compute the scattering phase matrix for concentrically stratified spheres. Using typical refractive indices for water and aerosols in the calculations, numerous rainbow features appear in the phase matrix that deviate from the results calculated from homogeneous spheres. In the context of geometric ray tracing, rainbows and glory are identified by means of their ray paths, which provide physical explanation for the features produced by the "exact" Lorenz-Mie theory. The computed results for the phase matrix, the single-scattering albedo, and the asymmetry factor for a size parameter of approximately 600 compared closely with those evaluated from the "exact" theory. PMID:20648178
Faraji-Dana, Zahra; Tam, Fred; Chen, J Jean; Graham, Simon J
2016-01-01
Echo planar imaging (EPI) suffers from geometric distortions caused by magnetic field inhomogeneities, which can be time-varying as a result of small amounts of head motion that occur over seconds and minutes during fMRI experiments, also known as "dynamic geometric distortion". Phase Labeling for Additional Coordinate Encoding (PLACE) is a promising technique for geometric distortion correction without reduced temporal resolution and in principle can be used to correct for motion-induced dynamic geometric distortion. PLACE requires at least two EPI images of the same anatomy that are ideally acquired with no variation in the magnetic field inhomogeneities. However, head motion and lung ventilation during the respiratory cycle can cause changes in magnetic field inhomogeneities within the EPI pair used for PLACE. In this work, we exploited dynamic off-resonance in k-space (DORK) and averaging to correct the within EPI pair magnetic field inhomogeneities; and hence proposed a combined technique (DORK+PLACE+averaging) to mitigate dynamic geometric distortion in EPI-based fMRI while preserving the temporal resolution. The performance of the combined DORK, PLACE and averaging technique was characterized through several imaging experiments involving test phantoms and six healthy adult volunteers. Phantom data illustrate reduced temporal standard deviation of fMRI signal intensities after use of combined dynamic PLACE, DORK and averaging compared to the standard processing and static geometric distortion correction. The combined technique also substantially improved the temporal standard deviation and activation maps obtained from human fMRI data in comparison to the results obtained by standard processing and static geometric distortion correction, highlighting the utility of the approach. PMID:27258194
Faraji-Dana, Zahra; Tam, Fred; Chen, J. Jean; Graham, Simon J.
2016-01-01
Echo planar imaging (EPI) suffers from geometric distortions caused by magnetic field inhomogeneities, which can be time-varying as a result of small amounts of head motion that occur over seconds and minutes during fMRI experiments, also known as “dynamic geometric distortion”. Phase Labeling for Additional Coordinate Encoding (PLACE) is a promising technique for geometric distortion correction without reduced temporal resolution and in principle can be used to correct for motion-induced dynamic geometric distortion. PLACE requires at least two EPI images of the same anatomy that are ideally acquired with no variation in the magnetic field inhomogeneities. However, head motion and lung ventilation during the respiratory cycle can cause changes in magnetic field inhomogeneities within the EPI pair used for PLACE. In this work, we exploited dynamic off-resonance in k-space (DORK) and averaging to correct the within EPI pair magnetic field inhomogeneities; and hence proposed a combined technique (DORK+PLACE+averaging) to mitigate dynamic geometric distortion in EPI-based fMRI while preserving the temporal resolution. The performance of the combined DORK, PLACE and averaging technique was characterized through several imaging experiments involving test phantoms and six healthy adult volunteers. Phantom data illustrate reduced temporal standard deviation of fMRI signal intensities after use of combined dynamic PLACE, DORK and averaging compared to the standard processing and static geometric distortion correction. The combined technique also substantially improved the temporal standard deviation and activation maps obtained from human fMRI data in comparison to the results obtained by standard processing and static geometric distortion correction, highlighting the utility of the approach. PMID:27258194
Effect of the geometric phase on the dynamics of the hydrogen-exchange reaction.
Juanes-Marcos, Juan Carlos; Althorpe, Stuart C; Wrede, Eckart
2007-01-28
A recent puzzle in nonadiabatic quantum dynamics is that geometric phase (GP) effects are present in the state-to-state opacity functions of the hydrogen-exchange reaction, but cancel out in the state-to-state integral cross sections (ICSs). Here the authors explain this result by using topology to separate the scattering amplitudes into contributions from Feynman paths that loop in opposite senses around the conical intersection. The clockwise-looping paths pass over one transition state (1-TS) and scatter into positive deflection angles; the counterclockwise-looping paths pass over two transition states (2-TS) and scatter into negative deflection angles. The interference between the 1-TS and 2-TS paths thus integrates to a very small value, which cancels the GP effects in the ICS. Quasiclassical trajectory (QCT) calculations reproduce the scattering of the 1-TS and 2-TS paths into positive and negative deflection angles and show that the 2-TS paths describe a direct insertion mechanism. The inserting atom follows a highly constrained "S-bend" path, which allows it to avoid both the other atoms and the conical intersection and forces the product diatom to scatter into high rotational states. By contrast, the quantum 2-TS paths scatter into a mainly statistical distribution of rotational states, so that the quantum 2-TS total ICS is roughly twice the QCT ICS at 2.3 eV total energy. This suggests that the S-bend constraint is relaxed by tunneling in the quantum system. These findings on H+H(2) suggest that similar cancellations or reductions in GP effects are likely in many other reactions.
Accurate potential energy functions, non-adiabatic and spin-orbit couplings in the ZnH(+) system.
Liang, Guiying; Liu, Xiaoting; Zhang, Xiaomei; Xu, Haifeng; Yan, Bing
2016-03-01
A high-level ab initio calculation on the ZnH(+) cation has been carried out with the multi-reference configuration interaction method plus Davison correction (MRCI+Q). The scalar relativistic effect is included by using the Douglas-Kroll-Hess (DKH) method. The calculated potential energy curves (PECs) of the 7 Λ-S states are associated with the dissociation limits of Zn(+)((2)Sg)+H((2)Sg), Zn((1)Sg)+H(+)((1)Sg), and Zn(+)((2)Pu)+H((2)Sg), respectively (The Λ-S state is labeled as (2S+1)Λ, in which Λ is the quantum number for the projection along the internuclear axis of the total electronic orbital angular momentum and S is the total electron spin). The spectroscopic constants of the bound states are determined and in good agreement with the available theoretical and experimental results. The permanent dipole moments (PDMs) of Λ-S states and the spin-orbit (SO) matrix elements between Λ-S states are also computed. The results show that the abrupt changes of the PDMs and SO matrix elements come into being for the reason of the avoided crossing between the states with the same symmetry. In addition, the non-adiabatic couplings matrix elements between Λ-S states are also evaluated. Finally, the spin-orbit couplings (SOCs) for the low-lying states are considered with Breit-Pauli operator. The SOC effect makes the 7 Λ-S states of the ZnH(+) cation split into 12 Ω states (Ω=Λ+Sz, in which Sz is projection of the total electron spin S along the internuclear Z-axis). For the (3)0(+) state, the two energy minima exhibit in the potential, which could be attributed to the formation of the new avoided crossing point. The transition dipole moments (TDMs), Franck-Condon factors, and the radiative lifetimes of the selected transitions (2)0(+)-X0(+), (3)0(+)-X0(+), (2)1-X0(+) and (3)1-X0(+) have been reported.
Accurate potential energy functions, non-adiabatic and spin-orbit couplings in the ZnH+ system
NASA Astrophysics Data System (ADS)
Liang, Guiying; Liu, Xiaoting; Zhang, Xiaomei; Xu, Haifeng; Yan, Bing
2016-03-01
A high-level ab initio calculation on the ZnH+ cation has been carried out with the multi-reference configuration interaction method plus Davison correction (MRCI + Q). The scalar relativistic effect is included by using the Douglas-Kroll-Hess (DKH) method. The calculated potential energy curves (PECs) of the 7 Λ-S states are associated with the dissociation limits of Zn+(2Sg) + H(2Sg), Zn(1Sg) + H+(1Sg), and Zn+(2Pu) + H(2Sg), respectively (The Λ-S state is labeled as 2S + 1Λ, in which Λ is the quantum number for the projection along the internuclear axis of the total electronic orbital angular momentum and S is the total electron spin). The spectroscopic constants of the bound states are determined and in good agreement with the available theoretical and experimental results. The permanent dipole moments (PDMs) of Λ-S states and the spin-orbit (SO) matrix elements between Λ-S states are also computed. The results show that the abrupt changes of the PDMs and SO matrix elements come into being for the reason of the avoided crossing between the states with the same symmetry. In addition, the non-adiabatic couplings matrix elements between Λ-S states are also evaluated. Finally, the spin-orbit couplings (SOCs) for the low-lying states are considered with Breit-Pauli operator. The SOC effect makes the 7 Λ-S states of the ZnH+ cation split into 12 Ω states (Ω = Λ + Sz, in which Sz is projection of the total electron spin S along the internuclear Z-axis). For the (3)0+ state, the two energy minima exhibit in the potential, which could be attributed to the formation of the new avoided crossing point. The transition dipole moments (TDMs), Franck-Condon factors, and the radiative lifetimes of the selected transitions (2)0+-X0+, (3)0+-X0+, (2)1-X0+ and (3)1-X0+ have been reported.
Experimental realization of non-abelian geometric gates with a superconducting three-level system
NASA Astrophysics Data System (ADS)
Abdumalikov, Abdufarrukh; Fink, J. M.; Juliusson, K.; Pechal, M.; Berger, S.; Wallraff, A.; Filipp, S.
2013-03-01
Geometric gates hold promise to provide the building blocks for robust quantum computation. In our experiments, we use a superconducting three-level system (transmon) to realize non-adiabatic non-abelian geometric gates. As computational basis we choose the ground and second excited states, while the first excited state acts as an ancilla state. The gates are realized by applying two resonant drives between the transmon levels. During the geometric gate ration of the amplitudes of the two drive tone is kept constant. Different gates are obtained for different ratio of the drive tones. We implement a Hadamard, a NOT and a phase gates with the fidelities of 95 % , 98 % , and 97 % as determined by full process tomography and maximum likelihood methods. We explicitly show the non-abelian nature of gates by applying two non-commuting gates in alternating order. The demonstrated holonomic gates are not exclusive to superconducting quantum devices, but can also be applied to other three level systems with similar energy level structure.
Jian Liu and Hong Qin
2012-08-22
The reformulation of our analysis on the geometric phase of the gyromotion [J. Liu and H. Qin, Phys. Plasmas 18, 072505 (2011)] in terms of spatial angles presented in the comment by Brizard and Guillebon is interesting and correct. The subtlety of whether the adiabatic term associated with the long term average of the variation of pitch angle completely disappears after the gyrophase average is related to where valid approximations are applied. But it has no impact on the main conclusions.
NASA Astrophysics Data System (ADS)
Nagarajan, Mahesh B.; Coan, Paola; Huber, Markus B.; Diemoz, Paul C.; Wismüller, Axel
2014-03-01
Current assessment of cartilage is primarily based on identification of indirect markers such as joint space narrowing and increased subchondral bone density on x-ray images. In this context, phase contrast CT imaging (PCI-CT) has recently emerged as a novel imaging technique that allows a direct examination of chondrocyte patterns and their correlation to osteoarthritis through visualization of cartilage soft tissue. This study investigates the use of topological and geometrical approaches for characterizing chondrocyte patterns in the radial zone of the knee cartilage matrix in the presence and absence of osteoarthritic damage. For this purpose, topological features derived from Minkowski Functionals and geometric features derived from the Scaling Index Method (SIM) were extracted from 842 regions of interest (ROI) annotated on PCI-CT images of healthy and osteoarthritic specimens of human patellar cartilage. The extracted features were then used in a machine learning task involving support vector regression to classify ROIs as healthy or osteoarthritic. Classification performance was evaluated using the area under the receiver operating characteristic (ROC) curve (AUC). The best classification performance was observed with high-dimensional geometrical feature vectors derived from SIM (0.95 ± 0.06) which outperformed all Minkowski Functionals (p < 0.001). These results suggest that such quantitative analysis of chondrocyte patterns in human patellar cartilage matrix involving SIM-derived geometrical features can distinguish between healthy and osteoarthritic tissue with high accuracy.
NASA Astrophysics Data System (ADS)
Casana, R.; Ferreira, M. M.; Mouchrek-Santos, V. E.; Silva, Edilberto O.
2015-06-01
We have demonstrated that Lorentz-violating terms stemming from the fermion sector of the SME are able to generate geometrical phases on the wave function of electrons confined in 1-dimensional rings, as well as persistent spin currents, in the total absence of electromagnetic fields. We have explicitly evaluated the eigenenergies and eigenspinors of the electrons modified by the Lorentz-violating terms, using them to calculate the dynamic and the Aharonov-Anandan phases in the sequel. The total phase presents a pattern very similar to the Aharonov-Casher phase accumulated by electrons in rings under the action of the Rashba interaction. Finally, the persistent spin current were carried out and used to impose upper bounds on the Lorentz-violating parameters.
Geometric phase and o-mode blueshift in a chiral anisotropic medium inside a Fabry-Pérot cavity.
Timofeev, Ivan V; Gunyakov, Vladimir A; Sutormin, Vitaly S; Myslivets, Sergey A; Arkhipkin, Vasily G; Vetrov, Stepan Ya; Lee, Wei; Zyryanov, Victor Ya
2015-11-01
Anomalous spectral shift of transmission peaks is observed in a Fabry-Pérot cavity filled with a chiral anisotropic medium. The effective refractive index value resides out of the interval between the ordinary and the extraordinary refractive indices. The spectral shift is explained by contribution of a geometric phase. The problem is solved analytically using the approximate Jones matrix method, numerically using the accurate Berreman method, and geometrically using the generalized Mauguin-Poincaré rolling cone method. The o-mode blueshift is measured for a 4-methoxybenzylidene-4'-n-butylaniline twisted-nematic layer inside the Fabry-Pérot cavity. The twist is electrically induced due to the homeoplanar-twisted configuration transition in an ionic-surfactant-doped liquid crystal layer. Experimental evidence confirms the validity of the theoretical model.
NASA Astrophysics Data System (ADS)
Akopyan, M. E.; Chinkova, I. Yu.; Fedorova, T. V.; Poretsky, S. A.; Pravilov, A. M.
2004-07-01
Non-adiabatic transitions from the f0 g+ state of the iodine ion-pair (IP) second tier induced by collision with iodine ground state molecules have been studied for the first time. The only I 2( f0g+,v f,J f limit→I2( X) F0u+,v F,J F) transition has been observed. No transitions between the states of the first and second tiers have been found. The dependences of the I 2( f0g+,v f,J f limit→I2( X) F0u+,v F,J F) transition rate constants on the vibrational vf=8-19, vF, rotational Jf≈55,85,105, JF quantum numbers, energy gaps, as well as their correlations with Franck-Condon factors (FCFs) of the initial and final levels have been studied. The principal features of the collision-induced non-adiabatic transitions in the first and second tiers are very similar.
Cotton, Stephen J; Miller, William H
2016-03-01
In a recent series of papers, it has been illustrated that a symmetrical quasi-classical (SQC) windowing model applied to the Meyer-Miller (MM) classical vibronic Hamiltonian provides an excellent description of a variety of electronically non-adiabatic benchmark model systems for which exact quantum results are available for comparison. In this paper, the SQC/MM approach is used to treat energy transfer dynamics in site-exciton models of light-harvesting complexes, and in particular, the well-known 7-state Fenna-Mathews-Olson (FMO) complex. Again, numerically "exact" results are available for comparison, here via the hierarchical equation of motion (HEOM) approach of Ishizaki and Fleming, and it is seen that the simple SQC/MM approach provides very reasonable agreement with the previous HEOM results. It is noted, however, that unlike most (if not all) simple approaches for treating these systems, because the SQC/MM approach presents a fully atomistic simulation based on classical trajectory simulation, it places no restrictions on the characteristics of the thermal baths coupled to each two-level site, e.g., bath spectral densities (SD) of any analytic functional form may be employed as well as discrete SD determined experimentally or from MD simulation (nor is there any restriction that the baths be harmonic), opening up the possibility of simulating more realistic variations on the basic site-exciton framework for describing the non-adiabatic dynamics of photosynthetic pigment complexes. PMID:26761191
Sinitsyn, Nikolai A
2008-01-01
We generalize the concept of the geometric phase in stochastic kinetics to a noncyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the noncyclic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. We also discuss a model, where this correction qualitatively changes the outcome of reaction kinetics.
A composite phase diagram of structure H hydrates using Schreinemakers' geometric approach
Mehta, A.P.; Makogon, T.Y.; Burruss, R.C.; Wendlandt, R.F.; Sloan, E.D.
1996-01-01
A composite phase diagram is presented for Structure H (sH) clathrate hydrates. In this work, we derived the reactions occurring among the various phases along each four-phase (Ice/Liquid water, liquid hydrocarbon, vapor, and hydrate) equilibrium line. A powerful method (though seldom used in chemical engineering) for multicomponent equilibria developed by Schreinemakers is applied to determine the relative location of all quadruple (four-phase) lines emanating from three quintuple (five-phase) points. Experimental evidence validating the approximate phase diagram is also provided. The use of Schreinemakers' rules for the development of the phase diagram is novel for hydrates, but these rules may be extended to resolve the phase space of other more complex systems commonly encountered in chemical engineering.
On a relation of the angular frequency to the Aharonov-Casher geometric phase in a quantum dot
NASA Astrophysics Data System (ADS)
Barboza, P. M. T.; Bakke, K.
2016-09-01
By analysing the behaviour of a neutral particle with permanent magnetic dipole moment confined to a quantum dot in the presence of a radial electric field, Coulomb-type and linear confining potentials, then, an Aharonov-Bohm-type effect for bound states and a dependence of the angular frequency of the system on the Aharonov-Casher geometric phase and the quantum numbers associated with the radial modes, the angular momentum and the spin are obtained. In particular, the possible values of the angular frequency and the persistent spin currents associated with the ground state are investigated in two different cases.
Competing Ferri- and Antiferromagnetic Phases in Geometrically Frustrated LuFe2O4
De Groot, J.; Marty, Karol J; Lumsden, Mark D; Christianson, Andrew D; Nagler, Stephen E; Adiga, Shilpa; Borghols, Wouter; Schmalzl, Karin; Yamani, Z.; Bland, S. R.; de Souza, R.; Staub, U.; Schweika, Werner; Su, Y.; Angst, Manuel
2012-01-01
We present a detailed study of magnetism in LuFe2O4, combining magnetization measurements with neutron and soft x-ray diffraction. The magnetic phase diagram in the vicinity of TN involves a metamagnetic transition separating an antiferro- and a ferrimagnetic phase. For both phases the spin structure is refined by neutron diffraction. Observed diffuse magnetic scattering far above TN is explained in terms of near degeneracy of the magnetic phases.
Zhang, Ruihua; Guo, Hongwei; Asundi, Anand K
2016-09-20
In fringe projection profilometry, phase sensitivity is one of the important factors affecting measurement accuracy. A typical fringe projection system consists of one camera and one projector. To gain insight into its phase sensitivity, we perform in this paper a strict analysis in theory about the dependence of phase sensitivities on fringe directions. We use epipolar geometry as a tool to derive the relationship between fringe distortions and depth variations of the measured surface, and further formularize phase sensitivity as a function of the angle between fringe direction and the epipolar line. The results reveal that using the fringes perpendicular to the epipolar lines enables us to achieve the maximum phase sensitivities, whereas if the fringes have directions along the epipolar lines, the phase sensitivities decline to zero. Based on these results, we suggest the optimal fringes being circular-arc-shaped and centered at the epipole, which enables us to give the best phase sensitivities over the whole fringe pattern, and the quasi-optimal fringes, being straight and perpendicular to the connecting line between the fringe pattern center and the epipole, can achieve satisfyingly high phase sensitivities over whole fringe patterns in the situation that the epipole locates far away from the fringe pattern center. The experimental results demonstrate that our analyses are practical and correct, and that our optimized fringes are effective in improving the phase sensitivities and, further, the measurement accuracies. PMID:27661597
Reichardt, J; Hess, M; Macke, A
2000-04-20
Multiple-scattering correction factors for cirrus particle extinction coefficients measured with Raman and high spectral resolution lidars are calculated with a radiative-transfer model. Cirrus particle-ensemble phase functions are computed from single-crystal phase functions derived in a geometrical-optics approximation. Seven crystal types are considered. In cirrus clouds with height-independent particle extinction coefficients the general pattern of the multiple-scattering parameters has a steep onset at cloud base with values of 0.5-0.7 followed by a gradual and monotonic decrease to 0.1-0.2 at cloud top. The larger the scattering particles are, the more gradual is the rate of decrease. Multiple-scattering parameters of complex crystals and of imperfect hexagonal columns and plates can be well approximated by those of projected-area equivalent ice spheres, whereas perfect hexagonal crystals show values as much as 70% higher than those of spheres. The dependencies of the multiple-scattering parameters on cirrus particle spectrum, base height, and geometric depth and on the lidar parameters laser wavelength and receiver field of view, are discussed, and a set of multiple-scattering parameter profiles for the correction of extinction measurements in homogeneous cirrus is provided.
High-efficiency beam manipulation combining geometric phase with anisotropic Huygens surface
NASA Astrophysics Data System (ADS)
Zhao, Wenyu; Jiang, Huan; Liu, Bingyi; Song, Jie; Jiang, Yongyuan
2016-05-01
Conventional geometric metasurfaces relying on space-variant metal antennas for beam manipulation suffer from strong Ohmic loss and incomplete polarization conversion. The efficiency is often limited to rather small values, especially when operating in transmission mode. Here, we tackle this challenge by deliberately constructing an equivalent sheet with anisotropic surface electric and magnetic polarizabilities using cross-shaped dielectric antennas. An incident circularly polarized light can be almost fully converted to a transmitted light of opposite helicity with an unprecedented efficiency up to 98%. Such a transmissive metasurface possessing the merits of high-efficiency, non-dispersion, and robust against variations can serve as an outstanding candidate for flat optics, such as anomalous refraction and beam focusing.
NASA Astrophysics Data System (ADS)
Samadi, R.; Belkacem, K.; Dupret, M.-A.; Ludwig, H.-G.; Baudin, F.; Caffau, E.; Goupil, M.-J.; Barban, C.
2012-07-01
Context. A growing number of solar-like oscillations has been detected in red giant stars thanks to the CoRoT and Kepler space-crafts. In the same way as for main-sequence stars, mode driving is attributed to turbulent convection in the uppermost convective layers of those stars. Aims: The seismic data gathered by CoRoT on red giant stars allow us to test the mode driving theory in physical conditions different from main-sequence stars. Methods: Using a set of 3D hydrodynamical models representative of the upper layers of sub- and red giant stars, we computed the acoustic mode energy supply rate ({p_max}). Assuming adiabatic pulsations and using global stellar models that assume that the surface stratification comes from the 3D hydrodynamical models, we computed the mode amplitude in terms of surface velocity. This was converted into intensity fluctuations using either a simplified adiabatic scaling relation or a non-adiabatic one. Results: From L and M (the luminosity and mass), the energy supply rate {p_max} is found to scale as (L/M)2.6 for both main-sequence and red giant stars, extending previous results. The theoretical amplitudes in velocity under-estimate the Doppler velocity measurements obtained so far from the ground for red giant stars by about 30%. In terms of intensity, the theoretical scaling law based on the adiabatic intensity-velocity scaling relation results in an under-estimation by a factor of about 2.5 with respect to the CoRoT seismic measurements. On the other hand, using the non-adiabatic intensity-velocity relation significantly reduces the discrepancy with the CoRoT data. The theoretical amplitudes remain 40% below, however, the CoRoT measurements. Conclusions: Our results show that scaling relations of mode amplitudes cannot be simply extended from main-sequence to red giant stars in terms of intensity on the basis of adiabatic relations because non-adiabatic effects for red giant stars are important and cannot be neglected. We discuss
Benabbas, Abdelkrim; Salna, Bridget; Sage, J Timothy; Champion, Paul M
2015-03-21
Analytical models describing the temperature dependence of the deep tunneling rate, useful for proton, hydrogen, or hydride transfer in proteins, are developed and compared. Electronically adiabatic and non-adiabatic expressions are presented where the donor-acceptor (D-A) motion is treated either as a quantized vibration or as a classical "gating" distribution. We stress the importance of fitting experimental data on an absolute scale in the electronically adiabatic limit, which normally applies to these reactions, and find that vibrationally enhanced deep tunneling takes place on sub-ns timescales at room temperature for typical H-bonding distances. As noted previously, a small room temperature kinetic isotope effect (KIE) does not eliminate deep tunneling as a major transport channel. The quantum approach focuses on the vibrational sub-space composed of the D-A and hydrogen atom motions, where hydrogen bonding and protein restoring forces quantize the D-A vibration. A Duschinsky rotation is mandated between the normal modes of the reactant and product states and the rotation angle depends on the tunneling particle mass. This tunnel-mass dependent rotation contributes substantially to the KIE and its temperature dependence. The effect of the Duschinsky rotation is solved exactly to find the rate in the electronically non-adiabatic limit and compared to the Born-Oppenheimer (B-O) approximation approach. The B-O approximation is employed to find the rate in the electronically adiabatic limit, where we explore both harmonic and quartic double-well potentials for the hydrogen atom bound states. Both the electronically adiabatic and non-adiabatic rates are found to diverge at high temperature unless the proton coupling includes the often neglected quadratic term in the D-A displacement from equilibrium. A new expression is presented for the electronically adiabatic tunnel rate in the classical limit for D-A motion that should be useful to experimentalists working near
Benabbas, Abdelkrim; Salna, Bridget; Sage, J. Timothy; Champion, Paul M.
2015-03-21
Analytical models describing the temperature dependence of the deep tunneling rate, useful for proton, hydrogen, or hydride transfer in proteins, are developed and compared. Electronically adiabatic and non-adiabatic expressions are presented where the donor-acceptor (D-A) motion is treated either as a quantized vibration or as a classical “gating” distribution. We stress the importance of fitting experimental data on an absolute scale in the electronically adiabatic limit, which normally applies to these reactions, and find that vibrationally enhanced deep tunneling takes place on sub-ns timescales at room temperature for typical H-bonding distances. As noted previously, a small room temperature kinetic isotope effect (KIE) does not eliminate deep tunneling as a major transport channel. The quantum approach focuses on the vibrational sub-space composed of the D-A and hydrogen atom motions, where hydrogen bonding and protein restoring forces quantize the D-A vibration. A Duschinsky rotation is mandated between the normal modes of the reactant and product states and the rotation angle depends on the tunneling particle mass. This tunnel-mass dependent rotation contributes substantially to the KIE and its temperature dependence. The effect of the Duschinsky rotation is solved exactly to find the rate in the electronically non-adiabatic limit and compared to the Born-Oppenheimer (B-O) approximation approach. The B-O approximation is employed to find the rate in the electronically adiabatic limit, where we explore both harmonic and quartic double-well potentials for the hydrogen atom bound states. Both the electronically adiabatic and non-adiabatic rates are found to diverge at high temperature unless the proton coupling includes the often neglected quadratic term in the D-A displacement from equilibrium. A new expression is presented for the electronically adiabatic tunnel rate in the classical limit for D-A motion that should be useful to experimentalists working
Benabbas, Abdelkrim; Salna, Bridget; Sage, J Timothy; Champion, Paul M
2015-03-21
Analytical models describing the temperature dependence of the deep tunneling rate, useful for proton, hydrogen, or hydride transfer in proteins, are developed and compared. Electronically adiabatic and non-adiabatic expressions are presented where the donor-acceptor (D-A) motion is treated either as a quantized vibration or as a classical "gating" distribution. We stress the importance of fitting experimental data on an absolute scale in the electronically adiabatic limit, which normally applies to these reactions, and find that vibrationally enhanced deep tunneling takes place on sub-ns timescales at room temperature for typical H-bonding distances. As noted previously, a small room temperature kinetic isotope effect (KIE) does not eliminate deep tunneling as a major transport channel. The quantum approach focuses on the vibrational sub-space composed of the D-A and hydrogen atom motions, where hydrogen bonding and protein restoring forces quantize the D-A vibration. A Duschinsky rotation is mandated between the normal modes of the reactant and product states and the rotation angle depends on the tunneling particle mass. This tunnel-mass dependent rotation contributes substantially to the KIE and its temperature dependence. The effect of the Duschinsky rotation is solved exactly to find the rate in the electronically non-adiabatic limit and compared to the Born-Oppenheimer (B-O) approximation approach. The B-O approximation is employed to find the rate in the electronically adiabatic limit, where we explore both harmonic and quartic double-well potentials for the hydrogen atom bound states. Both the electronically adiabatic and non-adiabatic rates are found to diverge at high temperature unless the proton coupling includes the often neglected quadratic term in the D-A displacement from equilibrium. A new expression is presented for the electronically adiabatic tunnel rate in the classical limit for D-A motion that should be useful to experimentalists working near
Revealing geometric phases in modular and weak values with a quantum eraser
NASA Astrophysics Data System (ADS)
Cormann, Mirko; Remy, Mathilde; Kolaric, Branko; Caudano, Yves
2016-04-01
We present a procedure to completely determine the complex modular values of arbitrary observables of pre- and postselected ensembles, which works experimentally for all measurement strengths and all postselected states. This procedure allows us to discuss the physics of modular and weak values in interferometric experiments involving a qubit meter. We determine both the modulus and the argument of the modular value for any measurement strength in a single step, by simultaneously controlling the visibility and the phase in a quantum eraser interference experiment. Modular and weak values are closely related. Using entangled qubits for the probed and meter systems, we show that the phase of the modular and weak values has a topological origin. This phase is completely defined by the intrinsic physical properties of the probed system and its time evolution. The physical significance of this phase can thus be used to evaluate the quantumness of weak values.
NASA Astrophysics Data System (ADS)
Diniz, Leonardo G.; Kirnosov, Nikita; Alijah, Alexander; Mohallem, José R.; Adamowicz, Ludwik
2016-04-01
A very accurate dipole moment curve (DMC) for the ground X1Σ+ electronic state of the 7LiH molecule is reported. It is calculated with the use of all-particle explicitly correlated Gaussian functions with shifted centers. The DMC - the most accurate to our knowledge - and the corresponding highly accurate potential energy curve are used to calculate the transition energies, the transition dipole moments, and the Einstein coefficients for the rovibrational transitions with ΔJ = - 1 and Δv ⩽ 5 . The importance of the non-adiabatic effects in determining these properties is evaluated using the model of a vibrational R-dependent effective reduced mass in the rovibrational calculations introduced earlier (Diniz et al., 2015). The results of the present calculations are used to assess the quality of the two complete linelists of 7LiH available in the literature.
NASA Astrophysics Data System (ADS)
Diniz, Leonardo G.; Alijah, Alexander; Adamowicz, Ludwik; Mohallem, José R.
2015-07-01
Non-adiabatic vibrational calculations performed with the accuracy of 0.2 cm-1 spanning the whole energy spectrum up to the dissociation limit for 7LiH are reported. A so far unknown v = 23 energy level is predicted. The key feature of the approach used in the calculations is a valence-bond (VB) based procedure for determining the effective masses of the two vibrating atoms, which depend on the internuclear distance, R. It is found that all LiH electrons participate in the vibrational motion. The R-dependent masses are obtained from the analysis of the simple VB two-configuration ionic-covalent representation of the electronic wave function. These findings are consistent with an interpretation of the chemical bond in LiH as a quantum mechanical superposition of one-electron ionic and covalent states.
NASA Astrophysics Data System (ADS)
Dobbyn, Abigail J.; Knowles, Peter J.
A number of established techniques for obtaining diabatic electronic states in small molecules are critically compared for the example of the X and B states in the water molecule, which contribute to the two lowest-energy conical intersections. Integration of the coupling matrix elements and analysis of configuration mixing coefficients both produce reliable diabatic states globally. Methods relying on diagonalization of dipole moment and angular momentum operators are shown to fail in large regions of coordinate space. However, the use of transition angular momentum matrix elements involving the A state, which is degenerate with B at the conical intersections, is successful globally, provided that an appropriate choice of coordinates is made. Long range damping of non-adiabatic coupling to give correct asymptotic mixing angles also is investigated.
Kittell, Aaron W; Hyde, James S
2015-06-01
Non-adiabatic rapid passage (NARS) electron paramagnetic resonance (EPR) spectroscopy was introduced by Kittell et al. (2011) as a general purpose technique to collect the pure absorption response. The technique has been used to improve sensitivity relative to sinusoidal magnetic field modulation, increase the range of inter-spin distances that can be measured under near physiological conditions (Kittell et al., 2012), and enhance spectral resolution in copper (II) spectra (Hyde et al., 2013). In the present work, the method is extended to CW microwave power saturation of spin-labeled T4 Lysozyme (T4L). As in the cited papers, rapid triangular sweep of the polarizing magnetic field was superimposed on slow sweep across the spectrum. Adiabatic rapid passage (ARP) effects were encountered in samples undergoing very slow rotational diffusion as the triangular magnetic field sweep rate was increased. The paper reports results of variation of experimental parameters at the interface of adiabatic and non-adiabatic rapid sweep conditions. Comparison of the forward (up) and reverse (down) triangular sweeps is shown to be a good indicator of the presence of rapid passage effects. Spectral turning points can be distinguished from spectral regions between turning points in two ways: differential microwave power saturation and differential passage effects. Oxygen accessibility data are shown under NARS conditions that appear similar to conventional field modulation data. However, the sensitivity is much higher, permitting, in principle, experiments at substantially lower protein concentrations. Spectral displays were obtained that appear sensitive to rotational diffusion in the range of rotational correlation times of 10(-3) to 10(-7) s in a manner that is analogous to saturation transfer spectroscopy.
NASA Astrophysics Data System (ADS)
Kittell, Aaron W.; Hyde, James S.
2015-06-01
Non-adiabatic rapid passage (NARS) electron paramagnetic resonance (EPR) spectroscopy was introduced by Kittell et al. (2011) as a general purpose technique to collect the pure absorption response. The technique has been used to improve sensitivity relative to sinusoidal magnetic field modulation, increase the range of inter-spin distances that can be measured under near physiological conditions (Kittell et al., 2012), and enhance spectral resolution in copper (II) spectra (Hyde et al., 2013). In the present work, the method is extended to CW microwave power saturation of spin-labeled T4 Lysozyme (T4L). As in the cited papers, rapid triangular sweep of the polarizing magnetic field was superimposed on slow sweep across the spectrum. Adiabatic rapid passage (ARP) effects were encountered in samples undergoing very slow rotational diffusion as the triangular magnetic field sweep rate was increased. The paper reports results of variation of experimental parameters at the interface of adiabatic and non-adiabatic rapid sweep conditions. Comparison of the forward (up) and reverse (down) triangular sweeps is shown to be a good indicator of the presence of rapid passage effects. Spectral turning points can be distinguished from spectral regions between turning points in two ways: differential microwave power saturation and differential passage effects. Oxygen accessibility data are shown under NARS conditions that appear similar to conventional field modulation data. However, the sensitivity is much higher, permitting, in principle, experiments at substantially lower protein concentrations. Spectral displays were obtained that appear sensitive to rotational diffusion in the range of rotational correlation times of 10-3 to 10-7 s in a manner that is analogous to saturation transfer spectroscopy.
Kittell, Aaron W; Hyde, James S
2015-06-01
Non-adiabatic rapid passage (NARS) electron paramagnetic resonance (EPR) spectroscopy was introduced by Kittell et al. (2011) as a general purpose technique to collect the pure absorption response. The technique has been used to improve sensitivity relative to sinusoidal magnetic field modulation, increase the range of inter-spin distances that can be measured under near physiological conditions (Kittell et al., 2012), and enhance spectral resolution in copper (II) spectra (Hyde et al., 2013). In the present work, the method is extended to CW microwave power saturation of spin-labeled T4 Lysozyme (T4L). As in the cited papers, rapid triangular sweep of the polarizing magnetic field was superimposed on slow sweep across the spectrum. Adiabatic rapid passage (ARP) effects were encountered in samples undergoing very slow rotational diffusion as the triangular magnetic field sweep rate was increased. The paper reports results of variation of experimental parameters at the interface of adiabatic and non-adiabatic rapid sweep conditions. Comparison of the forward (up) and reverse (down) triangular sweeps is shown to be a good indicator of the presence of rapid passage effects. Spectral turning points can be distinguished from spectral regions between turning points in two ways: differential microwave power saturation and differential passage effects. Oxygen accessibility data are shown under NARS conditions that appear similar to conventional field modulation data. However, the sensitivity is much higher, permitting, in principle, experiments at substantially lower protein concentrations. Spectral displays were obtained that appear sensitive to rotational diffusion in the range of rotational correlation times of 10(-3) to 10(-7) s in a manner that is analogous to saturation transfer spectroscopy. PMID:25917132
Qu, Zexing Liu, Chungen
2013-12-28
Simulation of the excited state dynamics of all-trans-1,3,5,7-octatetraene has been performed to investigate the ultrafast radiationless S{sub 2} → S{sub 1} internal conversion process. Multireference configuration interaction with single excitation method has been employed to optimize the equilibrium structure of the excited states, as well as the S{sub 2}/S{sub 1} conical intersection, and to investigate the non-adiabatic molecular dynamics of the S{sub 2}/S{sub 1} state transition. At the conical intersection, the molecule is found to be distorted from the original planar trans structure to a nearly perpendicular conformation around C{sub 3}−C{sub 4} bond, with the torsion angle being about 107°. Such structural change can result in mutual approaching of states S{sub 2} and S{sub 1} in energy, and drastically increase the nonadiabatic coupling between the two states by destroying the inter-state symmetry prohibition in the electronic wavefunctions. Surface-hopping molecular dynamics simulations are performed to describe the non-adiabatic process. Upon the Franck-Condon excitation to the S{sub 2} state, the molecule quickly twists its C{sub 3}−C{sub 4} bond and approaches the conical intersection region, where it can undergo efficient internal conversion to S{sub 1}. The decay time constant (τ) of S{sub 2} state is estimated to be around 251 fs by fitting the occupation number of average fraction of trajectories using an exponential damping function. This value is reasonably consistent with previous experimental measurements of around 300–400 fs.
Shekhar, Raj; Lei, Peng; Castro-Pareja, Carlos R.; Plishker, William L.; D'Souza, Warren D.
2007-07-15
Conventional radiotherapy is planned using free-breathing computed tomography (CT), ignoring the motion and deformation of the anatomy from respiration. New breath-hold-synchronized, gated, and four-dimensional (4D) CT acquisition strategies are enabling radiotherapy planning utilizing a set of CT scans belonging to different phases of the breathing cycle. Such 4D treatment planning relies on the availability of tumor and organ contours in all phases. The current practice of manual segmentation is impractical for 4D CT, because it is time consuming and tedious. A viable solution is registration-based segmentation, through which contours provided by an expert for a particular phase are propagated to all other phases while accounting for phase-to-phase motion and anatomical deformation. Deformable image registration is central to this task, and a free-form deformation-based nonrigid image registration algorithm will be presented. Compared with the original algorithm, this version uses novel, computationally simpler geometric constraints to preserve the topology of the dense control-point grid used to represent free-form deformation and prevent tissue fold-over. Using mean squared difference as an image similarity criterion, the inhale phase is registered to the exhale phase of lung CT scans of five patients and of characteristically low-contrast abdominal CT scans of four patients. In addition, using expert contours for the inhale phase, the corresponding contours were automatically generated for the exhale phase. The accuracy of the segmentation (and hence deformable image registration) was judged by comparing automatically segmented contours with expert contours traced directly in the exhale phase scan using three metrics: volume overlap index, root mean square distance, and Hausdorff distance. The accuracy of the segmentation (in terms of radial distance mismatch) was approximately 2 mm in the thorax and 3 mm in the abdomen, which compares favorably to the
Geometric quantum phase for displaced states for a particle with an induced electric dipole moment
NASA Astrophysics Data System (ADS)
Lemos de Melo, J.; Bakke, K.; Furtado, C.
2016-07-01
Basing on the analogue Landau levels for a neutral particle possessing an induced electric dipole moment, we show that displaced states can be built in the presence of electric and magnetic fields. Besides, the Berry phase associated with these displaced quantum states is obtained by performing an adiabatic cyclic evolution in series of paths in parameter space.
On a relation of the angular frequency to the Aharonov-Casher geometric phase in a quantum dot
NASA Astrophysics Data System (ADS)
Barboza, P. M. T.; Bakke, K.
2016-09-01
By analysing the behaviour of a neutral particle with permanent magnetic dipole moment confined to a quantum dot in the presence of a radial electric field, Coulomb-type and linear confining potentials, then, an Aharonov-Bohm-type effect for bound states and a dependence of the angular frequency of the system on the Aharonov-Casher geometric phase and the quantum numbers associated with the radial modes, the angular momentum and the spin are obtained. In particular, the possible values of the angular frequency and the persistent spin currents associated with the ground state are investigated in two different cases.
Karimi, Ebrahim; Marrucci, Lorenzo; Slussarenko, Sergei; Piccirillo, Bruno; Santamato, Enrico
2010-05-15
We present an easy, efficient, and fast method to generate arbitrary linear combinations of light orbital angular-momentum eigenstates l={+-}2 starting from a linearly polarized TEM{sub 00} laser beam. The method exploits the spin-to-orbital angular-momentum conversion capability of a liquid-crystal-based q plate and a Dove prism inserted into a Sagnac polarizing interferometer. The nominal generation efficiency is 100%, being limited only by reflection and scattering losses in the optical components. When closed paths are followed on the polarization Poincare sphere of the input beam, the associated Pancharatnam geometric phase is transferred unchanged to the orbital angular momentum state of the output beam.
Geometric diffusion of quantum trajectories.
Yang, Fan; Liu, Ren-Bao
2015-07-16
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov-Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects.
NASA Astrophysics Data System (ADS)
Mauguière, Frédéric A. L.; Collins, Peter; Ezra, Gregory S.; Farantos, Stavros C.; Wiggins, Stephen
2014-04-01
A model Hamiltonian for the reaction CH_4^+ rArr CH_3^+ + H, parametrized to exhibit either early or late inner transition states, is employed to investigate the dynamical characteristics of the roaming mechanism. Tight/loose transition states and conventional/roaming reaction pathways are identified in terms of time-invariant objects in phase space. These are dividing surfaces associated with normally hyperbolic invariant manifolds (NHIMs). For systems with two degrees of freedom NHIMS are unstable periodic orbits which, in conjunction with their stable and unstable manifolds, unambiguously define the (locally) non-recrossing dividing surfaces assumed in statistical theories of reaction rates. By constructing periodic orbit continuation/bifurcation diagrams for two values of the potential function parameter corresponding to late and early transition states, respectively, and using the total energy as another parameter, we dynamically assign different regions of phase space to reactants and products as well as to conventional and roaming reaction pathways. The classical dynamics of the system are investigated by uniformly sampling trajectory initial conditions on the dividing surfaces. Trajectories are classified into four different categories: direct reactive and non-reactive trajectories, which lead to the formation of molecular and radical products respectively, and roaming reactive and non-reactive orbiting trajectories, which represent alternative pathways to form molecular and radical products. By analysing gap time distributions at several energies, we demonstrate that the phase space structure of the roaming region, which is strongly influenced by nonlinear resonances between the two degrees of freedom, results in nonexponential (nonstatistical) decay.
Internal phase transition induced by external forces in Finsler geometric model for membranes
NASA Astrophysics Data System (ADS)
Koibuchi, Hiroshi; Shobukhov, Andrey
2016-10-01
In this paper, we numerically study an anisotropic shape transformation of membranes under external forces for two-dimensional triangulated surfaces on the basis of Finsler geometry. The Finsler metric is defined by using a vector field, which is the tangential component of a three-dimensional unit vector σ corresponding to the tilt or some external macromolecules on the surface of disk topology. The sigma model Hamiltonian is assumed for the tangential component of σ with the interaction coefficient λ. For large (small) λ, the surface becomes oblong (collapsed) at relatively small bending rigidity. For the intermediate λ, the surface becomes planar. Conversely, fixing the surface with the boundary of area A or with the two-point boundaries of distance L, we find that the variable σ changes from random to aligned state with increasing of A or L for the intermediate region of λ. This implies that an internal phase transition for σ is triggered not only by the thermal fluctuations, but also by external mechanical forces. We also find that the frame (string) tension shows the expected scaling behavior with respect to A/N (L/N) at the intermediate region of A (L) where the σ configuration changes between the disordered and ordered phases. Moreover, we find that the string tension γ at sufficiently large λ is considerably smaller than that at small λ. This phenomenon resembles the so-called soft-elasticity in the liquid crystal elastomer, which is deformed by small external tensile forces.
Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
Bliokh, Konstantin Yu.
2006-07-28
We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.
Geometrically induced phase transitions in two-dimensional dumbbell-shaped domains
NASA Astrophysics Data System (ADS)
Morini, M.; Slastikov, V.
2015-08-01
We continue the analysis, started in [23], of a two-dimensional non-convex variational problem, motivated by studies on magnetic domain walls trapped by thin necks. The main focus is on the impact of extreme geometry on the structure of local minimizers representing the transition between two different constant phases. We address here the case of general non-symmetric dumbbell-shaped domains with a small constriction and general multi-well potentials. Our main results concern the existence and uniqueness of non-constant local minimizers, their full classification in the case of convex bulks, and the complete description of their asymptotic behavior, as the size of the constriction tends to zero.
NASA Astrophysics Data System (ADS)
Han, Taeyoung; Schubert, Frank; Hillmann, Susanne; Meyendorf, Norbert
2015-03-01
Phased array ultrasonic testing (PAUT) techniques are widely used for the non-destructive testing (NDT) of austenitic welds to find defects like cracks. However, the propagation of ultrasound waves through the austenitic material is intricate due to its inhomogeneous and anisotropic nature. Such a characteristic leads beam path distorted which causes the signal to be misinterpreted. By employing a reference block which is cutout from the mockup of which the structure is a dissimilar metal weld (DMW), a new method of PAUT named as Referencing Delay Law Technique (RDLT) is introduced. With the RDLT, full matrix capture (FMC) was used for data acquisition. To reconstruct the images, total focusing method (TFM) was used. After the focal laws were calculated, PAUT was then performed. As a result, the flaws are more precisely positioned with significantly increased signal-to-noise ratio (SNR).
The dynamic and geometric phase transition in the cellular network of pancreatic islet
NASA Astrophysics Data System (ADS)
Wang, Xujing
2013-03-01
The pancreatic islet is a micro-organ that contains several thousands of endocrine cells, majority of which being the insulin releasing β - cells . - cellsareexcitablecells , andarecoupledtoeachother through gap junctional channels. Here, using percolation theory, we investigate the role of network structure in determining the dynamics of the β-cell network. We show that the β-cell synchronization depends on network connectivity. More specifically, as the site occupancy is reducing, initially the β-cell synchronization is barely affected, until it reaches around a critical value, where the synchronization exhibit a sudden rapid decline, followed by an slow exponential tail. This critical value coincides with the critical site open probability for percolation transition. The dependence over bond strength is similar, exhibiting critical-behavior like dependence around a certain value of bond strength. These results suggest that the β-cell network undergoes a dynamic phase transition when the network is percolated. We further apply the findings to study diabetes. During the development of diabetes, the β - cellnetworkconnectivitydecreases . Siteoccupancyreducesfromthe reducing β-cell mass, and the bond strength is increasingly impaired from β-cell stress and chronic hyperglycemia. We demonstrate that the network dynamics around the percolation transition explain the disease dynamics around onset, including a long time mystery in diabetes, the honeymoon phenomenon.
NASA Astrophysics Data System (ADS)
Liang, H.; Ashour-Abdalla, M.; Richard, R. L.; Schriver, D.; El-Alaoui, M.; Walker, R. J.
2013-12-01
We investigate the spatial evolution of energetic electron distribution functions in the near-Earth plasma sheet associated with earthward propagating dipolarization fronts by using in situ observations as well as magnetohydrodynamic (MHD) and large scale kinetic (LSK) simulations. We have investigated two substorms, one on February 15, 2008 and the other on August 15, 2001. The February 15 event was observed by one of the THEMIS spacecraft at X_{GSM} -10RE, while the August 15 event was observed by Cluster at X -18RE. Both the MHD and LSK simulation results are compared to these spacecraft observations. Earthward propagating dipolarization fronts are found in both the observations and the MHD simulations, which exhibit very different magnetotail configurations, with contrasting flows, magnetic reconnection configuration, and plasma sheet structure. Electron LSK simulations were performed by using the time-varying magnetic and electric fields from the global MHD simulations. For the February 15, 2008 event, the electrons were launched near X = -20 RE with a thermal energy of 1 keV and for August 15, 2001 event, they were launched at 4 keV near X = -22 RE. These electrons undergo both non-adiabatic acceleration near the magnetotail reconnection region and adiabatic acceleration as they propagate earthward from the launch region. We compute the electron distribution functions parallel and perpendicular to the magnetic field at different locations between X = -18 RE and X = -10 RE in the plasma sheet. We find that for the February 15, 2008 event, reconnection is localized with a narrow region of high-speed flows ( 300 km/s). For this event the distribution functions show mainly f(v_perp) > f(v_par) ("par" and "perp" correspond to parallel and perpendicular to magnetic field). On August 15, 2001, there is a neutral line extending across the tail with relatively low-speed flows ( 100 km/s). For this event the distribution functions show mainly f(v_par) > f(v_perp). The
NASA Astrophysics Data System (ADS)
Dai, Xianglu; Xie, Huimin; Wang, Huaixi; Li, Chuanwei; Liu, Zhanwei; Wu, Lifu
2014-02-01
The geometric phase analysis (GPA) method based on the local high resolution discrete Fourier transform (LHR-DFT) for deformation measurement, defined as LHR-DFT GPA, is proposed to improve the measurement accuracy. In the general GPA method, the fundamental frequency of the image plays a crucial role. However, the fast Fourier transform, which is generally employed in the general GPA method, could make it difficult to locate the fundamental frequency accurately when the fundamental frequency is not located at an integer pixel position in the Fourier spectrum. This study focuses on this issue and presents a LHR-DFT algorithm that can locate the fundamental frequency with sub-pixel precision in a specific frequency region for the GPA method. An error analysis is offered and simulation is conducted to verify the effectiveness of the proposed method; both results show that the LHR-DFT algorithm can accurately locate the fundamental frequency and improve the measurement accuracy of the GPA method. Furthermore, typical tensile and bending tests are carried out and the experimental results verify the effectiveness of the proposed method.
NASA Astrophysics Data System (ADS)
Mátyus, Edit; Szidarovszky, Tamás; Császár, Attila G.
2014-10-01
Introducing different rotational and vibrational masses in the nuclear-motion Hamiltonian is a simple phenomenological way to model rovibrational non-adiabaticity. It is shown on the example of the molecular ion H_3^+, for which a global adiabatic potential energy surface accurate to better than 0.1 cm-1 exists [M. Pavanello, L. Adamowicz, A. Alijah, N. F. Zobov, I. I. Mizus, O. L. Polyansky, J. Tennyson, T. Szidarovszky, A. G. Császár, M. Berg et al., Phys. Rev. Lett. 108, 023002 (2012)], that the motion-dependent mass concept yields much more accurate rovibrational energy levels but, unusually, the results are dependent upon the choice of the embedding of the molecule-fixed frame. Correct degeneracies and an improved agreement with experimental data are obtained if an Eckart embedding corresponding to a reference structure of D3h point-group symmetry is employed. The vibrational mass of the proton in H_3^+ is optimized by minimizing the root-mean-square (rms) deviation between the computed and recent high-accuracy experimental transitions. The best vibrational mass obtained is larger than the nuclear mass of the proton by approximately one third of an electron mass, m^(v)_opt,p=m_nuc,p+0.31224 m_e. This optimized vibrational mass, along with a nuclear rotational mass, reduces the rms deviation of the experimental and computed rovibrational transitions by an order of magnitude. Finally, it is shown that an extension of the algorithm allowing the use of motion-dependent masses can deal with coordinate-dependent mass surfaces in the rovibrational Hamiltonian, as well.
Mátyus, Edit; Szidarovszky, Tamás
2014-10-21
Introducing different rotational and vibrational masses in the nuclear-motion Hamiltonian is a simple phenomenological way to model rovibrational non-adiabaticity. It is shown on the example of the molecular ion H{sub 3}{sup +}, for which a global adiabatic potential energy surface accurate to better than 0.1 cm{sup −1} exists [M. Pavanello, L. Adamowicz, A. Alijah, N. F. Zobov, I. I. Mizus, O. L. Polyansky, J. Tennyson, T. Szidarovszky, A. G. Császár, M. Berg et al., Phys. Rev. Lett. 108, 023002 (2012)], that the motion-dependent mass concept yields much more accurate rovibrational energy levels but, unusually, the results are dependent upon the choice of the embedding of the molecule-fixed frame. Correct degeneracies and an improved agreement with experimental data are obtained if an Eckart embedding corresponding to a reference structure of D{sub 3h} point-group symmetry is employed. The vibrational mass of the proton in H{sub 3}{sup +} is optimized by minimizing the root-mean-square (rms) deviation between the computed and recent high-accuracy experimental transitions. The best vibrational mass obtained is larger than the nuclear mass of the proton by approximately one third of an electron mass, m{sub opt,p}{sup (v)}=m{sub nuc,p}+0.31224 m{sub e}. This optimized vibrational mass, along with a nuclear rotational mass, reduces the rms deviation of the experimental and computed rovibrational transitions by an order of magnitude. Finally, it is shown that an extension of the algorithm allowing the use of motion-dependent masses can deal with coordinate-dependent mass surfaces in the rovibrational Hamiltonian, as well.
Kittell, Aaron W.; Hustedt, Eric J.; Hyde, James S.
2014-01-01
Site-directed spin-labeling electron paramagnetic resonance (SDSL EPR) provides insight into the local structure and motion of a spin probe strategically attached to a molecule. When a second spin is introduced to the system, macromolecular information can be obtained through measurement of inter-spin distances either by continuous wave (CW) or pulsed electron double resonance (ELDOR) techniques. If both methodologies are considered, inter-spin distances of 8 to 80 Å can be experimentally determined. However, there exists a region at the upper limit of the conventional X-band (9.5 GHz) CW technique and the lower limit of the four-pulse double electron-electron resonance (DEER) experiment where neither method is particularly reliable. The work presented here utilizes L-band (1.9 GHz) in combination with non-adiabatic rapid sweep (NARS) EPR to address this opportunity by increasing the upper limit of the CW technique. Because L-band linewidths are three to seven times narrower than those at X-band, dipolar broadenings that are small relative to the X-band inhomogeneous linewidth become observable, but the signal loss due to the frequency dependence of the Boltzmann factor, has made L-band especially challenging. NARS has been shown to increase sensitivity by a factor of five, and overcomes much of this loss, making L-band distance determination more feasible [1]. Two different systems are presented and distances of 18–30 Å have been experimentally determined at physiologically relevant temperatures. Measurements are in excellent agreement with a helical model and values determined by DEER. PMID:22750251
NASA Astrophysics Data System (ADS)
Bakke, K.; Belich, H.
2015-11-01
We discuss the appearance of geometric quantum phases for a Dirac neutral particle in the context of relativistic quantum mechanics based on possible scenarios of the Lorentz symmetry violation tensor background in the CPT-even gauge sector of Standard Model Extension. We assume that the Lorentz symmetry breaking is determined by a tensor background given by (KF)μναβ, then, relativistic analogues of the Anandan quantum phase [J. Anandan, Phys. Lett. A 138, 347 (1989)] are obtained based on the parity-even and parity-odd sectors of the tensor (KF)μναβ.
NASA Astrophysics Data System (ADS)
Lindlein, Norbert; Leuchs, Gerd
This chapter shall discuss the basics and the applications of geometrical optical methods in modern optics. Geometrical optics has a long tradition and some ideas are many centuries old. Nevertheless, the invention of modern personal computers which can perform several million floating-point operations in a second also revolutionized the methods of geometrical optics and so several analytical methods lost importance whereas numerical methods such as ray tracing became very important. Therefore, the emphasis in this chapter is also on modern numerical methods such as ray tracing and some other systematic methods such as the paraxial matrix theory.
NASA Astrophysics Data System (ADS)
Lu, Ying-Bo; Li, Y. H.; Ling, Z. C.; Cong, Wei-Yan; Zhang, Peng; Xin, Y. Q.; Yang, T. L.
2016-02-01
As transparent conducting oxides (TCOs), In2O3 in the high pressure phase attracts extensive research interests. Because physical properties are determined by the geometric structures, we investigate the electronic and optical properties of Zn/Sn codoped In2O3 materials (IZTO) being modulated by the bixbyite/corundum phase transition via Density Functional Theory calculations. For IZTO in high pressure phase, i.e. corundum phase, Sn/Zn dopant pair tends to form face-sharing ZnO6 and SnO6 octahedrons. The radius differences between Zn2+/Sn4+ dopants and In3+ host cations make Jahn-Teller effect occur and IZTO transform from bixbyite to corundum phase under a slight higher pressure than that of pure In2O3. Although Zn/Sn cosubstitution of In ions may increase the free carrier effective mass m * near the band edge, when IZTO crystal transforms to corundum phase, the more dense packing structure results in stronger cation s-orbital overlaps than in bixbyite phase, which makes m * recover to a smaller value. In addition, corundum IZTO has a larger indirect band gap and a high dopant solubility. So these investigations may open a new way to search for TCOs materials with low indium content.
NASA Astrophysics Data System (ADS)
Zhang, Duo; Papadikis, K.; Gu, Sai
2016-09-01
In the current paper, the effect of the geometrical characteristics of 2-D porous media on the relative permeability in immiscible two-phase flows is studied. The generation of the different artificial porous media is performed using a Boolean model based on a random distribution of overlapping circles/ellipses, the size and shape of which are chosen to satisfy the specific Minkowski functionals (i.e. volume fraction, solid line contour length, connectivity). The study aims to identify how each different Minkowski functional affects the relative permeability of each phase at various saturations of the non-wetting phase. A 2-D multi-relaxation time (MRT) lattice Boltzmann model (LBM) that can handle high density ratios is employed in the simulation. The relationship between the driving forces G and the relative permeabilities of the two phases for every artificial structure is quantified. It is found that for high non-wetting phase saturations (fully connected flow), a non-linear relationship exists between the non-wetting phase flow rate and the driving force, whilst this relationship becomes linear at higher magnitudes of the latter. The force magnitude required to approach the linear region is highly influenced by the pore size distribution and the connectivity of the solid phase. For lower non-wetting phase saturation values, its relative permeability in the linear regime decreases as the fraction of small pores in the structure increases and the non-wetting phase flow becomes disconnected. A strong influence of the solid phase connectivity is also observed.
Oh, Aram; Baik, Hionsuck; Choi, Dong Shin; Cheon, Jae Yeong; Kim, Byeongyoon; Kim, Heejin; Kwon, Seong Jung; Joo, Sang Hoon; Jung, Yousung; Lee, Kwangyeol
2015-03-24
Catalytic properties of nanoparticles can be significantly enhanced by controlling nanoscale alloying and its structure. In this work, by using a facet-controlled Pt@Ni core-shell octahedron nanoparticle, we show that the nanoscale phase segregation can have directionality and be geometrically controlled to produce a Ni octahedron that is penetrated by Pt atoms along three orthogonal Cartesian axes and is coated by Pt atoms along its edges. This peculiar anisotropic diffusion of Pt core atoms along the ⟨100⟩ vertex, and then toward the ⟨110⟩ edges, is explained via the minimum strain energy for Ni-Ni pair interactions. The selective removal of the Ni-rich phase by etching then results in structurally fortified Pt-rich skeletal PtNi alloy framework nanostructures. Electrochemical evaluation of this hollow nanoframe suggests that the oxygen reduction reaction (ORR) activity is greatly improved compared to conventional Pt catalysts. PMID:25734892
NASA Astrophysics Data System (ADS)
Zhou, Linsen; Xie, Daiqian; Guo, Hua
2015-03-01
A detailed quantum mechanical characterization of the photodissociation dynamics of H2O at 121.6 nm is presented. The calculations were performed using a full-dimensional wave packet method on coupled potential energy surfaces of all relevant electronic states. Our state-to-state model permits a detailed analysis of the OH( X ˜ / A ˜ ) product fine-structure populations as a probe of the non-adiabatic dissociation dynamics. The calculated rotational state distributions of the two Λ-doublet levels of OH( X ˜ , v = 0) exhibit very different characteristics. The A' states, produced mostly via the B ˜ → X ˜ conical intersection pathway, have significantly higher populations than the A″ counterparts, which are primarily from the B ˜ → A ˜ Renner-Teller pathway. The former features a highly inverted and oscillatory rotational state distribution, while the latter has a smooth distribution with much less rotational excitation. In good agreement with experiment, the calculated total OH( X ˜ ) rotational state distribution and anisotropy parameters show clear even-odd oscillations, which can be attributed to a quantum mechanical interference between waves emanating from the HOH and HHO conical intersections in the B ˜ → X ˜ non-adiabatic pathway. On the other hand, the experiment-theory agreement for the OH( A ˜ ) fragment is also satisfactory, although some small quantitative differences suggest remaining imperfections of the ab initio based potential energy surfaces.
Zhou, Linsen; Xie, Daiqian E-mail: hguo@unm.edu; Guo, Hua E-mail: hguo@unm.edu
2015-03-28
A detailed quantum mechanical characterization of the photodissociation dynamics of H{sub 2}O at 121.6 nm is presented. The calculations were performed using a full-dimensional wave packet method on coupled potential energy surfaces of all relevant electronic states. Our state-to-state model permits a detailed analysis of the OH(X{sup ~}/A{sup ~}) product fine-structure populations as a probe of the non-adiabatic dissociation dynamics. The calculated rotational state distributions of the two Λ-doublet levels of OH(X{sup ~}, v = 0) exhibit very different characteristics. The A′ states, produced mostly via the B{sup ~}→X{sup ~} conical intersection pathway, have significantly higher populations than the A″ counterparts, which are primarily from the B{sup ~}→A{sup ~} Renner-Teller pathway. The former features a highly inverted and oscillatory rotational state distribution, while the latter has a smooth distribution with much less rotational excitation. In good agreement with experiment, the calculated total OH(X{sup ~}) rotational state distribution and anisotropy parameters show clear even-odd oscillations, which can be attributed to a quantum mechanical interference between waves emanating from the HOH and HHO conical intersections in the B{sup ~}→X{sup ~} non-adiabatic pathway. On the other hand, the experiment-theory agreement for the OH(A{sup ~}) fragment is also satisfactory, although some small quantitative differences suggest remaining imperfections of the ab initio based potential energy surfaces.
NASA Astrophysics Data System (ADS)
Talman, Richard
1999-10-01
Mechanics for the nonmathematician-a modern approach For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for nonmathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, Dr. Talman treats separately Lagrangian, Hamiltonian, and Newtonian mechanics-exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. Geometric Mechanics features illustrative examples and assumes only basic knowledge of Lagrangian mechanics. Of related interest . . . APPLIED DYNAMICS With Applications to Multibody and Mechatronic Systems Francis C. Moon A contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics. 1998 (0-471-13828-2) 504 pp. MATHEMATICAL PHYSICS Applied Mathematics for Scientists and Engineers Bruce Kusse and Erik Westwig A comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering. 1998 (0-471-15431-8) 680 pp.
NASA Astrophysics Data System (ADS)
Thurston, George; Hayden, Douglas; Ross, David; Pande, Ajay; Pande, Jayanti; Foffi, Giuseppe; Stradner, Anna; Schurtenberger, Peter
2014-03-01
Ternary, quaternary, and multi-component phase separations are common in biological systems, and their properties have many physiological and pathological consequences. As one example, understanding the molecular origins of the phase boundaries of eye lens protein solutions can help understand loss of transparency of the eye lens in cataract, a leading cause of blindness. The phase boundaries respond in a sensitive and non-monotonic fashion to small changes in molecular interaction strengths. We show how the geometry of relevant intersections, in the space of the components of the Hessian of the intensive Gibbs free energy with respect to relative compositions, can assist in comprehending the origins of such non-monotonic and sensitive changes of the phase boundaries. We apply this construction to analyze recent results about non-monotonic dependence of the phase boundaries of eye lens protein solutions on interprotein interaction strengths. Supported by NIH R15EY018249.
Ghani, Muhammad. U.; Yan, Aimin; Wong, Molly. D.; Li, Yuhua; Ren, Liqiang; Wu, Xizeng; Liu, Hong
2016-01-01
The objective of this study was to investigate the optimization of a high energy in-line phase sensitive x-ray imaging prototype under different geometric and operating conditions for mammography application. A phase retrieval algorithm based on phase attenuation duality (PAD) was applied to the phase contrast images acquired by the prototype. Imaging performance was investigated at four magnification values of 1.67, 2, 2.5 and 3 using an acrylic edge, an American College of Radiology (ACR) mammography phantom and contrast detail (CD) phantom with tube potentials of 100, 120 and 140 kVp. The ACR and CD images were acquired at the same mean glandular dose (MGD) of 1.29 mGy with a computed radiography (CR) detector of 43.75 µm pixel pitch at a fixed source to image distance (SID) of 170 cm. The x-ray tube focal spot size was kept constant as 7 µm while a 2.5 mm thick aluminum (Al) filter was used for beam hardening. The performance of phase contrast and phase retrieved images were compared with computer simulations based on the relative phase contrast factor (RPF) at high x-ray energies. The imaging results showed that the x-ray tube operated at 100 kVp under the magnification of 2.5 exhibits superior imaging performance which is in accordance to the computer simulations. As compared to the phase contrast images, the phase retrieved images of the ACR and CD phantoms demonstrated improved imaging contrast and target discrimination. We compared the CD phantom images acquired in conventional contact mode with and without the anti-scatter grid using the same prototype at 1.295 mGy and 2.59 mGy using 40 kVp, a 25 µm rhodium (Rh) filter. At the same radiation dose, the phase sensitive images provided improved detection capabilities for both the large and small discs, while compared to the double dose image acquired in conventional mode, the observer study also indicated that the phase sensitive images provided improved detection capabilities for the large discs. This
Ghani, Muhammad U; Yan, Aimin; Wong, Molly D; Li, Yuhua; Ren, Liqiang; Wu, Xizeng; Liu, Hong
2015-01-01
The objective of this study was to investigate the optimization of a high energy in-line phase sensitive x-ray imaging prototype under different geometric and operating conditions for mammography application. A phase retrieval algorithm based on phase attenuation duality (PAD) was applied to the phase contrast images acquired by the prototype. Imaging performance was investigated at four magnification values of 1.67, 2, 2.5 and 3 using an acrylic edge, an American College of Radiology (ACR) mammography phantom and contrast detail (CD) phantom with tube potentials of 100, 120 and 140 kVp. The ACR and CD images were acquired at the same mean glandular dose (MGD) of 1.29 mGy with a computed radiography (CR) detector of 43.75 μm pixel pitch at a fixed source to image distance (SID) of 170 cm. The x-ray tube focal spot size was kept constant as 7 μm while a 2.5 mm thick aluminum (Al) filter was used for beam hardening. The performance of phase contrast and phase retrieved images were compared with computer simulations based on the relative phase contrast factor (RPF) at high x-ray energies. The imaging results showed that the x-ray tube operated at 100 kVp under the magnification of 2.5 exhibits superior imaging performance which is in accordance to the computer simulations. As compared to the phase contrast images, the phase retrieved images of the ACR and CD phantoms demonstrated improved imaging contrast and target discrimination. We compared the CD phantom images acquired in conventional contact mode with and without the anti-scatter grid using the same prototype at 1.295 mGy and 2.59 mGy using 40 kVp, a 25 μm rhodium (Rh) filter. At the same radiation dose, the phase sensitive images provided improved detection capabilities for both the large and small discs, while compared to the double dose image acquired in conventional mode, the observer study also indicated that the phase sensitive images provided improved detection capabilities for the large discs. This
NASA Astrophysics Data System (ADS)
You, Yizhi; Cho, Gil Young; Fradkin, Eduardo
2016-05-01
We present a theory of the isotropic-nematic quantum phase transition in the composite Fermi liquid arising in half-filled Landau levels. We show that the quantum phase transition between the isotropic and the nematic phase is triggered by an attractive quadrupolar interaction between electrons, as in the case of conventional Fermi liquids. We derive the theory of the nematic state and of the phase transition. This theory is based on the flux attachment procedure, which maps an electron liquid in half-filled Landau levels into the composite Fermi liquid close to a nematic transition. We show that the local fluctuations of the nematic order parameters act as an effective dynamical metric interplaying with the underlying Chern-Simons gauge fields associated with the flux attachment. Both the fluctuations of the Chern-Simons gauge field and the nematic order parameter can destroy the composite fermion quasiparticles and drive the system into a non-Fermi liquid state. The effective-field theory for the isotropic-nematic phase transition is shown to have z =3 dynamical exponent due to the Landau damping of the dense Fermi system. We show that there is a Berry-phase-type term that governs the effective dynamics of the nematic order parameter fluctuations, which can be interpreted as a nonuniversal "Hall viscosity" of the dynamical metric. We also show that the effective-field theory of this compressible fluid has a Wen-Zee-type term. Both terms originate from the time-reversal breaking fluctuation of the Chern-Simons gauge fields. We present a perturbative (one-loop) computation of the Hall viscosity and also show that this term is also obtained by a Ward identity. We show that the topological excitation of the nematic fluid, the disclination, carries an electric charge. We show that a resonance observed in radio-frequency conductivity experiments can be interpreted as a Goldstone nematic mode gapped by lattice effects.
NASA Astrophysics Data System (ADS)
You, Yizhi; Cho, Gil Young; Fradkin, Eduardo
We present a theory of isotropic-nematic quantum phase transition in the composite Fermi liquid arising in the half-filled Landau levels. We show that the quantum phase transition is triggered by the attractive quadrupolar interaction. By performing flux attachment, system turns into a composite Fermi liquid. The nematic order parameters act as the dynamical metric interplaying with the underlying topology, the Chern-Simons theory. Here both the fluctuations of the gauge field and the nematic order parameter can soften the Fermi surface and thus the fermions form a non-Fermi liquid. The effective field theory for the isotropic-nematic phase transition has z = 3 dynamical exponent due to the Landau damping due to the finite density of the fermions. We show that there is a Berry phase term of the nematic order parameter, which can be interpreted as the ``Hall viscosity'' of the dynamical metric. We also find the Wen-Zee-like term, which effectively dresses the nematic vortex with the electric charge. Both of the terms are originated from the time reversal breaking fluctuation of the Chern-Simons gauge fields. This indicates the fluctuations of the gauge fields modify the Hall viscosity and orbital spin of the compressible half-filled Landau level.
NASA Astrophysics Data System (ADS)
Har-Shemesh, Omri; Quax, Rick; Hoekstra, Alfons G.; Sloot, Peter M. A.
2016-04-01
The Fisher–Rao metric from information geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of information geometry to study more general phase transitions in complex systems. However, it is unclear whether the Fisher–Rao metric does indeed detect these more general transitions, especially in the absence of a statistical model. In this paper we study the transitions between patterns in the Gray-Scott reaction–diffusion model using Fisher information. We describe the system by a probability density function that represents the size distribution of blobs in the patterns and compute its Fisher information with respect to changing the two rate parameters of the underlying model. We estimate the distribution non-parametrically so that we do not assume any statistical model. The resulting Fisher map can be interpreted as a phase-map of the different patterns. Lines with high Fisher information can be considered as boundaries between regions of parameter space where patterns with similar characteristics appear. These lines of high Fisher information can be interpreted as phase transitions between complex patterns.
NASA Astrophysics Data System (ADS)
Enjalran, Matthew; Del Maestro, Adrian; Gingras, Michel J. P.
2008-03-01
The rare-earth pyrochlore gadolinium titanate, Gd2Ti2O7, represents an excellent experimental realization of a Heisenberg antiferromagnet (AFM) in a frustrated geometry with weak long-range dipole-dipole interactions (approximately 20% of nearest neighbor AFM exchange). Experiments on Gd2Ti2O7 in a magnetic field reveal a complex phase diagram associated with the breaking of spatial symmetries of the pyrochlore lattice as the field is applied along select symmetry directions. We study a model of classical Heisenberg spins (O(3) symmetry) on a pyrochlore lattice with exchange and dipolar interactions within mean-field theory. Using parameters relevant to the material system, we develop phase diagrams in finite magnetic fields. Our results our compared to experiments on Gd2Ti2O7 (and Gd2Sn2O7).
NASA Astrophysics Data System (ADS)
Wang, Xujing
Living systems are characterized by complexity in structure and emergent dynamic orders. In many aspects the onset of a chronic disease resembles phase transition in a dynamic system: quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. In this study we investigate this idea in a real example, the insulin-producing pancreatic islet β-cells and the onset of type 1 diabetes. Within each islet, the β-cells are electrically coupled to each other, and function as a network with synchronized actions. Using percolation theory we show how normal islet function is intrinsically linked to network connectivity, and the critical point where the islet cellular network loses site percolation, is consistent with laboratory and clinical observations of the threshold β-cell loss that causes islet functional failure. Numerical simulations confirm that the islet cellular network needs to be percolated for β-cells to synchronize. Furthermore, the interplay between site percolation and bond strength predicts the existence of a transient phase of islet functional recovery after disease onset and introduction of treatment, potentially explaining a long time mystery in the clinical study of type 1 diabetes: the honeymoon phenomenon. Based on these results, we hypothesized that the onset of T1D may be the result of a phase transition of the islet β-cell network. We further discuss the potential applications in identifying disease-driving factors, and the critical parameters that are predictive of disease onset.
NASA Technical Reports Server (NTRS)
Grebowsky, G. J.
1982-01-01
Present LANDSAT data formats are reviewed to clarify how the geodetic location and registration capabilities were defined for P-tape products and RBV data. Since there is only one geometric model used in the master data processor, geometric location accuracy of P-tape products depends on the absolute accuracy of the model and registration accuracy is determined by the stability of the model. Due primarily to inaccuracies in data provided by the LANDSAT attitude management system, desired accuracies are obtained only by using ground control points and a correlation process. The verification of system performance with regards to geodetic location requires the capability to determine pixel positions of map points in a P-tape array. Verification of registration performance requires the capability to determine pixel positions of common points (not necessarily map points) in 2 or more P-tape arrays for a given world reference system scene. Techniques for registration verification can be more varied and automated since map data are not required. The verification of LACIE extractions is used as an example.
NASA Astrophysics Data System (ADS)
Li, Tang-Jing; Liang, Jian-Gang; Li, Hai-Peng; Liu, Ya-Qiao
2016-09-01
A new method to design an ultra-thin high-gain circularly-polarized antenna system with high efficiency is proposed based on the geometrical phase gradient metasurface (GPGM). With an accuracy control of the transmission phase and also the high transmission amplitude, the GPGM is capable of manipulating an electromagnetic wave arbitrarily. A focusing transmission lens working at Ku band is well optimized with the F/D of 0.32. A good focusing effect is demonstrated clearly by theoretical calculation and electromagnetic simulation. For further application, an ultra-thin single-layer transmissive lens antenna based on the proposed focusing metasurface operating at 13 GHz is implemented and launched by an original patch antenna from the perspective of high integration, simple structure, and low cost. Numerical and experimental results coincide well, indicating the advantages of the antenna system, such as a high gain of 17.6 dB, the axis ratio better than 2 dB, a high aperture efficiency of 41%, and also a simple fabrication process based on the convenient print circuit board technology. The good performance of the proposed antenna indicates promising applications in portable communication systems. Project supported by the National Natural Science Foundation of China (Grant No. 61372034).
Juanes-Marcos, Juan Carlos; Althorpe, Stuart C
2005-05-22
We report quantum wave-packet calculations on the H+H(2) reaction, aimed at resolving the controversy over whether geometric phase (GP) effects can be observed in this reaction. Two sets of calculations are reported of the state-to-state reaction probabilities, and integral and differential cross sections (ICSs and DCSs). One set includes the GP using the vector potential approach of Mead and Truhlar; the other set neglects the phase. We obtain unequivocal agreement with recent results of Kendrick [J. Phys. Chem. A 107, 6739 (2003)], predicting GP effects in the state-to-state reaction probabilities, which cancel exactly on summing the partial waves to yield the ICS. Our results therefore contradict those of Kuppermann and Wu [Chem. Phys. Lett. 349 537 (2001)], which predicted pronounced GP effects in the cross sections. We also agree with Kendrick in predicting that there are no significant GP effects in the full DCS at energies below 1.8 eV, and in the partial (0
Gaitan, F.
1998-09-01
The generic Berry phase scenario in which a two-level system is coupled to a second system whose dynamical coordinate is slowly varying is generalized to allow for stochastic evolution of the slow system. The stochastic behavior is produced by coupling the slow system to a heat reservoir, which is modeled by a bath of harmonic oscillators initially in equilibrium at temperature T, and whose spectral density has a bandwidth that is small compared to the energy-level spacing of the fast system. The well-known energy-level shifts produced by Berry{close_quote}s phase in the fast system, in conjunction with the stochastic motion of the slow system, leads to a broadening of the fast system energy levels. In the limit of strong damping and sufficiently low temperature, we determine the degree of level broadening analytically, and show that the slow system dynamics satisfies a Langevin equation in which Lorentz-like and electriclike forces appear as a consequence of geometrical effects. We also determine the average energy level shift produced in the fast system by this mechanism. {copyright} {ital 1998} {ital The American Physical Society}
NASA Astrophysics Data System (ADS)
Li, Tang-Jing; Liang, Jian-Gang; Li, Hai-Peng; Liu, Ya-Qiao
2016-09-01
A new method to design an ultra-thin high-gain circularly-polarized antenna system with high efficiency is proposed based on the geometrical phase gradient metasurface (GPGM). With an accuracy control of the transmission phase and also the high transmission amplitude, the GPGM is capable of manipulating an electromagnetic wave arbitrarily. A focusing transmission lens working at Ku band is well optimized with the F/D of 0.32. A good focusing effect is demonstrated clearly by theoretical calculation and electromagnetic simulation. For further application, an ultra-thin single-layer transmissive lens antenna based on the proposed focusing metasurface operating at 13 GHz is implemented and launched by an original patch antenna from the perspective of high integration, simple structure, and low cost. Numerical and experimental results coincide well, indicating the advantages of the antenna system, such as a high gain of 17.6 dB, the axis ratio better than 2 dB, a high aperture efficiency of 41%, and also a simple fabrication process based on the convenient print circuit board technology. The good performance of the proposed antenna indicates promising applications in portable communication systems. Project supported by the National Natural Science Foundation of China (Grant No. 61372034).
NASA Astrophysics Data System (ADS)
Ekberg, Peter; Stiblert, Lars; Mattsson, Lars
2010-12-01
Mask writers and large area measurements systems are key systems for production of large liquid crystal displays (LCD) and image devices. With position tolerances in the sub-µm range over square meter sized masks, the metrology challenges are indeed demanding. Most systems used for this type of measurement rely on a microscope camera imaging system, provided with a charge coupled device, a complementary metal-oxide-semiconductor sensor or a time delay and integration sensor to transform the optical image to a digital gray-level image. From this image, processing algorithms are used to extract information such as location of edges. The drawback of this technique is the vast amount of data captured but never used. This paper presents a new approach for ultra-high-precision lateral measurement at nm-levels of chrome/glass patterns separated by centimeters, so called registration marks, on masks used for the LCD manufacturing. Registration specifications demand a positioning accuracy <200 nm and critical dimensions, i.e. chrome line widths, which need to be accurate in the 80 nm range. This accuracy has to be achieved on glass masks of 2.4 × 1.6 m2 size. Our new measurement method is based on nm-precise lateral scanning of a focused laser beam combined with statistical random phase sampling of the reflected signal. The precise scanning is based on an extremely accurate time measuring device controlling an acousto optic deflector crystal. The method has been successfully applied in measuring the 4 µm pitch of reference gratings at standard deviations σ of 0.5 nm and registration marks separated by several cm at standard deviations of 23 nm.
NASA Astrophysics Data System (ADS)
Zhu, Ronghua; Xie, Huimin; Dai, Xianglu; Zhu, Jianguo; Jin, Aizi
2014-09-01
Stress generated during thin film deposition is a critical issue for many applications. In general, the possible origins of the residual stress include intrinsic and extrinsic stresses. Since high residual stresses can cause detrimental effects on the film, such as delamination and wrinkle, it is of great importance to quantify the residual stress for the optimal design and the evaluation of its mechanical behavior. In this study, a method combining focused ion beam (FIB) milling and geometric phase analysis (GPA) is developed to assess the residual stress of thin films. The procedures of the residual stress measurement using this method include grating fabrication and slot milling by FIB, high-resolution scanning electron microscope (SEM) imaging of the grating before and after stress relaxation, and deformation analysis by GPA. The residual stress can be inferred from the released deformation using the reference displacements of the finite element model. As an application, this method was utilized to measure the residual stress in a TiAlSiN film, and the measured result is in good agreement with that obtained by the curvature method. In order to analyze the measurement error, the influence factors of Ga+ bombardment and the deposited platinum layer on the stress calculation are also discussed in detail.
Geometric time delay interferometry
NASA Astrophysics Data System (ADS)
Vallisneri, Michele
2005-08-01
The space-based gravitational-wave observatory LISA, a NASA-ESA mission to be launched after 2012, will achieve its optimal sensitivity using time delay interferometry (TDI), a LISA-specific technique needed to cancel the otherwise overwhelming laser noise in the interspacecraft phase measurements. The TDI observables of the Michelson and Sagnac types have been interpreted physically as the virtual measurements of a synthesized interferometer. In this paper, I present Geometric TDI, a new and intuitive approach to extend this interpretation to all TDI observables. Unlike the standard algebraic formalism, Geometric TDI provides a combinatorial algorithm to explore exhaustively the space of second-generation TDI observables (i.e., those that cancel laser noise in LISA-like interferometers with time-dependent arm lengths). Using this algorithm, I survey the space of second-generation TDI observables of length (i.e., number of component phase measurements) up to 24, and I identify alternative, improved forms of the standard second-generation TDI observables. The alternative forms have improved high-frequency gravitational-wave sensitivity in realistic noise conditions (because they have fewer nulls in the gravitational-wave and noise response functions), and are less susceptible to instrumental gaps and glitches (because their component phase measurements span shorter time periods).
Perspective: Geometrically frustrated assemblies
NASA Astrophysics Data System (ADS)
Grason, Gregory M.
2016-09-01
This perspective will overview an emerging paradigm for self-organized soft materials, geometrically frustrated assemblies, where interactions between self-assembling elements (e.g., particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including self-twisting protein filament bundles, amyloid fibers, chiral smectics and membranes, particle-coated droplets, curved protein shells, and phase-separated lipid vesicles. In assemblies, geometric frustration leads to a host of anomalous structural and thermodynamic properties, including heterogeneous and internally stressed equilibrium structures, self-limiting assembly, and topological defects in the equilibrium assembly structures. The purpose of this perspective is to (1) highlight the unifying principles and consequences of geometric frustration in soft matter assemblies; (2) classify the known distinct modes of frustration and review corresponding experimental examples; and (3) describe outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems.
Geometrically representing spin correlations
NASA Astrophysics Data System (ADS)
White, Ian G.; Mirasola, Anthony; Hollingsworth, Jacob; Mukherjee, Rick; Hazzard, Kaden R. A.
2016-05-01
We develop a general method to visualize spin correlations, and we demonstrate its usefulness in ultracold matter from fermions in lattices to trapped ions and ultracold molecules. Correlations are of fundamental interest in many-body physics: they characterize phases in condensed matter and AMO, and are required for quantum sensing and computing. However, it is often difficult to understand even the simplest correlations - for example between two spin-1/2's - directly from the components Cab =
Medvedev, Igor G
2011-11-01
A theory of electrochemical behavior of small metal nanoparticles (NPs) which is governed both by the charging effect and the effect of the solvent reorganization on the dynamic of the electron transfer (ET) is considered under ambient conditions. The exact expression for the rate constant of ET from an electrode to NP which is valid for all values of the reorganization free energy E(r), bias voltage, and overpotential is obtained in the non-adiabatic limit. The tunnel current/overpotential relations are studied and calculated for different values of the bias voltage and E(r). The effect of E(r) on the full width at half maximum of the charging peaks is investigated at different values of the bias voltage. The differential conductance/bias voltage and the tunnel current/bias voltage dependencies are also studied and calculated. It is shown that, at room temperature, the pronounced Coulomb blockade oscillations in the differential conductance/bias voltage curves and the noticeable Coulomb staircase in the tunnel current/bias voltage relations are observed only at rather small values of E(r) in the case of the strongly asymmetric tunneling contacts.
NASA Astrophysics Data System (ADS)
Boering, Kristie
2015-03-01
Reactions of the first excited state of atomic oxygen, O(1D), with small molecules such as CO, NO2, and CO2 continue to be of interest in aeronomy and atmospheric chemistry, thus providing additional motivation to understand the dynamics of these reactions and how well they are predicted by theory. In collaboration with Prof. Jim Lin of the Institute of Atomic and Molecular Sciences, Academia Sinica, Taiwan, we have studied the dynamics of quenching and non-quenching reactions between O(1D) and various small molecules using a universal crossed atomic and molecular beam apparatus. New experimental results for the dynamics of quenching of O(1D) by Xe and CO will be presented and compared with previous results for NO2 (K.A. Mar, A.L. Van Wyngarden, C.-W. Liang, Y.T. Lee, J.J. Lin, K.A. Boering, J. Chem. Phys., 137, 044302, doi: 10.1063/1.4736567, 2012) and CO2 (M.J. Perri, A.L. Van Wyngarden, K.A. Boering, J.J. Lin, and Y.T. Lee, J. Chem. Phys., 119(16), 8213-8216, 2003; M.J. Perri, A.L. Van Wyngarden, J.J. Lin, Y.T. Lee, and K.A. Boering, J. Phys. Chem. A, 108(39), 7995-8001, doi: 10.1021/jp0485845, 2004). Among the most intriguing of the new results are for quenching of O(1D) by Xe, for which marked oscillations in the differential cross sections were observed for the O(3P) and Xe products. The shape and relative phase of the oscillatory structure depended strongly on collision energy. This behavior is likely due to the quantum nature of the collision dynamics, caused by interferences among multiple curve crossing pathways accessible during electronic quenching, known as Stueckelberg oscillations.
PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism
NASA Astrophysics Data System (ADS)
Gardner, Jason S.
2011-04-01
Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rønnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: μSR measurements on single crystals
NASA Astrophysics Data System (ADS)
Golub, R.; Kaufman, C.; Müller, G.; Steyerl, A.
2015-12-01
The important role of geometric phases in searches for a permanent electric dipole moment of the neutron, using Ramsey separated oscillatory field nuclear magnetic resonance, was first noted by Commins [Am. J. Phys. 59, 1077 (1991), 10.1119/1.16616] and investigated in detail by Pendlebury et al. [Phys. Rev. A 70, 032102 (2004), 10.1103/PhysRevA.70.032102]. Their analysis was based on the Bloch equations. In subsequent work using the spin-density matrix, Lamoreaux and Golub [Phys. Rev. A 71, 032104 (2005), 10.1103/PhysRevA.71.032104] showed the relation between the frequency shifts and the correlation functions of the fields seen by trapped particles in general fields (Redfield theory). More recently, we presented a solution of the Schrödinger equation for spin-1 /2 particles in circular cylindrical traps with smooth walls and exposed to arbitrary fields [A. Steyerl et al., Phys. Rev. A 89, 052129 (2014), 10.1103/PhysRevA.89.052129]. Here, we extend this work to show how the Redfield theory follows directly from the Schrödinger equation solution. This serves to highlight the conditions of validity of the Redfield theory, a subject of considerable discussion in the literature [e.g., M. P. Nicholas et al., Prog. Nucl. Magn. Reson. Spectrosc. 57, 111 (2010), 10.1016/j.pnmrs.2010.04.003]. Our results can be applied where the Redfield result no longer holds, such as observation times on the order of or shorter than the correlation time and nonstochastic systems, and thus we can illustrate the transient spin dynamics, i.e., the gradual development of the shift with increasing time subsequent to the start of the free precession. We consider systems with rough, diffuse reflecting walls, cylindrical trap geometry with arbitrary cross section, and field perturbations that do not, in the frame of the moving particles, average to zero in time. We show by direct, detailed, calculation the agreement of the results from the Schrödinger equation with the Redfield theory for the
Geometric quantum noise of spin.
Shnirman, Alexander; Gefen, Yuval; Saha, Arijit; Burmistrov, Igor S; Kiselev, Mikhail N; Altland, Alexander
2015-05-01
The presence of geometric phases is known to affect the dynamics of the systems involved. Here, we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum noise. We show that geometric phases enter the stochastic noise terms. Specifically, we consider small ferromagnetic particles (nanomagnets) or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Schön effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application, we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon.
ERIC Educational Resources Information Center
Sherrod, Sonya Ellouise; Wilhelm, Jennifer
2009-01-01
Research indicates that student understanding is either confirmed or reformed when given opportunities to share what they know. This study was conducted to answer the research question: Will classroom dialogue facilitate students' understanding of lunar concepts related to geometric spatial visualisation? Ninety-two middle school students engaged…
Conceptual aspects of geometric quantum computation
NASA Astrophysics Data System (ADS)
Sjöqvist, Erik; Azimi Mousolou, Vahid; Canali, Carlo M.
2016-07-01
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates and find an explicit physical example where the two types of gates coincide. We identify differences and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases.
Conceptual aspects of geometric quantum computation
NASA Astrophysics Data System (ADS)
Sjöqvist, Erik; Azimi Mousolou, Vahid; Canali, Carlo M.
2016-10-01
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates and find an explicit physical example where the two types of gates coincide. We identify differences and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases.
NASA Astrophysics Data System (ADS)
Bouchiat, Marie-Anne; Bouchiat, Claude
2012-10-01
We have constructed the geometric phases emerging from the non-trivial topology of a space-dependent magnetic field B(r), interacting with the spin magnetic moment of a neutral particle. Our basic tool, adapted from a previous work on Berry’s phases, is the space-dependent unitary transformation {U}({\\mathbf {r}}), which leads to the identity, {U}({\\mathbf {r}})^{\\dag }\\, {\\mathbf {S}}\\,{\\bm \\cdot}\\, {\\mathbf {B}}({\\mathbf {r}}) \\, {U}({\\mathbf {r}}) = \\vert {\\mathbf {B}}({\\mathbf {r}}) \\vert \\, S_z, at each point r. In the ‘rotated’ Hamiltonian \\widehat{ H}, \\frac{ \\partial }{\\partial {\\mathbf {r}}} is replaced by the non-Abelian covariant derivative \\frac{ \\partial }{\\partial {\\mathbf {r}}}- \\frac{i}{\\hbar } {A}({\\mathbf {r}}) where {A}({\\mathbf {r}}) = i \\hbar \\, {U}^{\\dag }\\,{\\bm\\cdot}\\, \\frac{ \\partial }{\\partial {\\mathbf {r}}} {U} can be written as A1(r)Sx + A2(r)Sy + A3(r)Sz. The Abelian differentials Ak(r)·dr are given in terms of the Euler angles defining the orientation of B(r). The non-Abelian field {A}({\\mathbf {r}}) transforms as a Yang-Mills field; however, its vanishing ‘curvature’ reveals its purely geometric character. We have defined a perturbation scheme based upon the assumption that in \\widehat{ H} the longitudinal field A3(r) dominates the transverse field A1, 2(r) contributions, evaluated to second order. The geometry embedded in both the vector field A3(r) and the geometric magnetic field \\mathbf { B}_3 ({\\mathbf {r}}) = \\frac{ \\partial }{\\partial {\\mathbf {r}}}\\wedge {{\\mathbf {A}}}_3({\\mathbf {r}}) is described by their associated Aharonov-Bohm phase. As an illustration we study the physics of cold 171Yb atoms dressed by overlaying two circularly polarized stationary waves with orthogonal directions, which form a 2D square optical lattice. The frequency is tuned midway between the two hyperfine levels of the (6s6p)3P1 states to protect the optical B(r) field generated by the
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
NASA Astrophysics Data System (ADS)
Sarkar, B.; Varandas, A. J. C.
2011-11-01
The Longuet-Higgins theorem has recently been extended to Jahn-Teller type electronic degeneracy manifolds of arbitrary dimension and suggested to obtain generalized Born-Oppenheimer equations including the geometrical phase effect [A.J.C. Varandas, Chem. Phys. Lett. 487 (2010) 139]. By replacing the traditional sign-change diagnostic of the adiabatic electronic wave vectors (upon adiabatic transportation in configuration space along a loop that encircles the point of degeneracy) with a sign-change criterion based upon their rotation by π in the N-dimensional electronic wave-vector space, it has been shown that only one pair of adiabatic electronic states changes sign upon encircling the degeneracy in configuration space. Here, we examine in detail the four-fold problem and report relevant dynamics studies. The results are compared with those obtained from the simple Born-Oppenheimer approximation (geometrical phase ignored) as well as two- and three-fold single-surface generalized Born-Oppenheimer equations. A rationalization is provided based on the symmetry-allowed reactive probabilities.
Exploring New Geometric Worlds
ERIC Educational Resources Information Center
Nirode, Wayne
2015-01-01
When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…
Geometrical expression of excess entropy production.
Sagawa, Takahiro; Hayakawa, Hisao
2011-11-01
We derive a geometrical expression of the excess entropy production for quasistatic transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct the thermodynamics of nonequilibrium steady states. PMID:22181372
Xu, Zhijie; Meakin, Paul
2009-06-21
Dissipative particle dynamics (DPD) is an effective mesoscopic particle model with a lower computational cost than molecular dynamics because of the soft potentials that it employs. However, the soft potential is not strong enough to prevent the DPD particles that are used to represent the fluid from penetrating solid boundaries represented by stationary DPD particles. A phase-field variable, phi(x,t), is used to indicate the phase at point x and time t, with a smooth transition from -1 (phase 1) to +1 (phase 2) across the interface. We describe an efficient implementation of no-slip boundary conditions in DPD models that combines solid-liquid particle-particle interactions with reflection at a sharp boundary located with subgrid scale accuracy using the phase field. This approach can be used for arbitrarily complex flow geometries and other similar particle models (such as smoothed particle hydrodynamics), and the validity of the model is demonstrated by DPD simulations of flow in confined systems with various geometries.
Geometric intrinsic symmetries
Gozdz, A. Szulerecka, A.; Pedrak, A.
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
Polar metals by geometric design.
Kim, T H; Puggioni, D; Yuan, Y; Xie, L; Zhou, H; Campbell, N; Ryan, P J; Choi, Y; Kim, J-W; Patzner, J R; Ryu, S; Podkaminer, J P; Irwin, J; Ma, Y; Fennie, C J; Rzchowski, M S; Pan, X Q; Gopalan, V; Rondinelli, J M; Eom, C B
2016-05-01
Gauss's law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions. Quantum physics supports this view, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals--it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedral--the structural signatures of perovskites--owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties. PMID:27096369
Polar metals by geometric design
NASA Astrophysics Data System (ADS)
Kim, T. H.; Puggioni, D.; Yuan, Y.; Xie, L.; Zhou, H.; Campbell, N.; Ryan, P. J.; Choi, Y.; Kim, J.-W.; Patzner, J. R.; Ryu, S.; Podkaminer, J. P.; Irwin, J.; Ma, Y.; Fennie, C. J.; Rzchowski, M. S.; Pan, X. Q.; Gopalan, V.; Rondinelli, J. M.; Eom, C. B.
2016-05-01
Gauss’s law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions. Quantum physics supports this view, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals—it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedra—the structural signatures of perovskites—owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.
Polar metals by geometric design.
Kim, T H; Puggioni, D; Yuan, Y; Xie, L; Zhou, H; Campbell, N; Ryan, P J; Choi, Y; Kim, J-W; Patzner, J R; Ryu, S; Podkaminer, J P; Irwin, J; Ma, Y; Fennie, C J; Rzchowski, M S; Pan, X Q; Gopalan, V; Rondinelli, J M; Eom, C B
2016-05-01
Gauss's law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions. Quantum physics supports this view, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals--it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedral--the structural signatures of perovskites--owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.
Descriptive Geometry and Geometric Modeling.
ERIC Educational Resources Information Center
Adams, J. Alan
1988-01-01
Describes experiences for engineering students to develop spatial awareness and reasoning capability. Describes geometric modeling, basic geometric concepts, operations, surface modeling, and conclusions. (YP)
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly.
Inflation from geometrical tachyons
Thomas, Steven; Ward, John
2005-10-15
We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS D3-brane in the background geometry due to k parallel NS5-branes arranged around a ring of radius R. Because of the fact that the mass of this geometrical tachyon field is {radical}(2/k) times smaller than the corresponding open-string tachyon mass, we find that the slow-roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. We also show that the metric perturbations produced at the end of inflation can be sufficiently small and do not lead to the inconsistencies that plague the open-string tachyon models. Finally we argue for the existence of a minimum of the geometrical tachyon potential which could give rise to a traditional reheating mechanism.
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly. PMID:25507310
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly. PMID:25420326
Geometric precipices in string cosmology
Kaloper, Nemanja; Watson, Scott
2008-03-15
We consider the effects of graviton multiplet fields on transitions between string gas phases. Focusing on the dilaton field, we show that it may obstruct transitions between different thermodynamic phases of the string gas, because the sign of its dimensionally reduced, T-duality invariant, part is conserved when the energy density of the Universe is positive. Thus, many interesting solutions for which this sign is positive end up in a future curvature singularity. Because of this, some of the thermodynamic phases of the usual gravitating string gases behave like superselection sectors. For example, a past-regular Hagedorn phase and an expanding Friedmann-Robertson-Walker (FRW) phase dominated by string momentum modes cannot be smoothly connected in the framework of string cosmology with positive sources. The singularity separates them like a geometric precipice in the moduli space, preventing the dynamics of the theory from bridging across. Sources which simultaneously violate the positivity of energy and null energy condition (NEC) could modify these conclusions. We provide a quantitative measure of positivity of energy and NEC violations that would be necessary for such transitions. These effects must dominate the Universe at the moment of transition, altering the standard gas pictures. At present, it is not known how to construct such sources from first principles in string theory.
Geometric Series via Probability
ERIC Educational Resources Information Center
Tesman, Barry
2012-01-01
Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…
NASA Technical Reports Server (NTRS)
Ives, David
1995-01-01
This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.
1500 System Geometric Dictionary.
ERIC Educational Resources Information Center
Peloquin, Paul V.
A general description is provided of the "geometric dictionary," a graphic display aid, used by the Computer-Assisted Instruction Laboratory at the Pennsylvania State University. The purpose of the description is to enable the reader to duplicate and use the dictionary on any cathode ray tube terminal of the IBM 1500 system. The major advantages…
ERIC Educational Resources Information Center
Smart, Julie; Marshall, Jeff
2007-01-01
Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…
Pragmatic geometric model evaluation
NASA Astrophysics Data System (ADS)
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to
Błoński, Piotr; Hafner, Jürgen
2015-02-01
The structural and magnetic properties of mixed Pt-Co and Pt-Fe trimers and tetramers in the gas-phase and supported on a free-standing graphene layer have been calculated using density-functional theory. The influence of the strong magnetic moments of the 3d atoms on the Pt atoms and the influence of the strong spin-orbit coupling contributed by the Pt atoms on the 3d atoms have been studied in detail. All mixed trimers form isocele triangles in the gas-phase. On a graphene layer the structure is influenced by the strong binding of the 3d atoms, leading to an asymmetric configuration for Pt-rich and more symmetric structures for 3d-rich clusters. The magnetic anisotropy energy defined as the energy difference for easy and hard magnetization directions varies between 5 and 13 meV/atom for the free trimers, but is strongly reduced to values between 0.7 and 6.6 meV/atom for the graphene-supported clusters. The saddle-point energy representing the barrier against magnetization reversal is on average 3 meV/atom for free trimers, it is reduced to 2 meV/atom for the more symmetric PtCo(Fe)(2) clusters, and to only about 0.3 meV/atom for the asymmetric Pt(2)Co(Fe) cluster on graphene. For the mixed tetramers the strong magnetism stabilizes a flat geometric structure, except for Pt(3)Co which forms a distorted trigonal pyramid. The geometry of the graphene-supported tetramers is very different due to the requirement of a good match to the substrate. Large magnetic anisotropy energies are found for free Pt(3)Co where the change of the magnetization direction also induces a transition from a high- to a low-moment magnetic isomer. For all other free tetramers the magnetic anisotropy energy ranges between 3 to 5 meV/atom only, it is further reduced to 0.4 to 3.8 meV/atom for the graphene-supported tetramers. The reduction is strongest for Pt(3)Fe/graphene because of the asymmetric structure of the adsorption complex. The barriers against magnetization reversal range between
Representing geometrical knowledge.
Anderson, J A
1997-01-01
This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic. PMID:9304680
Howarth, P A
2011-02-23
Two aspects of the geometric horopter, which here is based on the criterion of equality of angle, are clarified. The first is that in the fixation plane (containing the nodal points and the fixation point) the locus of points lying on the horopter is the larger arc of a circle, and not a full circle as has been previously accepted. The second is that elsewhere, the locus of these points is a straight line perpendicular to this plane and midway between the eyes. These rules hold for both symmetric and asymmetric convergence, and for fixation elevated or depressed from the horizontal.
Multiphase flow in geometrically simple fracture intersections
Basagaoglu, H.; Meakin, P.; Green, C.T.; Mathew, M.; ,
2006-01-01
A two-dimensional lattice Boltzmann (LB) model with fluid-fluid and solid-fluid interaction potentials was used to study gravity-driven flow in geometrically simple fracture intersections. Simulated scenarios included fluid dripping from a fracture aperture, two-phase flow through intersecting fractures and thin-film flow on smooth and undulating solid surfaces. Qualitative comparisons with recently published experimental findings indicate that for these scenarios the LB model captured the underlying physics reasonably well.
Geometry and dynamics of one-norm geometric quantum discord
NASA Astrophysics Data System (ADS)
Huang, Zhiming; Qiu, Daowen; Mateus, Paulo
2016-01-01
We investigate the geometry of one-norm geometric quantum discord and present a geometric interpretation of one-norm geometric quantum discord for a class of two-qubit states. It is found that one-norm geometric quantum discord has geometric behavior different from that described in Lang and Caves (Phys Rev Lett 105:150501, 2010), Li et al. (Phys Rev A 83:022321, 2011) and Yao et al. (Phys Lett A 376:358-364, 2012). We also compare the dynamics of the one-norm geometric quantum discord and other measures of quantum correlations under correlated noise. It is shown that different decoherent channels bring different influences to quantum correlations measured by concurrence, entropic quantum discord and geometric quantum discord, which depend on the memory parameter and decoherence parameter. We lay emphasis on the behaviors such as entanglement sudden death and sudden transition of quantum discord. Finally, we study the dynamical behavior of one-norm geometric quantum discord in one-dimensional anisotropic XXZ model by utilizing the quantum renormalization group method. It is shown that the one-norm geometric quantum discord demonstrates quantum phase transition through renormalization group approach.
Geometrical Destabilization of Inflation
NASA Astrophysics Data System (ADS)
Renaux-Petel, Sébastien; Turzyński, Krzysztof
2016-09-01
We show the existence of a general mechanism by which heavy scalar fields can be destabilized during inflation, relying on the fact that the curvature of the field space manifold can dominate the stabilizing force from the potential and destabilize inflationary trajectories. We describe a simple and rather universal setup in which higher-order operators suppressed by a large energy scale trigger this instability. This phenomenon can prematurely end inflation, thereby leading to important observational consequences and sometimes excluding models that would otherwise perfectly fit the data. More generally, it modifies the interpretation of cosmological constraints in terms of fundamental physics. We also explain how the geometrical destabilization can lead to powerful selection criteria on the field space curvature of inflationary models.
Geometrical aspects of entanglement
Leinaas, Jon Magne; Myrheim, Jan; Ovrum, Eirik
2006-07-15
We study geometrical aspects of entanglement, with the Hilbert-Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a 'relativistic' formulation leads to a complete analysis of the question of separability. Our approach is based on Schmidt decomposition of density matrices for a composite system and nonunitary transformations to a standard form. The positivity of the density matrices is crucial for the method to work. A similar approach works to some extent in higher dimensions, but is a less powerful tool. We further present a numerical method for examining separability and illustrate the method by a numerical study of bound entanglement in a composite system of two three-level systems.
Goldberg, P.W.
1993-04-01
In this paper we consider the problem of learning the positions of spheres in metric spaces, given as data randomly drawn points classified according to whether they are internal or external to an unknown sphere. The particular metrics under consideration are geometrical shape metrics, and the results are intended to be applicable to the problem of learning to identify a shape from related shapes classified according to whether they resemble it visually. While it is typically NP-hard to locate a central point for a hypothesis sphere, we find that it is however often possible to obtain a non-spherical hypothesis which can accurately predict whether further random points lie within the unknown sphere. We exhibit algorithms which achieve this, and in the process indicate useful general techniques for computational learning. Finally we exhibit a natural shape metric and show that it defines a class of spheres not predictable in this sense, subject to standard cryptographic assumptions.
Geometric Frustration with Disorder
NASA Astrophysics Data System (ADS)
Woo, Nayoon; Silevitch, Daniel M.; Rosenbaum, Thomas F.
2014-03-01
We study the effects of Nd doping on the geometrically-frustrated Heisenberg antiferromagnet Gadolinium Gallium Garnet (GGG), using linear and nonlinear ac magnetic susceptibility. Doping levels from 0.1 to 1 percent Nd alleviate the intrinsic frustration of pure GGG and elevate the ordering temperature compared to the pure material. We use nonlinear pump-probe magnetic susceptometry to examine cluster dynamics for both the pure and the doped series. At low frequency (~10 Hz), spectral hole burning is possible, indicating the presence of spin clusters with discrete energy levels largely decoupled from the overall spin bath. At kHz, we find a Fano resonance, revealing scattering pathways between spin cluster excitations and the bath. We trace the evolution of this resonance behavior as a function of dopant concentration.
Phenomenological modeling of geometric metasurfaces.
Ye, Weimin; Guo, Qinghua; Xiang, Yuanjiang; Fan, Dianyuan; Zhang, Shuang
2016-04-01
Metasurfaces, with their superior capability in manipulating the optical wavefront at the subwavelength scale and low manufacturing complexity, have shown great potential for planar photonics and novel optical devices. However, vector field simulation of metasurfaces is so far limited to periodic-structured metasurfaces containing a small number of meta-atoms in the unit cell by using full-wave numerical methods. Here, focusing on achiral meta-atoms only with electric polarizability and thickness far less than the wavelength of light, and ignoring the coupling between meta-atoms, we propose a general phenomenological method to analytically model the metasurfaces based on the assumption that the meta-atoms possess localized resonances with Lorentz-Drude forms, whose exact form can be retrieved from the full wave simulation of a single element. Applied to phase modulated geometric metasurfaces constituted by identical meta-atoms with different orientations, our analytical results show good agreement with full-wave numerical simulations. The proposed theory provides an efficient method to model and design optical devices based on metasurfaces.
Phenomenological modeling of geometric metasurfaces.
Ye, Weimin; Guo, Qinghua; Xiang, Yuanjiang; Fan, Dianyuan; Zhang, Shuang
2016-04-01
Metasurfaces, with their superior capability in manipulating the optical wavefront at the subwavelength scale and low manufacturing complexity, have shown great potential for planar photonics and novel optical devices. However, vector field simulation of metasurfaces is so far limited to periodic-structured metasurfaces containing a small number of meta-atoms in the unit cell by using full-wave numerical methods. Here, focusing on achiral meta-atoms only with electric polarizability and thickness far less than the wavelength of light, and ignoring the coupling between meta-atoms, we propose a general phenomenological method to analytically model the metasurfaces based on the assumption that the meta-atoms possess localized resonances with Lorentz-Drude forms, whose exact form can be retrieved from the full wave simulation of a single element. Applied to phase modulated geometric metasurfaces constituted by identical meta-atoms with different orientations, our analytical results show good agreement with full-wave numerical simulations. The proposed theory provides an efficient method to model and design optical devices based on metasurfaces. PMID:27137005
Early sex differences in weighting geometric cues.
Lourenco, Stella F; Addy, Dede; Huttenlocher, Janellen; Fabian, Lydia
2011-11-01
When geometric and non-geometric information are both available for specifying location, men have been shown to rely more heavily on geometry compared to women. To shed insight on the nature and developmental origins of this sex difference, we examined how 18- to 24-month-olds represented the geometry of a surrounding (rectangular) space when direct non-geometric information (i.e. a beacon) was also available for localizing a hidden object. Children were tested on a disorientation task with multiple phases. Across experiments, boys relied more heavily than girls on geometry to guide localization, as indicated by their errors during the initial phase of the task, and by their search choices following transformations that left only geometry available, or that, under limited conditions, created a conflict between beacon and geometry. Analyses of search times suggested that girls, like boys, had encoded geometry, and testing in a square space ruled out explanations concerned with motivational and methodological variables. Taken together, the findings provide evidence for an early sex difference in the weighting of geometry. This sex difference, we suggest, reflects subtle variation in how boys and girls approach the problem of combining multiple sources of location information.
Can EPR non-locality be geometrical?
Ne`eman, Y. |; Botero, A.
1995-10-01
The presence in Quantum Mechanics of non-local correlations is one of the two fundamentally non-intuitive features of that theory. The non-local correlations themselves fall into two classes: EPR and Geometrical. The non-local characteristics of the geometrical type are well-understood and are not suspected of possibly generating acausal features, such as faster-than-light propagation of information. This has especially become true since the emergence of a geometrical treatment for the relevant gauge theories, i.e. Fiber Bundle geometry, in which the quantum non-localities are seen to correspond to pure homotopy considerations. This aspect is reviewed in section 2. Contrary-wise, from its very conception, the EPR situation was felt to be paradoxical. It has been suggested that the non-local features of EPR might also derive from geometrical considerations, like all other non-local characteristics of QM. In[7], one of the authors was able to point out several plausibility arguments for this thesis, emphasizing in particular similarities between the non-local correlations provided by any gauge field theory and those required by the preservation of the quantum numbers of the original EPR state-vector, throughout its spatially-extended mode. The derivation was, however, somewhat incomplete, especially because of the apparent difference between, on the one hand, the closed spatial loops arising in the analysis of the geometrical non-localities, from Aharonov-Bohm and Berry phases to magnetic monopoles and instantons, and on the other hand, in the EPR case, the open line drawn by the positions of the two moving decay products of the disintegrating particle. In what follows, the authors endeavor to remove this obstacle and show that as in all other QM non-localities, EPR is somehow related to closed loops, almost involving homotopy considerations. They develop this view in section 3.
Measurement of geometric dephasing using a superconducting qubit
Berger, S.; Pechal, M.; Kurpiers, P.; Abdumalikov, A. A.; Eichler, C.; Mlynek, J. A.; Shnirman, A.; Gefen, Yuval; Wallraff, A.; Filipp, S.
2015-01-01
A quantum system interacting with its environment is subject to dephasing, which ultimately destroys the information it holds. Here we use a superconducting qubit to experimentally show that this dephasing has both dynamic and geometric origins. It is found that geometric dephasing, which is present even in the adiabatic limit and when no geometric phase is acquired, can either reduce or restore coherence depending on the orientation of the path the qubit traces out in its projective Hilbert space. It accompanies the evolution of any system in Hilbert space subjected to noise. PMID:26515812
Geometric Quantization and Foliation Reduction
NASA Astrophysics Data System (ADS)
Skerritt, Paul
A standard question in the study of geometric quantization is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether "quantization commutes with reduction." Guillemin and Sternberg first proposed this question, and answered it in the affirmative for the case of a free action of a compact Lie group on a compact Kahler manifold. Subsequent work has focused mainly on extending their proof to non-free actions and non-Kahler manifolds. For realistic physical examples, however, it is desirable to have a proof which also applies to non-compact symplectic manifolds. In this thesis we give a proof of the quantization-reduction problem for general symplectic manifolds. This is accomplished by working in a particular wavefunction representation, associated with a polarization that is in some sense compatible with reduction. While the polarized sections described by Guillemin and Sternberg are nonzero on a dense subset of the Kahler manifold, the ones considered here are distributional, having support only on regions of the phase space associated with certain quantized, or "admissible", values of momentum. We first propose a reduction procedure for the prequantum geometric structures that "covers" symplectic reduction, and demonstrate how both symplectic and prequantum reduction can be viewed as examples of foliation reduction. Consistency of prequantum reduction imposes the above-mentioned admissibility conditions on the quantized momenta, which can be seen as analogues of the Bohr-Wilson-Sommerfeld conditions for completely integrable systems. We then describe our reduction-compatible polarization, and demonstrate a one-to-one correspondence between polarized sections on the unreduced and reduced spaces. Finally, we describe a factorization of the reduced prequantum bundle, suggested by the structure of the underlying reduced symplectic manifold. This in turn induces a factorization of the space of polarized sections that agrees
Geometrical method of decoupling
NASA Astrophysics Data System (ADS)
Baumgarten, C.
2012-12-01
The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E→, B→, and P→, which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of) transformations must be symplectic and hence canonical. When used iteratively, the decoupling
Geometrical versus wave optics under gravitational waves
NASA Astrophysics Data System (ADS)
Angélil, Raymond; Saha, Prasenjit
2015-06-01
We present some new derivations of the effect of a plane gravitational wave on a light ray. A simple interpretation of the results is that a gravitational wave causes a phase modulation of electromagnetic waves. We arrive at this picture from two contrasting directions, namely, null geodesics and Maxwell's equations, or geometric and wave optics. Under geometric optics, we express the geodesic equations in Hamiltonian form and solve perturbatively for the effect of gravitational waves. We find that the well-known time-delay formula for light generalizes trivially to massive particles. We also recover, by way of a Hamilton-Jacobi equation, the phase modulation obtained under wave optics. Turning then to wave optics—rather than solving Maxwell's equations directly for the fields, as in most previous approaches—we derive a perturbed wave equation (perturbed by the gravitational wave) for the electromagnetic four-potential. From this wave equation it follows that the four-potential and the electric and magnetic fields all experience the same phase modulation. Applying such a phase modulation to a superposition of plane waves corresponding to a Gaussian wave packet leads to time delays.
Multi-stable dynamics of the non-adiabatic repressilator
Potapov, Ilya; Zhurov, Boris; Volkov, Evgeny
2015-01-01
The assumption of the fast binding of transcription factors (TFs) to promoters is a typical point in studies of synthetic genetic circuits functioning in bacteria. Although the assumption is effective for simplifying the models, it becomes questionable in the light of in vivo measurements of the times TF spends searching for its cognate DNA sites. We investigated the dynamics of the full idealized model of the paradigmatic genetic oscillator, the repressilator, using deterministic mathematical modelling and stochastic simulations. We found (using experimentally approved parameter values) that decreases in the TF binding rate changes the type of transition between steady state and oscillation. As a result, this gives rise to the hysteresis region in the parameter space, where both the steady state and the oscillation coexist. We further show that the hysteresis is persistent over a considerable range of the parameter values, but the presence of the oscillations is limited by the low rate of TF dimer degradation. Finally, the stochastic simulation of the model confirms the hysteresis with switching between the two attractors, resulting in highly skewed period distributions. Moreover, intrinsic noise stipulates trains of large-amplitude modulations around the stable steady state outside the hysteresis region, which makes the period distributions bimodal. PMID:25631570
Non-adiabatic corrections to the quasiparticle self-energy
NASA Astrophysics Data System (ADS)
Danylenko, Oleksiy V.; Dolgov, Oleg V.; Losyakov, Vladimir V.
1996-02-01
High T c superconductors and fullerenes seem to be characterized by very small bandwidths of the order of phonon frequencies. This may imply a breakdown of Migdal's theorem for the electron self-energy. There are two different approaches to the problem. The gauge-invariant self-consistent method proposed by Y. Takada includes many vertex corrections using the Ward identity. The other method by C. Grimaldi, L. Pietronero and S. Strässler (GPS) based on Migdal's idea uses the first correction to the unit vertex. These two approaches have been compared and the main results are the following: 1) Takada's method for the self-energy gives incorrect order in the Migdal parameter λΩ ph /ɛ F , 2) in GPS's method the momentum cut-off offered by the authors cannot be used as a free parameter, and 3) there is a possible instability which can be ascribed to appearing of polaron states.
Geometric Effects on Electron Cloud
Wang, L
2007-07-06
The development of an electron cloud in the vacuum chambers of high intensity positron and proton storage rings may limit the machine performances by inducing beam instabilities, beam emittance increase, beam loss, vacuum pressure increases and increased heat load on the vacuum chamber wall. The electron multipacting is a kind of geometric resonance phenomenon and thus is sensitive to the geometric parameters such as the aperture of the beam pipe, beam shape and beam bunch fill pattern, etc. This paper discusses the geometric effects on the electron cloud build-up in a beam chamber and examples are given for different beams and accelerators.
Guitars, Violins, and Geometric Sequences
ERIC Educational Resources Information Center
Barger, Rita; Haehl, Martha
2007-01-01
This article describes middle school mathematics activities that relate measurement, ratios, and geometric sequences to finger positions or the placement of frets on stringed musical instruments. (Contains 2 figures and 2 tables.)
Crystallization kinetics: A solution for geometrical impingement
NASA Astrophysics Data System (ADS)
Clemente, R. A.; Saleh, A. M.
2002-04-01
Starting from the wrong derivation by Erukhimovitch and Baram of an equation alternative to the classical Kolmogoroff-Johnson-Mehl-Avrami one for the transformed fraction in an infinite specimen, undergoing an isothermal first-order phase transformation, it is shown that a different exact solution of the geometrical problem of impingement can be obtained. Such solution is equivalent to the empirical one already presented by Austin and Rickett more than sixty years ago and allows to better fit experimental results for isothermal transformations. This also suggests that perhaps different statistical derivations could allow to reach the same result.
A geometric criterion for adiabatic chaos
Kaper, T.J. ); Kovacic, G. )
1994-03-01
Chaos in adiabatic Hamiltonian systems is a recent discovery and a pervasive phenomenon in physics. In this work, a geometric criterion is discussed based on the theory of action from classical mechanics to detect the existence of Smale horseshoe chaos in adiabatic systems. It is used to show that generic adiabatic planar Hamiltonian systems exhibit stochastic dynamics in large regions of phase space. To illustrate the method, results are obtained for three problems concerning relativistic particle dynamics, fluid mechanics, and passage through resonance, results which either could not be obtained with existing methods, or which were difficult and analytically impractical to obtain with them.
Antenna with Dielectric Having Geometric Patterns
NASA Technical Reports Server (NTRS)
Dudley, Kenneth L. (Inventor); Elliott, Holly A. (Inventor); Cravey, Robin L. (Inventor); Connell, John W. (Inventor); Ghose, Sayata (Inventor); Watson, Kent A. (Inventor); Smith, Jr., Joseph G. (Inventor)
2013-01-01
An antenna includes a ground plane, a dielectric disposed on the ground plane, and an electrically-conductive radiator disposed on the dielectric. The dielectric includes at least one layer of a first dielectric material and a second dielectric material that collectively define a dielectric geometric pattern, which may comprise a fractal geometry. The radiator defines a radiator geometric pattern, and the dielectric geometric pattern is geometrically identical, or substantially geometrically identical, to the radiator geometric pattern.
Geometric defects in quantum Hall states
NASA Astrophysics Data System (ADS)
Gromov, Andrey
2016-08-01
We describe a geometric (or gravitational) analog of the Laughlin quasiholes in fractional quantum Hall states. Analogously to the quasiholes, these defects can be constructed by an insertion of an appropriate vertex operator into the conformal block representation of a trial wave function; however, unlike the quasiholes these defects are extrinsic and do not correspond to true excitations of the quantum fluid. We construct a wave function in the presence of such defects and explain how to assign an electric charge and a spin to each defect and calculate the adiabatic, non-Abelian statistics of the defects. The defects turn out to be equivalent to the genons in that their adiabatic exchange statistics can be described in terms of representations of the mapping class group of an appropriate higher genus Riemann surface. We present a general construction that, in principle, makes it possible to calculate the statistics of Zn genons for any "parent" topological phase. We illustrate the construction on the example of the Laughlin state and perform an explicit calculation of the braiding matrices. In addition to non-Abelian statistics, geometric defects possess a universal Abelian overall phase, determined by the gravitational anomaly.
Structural phase transitions and topological defects in ion Coulomb crystals
Partner, Heather L.; Nigmatullin, Ramil; Burgermeister, Tobias; Keller, Jonas; Pyka, Karsten; Plenio, Martin B.; Retzker, Alex; Zurek, Wojciech Hubert; del Campo, Adolfo; Mehlstaubler, Tanja E.
2014-11-19
We use laser-cooled ion Coulomb crystals in the well-controlled environment of a harmonic radiofrequency ion trap to investigate phase transitions and defect formation. Topological defects in ion Coulomb crystals (kinks) have been recently proposed for studies of nonlinear physics with solitons and as carriers of quantum information. Defects form when a symmetry breaking phase transition is crossed non-adiabatically. For a second order phase transition, the Kibble-Zurek mechanism predicts that the formation of these defects follows a power law scaling in the rate of the transition. We demonstrate a scaling of defect density and describe kink dynamics and stability. We further discuss the implementation of mass defects and electric fields as first steps toward controlled kink preparation and manipulation.
Geometrical modelling of textile reinforcements
NASA Technical Reports Server (NTRS)
Pastore, Christopher M.; Birger, Alexander B.; Clyburn, Eugene
1995-01-01
The mechanical properties of textile composites are dictated by the arrangement of yarns contained with the material. Thus to develop a comprehensive understanding of the performance of these materials, it is necessary to develop a geometrical model of the fabric structure. This task is quite complex, as the fabric is made form highly flexible yarn systems which experience a certain degree of compressability. Furthermore there are tremendous forces acting on the fabric during densification typically resulting in yarn displacement and misorientation. The objective of this work is to develop a methodology for characterizing the geometry of yarns within a fabric structure including experimental techniques for evaluating these models. Furthermore, some applications of these geometric results to mechanical prediction models are demonstrated. Although more costly than its predecessors, the present analysis is based on the detailed architecture developed by one of the authors and his colleagues and accounts for many of the geometric complexities that other analyses ignore.
Geometric scalar theory of gravity
Novello, M.; Bittencourt, E.; Goulart, E.; Salim, J.M.; Toniato, J.D.; Moschella, U. E-mail: eduhsb@cbpf.br E-mail: egoulart@cbpf.br E-mail: toniato@cbpf.br
2013-06-01
We present a geometric scalar theory of gravity. Our proposal will be described using the ''background field method'' introduced by Gupta, Feynman, Deser and others as a field theory formulation of general relativity. We analyze previous criticisms against scalar gravity and show how the present proposal avoids these difficulties. This concerns not only the theoretical complaints but also those related to observations. In particular, we show that the widespread belief of the conjecture that the source of scalar gravity must be the trace of the energy-momentum tensor — which is one of the main difficulties to couple gravity with electromagnetic phenomenon in previous models — does not apply to our geometric scalar theory. From the very beginning this is not a special relativistic scalar gravity. The adjective ''geometric'' pinpoints its similarity with general relativity: this is a metric theory of gravity. Some consequences of this new scalar theory are explored.
Geometrical Optics of Dense Aerosols
Hay, Michael J.; Valeo, Ernest J.; Fisch, Nathaniel J.
2013-04-24
Assembling a free-standing, sharp-edged slab of homogeneous material that is much denser than gas, but much more rare ed than a solid, is an outstanding technological challenge. The solution may lie in focusing a dense aerosol to assume this geometry. However, whereas the geometrical optics of dilute aerosols is a well-developed fi eld, the dense aerosol limit is mostly unexplored. Yet controlling the geometrical optics of dense aerosols is necessary in preparing such a material slab. Focusing dense aerosols is shown here to be possible, but the nite particle density reduces the eff ective Stokes number of the flow, a critical result for controlled focusing. __________________________________________________
Geometrical spin symmetry and spin
Pestov, I. B.
2011-07-15
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
Geometric validation plan for ASTER
NASA Astrophysics Data System (ADS)
Iwasaki, Akira; Matsumoto, Ken; Fujisada, Hiroyuki
1998-12-01
The ASTER system is a multispectral imager which covers a spectral range from visible to thermal infrared light by combining three subsystems composed of four telescopes. To ensure the high-quality data products concerning to the geolocation and band-to-band matching performance, the geometric registration is needed. This paper describes the geometric validation procedure for a multi-telescope imager with a cross-track pointing function. The strategy for the maintenance of database files and the preparation a GCP library is also shown.
Teleportation of geometric structures in 3D
NASA Astrophysics Data System (ADS)
Aerts, Diederik; Czachor, Marek; Orłowski, Łukasz
2009-04-01
The simplest quantum teleportation algorithms can be represented in geometric terms in spaces of dimensions 3 (for real state vectors) and 4 (for complex state vectors). The geometric representation is based on geometric-algebra coding, a geometric alternative to the tensor-product coding typical of quantum mechanics. We discuss all the elementary ingredients of the geometric version of the algorithm: geometric analogs of states and controlled Pauli gates. A fully geometric presentation is possible if one employs a nonstandard representation of directed magnitudes, formulated in terms of colors defined via stereographic projection of a color wheel, and not by means of directed volumes.
Effect of geometrical frustration on inverse freezing.
Schmidt, M; Morais, C V; Zimmer, F M
2016-01-01
The interplay between geometrical frustration (GF) and inverse freezing (IF) is studied within a cluster approach. The model considers first-neighbor (J_{1}) and second-neighbor (J_{2}) intracluster antiferromagnetic interactions between Ising spins on a checkerboard lattice and long-range disordered couplings (J) among clusters. We obtain phase diagrams of temperature versus J_{1}/J in two cases: the absence of J_{2} interaction and the isotropic limit J_{2}=J_{1}, where GF takes place. An IF reentrant transition from the spin-glass (SG) to paramagnetic (PM) phase is found for a certain range of J_{1}/J in both cases. The J_{1} interaction leads to a SG state with high entropy at the same time that can introduce a low-entropy PM phase. In addition, it is observed that the cluster size plays an important role. The GF increases the PM phase entropy, but larger clusters can give an entropic advantage for the SG phase that favors IF. Therefore, our results suggest that disordered systems with antiferromagnetic clusters can exhibit an IF transition even in the presence of GF. PMID:26871062
Sigma models for genuinely non-geometric backgrounds
NASA Astrophysics Data System (ADS)
Chatzistavrakidis, Athanasios; Jonke, Larisa; Lechtenfeld, Olaf
2015-11-01
The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class of Courant algebroids as protobialgebroids with all types of geometric and non-geometric fluxes. For such structures we apply the mathematical result that any Courant algebroid gives rise to a 3D topological sigma model of the AKSZ type and we discuss the corresponding 2D field theories. It is found that these models are always geometric, even when both 2-form and 2-vector fields are neither vanishing nor inverse of one another. Taking a further step, we suggest an extended class of 3D sigma models, whose world volume is embedded in phase space, which allow for genuinely non-geometric backgrounds. Adopting the doubled formalism such models can be related to double field theory, albeit from a world sheet perspective.
Vergence, Vision, and Geometric Optics
ERIC Educational Resources Information Center
Keating, Michael P.
1975-01-01
Provides a definition of vergence in terms of the curvature of the wave fronts, and gives examples to illustrate the advantages of this approach. The vergence treatment of geometrical optics provides both conceptual and algebraic advantages, particularly for the life science student, over the traditional object distance-image distance-focal length…
Celestial mechanics with geometric algebra
NASA Technical Reports Server (NTRS)
Hestenes, D.
1983-01-01
Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.
The geometric oblateness of Uranus
NASA Technical Reports Server (NTRS)
Franklin, F. A.; Avis, C. C.; Colombo, G.; Shapiro, I. I.
1980-01-01
The paper considers photographs of Uranus obtained by the Stratoscope II balloon-borne telescope in 1970. These data have been redigitized and reanalyzed, and the geometric oblateness of Uranus was determined from the isophotes near the limb using an expression in terms of the equatorial and polar radii.
Platonic Symmetry and Geometric Thinking
ERIC Educational Resources Information Center
Zsombor-Murray, Paul
2007-01-01
Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…
Geometric hashing and object recognition
NASA Astrophysics Data System (ADS)
Stiller, Peter F.; Huber, Birkett
1999-09-01
We discuss a new geometric hashing method for searching large databases of 2D images (or 3D objects) to match a query built from geometric information presented by a single 3D object (or single 2D image). The goal is to rapidly determine a small subset of the images that potentially contain a view of the given object (or a small set of objects that potentially match the item in the image). Since this must be accomplished independent of the pose of the object, the objects and images, which are characterized by configurations of geometric features such as points, lines and/or conics, must be treated using a viewpoint invariant formulation. We are therefore forced to characterize these configurations in terms of their 3D and 2D geometric invariants. The crucial relationship between the 3D geometry and its 'residual' in 2D is expressible as a correspondence (in the sense of algebraic geometry). Computing a set of generating equations for the ideal of this correspondence gives a complete characterization of the view of independent relationships between an object and all of its possible images. Once a set of generators is in hand, it can be used to devise efficient recognition algorithms and to give an efficient geometric hashing scheme. This requires exploiting the form and symmetry of the equations. The result is a multidimensional access scheme whose efficiency we examine. Several potential directions for improving this scheme are also discussed. Finally, in a brief appendix, we discuss an alternative approach to invariants for generalized perspective that replaces the standard invariants by a subvariety of a Grassmannian. The advantage of this is that one can circumvent many annoying general position assumptions and arrive at invariant equations (in the Plucker coordinates) that are more numerically robust in applications.
Geometrical, response, and gap properties of Lindbladians
NASA Astrophysics Data System (ADS)
Albert, Victor V.; Bradlyn, Barry; Fraas, Martin; Jiang, Liang
We study Lindbladians admitting multi-dimensional steady-state subspaces (SSS) which can be used to store, protect, and process quantum information. We derive an analytical formula for the left eigenmatrices of such Lindbladians corresponding to purely imaginary eigenvalues. This formula resolves how Lindbladian evolution affects perturbative response and geometrical features of the SSS and allows us to generalize recent work to all types of SSS. We show that Hamiltonian and certain jump operator perturbations induce, to first order, exclusively unitary evolution on the SSS. Similarly, the holonomy (generalization of geometric phase) induced on the SSS after adiabatic traversal of a closed path in parameter space is unitary. We derive a new Riemannian metric tensor in parameter space induced by one type of SSS, generalizing the Fubini-Study metric to Lindbladians possessing one or more mixed steady states. We derive a Kubo formula governing linear response of the SSS to Hamiltonian perturbations. Finally, we show that the energy scale governing leakage out of the SSS is different from the conventional Lindbladian dissipative gap.
Cosmological models in Weyl geometrical scalar-tensor theory
NASA Astrophysics Data System (ADS)
Pucheu, M. L.; Alves Junior, F. A. P.; Barreto, A. B.; Romero, C.
2016-09-01
We investigate cosmological models in a recently proposed geometrical theory of gravity, in which the scalar field appears as part of the spacetime geometry. We extend the previous theory to include a scalar potential in the action. We solve the vacuum field equations for different choices of the scalar potential and give a detailed analysis of the solutions. We show that, in some cases, a cosmological scenario is found that seems to suggest the appearance of a geometric phase transition. We build a toy model, in which the accelerated expansion of the early Universe is driven by pure geometry.
C Patridge; C Jaye; T Abtew; B Ravel; D Fischer; A Marschilok; P Zhang; K Takeuchi; E Takeuchi; S Baneerjee
2011-12-31
Bimetallic phosphorus oxides have emerged as attractive candidates for use as cathode materials in the next generation of lithium-based batteries owing to the operation of multielectron transfer processes and thermochemical stabilities conferred by the incorporation of phosphate groups. In particular silver vanadium phosphorus oxide, Ag{sub 2}VO{sub 2}PO{sub 4}, shows a much desired in situ conductivity enhancement upon discharge resulting in inherently high power capability with minimal conductive additives needed. However, the amorphization of Ag{sub 2}VO{sub 2}PO{sub 4} during electrochemical discharge precludes the use of standard diffraction tools to monitor changes in the local electronic and geometric structure. Here, we have utilized a combination of V K-, V L-, Ag K-, and O K-edge X-ray absorption fine structure spectroscopy to determine the local vanadium and silver oxidation states, local coordination geometry, and stoichiometry for Ag{sub 2}VO{sub 2}PO{sub 4} samples with varying extents of electrochemical lithiation. Soft X-ray V L- and O K-edge measurements provide a detailed orbital-specific picture of changes in vanadium electronic structure upon discharge.
Geometrical modelling of textile reinforcements
NASA Technical Reports Server (NTRS)
Pastore, Christopher M.; Birger, Alexander B.; Clyburn, Eugene
1995-01-01
The mechanical properties of textile composites are dictated by the arrangement of yarns contained within the material. Thus, to develop a comprehensive understanding of the performance of these materials, it is necessary to develop a geometrical model of the fabric structure. This task is quite complex, as the fabric is made from highly flexible yarn systems which experience a certain degree of compressibility. Furthermore there are tremendous forces acting on the fabric during densification typically resulting in yarn displacement and misorientation. The objective of this work is to develop a methodology for characterizing the geometry of yarns within a fabric structure including experimental techniques for evaluating these models. Furthermore, some applications of these geometric results to mechanical property predictions models are demonstrated.
The verdict geometric quality library.
Knupp, Patrick Michael; Ernst, C.D. (Elemental Technologies, Inc., American Fork, UT); Thompson, David C.; Stimpson, C.J.; Pebay, Philippe Pierre
2006-03-01
Verdict is a collection of subroutines for evaluating the geometric qualities of triangles, quadrilaterals, tetrahedra, and hexahedra using a variety of metrics. A metric is a real number assigned to one of these shapes depending on its particular vertex coordinates. These metrics are used to evaluate the input to finite element, finite volume, boundary element, and other types of solvers that approximate the solution to partial differential equations defined over regions of space. The geometric qualities of these regions is usually strongly tied to the accuracy these solvers are able to obtain in their approximations. The subroutines are written in C++ and have a simple C interface. Each metric may be evaluated individually or in combination. When multiple metrics are evaluated at once, they share common calculations to lower the cost of the evaluation.
Geometric mean for subspace selection.
Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J
2009-02-01
Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions. PMID:19110492
Geometric mean for subspace selection.
Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J
2009-02-01
Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.
A geometric approach to quantum state separation
NASA Astrophysics Data System (ADS)
Bagan, E.; Yerokhin, V.; Shehu, A.; Feldman, E.; Bergou, J. A.
2015-12-01
Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure states in the general case where the known states have arbitrary a priori probabilities. The problem is formulated from a geometric perspective and shown to be equivalent to the problem of finding tangent curves within two families of conics that represent the unitarity constraints and the objective functions to be optimized, respectively. We present the corresponding analytical solutions in various forms. In the limit of perfect state separation, which is equivalent to unambiguous state discrimination, the solution exhibits a phenomenon analogous to a second order symmetry breaking phase transition. We also propose a linear optics implementation of separation which is based on the dual rail representation of qubits and single-photon multiport interferometry.
A geometric approach to spectral subtraction
Lu, Yang; Loizou, Philipos C.
2008-01-01
The traditional power spectral subtraction algorithm is computationally simple to implement but suffers from musical noise distortion. In addition, the subtractive rules are based on incorrect assumptions about the cross terms being zero. A new geometric approach to spectral subtraction is proposed in the present paper that addresses these shortcomings of the spectral subtraction algorithm. A method for estimating the cross terms involving the phase differences between the noisy (and clean) signals and noise is proposed. Analysis of the gain function of the proposed algorithm indicated that it possesses similar properties as the traditional MMSE algorithm. Objective evaluation of the proposed algorithm showed that it performed significantly better than the traditional spectral subtractive algorithm. Informal listening tests revealed that the proposed algorithm had no audible musical noise. PMID:19122867
Manipulating the spin-dependent splitting by geometric Doppler effect.
Liu, Yachao; Ke, Yougang; Zhou, Junxiao; Luo, Hailu; Wen, Shuangchun
2015-06-29
We report the manipulation of spin-dependent splitting by geometric Doppler effect based on dielectric metasurfaces. The extrapolation of rotational Doppler effect from temporal to spatial coordinate gives the phase change when the local optical axes of dielectric metasurfaces are rotating in space. Therefore, the continuous variation of local optical axes in a certain direction will introduce a phase gradient in the same direction at the beam cross section. This is additive to the phase gradient appeared when breaking the rotational symmetry of linearly polarized cylindrical vector beams, which leads to the deflections of different spin components of light, i.e., photonic spin Hall effect. Hence, it is possible to manipulate the spin-dependent splitting by introducing the geometric Doppler effect. Theoretically and experimentally, we show that the magnitude and orientation of the spin-dependent splitting are both tunable when changing the spatial rotation rate of local optical axes and incident polarization.
Universal Geometric Path to a Robust Majorana Magic Gate
NASA Astrophysics Data System (ADS)
Karzig, Torsten; Oreg, Yuval; Refael, Gil; Freedman, Michael H.
2016-07-01
A universal quantum computer requires a full set of basic quantum gates. With Majorana bound states one can form all necessary quantum gates in a topologically protected way, bar one. In this paper, we present a scheme that achieves the missing, so-called, π /8 magic phase gate without the need of fine-tuning for distinct physical realizations. The scheme is based on the manipulation of geometric phases described by a universal protocol and converges exponentially with the number of steps in the geometric path. Furthermore, our magic gate proposal relies on the most basic hardware previously suggested for topologically protected gates, and can be extended to an any-phase gate, where π /8 is substituted by any α .
Manipulating the spin-dependent splitting by geometric Doppler effect.
Liu, Yachao; Ke, Yougang; Zhou, Junxiao; Luo, Hailu; Wen, Shuangchun
2015-06-29
We report the manipulation of spin-dependent splitting by geometric Doppler effect based on dielectric metasurfaces. The extrapolation of rotational Doppler effect from temporal to spatial coordinate gives the phase change when the local optical axes of dielectric metasurfaces are rotating in space. Therefore, the continuous variation of local optical axes in a certain direction will introduce a phase gradient in the same direction at the beam cross section. This is additive to the phase gradient appeared when breaking the rotational symmetry of linearly polarized cylindrical vector beams, which leads to the deflections of different spin components of light, i.e., photonic spin Hall effect. Hence, it is possible to manipulate the spin-dependent splitting by introducing the geometric Doppler effect. Theoretically and experimentally, we show that the magnitude and orientation of the spin-dependent splitting are both tunable when changing the spatial rotation rate of local optical axes and incident polarization. PMID:26191680
Characteristic signatures of quantum criticality driven by geometrical frustration
Tokiwa, Yoshifumi; Stingl, Christian; Kim, Moo-Sung; Takabatake, Toshiro; Gegenwart, Philipp
2015-01-01
Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids. Whether geometrical frustration of magnetic interactions in metals can induce unconventional quantum critical points is an active area of research. We focus on the hexagonal heavy fermion metal CeRhSn, where the Kondo ions are located on distorted kagome planes stacked along the c axis. Low-temperature specific heat, thermal expansion, and magnetic Grüneisen parameter measurements prove a zero-field quantum critical point. The linear thermal expansion, which measures the initial uniaxial pressure derivative of the entropy, displays a striking anisotropy. Critical and noncritical behaviors along and perpendicular to the kagome planes, respectively, prove that quantum criticality is driven be geometrical frustration. We also discovered a spin flop–type metamagnetic crossover. This excludes an itinerant scenario and suggests that quantum criticality is related to local moments in a spin liquid–like state. PMID:26601165
NASA Astrophysics Data System (ADS)
Zhou, En-Bo; Zhang, Xin-Liang; Yu, Yu; Huang, De-Xiu
2009-03-01
Nonlinear patterning (NLP) effect in wavelength conversion based on transient cross-phase modulation (XPM) in semiconductor optical amplifier (SOA) assisted with a detuning filter is theoretically investigated. A non-adiabatic model is used to estimate the ultrafast dynamics of gain, phase and electron temperature in the SOA. Simulation results show that the NLP can be greatly suppressed by introducing an assist light, especially for the probe wavelength distant from gain peak. Furthermore, the results also indicate that the improvement is more evident for long wavelength probe light and assist light in counter-propagating configuration.
Geometrical Visualisation--Epistemic and Emotional
ERIC Educational Resources Information Center
Rodd, Melissa
2010-01-01
A well-documented experience of students of elementary Euclidean geometry is "seeing" a geometric result and being sure about its truth; this sort of experience gives rise to the notion of geometrical visualisation that is developed here. In this essay a philosophical argument for the epistemic potential of geometrical visualisation is reviewed,…
Development of a Geometric Spatial Visualization Tool
ERIC Educational Resources Information Center
Ganesh, Bibi; Wilhelm, Jennifer; Sherrod, Sonya
2009-01-01
This paper documents the development of the Geometric Spatial Assessment. We detail the development of this instrument which was designed to identify middle school students' strategies and advancement in understanding of four geometric concept domains (geometric spatial visualization, spatial projection, cardinal directions, and periodic patterns)…
Emergent geometric frustration of artificial magnetic skyrmion crystals
NASA Astrophysics Data System (ADS)
Ma, Fusheng; Reichhardt, C.; Gan, Weiliang; Reichhardt, C. J. Olson; Lew, Wen Siang
2016-10-01
Magnetic skyrmions have been receiving growing attention as potential information storage and magnetic logic devices since an increasing number of materials have been identified that support skyrmion phases. Explorations of artificial frustrated systems have led to new insights into controlling and engineering new emergent frustration phenomena in frustrated and disordered systems. Here, we propose a skyrmion spin ice, giving a unifying framework for the study of geometric frustration of skyrmion crystals (SCs) in a nonfrustrated artificial geometrical lattice as a consequence of the structural confinement of skyrmions in magnetic potential wells. The emergent ice rules from the geometrically frustrated SCs highlight a novel phenomenon in this skyrmion system: emergent geometrical frustration. We demonstrate how SC topology transitions between a nonfrustrated periodic configuration and a frustrated icelike ordering can also be realized reversibly. The proposed artificial frustrated skyrmion systems can be annealed into different ice phases with an applied current-induced spin-transfer torque, including a long-range ordered ice rule obeying ground state, as-relaxed random state, biased state, and monopole state. The spin-torque reconfigurability of the artificial skyrmion ice states, difficult to achieve in other artificial spin ice systems, is compatible with standard spintronic device fabrication technology, which makes the semiconductor industrial integration straightforward.
SQCD Vacua and Geometrical Engineering
Tatar, Radu; Wetenhall, Ben
2008-11-23
We consider the geometrical engineering constructions for the N = 1 SQCD vacua. After one T-duality, these geometries with wrapped D5 branes become N = 1 brane configurations with NS-branes and D4-branes. After performing a flop, the geometries contain branes, antibranes and branes wrapped on non-holomorphic cycles. The various tachyon condensations between pairs of wrapped D5 branes and anti-D5 branes together with deformations of the cycles give rise to a variety of supersymmetric and metastable non-supersymmetric vacua.
NASA Astrophysics Data System (ADS)
Cabrera, Ivelisse; Thompson, J. D.; Coldea, R.; Prabhakaran, D.; Bewley, R. I.; Guidi, T.; Rodriguez-Rivera, J. A.; Stock, C.
We report extensive single-crystal inelastic neutron scattering measurements of the magnetic excitations in the quasi 1D Ising ferromagnet CoNb2O6 in the quantum paramagnetic phase to characterize the effects of the finite interchain couplings. In this phase, we observe that excitations have a sharp, resolution-limited line shape at low energies and over most of the dispersion bandwidth, as expected for spin-flip quasiparticles. We map the full bandwidth along the strongly dispersive chain direction and resolve clear modulations of the dispersions in the plane normal to the chains, characteristic of frustrated interchain couplings in an antiferromagnetic isosceles triangular lattice. The dispersions can be well parametrized using a linear spin-wave model that includes interchain couplings and further neighbor exchanges. The observed dispersion bandwidth along the chain direction is smaller than that predicted by a linear spin-wave model using exchange values determined at zero field. We attribute this effect to quantum renormalization of the dispersion beyond the spin-wave approximation in fields slightly above the critical field, where quantum fluctuations are still significant. We acknowledge support from EPSRC Grant No. EP/H014934/1, the Oxford Clarendon Fund Scholarship and NSERC of Canada.
Measurement error in geometric morphometrics.
Fruciano, Carmelo
2016-06-01
Geometric morphometrics-a set of methods for the statistical analysis of shape once saluted as a revolutionary advancement in the analysis of morphology -is now mature and routinely used in ecology and evolution. However, a factor often disregarded in empirical studies is the presence and the extent of measurement error. This is potentially a very serious issue because random measurement error can inflate the amount of variance and, since many statistical analyses are based on the amount of "explained" relative to "residual" variance, can result in loss of statistical power. On the other hand, systematic bias can affect statistical analyses by biasing the results (i.e. variation due to bias is incorporated in the analysis and treated as biologically-meaningful variation). Here, I briefly review common sources of error in geometric morphometrics. I then review the most commonly used methods to measure and account for both random and non-random measurement error, providing a worked example using a real dataset.
NPP VIIRS Geometric Performance Status
NASA Technical Reports Server (NTRS)
Lin, Guoqing; Wolfe, Robert E.; Nishihama, Masahiro
2011-01-01
Visible Infrared Imager Radiometer Suite (VIIRS) instrument on-board the National Polar-orbiting Operational Environmental Satellite System (NPOESS) Preparatory Project (NPP) satellite is scheduled for launch in October, 2011. It is to provide satellite measured radiance/reflectance data for both weather and climate applications. Along with radiometric calibration, geometric characterization and calibration of Sensor Data Records (SDRs) are crucial to the VIIRS Environmental Data Record (EDR) algorithms and products which are used in numerical weather prediction (NWP). The instrument geometric performance includes: 1) sensor (detector) spatial response, parameterized by the dynamic field of view (DFOV) in the scan direction and instantaneous FOV (IFOV) in the track direction, modulation transfer function (MTF) for the 17 moderate resolution bands (M-bands), and horizontal spatial resolution (HSR) for the five imagery bands (I-bands); 2) matrices of band-to-band co-registration (BBR) from the corresponding detectors in all band pairs; and 3) pointing knowledge and stability characteristics that includes scan plane tilt, scan rate and scan start position variations, and thermally induced variations in pointing with respect to orbital position. They have been calibrated and characterized through ground testing under ambient and thermal vacuum conditions, numerical modeling and analysis. This paper summarizes the results, which are in general compliance with specifications, along with anomaly investigations, and describes paths forward for characterizing on-orbit BBR and spatial response, and for improving instrument on-orbit performance in pointing and geolocation.
Geometric pumping in autophoretic channels
NASA Astrophysics Data System (ADS)
Michelin, Sebastien; Montenegro Johnson, Thomas; de Canio, Gabriele; Lobatto-Dauzier, Nicolas; Lauga, Eric
2015-11-01
Pumping at the microscale has important applications from biological fluid handling to lab-on-a-chip systems. It can be achieved either from a global (e.g. imposed pressure gradient) or local forcing (e.g. ciliary pumping). Phoretic slip flows generated from concentration or temperature gradients are examples of such local flow forcing. Autophoresis is currently receiving much attention for the design of self-propelled particles achieving force- and torque-free locomotion by combining two essential surface properties: (i) an activity that modifies the solute content of the particle's environment (e.g. catalytic reaction or solute release), and (ii) a mobility that generates a slip flow from the resulting local concentration gradients. Recent work showed that geometric asymmetry is sufficient for a chemically-homogeneous particle to self-propel. Here we extend this idea to micro-pumping in active channels whose walls possess both chemical activity and phoretic mobility. Using a combination of theoretical analysis and numerical simulations, we show that geometrically-asymmetric but chemically-homogeneous channels can generate pumping and analyze the resulting flow patterns.
Geometrical deployment for braided stent.
Bouillot, Pierre; Brina, Olivier; Ouared, Rafik; Yilmaz, Hasan; Farhat, Mohamed; Erceg, Gorislav; Lovblad, Karl-Olof; Vargas, Maria Isabel; Kulcsar, Zsolt; Pereira, Vitor Mendes
2016-05-01
The prediction of flow diverter stent (FDS) implantation for the treatment of intracranial aneurysms (IAs) is being increasingly required for hemodynamic simulations and procedural planning. In this paper, a deployment model was developed based on geometrical properties of braided stents. The proposed mathematical description is first applied on idealized toroidal vessels demonstrating the stent shortening in curved vessels. It is subsequently generalized to patient specific vasculature predicting the position of the filaments along with the length and local porosity of the stent. In parallel, in-vitro and in-vivo FDS deployments were measured by contrast-enhanced cone beam CT (CBCT) in idealized and patient-specific geometries. These measurements showed a very good qualitative and quantitative agreement with the virtual deployments and provided experimental validations of the underlying geometrical assumptions. In particular, they highlighted the importance of the stent radius assessment in the accuracy of the deployment prediction. Thanks to its low computational cost, the proposed model is potentially implementable in clinical practice providing critical information for patient safety and treatment outcome assessment. PMID:26891065
Geometric optimization of thermal systems
NASA Astrophysics Data System (ADS)
Alebrahim, Asad Mansour
2000-10-01
The work in chapter 1 extends to three dimensions and to convective heat transfer the constructal method of minimizing the thermal resistance between a volume and one point. In the first part, the heat flow mechanism is conduction, and the heat generating volume is occupied by low conductivity material (k 0) and high conductivity inserts (kp) that are shaped as constant-thickness disks mounted on a common stem of kp material. In the second part the interstitial spaces once occupied by k0 material are bathed by forced convection. The internal and external geometric aspect ratios of the elemental volume and the first assembly are optimized numerically subject to volume constraints. Chapter 2 presents the constrained thermodynamic optimization of a cross-flow heat exchanger with ram air on the cold side, which is used in the environmental control systems of aircraft. Optimized geometric features such as the ratio of channel spacings and flow lengths are reported. It is found that the optimized features are relatively insensitive to changes in other physical parameters of the installation and relatively insensitive to the additional irreversibility due to discharging the ram-air stream into the atmosphere, emphasizing the robustness of the thermodynamic optimum. In chapter 3 the problem of maximizing exergy extraction from a hot stream by distributing streams over a heat transfer surface is studied. In the first part, the cold stream is compressed in an isothermal compressor, expanded in an adiabatic turbine, and discharged into the ambient. In the second part, the cold stream is compressed in an adiabatic compressor. Both designs are optimized with respect to the capacity-rate imbalance of the counter-flow and the pressure ratio maintained by the compressor. This study shows the tradeoff between simplicity and increased performance, and outlines the path for further conceptual work on the extraction of exergy from a hot stream that is being cooled gradually. The aim
NASA Astrophysics Data System (ADS)
Paik, Hanhee; Zhou, D.; Reed, M. D.; Kirchmair, G.; Frunzio, L.; Girvin, S. M.; Schoelkopf, R. J.
2013-03-01
We demonstrate a new all-microwave controlled phase entangling gate for the superconducting qubits in the three-dimensional circuit QED (3D cQED) architecture. The gate exploits the strong coupling between qubits and a cavity, wherein the cavity frequency dispersively shifts depending on the qubit register state. We off-resonantly displace the cavity vacuum state; each computational state evolves a different phase due to the dispersive coupling, yielding a conditional phase. While designed to exploit the advantages of the 3D cQED architecture, the gate requires only dispersive coupling, making the gate applicable to a wide variety of superconducting qubit architectures. We demonstrate 98% gate fidelity evaluated by quantum process tomography, and will discuss how appropriate choices of system parameters could increase this number and how we could minimize the gate infidelity due to measurement induced dephasing and non-adiabatic gate procedure.
Elastic scattering in geometrical model
NASA Astrophysics Data System (ADS)
Plebaniak, Zbigniew; Wibig, Tadeusz
2016-10-01
The experimental data on proton-proton elastic and inelastic scattering emerging from the measurements at the Large Hadron Collider, calls for an efficient model to fit the data. We have examined the optical, geometrical picture and we have found the simplest, linear dependence of this model parameters on the logarithm of the interaction energy with the significant change of the respective slopes at one point corresponding to the energy of about 300 GeV. The logarithmic dependence observed at high energies allows one to extrapolate the proton-proton elastic, total (and inelastic) cross sections to ultra high energies seen in cosmic rays events which makes a solid justification of the extrapolation to very high energy domain of cosmic rays and could help us to interpret the data from an astrophysical and a high energy physics point of view.
Geometrical setting of solid mechanics
Fiala, Zdenek
2011-08-15
Highlights: > Solid mechanics within the Riemannian symmetric manifold GL (3, R)/O (3, R). > Generalized logarithmic strain. > Consistent linearization. > Incremental principle of virtual power. > Time-discrete approximation. - Abstract: The starting point in the geometrical setting of solid mechanics is to represent deformation process of a solid body as a trajectory in a convenient space with Riemannian geometry, and then to use the corresponding tools for its analysis. Based on virtual power of internal stresses, we show that such a configuration space is the (globally) symmetric space of symmetric positive-definite real matrices. From this unifying point of view, we shall analyse the logarithmic strain, the stress rate, as well as linearization and intrinsic integration of corresponding evolution equation.
Geometrical characteristics of uniportal VATS
Rocco, Gaetano; Viti, Andrea; Terzi, Alberto
2013-01-01
In terms of accuracy and efficacy Uniportal Video-Assisted Thoracic Surgery (VATS) resections are comparable to standard VATS. In standard three-ports VATS, the geometric configuration of a parallelogram generates interference with the optical source, creating a plane with a torsion angle not favorable on the flat two-dimensional vision of currently available monitors. The potential advantages of single-port VATS approach include not only the one intercostal space incision (reduction of postoperative pain) but also a translational approach of VATS instruments along a sagittal plane. Accordingly, the Uniportal approach enables VATS instruments to draw two parallel lines on the plane, bringing them to approach the target lesion from a caudo-cranial perspective thus achieving a projective plane. As a consequence, taking advantage of the unique spatial features specific to uniportal VATS, the surgeon is enabled to bring the operative fulcrum inside the chest to address the target lesion in a fashion similar to open surgery. PMID:24040527
Bio-inspired interfacial strengthening strategy through geometrically interlocking designs.
Zhang, Yuming; Yao, Haimin; Ortiz, Christine; Xu, Jinquan; Dao, Ming
2012-11-01
Many biological materials, such as nacre and bone, are hybrid materials composed of stiff brittle ceramics and compliant organic materials. These natural organic/inorganic composites exhibit much enhanced strength and toughness in comparison to their constituents and inspires enormous biomimetic endeavors aiming to synthesize materials with superior mechanical properties. However, most current synthetic composites have not exhibited their full potential of property enhancement compared to the natural prototypes they are mimicking. One of the key issues is the weak junctions between stiff and compliant phases, which need to be optimized according to the intended functions of the composite material. Motivated by the geometrically interlocking designs of natural biomaterials, here we propose an interfacial strengthening strategy by introducing geometrical interlockers on the interfaces between compliant and stiff phases. Finite element analysis (FEA) shows that the strength of the composite depends strongly on the geometrical features of interlockers including shape, size, and structural hierarchy. Even for the most unfavorable scenario when neither adhesion nor friction is present between stiff and compliant phases, the tensile strength of the composites with proper interlocker design can reach up to 70% of the ideal value. The findings in this paper would provide guidelines to the improvement of the mechanical properties of current biomimetic composites. PMID:23032427
Geometric solitons of Hamiltonian flows on manifolds
Song, Chong; Sun, Xiaowei; Wang, Youde
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Splitting homomorphisms and the Geometrization Conjecture
NASA Astrophysics Data System (ADS)
Myers, Robert
2000-09-01
This paper gives an algebraic conjecture which is shown to be equivalent to Thurston's Geometrization Conjecture for closed, orientable 3-manifolds. It generalizes the Stallings-Jaco theorem which established a similar result for the Poincaré Conjecture. The paper also gives two other algebraic conjectures; one is equivalent to the finite fundamental group case of the Geometrization Conjecture and the other is equivalent to the union of the Geometrization Conjecture and Thurston's Virtual Bundle Conjecture.
Geometric Mathematical Framework for Multibody System Dynamics
NASA Astrophysics Data System (ADS)
Terze, Zdravko; Vrdoljak, Milan; Zlatar, Dario
2010-09-01
The paper surveys geometric mathematical framework for computational modeling of multibody system dynamics. Starting with the configuration space of rigid body motion and analysis of it's Lie group structure, the elements of respective Lie algebra are addressed and basic relations pertinent to geometrical formulations of multibody system dynamics are surveyed. Dynamical model of multibody system on manifold introduced, along with the outline of geometric characteristics of holonomic and non-holonomic kinematical constraints.
Frustrated topological symmetry breaking: Geometrical frustration and anyon condensation
NASA Astrophysics Data System (ADS)
Schulz, Marc D.; Burnell, Fiona J.
2016-10-01
We study the phase diagram of a topological string-net-type lattice model in the presence of geometrically frustrated interactions. These interactions drive several phase transitions that reduce the topological order, leading to a rich phase diagram including both Abelian (Z2) and non-Abelian (Ising×Ising¯ ) topologically ordered phases, as well as phases with broken translational symmetry. Interestingly, one of these phases simultaneously exhibits (Abelian) topological order and long-ranged order due to translational symmetry breaking, with nontrivial interactions between excitations in the topological order and defects in the long-ranged order. We introduce a variety of effective models, valid along certain lines in the phase diagram, which can be used to characterize both topological and symmetry-breaking order in these phases and in many cases allow us to characterize the phase transitions that separate them. We use exact diagonalization and high-order series expansion to study areas of the phase diagram where these models break down and to approximate the location of the phase boundaries.
Geometric Mechanics Reveals Optimal Complex Terrestrial Undulation Patterns
NASA Astrophysics Data System (ADS)
Gong, Chaohui; Astley, Henry; Schiebel, Perrin; Dai, Jin; Travers, Matthew; Goldman, Daniel; Choset, Howie; CMU Team; GT Team
Geometric mechanics offers useful tools for intuitively analyzing biological and robotic locomotion. However, utility of these tools were previously restricted to systems that have only two internal degrees of freedom and in uniform media. We show kinematics of complex locomotors that make intermittent contacts with substrates can be approximated as a linear combination of two shape bases, and can be represented using two variables. Therefore, the tools of geometric mechanics can be used to analyze motions of locomotors with many degrees of freedom. To demonstrate the proposed technique, we present studies on two different types of snake gaits which utilize combinations of waves in the horizontal and vertical planes: sidewinding (in the sidewinder rattlesnake C. cerastes) and lateral undulation (in the desert specialist snake C. occipitalis). C. cerastes moves by generating posteriorly traveling body waves in the horizontal and vertical directions, with a relative phase offset equal to +/-π/2 while C. occipitalismaintains a π/2 offset of a frequency doubled vertical wave. Geometric analysis reveals these coordination patterns enable optimal movement in the two different styles of undulatory terrestrial locomotion. More broadly, these examples demonstrate the utility of geometric mechanics in analyzing realistic biological and robotic locomotion.
Geometrical Quadrupolar Frustration in DyB4
NASA Astrophysics Data System (ADS)
Watanuki, Ryuta; Sato, Gou; Suzuki, Kazuya; Ishihara, Masaki; Yanagisawa, Tatsuya; Nemoto, Yuichi; Goto, Terutaka
2005-08-01
Physical properties of DyB4 have been studied by magnetization, specific heat, and ultrasonic measurements. The magnetic entropy change and ultrasonic properties in intermediate phase II indicate that the degeneracy of internal degrees of freedom is not fully lifted in spite of the formation of magnetic order. The ultrasonic attenuation and huge softening of C44 in phase II suggest the existence of electric-quadrupolar (orbital) fluctuations of 4 f-electrons. These unusual properties originate from a geometrical quadrupolar frustration.
Geometric asymmetry driven Janus micromotors
NASA Astrophysics Data System (ADS)
Zhao, Guanjia; Pumera, Martin
2014-09-01
The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a ``coconut'' micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors.The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a ``coconut'' micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors. Electronic supplementary information (ESI) available: Additional SEM images, data analysis, Videos S
Geometric perturbation theory and plasma physics
Omohundro, S.M.
1985-01-01
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory, and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure in five different ways. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle-group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a long-standing question posed by Kruskal about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no adhoc elements, which is then applied to gyromotion. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A theory motivated by free electron lasers gives new restrictions on the change of area of projected parallelepipeds under canonical transformations.
Geometric reasoning about assembly tools
Wilson, R.H.
1997-01-01
Planning for assembly requires reasoning about various tools used by humans, robots, or other automation to manipulate, attach, and test parts and subassemblies. This paper presents a general framework to represent and reason about geometric accessibility issues for a wide variety of such assembly tools. Central to the framework is a use volume encoding a minimum space that must be free in an assembly state to apply a given tool, and placement constraints on where that volume must be placed relative to the parts on which the tool acts. Determining whether a tool can be applied in a given assembly state is then reduced to an instance of the FINDPLACE problem. In addition, the author presents more efficient methods to integrate the framework into assembly planning. For tools that are applied either before or after their target parts are mated, one method pre-processes a single tool application for all possible states of assembly of a product in polynomial time, reducing all later state-tool queries to evaluations of a simple expression. For tools applied after their target parts are mated, a complementary method guarantees polynomial-time assembly planning. The author presents a wide variety of tools that can be described adequately using the approach, and surveys tool catalogs to determine coverage of standard tools. Finally, the author describes an implementation of the approach in an assembly planning system and experiments with a library of over one hundred manual and robotic tools and several complex assemblies.
Geometric Reasoning for Automated Planning
NASA Technical Reports Server (NTRS)
Clement, Bradley J.; Knight, Russell L.; Broderick, Daniel
2012-01-01
An important aspect of mission planning for NASA s operation of the International Space Station is the allocation and management of space for supplies and equipment. The Stowage, Configuration Analysis, and Operations Planning teams collaborate to perform the bulk of that planning. A Geometric Reasoning Engine is developed in a way that can be shared by the teams to optimize item placement in the context of crew planning. The ISS crew spends (at the time of this writing) a third or more of their time moving supplies and equipment around. Better logistical support and optimized packing could make a significant impact on operational efficiency of the ISS. Currently, computational geometry and motion planning do not focus specifically on the optimized orientation and placement of 3D objects based on multiple distance and containment preferences and constraints. The software performs reasoning about the manipulation of 3D solid models in order to maximize an objective function based on distance. It optimizes for 3D orientation and placement. Spatial placement optimization is a general problem and can be applied to object packing or asset relocation.
Geometric morphology of cellular solids
Schlei, B. R.; Prasad, L.; Skourikhine, A. N.
2001-01-01
We demonstrate how to derive morphological information from micrographs, i.e., grey-level images, of polymeric foams. The segmentation of the images is performed by applying a pulse-coupled neural network. This processing generates blobs of the foams walls/struts and voids, respectively. The contours of the blobs and their corresponding points form the input to a constrained Delaunay tessellation, which provides an unstructured grid of the material under consideration. The subsequently applied Chordal Axis Transform captures the intrinsic shape characteristics, and facilitates the identification and localization of key morphological features. While stochastic features of the polymeric foams struts/walls such as areas, aspect ratios, etc., already can be computed at this stage, the foams voids require further geometric processing. The voids are separated into single foam cells. This shape manipulation leads to a refinement of the initial blob contours, which then requires the repeated application of the constrained Delaunay tessellation and Chordal Axis Transform, respectively. Using minimum enclosing rectangles for each foam cell, finally the stochastic features of the foam voids are computed.
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-01
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
Solving Absolute Value Equations Algebraically and Geometrically
ERIC Educational Resources Information Center
Shiyuan, Wei
2005-01-01
The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.
Early Sex Differences in Weighting Geometric Cues
ERIC Educational Resources Information Center
Lourenco, Stella F.; Addy, Dede; Huttenlocher, Janellen; Fabian, Lydia
2011-01-01
When geometric and non-geometric information are both available for specifying location, men have been shown to rely more heavily on geometry compared to women. To shed insight on the nature and developmental origins of this sex difference, we examined how 18- to 24-month-olds represented the geometry of a surrounding (rectangular) space when…
Parabolas: Connection between Algebraic and Geometrical Representations
ERIC Educational Resources Information Center
Shriki, Atara
2011-01-01
A parabola is an interesting curve. What makes it interesting at the secondary school level is the fact that this curve is presented in both its contexts: algebraic and geometric. Being one of Apollonius' conic sections, the parabola is basically a geometric entity. It is, however, typically known for its algebraic characteristics, in particular…
Testing the geometric clutch hypothesis.
Lindemann, Charles B
2004-12-01
The Geometric Clutch hypothesis is based on the premise that transverse forces (t-forces) acting on the outer doublets of the eukaryotic axoneme coordinate the action of the dynein motors to produce flagellar and ciliary beating. T-forces result from tension and compression on the outer doublets when a bend is present on the flagellum or cilium. The t-force acts to pry the doublets apart in an active bend, and push the doublets together when the flagellum is passively bent and thus could engage and disengage the dynein motors. Computed simulations of this working mechanism have reproduced the beating pattern of simple cilia and flagella, and of mammalian sperm. Cilia-like beating, with a clearly defined effective and recovery stroke, can be generated using one uniformly applied switching algorithm. When the mechanical properties and dimensions appropriate to a specific flagellum are incorporated into the model the same algorithm can simulate a sea urchin or bull sperm-like beat. The computed model reproduces many of the observed behaviors of real flagella and cilia. The model can duplicate the results of outer arm extraction experiments in cilia and predicted two types of arrest behavior that were verified experimentally in bull sperm. It also successfully predicted the experimentally determined nexin elasticity. Calculations based on live and reactivated sea urchin and bull sperm yielded a value of 0.5 nN/microm for the t-force at the switch-point. This is a force sufficient to overcome the shearing force generated by all the dyneins on one micron of outer doublet. A t-force of this magnitude should produce substantial distortion of the axoneme at the switch-point, especially in spoke or spoke-head deficient motile flagella. This concrete and verifiable prediction is within the grasp of recent advances in imaging technology, specifically cryoelectron microscopy and atomic force microscopy. PMID:15567522
Mobility in geometrically confined membranes
Domanov, Yegor A.; Aimon, Sophie; Toombes, Gilman E. S.; Renner, Marianne; Quemeneur, François; Triller, Antoine; Turner, Matthew S.; Bassereau, Patricia
2011-01-01
Lipid and protein lateral mobility is essential for biological function. Our theoretical understanding of this mobility can be traced to the seminal work of Saffman and Delbrück, who predicted a logarithmic dependence of the protein diffusion coefficient (i) on the inverse of the size of the protein and (ii) on the “membrane size” for membranes of finite size [Saffman P, Delbrück M (1975) Proc Natl Acad Sci USA 72:3111—3113]. Although the experimental proof of the first prediction is a matter of debate, the second has not previously been thought to be experimentally accessible. Here, we construct just such a geometrically confined membrane by forming lipid bilayer nanotubes of controlled radii connected to giant liposomes. We followed the diffusion of individual molecules in the tubular membrane using single particle tracking of quantum dots coupled to lipids or voltage-gated potassium channels KvAP, while changing the membrane tube radius from approximately 250 to 10 nm. We found that both lipid and protein diffusion was slower in tubular membranes with smaller radii. The protein diffusion coefficient decreased as much as 5-fold compared to diffusion on the effectively flat membrane of the giant liposomes. Both lipid and protein diffusion data are consistent with the predictions of a hydrodynamic theory that extends the work of Saffman and Delbrück to cylindrical geometries. This study therefore provides strong experimental support for the ubiquitous Saffman–Delbrück theory and elucidates the role of membrane geometry and size in regulating lateral diffusion. PMID:21768336
Piezoelectricity in planar boron nitride via a geometric phase
NASA Astrophysics Data System (ADS)
Droth, Matthias; Burkard, Guido; Pereira, Vitor M.
2016-08-01
Due to their low surface mass density, two-dimensional materials with a strong piezoelectric response are interesting for nanoelectromechanical systems with high force sensitivity. Unlike graphene, the two sublattices in a monolayer of hexagonal boron nitride (hBN) are occupied by different elements, which breaks inversion symmetry and allows for piezoelectricity. This has been confirmed with density functional theory calculations of the piezoelectric constant of hBN. Here, we formulate an entirely analytical derivation of the electronic contribution to the piezoelectric response in this system based on the concepts of strain-induced pseudomagnetic vector potential and the modern theory of polarization that relates the polar moment to the Berry curvature. Our findings agree with the symmetry restrictions expected for the hBN lattice and reproduce well the magnitude of the piezoelectric effect previously obtained ab initio.
On geometric factors for neutral particle analyzers.
Stagner, L; Heidbrink, W W
2014-11-01
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
On geometric factors for neutral particle analyzers
Stagner, L.; Heidbrink, W. W.
2014-11-15
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, “Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry,” J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, “Geometric factor and directional response of single and multi-element particle telescopes,” Nucl. Instrum. Methods 95(1), 5–11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
Geometric quantum discord under noisy environment
NASA Astrophysics Data System (ADS)
Huang, Zhiming; Qiu, Daowen
2016-05-01
In this work, we mainly analyze the dynamics of geometric quantum discord under a common dissipating environment. Our results indicate that geometric quantum discord is generated when the initial state is a product state. The geometric quantum discord increases from zero to a stable value with the increasing time, and the variations of stable values depend on the system size. For different initial product states, geometric quantum discord has some different behaviors in contrast with entanglement. For initial maximally entangled state, it is shown that geometric quantum discord decays with the increasing dissipated time. It is found that for EPR state, entanglement is more robust than geometric quantum discord, which is a sharp contrast to the existing result that quantum discord is more robust than entanglement in noisy environments. However, for GHZ state and W state, geometric quantum discord is more stable than entanglement. By the comparison of quantum discord and entanglement, we find that a common dissipating environment brings complicated effects on quantum correlation, which may deepen our understanding of physical impacts of decohering environment on quantum correlation. In the end, we analyze the effects of collective dephasing noise and rotating noise to a class of two-qubit X states, and we find that quantum correlation is not altered by the collective noises.
On geometric factors for neutral particle analyzers
NASA Astrophysics Data System (ADS)
Stagner, L.; Heidbrink, W. W.
2014-11-01
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
Nonadditive Mixed State Phases in Neutron Optics
Klepp, J.; Sponar, S.; Filipp, S.; Lettner, M.; Badurek, G.; Hasegawa, Y.
2009-03-10
In a neutron polarimetry experiment mixed neutron spin phases are determined. We consider evolutions leading to purely geometric, purely dynamical and combined phases. It is experimentally demonstrated that the sum of the geometric and dynamical phases--both obtained in separate measurements--is not equal to the associated total phase as obtained from a third measurement, unless the system is in a pure state. In this sense, mixed state phases are not additive.
Geometric perturbation theory and plasma physics
Omohundro, S.M.
1985-04-04
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
The perception of geometrical structure from congruence
NASA Technical Reports Server (NTRS)
Lappin, Joseph S.; Wason, Thomas D.
1989-01-01
The principle function of vision is to measure the environment. As demonstrated by the coordination of motor actions with the positions and trajectories of moving objects in cluttered environments and by rapid recognition of solid objects in varying contexts from changing perspectives, vision provides real-time information about the geometrical structure and location of environmental objects and events. The geometric information provided by 2-D spatial displays is examined. It is proposed that the geometry of this information is best understood not within the traditional framework of perspective trigonometry, but in terms of the structure of qualitative relations defined by congruences among intrinsic geometric relations in images of surfaces. The basic concepts of this geometrical theory are outlined.
Geometric symmetries in superfluid vortex dynamics
Kozik, Evgeny; Svistunov, Boris
2010-10-01
Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, w(z)=x(z)+iy(z), describing the instant shape of the line. Along with a natural set of Noether's constants of motion, which - apart from their rather specific expressions in terms of w(z) - are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines, the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the wave-number space. Similar considerations apply to other systems with purely geometric degrees of freedom.
The Pentagon Problem: Geometric Reasoning with Technology.
ERIC Educational Resources Information Center
Zbiek, Rose Mary
1996-01-01
Presents an activity, involving pentagons and using a figure manipulator such as The Geometer's Sketchpad, that requires students to reason geometrically without making unsubstantiated assumptions based on diagrams. (MKR)
Geometric methods in computational fluid dynamics. [turbomachinery
NASA Technical Reports Server (NTRS)
Eiseman, P. R.
1980-01-01
General methods for the construction of geometric computational fluid dynamic algorithms are presented which simulate a variety of flow fields in various nontrivial regions. Included are: basic developments with tensors; various forms for the equations of motion; generalized numerical methods and boundary conditions; and methods for mesh generation to meet the strong geometric constraints of turbomachines. Coordinate generation is shown generally to yield mesh descriptions from one or more transformations that are smoothly joined together to form a composite mesh.
Machine Learning and Geometric Technique for SLAM
NASA Astrophysics Data System (ADS)
Bernal-Marin, Miguel; Bayro-Corrochano, Eduardo
This paper describes a new approach for building 3D geometric maps using a laser rangefinder, a stereo camera system and a mathematical system the Conformal Geometric Algebra. The use of a known visual landmarks in the map helps to carry out a good localization of the robot. A machine learning technique is used for recognition of objects in the environment. These landmarks are found using the Viola and Jones algorithm and are represented with their position in the 3D virtual map.
The Geometric Grids of the Hieratic Numeral.
NASA Astrophysics Data System (ADS)
Aboulfotouh, Hossam M. K.
The paper discusses the geometrical designs of the hieratic numeral signs. It shows the regular-grid-patterns of squares upon which, the shapes of the already decoded hieratic numeral-signs, have been designed. Also, it shows the design of some hieratic numeral signs, based on subdividing the circle; and the hieratic signs of modular notation. It might reveal the basic geometrical level of understanding of anonymous ancient Egyptians who designed them some four thousand years ago.
Percolation and cooperation with mobile agents: Geometric and strategy clusters
NASA Astrophysics Data System (ADS)
Vainstein, Mendeli H.; Brito, Carolina; Arenzon, Jeferson J.
2014-08-01
We study the conditions for persistent cooperation in an off-lattice model of mobile agents playing the Prisoner's Dilemma game with pure, unconditional strategies. Each agent has an exclusion radius rP, which accounts for the population viscosity, and an interaction radius rint, which defines the instantaneous contact network for the game dynamics. We show that, differently from the rP=0 case, the model with finite-sized agents presents a coexistence phase with both cooperators and defectors, besides the two absorbing phases, in which either cooperators or defectors dominate. We provide, in addition, a geometric interpretation of the transitions between phases. In analogy with lattice models, the geometric percolation of the contact network (i.e., irrespective of the strategy) enhances cooperation. More importantly, we show that the percolation of defectors is an essential condition for their survival. Differently from compact clusters of cooperators, isolated groups of defectors will eventually become extinct if not percolating, independently of their size.
Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector
NASA Technical Reports Server (NTRS)
Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)
2001-01-01
Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.
Fracture mechanics of hydroxyapatite single crystals under geometric confinement.
Libonati, Flavia; Nair, Arun K; Vergani, Laura; Buehler, Markus J
2013-04-01
Geometric confinement to the nanoscale, a concept that refers to the characteristic dimensions of structural features of materials at this length scale, has been shown to control the mechanical behavior of many biological materials or their building blocks, and such effects have also been suggested to play a crucial role in enhancing the strength and toughness of bone. Here we study the effect of geometric confinement on the fracture mechanism of hydroxyapatite (HAP) crystals that form the mineralized phase in bone. We report a series of molecular simulations of HAP crystals with an edge crack on the (001) plane under tensile loading, and we systematically vary the sample height whilst keeping the sample and the crack length constant. We find that by decreasing the sample height the stress concentration at the tip of the crack disappears for samples with a height smaller than 4.15nm, below which the material shows a different failure mode characterized by a more ductile mechanism with much larger failure strains, and the strength approaching that of a flaw-less crystal. This study directly confirms an earlier suggestion of a flaw-tolerant state that appears under geometric confinement and may explain the mechanical stability of the reinforcing HAP platelets in bone. PMID:23500480
Effects of imbalance and geometric error on precision grinding machines
Bibler, J.E.
1997-06-01
To study balancing in grinding, a simple mechanical system was examined. It was essential to study such a well-defined system, as opposed to a large, complex system such as a machining center. The use of a compact, well-defined system enabled easy quantification of the imbalance force input, its phase angle to any geometric decentering, and good understanding of the machine mode shapes. It is important to understand a simple system such as the one I examined given that imbalance is so intimately coupled to machine dynamics. It is possible to extend the results presented here to industrial machines, although that is not part of this work. In addition to the empirical testing, a simple mechanical system to look at how mode shapes, balance, and geometric error interplay to yield spindle error motion was modelled. The results of this model will be presented along with the results from a more global grinding model. The global model, presented at ASPE in November 1996, allows one to examine the effects of changing global machine parameters like stiffness and damping. This geometrically abstract, one-dimensional model will be presented to demonstrate the usefulness of an abstract approach for first-order understanding but it will not be the main focus of this thesis. 19 refs., 36 figs., 10 tables.
Performance Assessment and Geometric Calibration of RESOURCESAT-2
NASA Astrophysics Data System (ADS)
Radhadevi, P. V.; Solanki, S. S.; Akilan, A.; Jyothi, M. V.; Nagasubramanian, V.
2016-06-01
Resourcesat-2 (RS-2) has successfully completed five years of operations in its orbit. This satellite has multi-resolution and multi-spectral capabilities in a single platform. A continuous and autonomous co-registration, geo-location and radiometric calibration of image data from different sensors with widely varying view angles and resolution was one of the challenges of RS-2 data processing. On-orbit geometric performance of RS-2 sensors has been widely assessed and calibrated during the initial phase operations. Since then, as an ongoing activity, various geometric performance data are being generated periodically. This is performed with sites of dense ground control points (GCPs). These parameters are correlated to the direct geo-location accuracy of the RS-2 sensors and are monitored and validated to maintain the performance. This paper brings out the geometric accuracy assessment, calibration and validation done for about 500 datasets of RS-2. The objectives of this study are to ensure the best absolute and relative location accuracy of different cameras, location performance with payload steering and co-registration of multiple bands. This is done using a viewing geometry model, given ephemeris and attitude data, precise camera geometry and datum transformation. In the model, the forward and reverse transformations between the coordinate systems associated with the focal plane, payload, body, orbit and ground are rigorously and explicitly defined. System level tests using comparisons to ground check points have validated the operational geo-location accuracy performance and the stability of the calibration parameters.
Probabilistically Perfect Cloning of Two Pure States: Geometric Approach
NASA Astrophysics Data System (ADS)
Yerokhin, V.; Shehu, A.; Feldman, E.; Bagan, E.; Bergou, J. A.
2016-05-01
We solve the long-standing problem of making n perfect clones from m copies of one of two known pure states with minimum failure probability in the general case where the known states have arbitrary a priori probabilities. The solution emerges from a geometric formulation of the problem. This formulation reveals that cloning converges to state discrimination followed by state preparation as the number of clones goes to infinity. The convergence exhibits a phenomenon analogous to a second-order symmetry-breaking phase transition.
Modeling the Thermoelectric Properties of Ti5O9 Magnéli Phase Ceramics
NASA Astrophysics Data System (ADS)
Pandey, Sudeep J.; Joshi, Giri; Wang, Shidong; Curtarolo, Stefano; Gaume, Romain M.
2016-11-01
Magnéli phase Ti5O9 ceramics with 200-nm grain-size were fabricated by hot-pressing nanopowders of titanium and anatase TiO2 at 1223 K. The thermoelectric properties of these ceramics were investigated from room temperature to 1076 K. We show that the experimental variation of the electrical conductivity with temperature follows a non-adiabatic small-polaron model with an activation energy of 64 meV. In this paper, we propose a modified Heikes-Chaikin-Beni model, based on a canonical ensemble of closely spaced titanium t 2g levels, to account for the temperature dependency of the Seebeck coefficient. Modeling of the thermal conductivity data reveals that the phonon contribution remains constant throughout the investigated temperature range. The thermoelectric figure-of-merit ZT of this nanoceramic material reaches 0.3 K at 1076 K.
Modeling the Thermoelectric Properties of Ti5O9 Magnéli Phase Ceramics
NASA Astrophysics Data System (ADS)
Pandey, Sudeep J.; Joshi, Giri; Wang, Shidong; Curtarolo, Stefano; Gaume, Romain M.
2016-07-01
Magnéli phase Ti5O9 ceramics with 200-nm grain-size were fabricated by hot-pressing nanopowders of titanium and anatase TiO2 at 1223 K. The thermoelectric properties of these ceramics were investigated from room temperature to 1076 K. We show that the experimental variation of the electrical conductivity with temperature follows a non-adiabatic small-polaron model with an activation energy of 64 meV. In this paper, we propose a modified Heikes-Chaikin-Beni model, based on a canonical ensemble of closely spaced titanium t 2g levels, to account for the temperature dependency of the Seebeck coefficient. Modeling of the thermal conductivity data reveals that the phonon contribution remains constant throughout the investigated temperature range. The thermoelectric figure-of-merit ZT of this nanoceramic material reaches 0.3 K at 1076 K.
Introduction to Dynamical Systems and Geometric Mechanics
NASA Astrophysics Data System (ADS)
Maruskin, Jared M.
2012-01-01
Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explores similar systems that instead evolve on differentiable manifolds. In the study of geometric mechanics, however, additional geometric structures are often present, since such systems arise from the laws of nature that govern the motions of particles, bodies, and even galaxies. In the first part of the text, we discuss linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, PoincarÃ© maps, Floquet theory, the PoincarÃ©-Bendixson theorem, bifurcations, and chaos. The second part of the text begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms. The final chapters cover Lagrangian and Hamiltonian mechanics from a modern geometric perspective, mechanics on Lie groups, and nonholonomic mechanics via both moving frames and fiber bundle decompositions. The text can be reasonably digested in a single-semester introductory graduate-level course. Each chapter concludes with an application that can serve as a springboard project for further investigation or in-class discussion.
Morphing of geometric composites via residual swelling.
Pezzulla, Matteo; Shillig, Steven A; Nardinocchi, Paola; Holmes, Douglas P
2015-08-01
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such as fabricating smart actuators or mimicking living tissues. Here, we present the controlled growth-like morphing of 2D sheets into 3D shapes by preparing geometric composite structures that deform by residual swelling. The morphing of these geometric composites is dictated by both swelling and geometry, with diffusion controlling the swelling-induced actuation, and geometric confinement dictating the structure's deformed shape. Building on a simple mechanical analog, we present an analytical model that quantitatively describes how the Gaussian and mean curvatures of a thin disk are affected by the interplay among geometry, mechanics, and swelling. This model is in excellent agreement with our experiments and numerics. We show that the dynamics of residual swelling is dictated by a competition between two characteristic diffusive length scales governed by geometry. Our results provide the first 2D analog of Timoshenko's classical formula for the thermal bending of bimetallic beams - our generalization explains how the Gaussian curvature of a 2D geometric composite is affected by geometry and elasticity. The understanding conferred by these results suggests that the controlled shaping of geometric composites may provide a simple complement to traditional manufacturing techniques. PMID:26076671
Unifying Geometrical Representations of Gauge Theory
NASA Astrophysics Data System (ADS)
Alsid, Scott; Serna, Mario
2015-01-01
We unify three approaches within the vast body of gauge-theory research that have independently developed distinct representations of a geometrical surface-like structure underlying the vector-potential. The three approaches that we unify are: those who use the compactified dimensions of Kaluza-Klein theory, those who use Grassmannian models (also called gauge theory embedding or models) to represent gauge fields, and those who use a hidden spatial metric to replace the gauge fields. In this paper we identify a correspondence between the geometrical representations of the three schools. Each school was mostly independently developed, does not compete with other schools, and attempts to isolate the gauge-invariant geometrical surface-like structures that are responsible for the resulting physics. By providing a mapping between geometrical representations, we hope physicists can now isolate representation-dependent physics from gauge-invariant physical results and share results between each school. We provide visual examples of the geometrical relationships between each school for electric and magnetic fields. We highlight a first new result: in all three representations a static electric field (electric field from a fixed ring of charge or a sphere of charge) has a hidden gauge-invariant time dependent surface that is underlying the vector potential.
Geometrical methods in soft condensed-matter physics
NASA Astrophysics Data System (ADS)
Kung, William
We propose a geometrical picture of understanding the thermodynamic and elastic properties of charged and fuzzy colloidal crystals, by analogy to foams, as well as perform a computational exercise to confirm a new universality class for long polymers with non-trivial topologies. By the foam analogy, we relate the problem of thermodynamic stability to the Kelvin's problem of partitioning space into equal-volume cells of minimal surface area. In particular, we consider the face-centered cubic (FCC), body-centered cubic (BCC) and the beta-tungsten (A15) lattices. We write down the free energy of these solid phases directly in terms of geometric and microscopic parameters of the system, and we derive the theoretical phase diagram of an experimental charged colloidal systems [Phys. Rev. Lett. 62, 1524 (1989)]. By considering deformations to the foam cells, we also compute the cubic elastic constants of these three lattices for charged and fuzzy colloids. In the polymer problem, we consider the critical behavior of polymers much longer than their persistence length, with built-in topological constraint in the form of Fuller's relation: Lk = Tw + Wr in a theta-solvent. We map the problem to the three-dimensional symmetric U( N)-Chern Simons theory as N → 0. To two-loop order, we find a new scaling regime for the topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe which gives way to a fluctuation-induced first-order transition.
Geometrical aspects in optical wave-packet dynamics.
Onoda, Masaru; Murakami, Shuichi; Nagaosa, Naoto
2006-12-01
We construct a semiclassical theory for propagation of an optical wave packet in a nonconducting medium with a periodic structure of dielectric permittivity and magnetic permeability, i.e., a nonconducting photonic crystal. We employ a quantum-mechanical formalism in order to clarify its link to those of electronic systems. It involves the geometrical phase, i.e., Berry's phase, in a natural way, and describes an interplay between orbital motion and internal rotation. Based on the above theory, we discuss the geometrical aspects of the optical Hall effect. We also consider a reduction of the theory to a system without periodic structure and apply it to the transverse shift of an optical beam at an interface reflection or refraction. For a generic incident beam with an arbitrary polarization, an identical result for the transverse shift of each reflected or transmitted beam is given by the following different approaches: (i) analytic evaluation of wave-packet dynamics, (ii) total angular momentum (TAM) conservation for individual photons, and (iii) numerical simulation of wave-packet dynamics. It is consistent with a result by classical electrodynamics. This means that the TAM conservation for individual photons is already taken into account in wave optics, i.e., classical electrodynamics. Finally, we show an application of our theory to a two-dimensional photonic crystal, and propose an optimal design for the enhancement of the optical Hall effect in photonic crystals.
A Geometric Description of Raman Fingerprints on Spinor BECs
NASA Astrophysics Data System (ADS)
Schultz, Justin T.; Hansen, Azure; Murphree, Joseph D.; Jayaseelan, Maitreyi; Bigelow, Nicholas P.
2016-05-01
We employ a geometric description of a coherent, diabatic two-photon Raman interaction as a rotation on the Bloch sphere of a spin-1/2 system. The spin state of the system is described by a point on the sphere and the time evolution is described by a trajectory of the sphere's surface. The axis of rotation is determined by properties of the optical Raman beams: the pulse area, the relative intensities, relative phase, and relative frequencies. The two-photon detuning gives fine control over the sizes and phases of the imprinted features. This interpretation allows us not only to precisely engineer complex, spatially varying spin textures, but also to characterize these textures with a form of atomic polarimetry as we demonstrate on a coreless vortex in a spinor BEC.
Overview on METEOSAT geometrical image data processing
NASA Technical Reports Server (NTRS)
Diekmann, Frank J.
1994-01-01
Digital Images acquired from the geostationary METEOSAT satellites are processed and disseminated at ESA's European Space Operations Centre in Darmstadt, Germany. Their scientific value is mainly dependent on their radiometric quality and geometric stability. This paper will give an overview on the image processing activities performed at ESOC, concentrating on the geometrical restoration and quality evaluation. The performance of the rectification process for the various satellites over the past years will be presented and the impacts of external events as for instance the Pinatubo eruption in 1991 will be explained. Special developments both in hard and software, necessary to cope with demanding tasks as new image resampling or to correct for spacecraft anomalies, are presented as well. The rotating lens of MET-5 causing severe geometrical image distortions is an example for the latter.
Connexions for the nuclear geometrical collective model
NASA Astrophysics Data System (ADS)
Rosensteel, G.; Sparks, N.
2015-11-01
The Bohr-Mottelson-Frankfurt model of nuclear rotations and quadrupole vibrations is a foundational model in nuclear structure physics. The model, also called the geometrical collective model or simply GCM(3), has two hidden mathematical structures, one group theoretic and the other differential geometric. Although the group structure has been understood for some time, the geometric structure is a new feature that this paper investigates in some detail. Using the de Rham Laplacian \\triangle =\\star d \\star d for the kinetic energy extends significantly the physical scope of the GCM(3) model. This Laplacian contains a ‘magnetic’ term due to the connexion between base manifold rotational and fibre vortex degrees of freedom. When the connexion specializes to irrotational flow, the Laplacian reduces to the Bohr-Mottelson kinetic energy operator.
Geometric spin echo under zero field
NASA Astrophysics Data System (ADS)
Sekiguchi, Yuhei; Komura, Yusuke; Mishima, Shota; Tanaka, Touta; Niikura, Naeko; Kosaka, Hideo
2016-05-01
Spin echo is a fundamental tool for quantum registers and biomedical imaging. It is believed that a strong magnetic field is needed for the spin echo to provide long memory and high resolution, since a degenerate spin cannot be controlled or addressed under a zero magnetic field. While a degenerate spin is never subject to dynamic control, it is still subject to geometric control. Here we show the spin echo of a degenerate spin subsystem, which is geometrically controlled via a mediating state split by the crystal field, in a nitrogen vacancy centre in diamond. The demonstration reveals that the degenerate spin is protected by inherent symmetry breaking called zero-field splitting. The geometric spin echo under zero field provides an ideal way to maintain the coherence without any dynamics, thus opening the way to pseudo-static quantum random access memory and non-invasive biosensors.
MM Algorithms for Geometric and Signomial Programming.
Lange, Kenneth; Zhou, Hua
2014-02-01
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.
Geometric spin echo under zero field
Sekiguchi, Yuhei; Komura, Yusuke; Mishima, Shota; Tanaka, Touta; Niikura, Naeko; Kosaka, Hideo
2016-01-01
Spin echo is a fundamental tool for quantum registers and biomedical imaging. It is believed that a strong magnetic field is needed for the spin echo to provide long memory and high resolution, since a degenerate spin cannot be controlled or addressed under a zero magnetic field. While a degenerate spin is never subject to dynamic control, it is still subject to geometric control. Here we show the spin echo of a degenerate spin subsystem, which is geometrically controlled via a mediating state split by the crystal field, in a nitrogen vacancy centre in diamond. The demonstration reveals that the degenerate spin is protected by inherent symmetry breaking called zero-field splitting. The geometric spin echo under zero field provides an ideal way to maintain the coherence without any dynamics, thus opening the way to pseudo-static quantum random access memory and non-invasive biosensors. PMID:27193936
Telencephalon and geometric space in goldfish.
Vargas, Juan Pedro; Bingman, Verner Peter; Portavella, Manuel; López, Juan Carlos
2006-11-01
Neuroanatomical evidence indicates that the lateral pallium (LP) of ray-finned fishes could be homologous to the hippocampus of mammals and birds. Recent studies have found that hippocampus of mammals and birds is critical for learning geometric properties of space. In this work, we studied the effects of lesions to the lateral pallium of goldfish on the encoding of geometric spatial information. Goldfish with telencephalic lesions were trained to search for a goal in a rectangular-shaped arena containing one different wall that served as the only distinctive environmental feature. Although fish with lateral pallium lesions learned the task even faster than sham and medial pallium (MP)-lesioned animals, subsequent probe trials showed that they were insensitive to geometric information. Sham and medial pallium-lesioned animals could use both geometric and feature information to locate the goal. By contrast, fish with lateral palium lesions relied exclusively on the feature information provided by the wall of a different colour. These results indicate that lesions to the lateral pallium of goldfish, like hippocampal lesions in mammals and birds, selectively impair the encoding of geometric spatial information of environmental space. Thus, the forebrain structures of teleost fish that are neuroanatomically equivalent to the mammalian and avian hippocampus also share a central role in supporting spatial cognition. Present results suggest that the presence of a hippocampal-dependent memory system implicated in the processing of geometric spatial information is an ancient feature of the vertebrate forebrain that has been conserved during the divergent evolution of different vertebrate groups.
Primary School Teacher Candidates' Geometric Habits of Mind
ERIC Educational Resources Information Center
Köse, Nilu¨fer Y.; Tanisli, Dilek
2014-01-01
Geometric habits of mind are productive ways of thinking that support learning and using geometric concepts. Identifying primary school teacher candidates' geometric habits of mind is important as they affect the development of their future students' geometric thinking. Therefore, this study attempts to determine primary school…
A geometric approach to quantum vortices
NASA Astrophysics Data System (ADS)
Penna, Vittorio; Spera, Mauro
1989-12-01
In this paper a geometrical description is given of the theory of quantum vortices first developed by Rasetti and Regge [Physica A 80, 217 (1975)] relying on the symplectic techniques of Marsden and Weinstein [J. Phys. D 7, 305 (1983)], and Kirillov-Kostant-Souriau geometric quantization. The RR-current algebra is interpreted as the natural Hamiltonian algebra associated to a certain coadjoint orbit of the group G=SDiff(R3), the KKS prequantization condition of which is related to the Feynman-Onsager relation. This orbit is also shown to possess a G-invariant Kaehler structure, whence, in principle, it is possible to quantize it in a natural way.
Local Geometrical Machinery for Complexity and Control
NASA Astrophysics Data System (ADS)
Ivancevic, Vladimir G.; Reid, Darryn J.
2015-11-01
In this Chapter, we present local geometrical machinery for studying complexity and control, consisting of dynamics on Kähler manifolds, which combine three geometrical structures-Riemannian, symplectic and complex (Hermitian)-in a mutually compatible way. In other words, every Kähler manifold is simultaneously Riemannian, symplectic and complex (Hermitian). It is well known that Riemannian manifolds represent the stage on which Lagrangian dynamics is set, symplectic manifolds represent the stage for Hamiltonian dynamics, and complex (Hermitian) varieties comprise the stage for quantum dynamics. Therefore, Kähler manifolds represent the richest dynamical stage available where Lagrangian, Hamiltonian, and quantum dynamics all dance together.
Geometrical compression of lidar return signals.
Harms, J; Lahmann, W; Weitkamp, C
1978-04-01
The dynamic range of lidar return signals has been calculated for coaxial transmitter-receiver geometries via the spatial distribution of irradiance in the detector plane as a function of distance z. It is shown that the z(-2)dependence from the lidar equation can be converted to almost constant signal amplitude for distances up to 3 km by suitable and realistic choice of the geometric parameters. On the other hand, no signal degradation with respect to the lidar equation occurs at large distances. This geometrical compression of lidar return signal amplitudes is rated superior to electronic compression methods such as gain switching or logarithmic amplification. PMID:20197946
Model-based vision using geometric hashing
NASA Astrophysics Data System (ADS)
Akerman, Alexander, III; Patton, Ronald
1991-04-01
The Geometric Hashing technique developed by the NYU Courant Institute has been applied to various automatic target recognition applications. In particular, I-MATH has extended the hashing algorithm to perform automatic target recognition ofsynthetic aperture radar (SAR) imagery. For this application, the hashing is performed upon the geometric locations of dominant scatterers. In addition to being a robust model-based matching algorithm -- invariant under translation, scale, and 3D rotations of the target -- hashing is of particular utility because it can still perform effective matching when the target is partially obscured. Moreover, hashing is very amenable to a SIMD parallel processing architecture, and thus potentially realtime implementable.
Reinforcing Geometric Properties with Shapedoku Puzzles
ERIC Educational Resources Information Center
Wanko, Jeffrey J.; Nickell, Jennifer V.
2013-01-01
Shapedoku is a new type of puzzle that combines logic and spatial reasoning with understanding of basic geometric concepts such as slope, parallelism, perpendicularity, and properties of shapes. Shapedoku can be solved by individuals and, as demonstrated here, can form the basis of a review for geometry students as they create their own. In this…
Geometric Models for Collaborative Search and Filtering
ERIC Educational Resources Information Center
Bitton, Ephrat
2011-01-01
This dissertation explores the use of geometric and graphical models for a variety of information search and filtering applications. These models serve to provide an intuitive understanding of the problem domains and as well as computational efficiencies to our solution approaches. We begin by considering a search and rescue scenario where both…
How Do Young Children Learn Geometric Concepts.
ERIC Educational Resources Information Center
Ohe, Pia
Twenty children (ages 5 and 6) from each of seven cultural groups (Caucasian, Black, Jewish, Puerto Rican, Chinese, Korean-American and native Korean) were given a copying task of 21 geometric shapes to test the cultural invariancy of Piaget's topological-projective-Euclidean concept acquisition sequence. All subjects were either middle or lower…
Geometric Mean--What Does It Mean?
ERIC Educational Resources Information Center
Kalder, Robin S.
2012-01-01
The National Council of Teachers of Mathematics and numerous mathematics educators promote the combination of conceptual understanding and procedural learning in the successful instruction of mathematics. Despite this, when geometric mean is taught in a typical American geometry class, it is taught as a process only despite the many connections…
The geometrical significance of the Laplacian
NASA Astrophysics Data System (ADS)
Styer, Daniel F.
2015-12-01
The Laplacian operator can be defined, not only as a differential operator, but also through its averaging properties. Such a definition lends geometric significance to the operator: a large Laplacian at a point reflects a "nonconformist" (i.e., different from average) character for the function there. This point of view is used to motivate the wave equation for a drumhead.
Geometric interpretations for resonances of plasmonic nanoparticles
NASA Astrophysics Data System (ADS)
Liu, Wei; Oulton, Rupert F.; Kivshar, Yuri S.
2015-07-01
The field of plasmonics can be roughly categorized into two branches: surface plasmon polaritons (SPPs) propagating in waveguides and localized surface plasmons (LSPs) supported by scattering particles. Investigations along these two directions usually employ different approaches, resulting in more or less a dogma that the two branches progress almost independently of each other, with few interactions. Here in this work we interpret LSPs from a Bohr model based geometric perspective relying on SPPs, thus establishing a connection between these two sub-fields. Besides the clear explanations of conventional scattering features of plasmonic nanoparticles, based on this geometric model we further demonstrate other anomalous scattering features (higher order modes supported at lower frequencies, and blueshift of the resonance with increasing particle sizes) and multiple electric resonances of the same order supported at different frequencies, which have been revealed to originate from backward SPP modes and multiple dispersion bands supported in the corresponding plasmonic waveguides, respectively. Inspired by this geometric model, it is also shown that, through solely geometric tuning, the absorption of each LSP resonance can be maximized to reach the single channel absorption limit, provided that the scattering and absorption rates are tuned to be equal.
Geometric Interpretation of the Pauli Spinor.
ERIC Educational Resources Information Center
Frescura, F. A. M.; Hiley, B. J.
1981-01-01
Presents a reexamination of an intuitively geometric view of the nonrelativistic Pauli spinor in a simplified discussion of the connection between the rotation group and special transformations in the plane of projection. This view of the spinor is related to those based on the existence of an istropic or null vector. (SK)
Children's Learning of Geometrical Concepts Through Logo.
ERIC Educational Resources Information Center
Noss, Richard
1987-01-01
Exploratory study aimed to investigate elements of geometrical concepts that children learn through Logo programing. A test designed to assess three components of length and angle was administered to 84 children who had learned Logo for one year and 92 who had not. Data indicated a positive effect of Logo work on some items, but not all.…
Geometric Transformations in Middle School Mathematics Textbooks
ERIC Educational Resources Information Center
Zorin, Barbara
2011-01-01
This study analyzed treatment of geometric transformations in presently available middle grades (6, 7, 8) student mathematics textbooks. Fourteen textbooks from four widely used textbook series were evaluated: two mainline publisher series, Pearson (Prentice Hall) and Glencoe (Math Connects); one National Science Foundation (NSF) funded curriculum…
Modern Geometric Algebra: A (Very Incomplete!) Survey
ERIC Educational Resources Information Center
Suzuki, Jeff
2009-01-01
Geometric algebra is based on two simple ideas. First, the area of a rectangle is equal to the product of the lengths of its sides. Second, if a figure is broken apart into several pieces, the sum of the areas of the pieces equals the area of the original figure. Remarkably, these two ideas provide an elegant way to introduce, connect, and…
If Only Clairaut Had Dynamic Geometric Tools
ERIC Educational Resources Information Center
Chang, Hyewon; Reys, Barbara J.
2013-01-01
Geometry is a major area of study in middle school mathematics, yet middle school and secondary students have difficulty learning important geometric concepts. This article considers Alexis-Claude Clairaut's approach that emphasizes engaging student curiosity about key ideas and theorems instead of directly teaching theorems before their…
Impossible Geometric Constructions: A Calculus Writing Project
ERIC Educational Resources Information Center
Awtrey, Chad
2013-01-01
This article discusses a writing project that offers students the opportunity to solve one of the most famous geometric problems of Greek antiquity; namely, the impossibility of trisecting the angle [pi]/3. Along the way, students study the history of Greek geometry problems as well as the life and achievements of Carl Friedrich Gauss. Included is…
More Meaning from the Geometric Mean.
ERIC Educational Resources Information Center
Dorner, Bryan C.
2003-01-01
Provides classroom suggestions for combining numerical, algebraic, and geometric techniques with the understanding of a simple method for computing square roots. Historical origins of the method illustrate the debt owed to ancient minds living in what are now India, Pakistan, Iraq, and Egypt. (Author/NB)
Geometrizing the Quantum - A Toy Model
Koch, Benjamin
2009-12-15
It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally 'curved' space-time. This shows that it is possible to formulate quantum mechanics as a purely classical geometrical theory. The results are further generalized to interactions with an external electromagnetic field.
A Geometric Approach to Fair Division
ERIC Educational Resources Information Center
Barbanel, Julius
2010-01-01
We wish to divide a cake among some collection of people (who may have very different notions of the comparative value of pieces of cake) in a way that is both "fair" and "efficient." We explore the meaning of these terms, introduce two geometric tools to aid our analysis, and present a proof (due to Dietrich Weller) that establishes the existence…
Geometric Determinants of Human Spatial Memory
ERIC Educational Resources Information Center
Hartley, Tom; Trinkler, Iris; Burgess, Neil
2004-01-01
Geometric alterations to the boundaries of a virtual environment were used to investigate the representations underlying human spatial memory. Subjects encountered a cue object in a simple rectangular enclosure, with distant landmarks for orientation. After a brief delay, during which they were removed from the arena, subjects were returned to it…
Geometric approach to dislocation and disclination theory
Nesterov, A.I.; Ovchinnikov, S.G.
1988-05-01
Cartan structure equations are used to create a four-dimensional geometric description of dislocations in continuum theory. It is shown that the dislocation distribution is determined by the torsion tensor, while the disclination distribution is determined by the curvature tensor. An analogy to electrodynamics is offered.
Subgraphs and network motifs in geometric networks
NASA Astrophysics Data System (ADS)
Itzkovitz, Shalev; Alon, Uri
2005-02-01
Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in abstract spaces such as multivariate biological or economic data sets and models of social networks. These networks often display network motifs: subgraphs that recur in the network much more often than in randomized networks. To understand the origin of the network motifs in these networks, it is important to study the subgraphs and network motifs that arise solely from geometric constraints. To address this, we analyze geometric network models, in which nodes are arranged on a lattice and edges are formed with a probability that decays with the distance between nodes. We present analytical solutions for the numbers of all three- and four-node subgraphs, in both directed and nondirected geometric networks. We also analyze geometric networks with arbitrary degree sequences and models with a bias for directed edges in one direction. Scaling rules for scaling of subgraph numbers with system size, lattice dimension, and interaction range are given. Several invariant measures are found, such as the ratio of feedback and feed-forward loops, which do not depend on system size, dimension, or connectivity function. We find that network motifs in many real-world networks, including social networks and neuronal networks, are not captured solely by these geometric models. This is in line with recent evidence that biological network motifs were selected as basic circuit elements with defined information-processing functions.
A GEOMETRICAL HEIGHT SCALE FOR SUNSPOT PENUMBRAE
Puschmann, K. G.; Ruiz Cobo, B.; MartInez Pillet, V. E-mail: brc@iac.e
2010-09-10
Inversions of spectropolarimetric observations of penumbral filaments deliver the stratification of different physical quantities in an optical depth scale. However, without establishing a geometrical height scale, their three-dimensional geometrical structure cannot be derived. This is crucial in understanding the correct spatial variation of physical properties in the penumbral atmosphere and to provide insights into the mechanism capable of explaining the observed penumbral brightness. The aim of this work is to determine a global geometrical height scale in the penumbra by minimizing the divergence of the magnetic field vector and the deviations from static equilibrium as imposed by a force balance equation that includes pressure gradients, gravity, and the Lorentz force. Optical depth models are derived from the inversion of spectropolarimetric data of an active region observed with the Solar Optical Telescope on board the Hinode satellite. We use a genetic algorithm to determine the boundary condition for the inference of geometrical heights. The retrieved geometrical height scale permits the evaluation of the Wilson depression at each pixel and the correlation of physical quantities at each height. Our results fit into the uncombed penumbral scenario, i.e., a penumbra composed of flux tubes with channeled mass flow and with a weaker and more horizontal magnetic field as compared with the background field. The ascending material is hotter and denser than their surroundings. We do not find evidence of overturning convection or field-free regions in the inner penumbral area analyzed. The penumbral brightness can be explained by the energy transfer of the ascending mass carried by the Evershed flow, if the physical quantities below z = -75 km are extrapolated from the results of the inversion.
Geometrical heterogeneities and permeability anisotropy of rough fractures
NASA Astrophysics Data System (ADS)
MéHeust, Y.; Schmittbuhl, J.
2001-02-01
We develop a numerical model for describing a single phase viscous flow in a rough fracture and compare it successfully to previously-published experimental results. The aperture fluctuations are introduced as an isotropic self-affine fractal which includes geometrical heterogeneities, especially at the fracture scale. The model is based on the lubrication approximation and solutions are obtained from two independent numerical schemes. The curves describing the evolution of the hydraulic aperture as a function of the mean fracture separation are shown to be well fitted by power law functions. A grid rotation technique is developed to explore the influence of the pressure drop orientation over a continuous range of orientations. A single fracture is shown to be either flow enhancing or flow inhibiting by comparison to a parallel plate model of identical mean separation, depending on the pressure drop orientation. This anisotropy of the fluid flow results from the geometrical heterogeneities at the fracture scale. Statistical analyses of the results when exploring different apertures distributions with the same measured scale invariance property show a large variability of the permeability, which is due to the same phenomenon. A prediction of the hydraulic transmittivity that takes account of the pressure drop orientation is proposed.
Learning with touchscreen devices: game strategies to improve geometric thinking
NASA Astrophysics Data System (ADS)
Soldano, Carlotta; Arzarello, Ferdinando
2016-03-01
The aim of this paper is to reflect on the importance of the students' game-strategic thinking during the development of mathematical activities. In particular, we hypothesise that this type of thinking helps students in the construction of logical links between concepts during the "argumentation phase" of the proving process. The theoretical background of our study lies in the works of J. Hintikka, a Finnish logician, who developed a new type of logic, based on game theory, called the logic of inquiry. In order to experiment with this new approach to the teaching and learning of mathematics, we have prepared five game-activities based on geometric theorems in which two players play against each other in a multi-touch dynamic geometric environment (DGE). In this paper, we present the design of the first game-activity and the relationship between it and the logic of inquiry. Then, adopting the theoretical framework of the instrumental genesis by Vérillon and Rabardel (EJPE 10: 77-101, 1995), we will present and analyse significant actions and dialogues developed by students while they are solving the game. We focus on the presence of a particular way of playing the game introduced by the students, the "reflected game", and highlight its functions for the development of the task.
New geometrical perspective of fuzzy ART and fuzzy ARTMAP learning
NASA Astrophysics Data System (ADS)
Anagnostopoulos, Georgios C.; Georgiopoulos, Michael
2001-03-01
In this paper we introduce new useful, geometric concepts regarding categories in Fuzzy ART and Fuzzy ARTMAP, which shed more light into the process of category competition eligibility upon the presentation of input patterns. First, we reformulate the competition of committed nodes with uncommitted nodes in an F2 layer as a commitment test very similar to the vigilance test. Next, we introduce a category's match and choice regions, which are the geometric interpretation of the vigilance and commitment test respectively. After examining properties of these regions we reach three results applicable to both Fuzzy ART and Fuzzy ARTMAP. More specifically, we show that only one out of these two tests is required; which test needs to be performed depends on the values of the vigilance parameter (rho) and the choice parameter (alpha) . Also, we show that for a specific relation of (rho) and (alpha) , the vigilance (rho) does not influence the training or performance phase of Fuzzy ART and Fuzzy ARTMAP. Finally, we refine a previously published upper bound on the size of the categories created during training in Fuzzy ART and Fuzzy ARTMAP.
ERIC Educational Resources Information Center
Richards, Lynn V.; Coventry, Kenny R.; Clibbens, John
2004-01-01
The effect of both geometric and extra-geometric factors on children's production of "in" is reported (free-response paradigm). Eighty children across four age groups (means 4;1, 5;5, 6;1, and 7;1) were shown video scenes of puppets placing real objects in various positions with reference to a bowl and a plate. Located objects were placed at three…
Vallortigara, Giorgio; Pagni, Piero; Sovrano, Valeria Anna
2004-04-01
Research has proved that disoriented children and nonhuman animals can reorient themselves using geometric and nongeometric features of the environment, showing conjoined use of both types of information to different degree depending on species and developmental level. Little is known of the neurobiological bases of these spatial reorientation processes. Here we take advantage of the neuroanatomical peculiarities of the visual system of birds (showing segregation of information between the two sides of the brain to a considerable degree) to investigate the way in which geometric and nongeometric information is encoded and used by the left and right hemispheres. Domestic chicks were trained binocularly in an environment with a distinctive geometry (a rectangular cage) with panels at the corners providing nongeometric cues. Between trials, chicks were passively disoriented to disable dead reckoning. When tested after removal of the panels, left-eyed chicks, but not right-eyed chicks, reoriented using the residual information provided by the geometry of the cage. When tested after removal of geometric information (i.e., in a square-shaped cage), both right- and left-eyed chicks reoriented using the residual nongeometric information provided by the panels. When trained binocularly with only geometric information, at test, left-eyed chicks reoriented better than right-eyed chicks. Finally, when geometric and nongeometric cues provided contradictory information, left-eyed chicks showed more reliance on geometric cues, whereas right-eyed chicks showed more reliance on nongeometric cues. The results suggest separate mechanisms for dealing with spatial reorientation problems, with the right hemisphere taking charge of large-scale geometry of the environment and with both hemispheres taking charge of local, nongeometric cues when available in isolation, but with a predominance of the left hemisphere when competition between geometric and non-geometric information occurs
Geometric versus finite element modeling current and future trends at Northrop
NASA Technical Reports Server (NTRS)
Bajaj, Shiv K.
1987-01-01
Engineering Automation at Northrop encompasses the various design and analytical phases of air vehicle development. Design systems addresses automation of engineering/tooling design and computer aided manufacturing processes. The analysis systems automate aeroelastic modeling and postprocessing analysis results. These systems interface with aircraft loft and geometric entities thru localized transfer techniques. However, total integration effort based on a geometric database nucleus with peripheral design, analytical and manufacturing systems is well underway. An outline of the present and future trends is presented to help channel the RPI effort in this direction.
Geometric modeling for computer aided design
NASA Technical Reports Server (NTRS)
Schwing, James L.
1993-01-01
Over the past several years, it has been the primary goal of this grant to design and implement software to be used in the conceptual design of aerospace vehicles. The work carried out under this grant was performed jointly with members of the Vehicle Analysis Branch (VAB) of NASA LaRC, Computer Sciences Corp., and Vigyan Corp. This has resulted in the development of several packages and design studies. Primary among these are the interactive geometric modeling tool, the Solid Modeling Aerospace Research Tool (smart), and the integration and execution tools provided by the Environment for Application Software Integration and Execution (EASIE). In addition, it is the purpose of the personnel of this grant to provide consultation in the areas of structural design, algorithm development, and software development and implementation, particularly in the areas of computer aided design, geometric surface representation, and parallel algorithms.
a Modular Geometric Model for Underwater Photogrammetry
NASA Astrophysics Data System (ADS)
Maas, H.-G.
2015-04-01
Underwater applications of photogrammetric measurement techniques usually need to deal with multimedia photogrammetry aspects, which are characterized by the necessity of handling optical rays that are broken at interfaces between optical media with different refrative indices according to Snell's Law. This so-called multimedia geometry has to be incorporated into geometric models in order to achieve correct measurement results. The paper shows a flexible yet strict geometric model for the handling of refraction effects on the optical path, which can be implemented as a module into photogrammetric standard tools such as spatial resection, spatial intersection, bundle adjustment or epipolar line computation. The module is especially well suited for applications, where an object in water is observed by cameras in air through one or more plane parallel glass interfaces, as it allows for some simplifications here.
Quantum state discrimination: A geometric approach
NASA Astrophysics Data System (ADS)
Markham, Damian; Miszczak, Jarosław Adam; Puchała, Zbigniew; Życzkowski, Karol
2008-04-01
We analyze the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view, this problem is equivalent to that of embedding a simplex of points whose distances are maximal with respect to the Bures distance (or trace distance). We derive upper and lower bounds for the trace distance and for the fidelity between two quantum states, which imply bounds for the Bures distance between the unitary orbits of both states. We thus show that, when analyzing minimal and maximal distances between states of fixed spectra, it is sufficient to consider diagonal states only. Hence when optimal discrimination is considered, given freedom up to unitary orbits, it is sufficient to consider diagonal states. This is illustrated geometrically in terms of Weyl chambers.
Finsler geometric extension of Einstein gravity
NASA Astrophysics Data System (ADS)
Pfeifer, Christian; Wohlfarth, Mattias N. R.
2012-03-01
We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle. These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties. A coupling procedure for matter fields to Finsler gravity completes our new theory that consistently becomes equivalent to Einstein gravity in the limit of metric geometry. We provide a precise geometric definition of observers and their measurements and show that the transformations, by means of which different observers communicate, form a groupoid that generalizes the usual Lorentz group. Moreover, we discuss the implementation of Finsler spacetime symmetries. We use our results to analyze a particular spacetime model that leads to Finsler geometric refinements of the linearized Schwarzschild solution.
Scale-invariant geometric random graphs.
Xie, Zheng; Rogers, Tim
2016-03-01
We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to influence zones that depend on node position in space and time, mimicking the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale invariance for geometric random graphs generated this way. Our analysis reveals a dichotomy between scale-free and Poisson distributions of in- and out-degree, the existence of a random number of hub nodes, high clustering, and unusual percolation behavior. These properties are similar to those of empirically observed web graphs. PMID:27078369
Topological minimally entangled states via geometric measure
NASA Astrophysics Data System (ADS)
Buerschaper, Oliver; García-Saez, Artur; Orús, Román; Wei, Tzu-Chieh
2014-11-01
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and toric code models on a torus with non-trivial topological partitions. Our calculations are done either quasi-exactly for small system sizes, or using the tensor network approach in Orús et al (arXiv:1406.0585) for large sizes. As a byproduct of our methods, we see that the minimisation of the geometric entanglement can also determine the number of Abelian quasiparticle excitations in a given model. The results in this paper provide a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states.
The classical geometrization of the electromagnetism
NASA Astrophysics Data System (ADS)
de Araujo Duarte, Celso
2015-08-01
Following the line of the history, if by one side the electromagnetic theory was consolidated on the 19th century, the emergence of the special and the general relativity theories on the 20th century opened possibilities of further developments, with the search for the unification of the gravitation and the electromagnetism on a single unified theory. Some attempts to the geometrization of the electromagnetism emerged in this context, where these first models resided strictly on a classical basis. Posteriorly, they were followed by more complete and embracing quantum field theories. The present work reconsiders the classical viewpoint, with the purpose of showing that at first-order of approximation the electromagnetism constitutes a geometric structure aside other phenomena as gravitation, and that magnetic monopoles do not exist at least up to this order of approximation. Even though being limited, the model is consistent and offers the possibility of an experimental test of validity.
The bouncing ball through a geometrical series
NASA Astrophysics Data System (ADS)
Flores, Sergio; Alfaro, Luis L.; Chavez, Juan E.; Bastarrachea, Aztlan; Hurtado, Jazmin
2008-10-01
The mathematical representation of the physical situation related to a bouncing ball on the floor is an important understanding difficulty for most of the students during the introductory mechanics and mathematics courses. The research group named Physics and mathematics in context from the University of Ciudad Juarez is concerned about the versatility in the change from a mathematical representation to the own physical context of any problem under a traditional instruction. In this case, the main idea is the association of the physical properties of the bouncing ball situation to the nearest mathematical model based on a geometrical series. The proposal of the cognitive development is based on a geometrical series that shows the time the ball takes to stop. In addition, we show the behavior of the ratio of the consecutive heights during the motion.
Robot arm geometric link parameter estimation
NASA Astrophysics Data System (ADS)
Hayati, S. A.
A general method for estimating serial link manipulator geometric parameter errors is proposed in this paper. The positioning accuracy of the end-effector may be increased significantly by updating the nominal link parameters in the control software to represent the physical system more accurately. The proposed method is applicable for serial link manipulators with any combination of revolute or prismatic joints, and is not limited to a specific measurement technique.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Chirality: a relational geometric-physical property.
Gerlach, Hans
2013-11-01
The definition of the term chirality by Lord Kelvin in 1893 and 1904 is analyzed by taking crystallography at that time into account. This shows clearly that chirality is a relational geometric-physical property, i.e., two relations between isometric objects are possible: homochiral or heterochiral. In scientific articles the relational term chirality is often mistaken for the two valued measure for the individual (absolute) sense of chirality, an arbitrary attributive term.
Geometric simulation of structures containing rigid units
NASA Astrophysics Data System (ADS)
Wells, Stephen
2005-03-01
Much insight into the behaviour of the framework silicates can be obtained from the Rigid Unit model. I review results from geometric analyses [1] of framework structures, quantifying the significance of rigid unit motion in thermal disorder and in defect accomodation, and from a method of simulation [2,3] based on a whole-body `geometric potential' rather than on interatomic potentials. I show the application of the geometric potential to the symmetry-constrained generation of hypothetical zeolite frameworks [4], and to the rapid generation of protein conformations using insights from rigid cluster decomposition [5]. 1. Wells, Dove and Tucker, Journal of Applied Crystallography, 37:536--544 (2004). 2. G.D. Gatta and S.A. Wells, Phys. Chem. Min. 31:1--10 (2004). 3. A. Sartbaeva, S. A. Wells, S. A. T. Redfern, J. Phys.: Condens. Matter 16, 8173 (2004) 4. M. M. J. Treacy, I. Rivin, E. Balkovsky, K. H. Randall and M. D. Foster, Micropor. Mesopor. Mater. 74, 121-132 (2004). 5. M.F. Thorpe, Ming Lei, A.J. Rader, Donald J. Jacobs, and Leslie A. Kuhn, Journal of Molecular Graphics and Modelling 19, 1:60 - 69, (2001).
Salt Bridges: Geometrically Specific, Designable Interactions
Donald, Jason E.; Kulp, Daniel W.; DeGrado, William F.
2010-01-01
Salt bridges occur frequently in proteins, providing conformational specificity and contributing to molecular recognition and catalysis. We present a comprehensive analysis of these interactions in protein structures by surveying a large database of protein structures. Salt bridges between Asp or Glu and His, Arg, or Lys display extremely well-defined geometric preferences. Several previously observed preferences are confirmed and others that were previously unrecognized are discovered. Salt bridges are explored for their preferences for different separations in sequence and in space, geometric preferences within proteins and at protein-protein interfaces, cooperativity in networked salt bridges, inclusion within metal-binding sites, preference for acidic electrons, apparent conformational side chain entropy reduction upon formation, and degree of burial. Salt bridges occur far more frequently between residues at close than distant sequence separations, but at close distances there remain strong preferences for salt bridges at specific separations. Specific types of complex salt bridges, involving three or more members, are also discovered. As we observe a strong relationship between the propensity to form a salt bridge and the placement of salt-bridging residues in protein sequences, we discuss the role that salt bridges might play in kinetically influencing protein folding and thermodynamically stabilizing the native conformation. We also develop a quantitative method to select appropriate crystal structure resolution and B-factor cutoffs. Detailed knowledge of these geometric and sequence dependences should aid de novo design and prediction algorithms. PMID:21287621
Salt bridges: geometrically specific, designable interactions.
Donald, Jason E; Kulp, Daniel W; DeGrado, William F
2011-03-01
Salt bridges occur frequently in proteins, providing conformational specificity and contributing to molecular recognition and catalysis. We present a comprehensive analysis of these interactions in protein structures by surveying a large database of protein structures. Salt bridges between Asp or Glu and His, Arg, or Lys display extremely well-defined geometric preferences. Several previously observed preferences are confirmed, and others that were previously unrecognized are discovered. Salt bridges are explored for their preferences for different separations in sequence and in space, geometric preferences within proteins and at protein-protein interfaces, co-operativity in networked salt bridges, inclusion within metal-binding sites, preference for acidic electrons, apparent conformational side chain entropy reduction on formation, and degree of burial. Salt bridges occur far more frequently between residues at close than distant sequence separations, but, at close distances, there remain strong preferences for salt bridges at specific separations. Specific types of complex salt bridges, involving three or more members, are also discovered. As we observe a strong relationship between the propensity to form a salt bridge and the placement of salt-bridging residues in protein sequences, we discuss the role that salt bridges might play in kinetically influencing protein folding and thermodynamically stabilizing the native conformation. We also develop a quantitative method to select appropriate crystal structure resolution and B-factor cutoffs. Detailed knowledge of these geometric and sequence dependences should aid de novo design and prediction algorithms.
Evolutionary Optimization of a Geometrically Refined Truss
NASA Technical Reports Server (NTRS)
Hull, P. V.; Tinker, M. L.; Dozier, G. V.
2007-01-01
Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.
Interacting geometric priors for robust multimodel fitting.
Pham, Trung Thanh; Chin, Tat-Jun; Schindler, Konrad; Suter, David
2014-10-01
Recent works on multimodel fitting are often formulated as an energy minimization task, where the energy function includes fitting error and regularization terms, such as low-level spatial smoothness and model complexity. In this paper, we introduce a novel energy with high-level geometric priors that consider interactions between geometric models, such that certain preferred model configurations may be induced.We argue that in many applications, such prior geometric properties are available and should be fruitfully exploited. For example, in surface fitting to point clouds, the building walls are usually either orthogonal or parallel to each other. Our proposed energy function is useful in dealing with unknown distributions of data errors and outliers, which are often the factors leading to biased estimation. Furthermore, the energy can be efficiently minimized using the expansion move method. We evaluate the performance on several vision applications using real data sets. Experimental results show that our method outperforms the state-of-the-art methods without significant increase in computation.
A Geometric Theory of Nonlinear Morphoelastic Shells
NASA Astrophysics Data System (ADS)
Sadik, Souhayl; Angoshtari, Arzhang; Goriely, Alain; Yavari, Arash
2016-08-01
Many thin three-dimensional elastic bodies can be reduced to elastic shells: two-dimensional elastic bodies whose reference shape is not necessarily flat. More generally, morphoelastic shells are elastic shells that can remodel and grow in time. These idealized objects are suitable models for many physical, engineering, and biological systems. Here, we formulate a general geometric theory of nonlinear morphoelastic shells that describes both the evolution of the body shape, viewed as an orientable surface, as well as its intrinsic material properties such as its reference curvatures. In this geometric theory, bulk growth is modeled using an evolving referential configuration for the shell, the so-called material manifold. Geometric quantities attached to the surface, such as the first and second fundamental forms, are obtained from the metric of the three-dimensional body and its evolution. The governing dynamical equations for the body are obtained from variational consideration by assuming that both fundamental forms on the material manifold are dynamical variables in a Lagrangian field theory. In the case where growth can be modeled by a Rayleigh potential, we also obtain the governing equations for growth in the form of kinetic equations coupling the evolution of the first and the second fundamental forms with the state of stress of the shell. We apply these ideas to obtain stress-free growth fields of a planar sheet, the time evolution of a morphoelastic circular cylindrical shell subject to time-dependent internal pressure, and the residual stress of a morphoelastic planar circular shell.
Landsat-5 bumper-mode geometric correction
Storey, J.C.; Choate, Michael J.
2004-01-01
The Landsat-5 Thematic Mapper (TM) scan mirror was switched from its primary operating mode to a backup mode in early 2002 in order to overcome internal synchronization problems arising from long-term wear of the scan mirror mechanism. The backup bumper mode of operation removes the constraints on scan start and stop angles enforced in the primary scan angle monitor operating mode, requiring additional geometric calibration effort to monitor the active scan angles. It also eliminates scan timing telemetry used to correct the TM scan geometry. These differences require changes to the geometric correction algorithms used to process TM data. A mathematical model of the scan mirror's behavior when operating in bumper mode was developed. This model includes a set of key timing parameters that characterize the time-varying behavior of the scan mirror bumpers. To simplify the implementation of the bumper-mode model, the bumper timing parameters were recast in terms of the calibration and telemetry data items used to process normal TM imagery. The resulting geometric performance, evaluated over 18 months of bumper-mode operations, though slightly reduced from that achievable in the primary operating mode, is still within the Landsat specifications when the data are processed with the most up-to-date calibration parameters.
Geometrical branching model: Correlations and jets
NASA Astrophysics Data System (ADS)
Hwa, Rudolph C.
1988-04-01
A geometrical model for multiparticle production at low as well as high pT is discussed. Below the threshold of substantial production of jets, the model has geometrical scaling and Koba-Nielsen-Olesen scaling, the latter being a result of Furry branching in multiplicity distribution at each impact parameter. Above the threshold the production of jets is explicitly taken into account by use of perturbative QCD. The separation into soft and hard components is done in the eikonal formalism consistent with unitarity. Geometrical scaling defines the soft component of the eikonal function. The hard component is related to the jet-production cross section; the pT cutoff is not chosen arbitrarily, but is to be determined by σel and σtot. Forward-backward multiplicity correlation can be calculated separately for the cases of no jets and with jets. The emphasis in this paper is on the formalism of the model. The procedure to determine the multiplicity distribution at all s is discussed.
NASA Astrophysics Data System (ADS)
Goswami, Himangshu Prabal; Agarwalla, Bijay Kumar; Harbola, Upendra
2016-05-01
Cyclic Pancharatnam-Berry (PB) and adiabatic noncyclic geometric (ANG) effects are investigated in a single electron orbital system connected to two metal contacts with externally driven chemical potential and/or temperatures. The PB contribution doesn't affect the density matrix evolution, but has a quantitative effect on the statistics (fluctuations) of electron transfer. The ANG contribution, on the other hand, affects the net flux across the junction. Unlike the PB, the ANG contribution is nonzero when two parameters are identically driven. Closed analytical expressions are derived for the ANG contribution to the flux, and the PB contribution to the first two leading order fluctuations. Fluctuations can be modified by manipulating the relative phases of the drivings. Interestingly, we find that the fluctuations of the pumped charge do not satisfy the steady state fluctuation theorem in presence of nonzero geometric contribution, but can be recovered for a vanishing geometric contribution even in presence of the external driving.
NASA Astrophysics Data System (ADS)
Schmitz, Martin; Bryngdahl, Olof
1998-07-01
A concept is presented for the analysis of diffractive cylindrical lenses with apertures larger than 100 wavelengths which are denoted as large geometrical apertures throughout this paper. The transmitted field of a cylindrical lens is calculated by the use of rigorous electromagnetic diffraction theory. Large geometrical apertures are subdivided into smaller overlapping areas that are treated in sequence. The wave propagation from the lens plane to the focal plane is calculated with the spectrum of plane waves. A design concept is presented which ensures that the performance of diffractive cylindrical lenses with high numerical apertures (NA≥0.3) is almost independent of the polarization of the illuminating light. The design concept is based on the local grating model in combination with the phase detour principle. As an example we design and analyze a F/0.5 cylindrical lens (NA=0.71) with a geometrical aperture of 600 wavelengths.
Geometrization of the physics with teleparallelism. II. Towards a fully geometric Dirac equation
NASA Astrophysics Data System (ADS)
Vargas, José G.; Torr, Douglas G.; Lecompte, Alvaro
1992-04-01
In an accompanying paper (I), it is shown that the basic equations of the theory of Lorentzian connections with teleparallelism (TP) acquire standard forms of physical field equations upon removal of the constraints represented by the Bianchi identities. A classical physical theory results that supersedes general relativity and Maxwell-Lorentz electrodynamics if the connection is viewed as Finslerian. The theory also encompasses a short-range, strong, classical interaction. It has, however, an open end, since the source side of the torsion field equation is not geometric. In this paper, Kaehler's partial geometrization of the Dirac equation is taken as a starting point for the development of fully geometric Dirac equations via the correspondence principle given in I. For this purpose, Kaehler's calculus (where the spinors are differential forms) is generalized so that it also applies when the torsion is not zero. The point is then made that the forms can take values in tangent Clifford algebras rather than in tensor algebras. The basic “Eigenschaft” of the Kaehler calculus also is examined from the physical perspective of dimensional analysis. Geometric Dirac equations of great structural simplicity are finally inferred from the standard Dirac equation by using the aforementioned correspondence principle. The realm of application of the Dirac theory is thus enriched in principle, though only at an abstract level at this point: the standard spinors, which are scalar-valued forms in the Kaehler version of that theory, become Clifford-valued. In addition, the geometrization of the Dirac equation implies a geometrization of the Dirac current. When this current is replaced in the field equations for the torsion, the theory of Paper I becomes fully geometric.
Geometric Approaches to Quadratic Equations from Other Times and Places.
ERIC Educational Resources Information Center
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Identifying and Fostering Higher Levels of Geometric Thinking
ERIC Educational Resources Information Center
Škrbec, Maja; Cadež, Tatjana Hodnik
2015-01-01
Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…
Children's Use of Geometric Information in Mapping Tasks
ERIC Educational Resources Information Center
Vasilyeva, Marina; Bowers, Edmond
2006-01-01
Accumulating evidence, particularly from research using the disorientation technique, demonstrates early sensitivity to geometric properties of space. However, it is not known whether children can use geometric cues to interpret a map. The current study examined how 3- to 6-year-olds use geometric features of layouts in solving mapping tasks.…
Optimization of biotechnological systems through geometric programming
Marin-Sanguino, Alberto; Voit, Eberhard O; Gonzalez-Alcon, Carlos; Torres, Nestor V
2007-01-01
Background In the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM) was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary. Results A new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA) system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency. Conclusion GMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into the GMA form. Thus
Geometrical confining effects in compression molding of co-continuous polymer blends.
Zhang, Wei; Deodhar, Sarang; Yao, Donggang
2010-06-01
Polymer blending is a versatile method for production of co-continuous porous materials. While numerous studies have been performed to elucidate the thermal annealing effects on the bulk structure, the effect of geometrical confinement is little understood. In the present work, possible effects from geometrical confinement during in-mold annealing were explored. A 50/50 wt.% poly (lactic acid)/polystyrene (PLA/PS) blend was compression molded and annealed between two parallel plates without being confined circumferentially during the compression molding process. Different conditions for geometrical confinement, including varied gap size and compression ratio (initial to final thickness ratio), as well as modified surface properties, were employed. The experimental results indicated that the gap size played a profound role in affecting the structural development; the phase size near the mold surface was smaller than away from the surface. The actual phase structure and the resulting gradient in pore size were further affected by the mold surface properties. Additionally, the compression ratio was found to affect the morphological development especially near the mold surface. At a high compression ratio, a thin layer of PLA was formed immediately during compression. The thickness of this layer either grew or reduced in size depending on the mold surface properties. Understanding of these geometrical confining effects and implementing them in processing may lead to the development of innovative porous materials.
Aerospace plane guidance using geometric control theory
NASA Technical Reports Server (NTRS)
Van Buren, Mark A.; Mease, Kenneth D.
1990-01-01
A reduced-order method employing decomposition, based on time-scale separation, of the 4-D state space in a 2-D slow manifold and a family of 2-D fast manifolds is shown to provide an excellent approximation to the full-order minimum-fuel ascent trajectory. Near-optimal guidance is obtained by tracking the reduced-order trajectory. The tracking problem is solved as regulation problems on the family of fast manifolds, using the exact linearization methodology from nonlinear geometric control theory. The validity of the overall guidance approach is indicated by simulation.
Geometric Aspects of Biological Sequence Comparison
Stojmirović, Aleksandar
2009-01-01
Abstract We introduce a geometric framework suitable for studying the relationships among biological sequences. In contrast to previous works, our formulation allows asymmetric distances (quasi-metrics), originating from uneven weighting of strings, which may induce non-trivial partial orders on sets of biosequences. The distances considered are more general than traditional generalized string edit distances. In particular, our framework enables non-trivial conversion between sequence similarities, both local and global, and distances. Our constructions apply to a wide class of scoring schemes and require much less restrictive gap penalties than the ones regularly used. Numerous examples are provided to illustrate the concepts introduced and their potential applications. PMID:19361329
Geometric derivation of the chronometric redshift.
Segal, I E
1993-01-01
The chronometric redshift-distance relation z = tan 2(1/2rho), where rho is the distance in radians in the Einstein metric, is derived by an elementary geometric analysis comparable to that in traditional analysis of the expanding universe model. The differential dTt of Einstein time evolution Tt through time t, as applied to the local Minkowski coordinates x, takes the form sec2(1/2t). At the point of observation t = rho, implying that for a sufficiently localized source, observed wave lengths are a factor of sec2(1/2rho) greater than the corresponding emitted wave lengths. PMID:11607440
Geometrical Wake of a Smooth Flat Collimator
Stupakov, G.V.; /SLAC
2011-09-09
A transverse geometrical wake generated by a beam passing through a smooth flat collimator with a gradually varying gap between the upper and lower walls is considered. Based on generalization of the approach recently developed for a smooth circular taper we reduce the electromagnetic problem of the impedance calculation to the solution of two much simpler static problems - a magnetostatic and an electrostatic ones. The solution shows that in the limit of not very large frequencies, the impedance increases with the ratio h/d where h is the width and d is the distance between the collimating jaws. Numerical results are presented for the NLC Post Linac collimator.
State-Space Regularization: Geometric Theory
Chavent, G.; Kunisch, K.
1998-05-15
Regularization of nonlinear ill-posed inverse problems is analyzed for a class of problems that is characterized by mappings which are the composition of a well-posed nonlinear and an ill-posed linear mapping. Regularization is carried out in the range of the nonlinear mapping. In applications this corresponds to the state-space variable of a partial differential equation or to preconditioning of data. The geometric theory of projection onto quasi-convex sets is used to analyze the stabilizing properties of this regularization technique and to describe its asymptotic behavior as the regularization parameter tends to zero.
The minimal geometric deformation approach extended
NASA Astrophysics Data System (ADS)
Casadio, R.; Ovalle, J.; da Rocha, Roldão
2015-11-01
The minimal geometric deformation approach was introduced in order to study the exterior spacetime around spherically symmetric self-gravitating systems, such as stars or similar astrophysical objects, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application, and a new solution that is potentially useful to describe stars in the brane-world is also presented.
Some Geometrical Aspects of M-Theory
NASA Astrophysics Data System (ADS)
de Azcárraga, José A.; Izquierdo, José M.
2008-06-01
Some geometrical aspects of super-p-brane theory, M-theory, and their connection with supergravity, are reviewed. In particular, the different fractions of preserved supersymmetries are discussed both from the algebraic and the supergravity solutions point of view. We also review the `preon conjecture' according to which states preserving a 31/32 fraction of supersymmetries would be the building blocks of M-theory, and on the failed attempts made so far to find these states in terms of supergravity solutions.
Geometric derivation of the quantum speed limit
Jones, Philip J.; Kok, Pieter
2010-08-15
The Mandelstam-Tamm and Margolus-Levitin inequalities play an important role in the study of quantum-mechanical processes in nature since they provide general limits on the speed of dynamical evolution. However, to date there has been only one derivation of the Margolus-Levitin inequality. In this paper, alternative geometric derivations for both inequalities are obtained from the statistical distance between quantum states. The inequalities are shown to hold for unitary evolution of pure and mixed states, and a counterexample to the inequalities is given for evolution described by completely positive trace-preserving maps. The counterexample shows that there is no quantum speed limit for nonunitary evolution.
On the minimum of independent geometrically distributed random variables
NASA Technical Reports Server (NTRS)
Ciardo, Gianfranco; Leemis, Lawrence M.; Nicol, David
1994-01-01
The expectations E(X(sub 1)), E(Z(sub 1)), and E(Y(sub 1)) of the minimum of n independent geometric, modifies geometric, or exponential random variables with matching expectations differ. We show how this is accounted for by stochastic variability and how E(X(sub 1))/E(Y(sub 1)) equals the expected number of ties at the minimum for the geometric random variables. We then introduce the 'shifted geometric distribution' and show that there is a unique value of the shift for which the individual shifted geometric and exponential random variables match expectations both individually and in the minimums.
Finite octree meshing through topologically driven geometric operators
NASA Technical Reports Server (NTRS)
Grice, Kurt R.
1987-01-01
The octree technique is developed into the finite octree, and an overview is given. Modeler requirements are given. The octree discretization is discussed along with geometric communication operators. Geometric communication operators returning topological associativity and geometric communication operators returning spatial data are also discussed and illustrated. The advantages are given of the boundary representation and of geometric communication operators. The implementation plays an important role in the integration with a variety of geometric modelers. The capabilities of closed loop processes within a complete finite element system are presented.
A geometric approach to direct minimization
NASA Astrophysics Data System (ADS)
van Voorhis, Troy; Head-Gordon, Martin
The approach presented, geometric direct minimization (GDM), is derived from purely geometrical arguments, and is designed to minimize a function of a set of orthonormal orbitals. The optimization steps consist of sequential unitary transformations of the orbitals, and convergence is accelerated using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) approach in the iterative subspace, together with a diagonal approximation to the Hessian for the remaining degrees of freedom. The approach is tested by implementing the solution of the self-consistent field (SCF) equations and comparing results with the standard direct inversion in the iterative subspace (DIIS) method. It is found that GDM is very robust and converges in every system studied, including several cases in which DIIS fails to find a solution. For main group compounds, GDM convergence is nearly as rapid as DIIS, whereas for transition metalcontaining systems we find that GDM is significantly slower than DIIS. A hybrid procedure where DIIS is used for the first several iterations and GDM is used thereafter is found to provide a robust solution for transition metal-containing systems.
Geometric representation of fundamental particles' inertial mass
Schachter, L.; Spencer, James
2015-07-22
A geometric representation of the (N = 279) masses of quarks, leptons, hadrons and gauge bosons was introduced by employing a Riemann Sphere facilitating the interpretation of the N masses in terms of a single particle, the Masson, which might be in one of the N eigen-states. Geometrically, its mass is the radius of the Riemann Sphere. Dynamically, its derived mass is near the mass of the nucleon regardless of whether it is determined from all N particles of only the hadrons, the mesons or the baryons separately. Ignoring all the other properties of these particles, it is shown that the eigen-values, the polar representation θ_{ν} of the masses on the Sphere, satisfy the symmetry θ_{ν} + θ_{N+1-ν} = π within less than 1% relative error. In addition, these pair correlations include the pairs θ_{γ} + θ_{top} ≃ π and θ_{gluon} + θ_{H} ≃ π as well as pairing the weak gauge bosons with the three neutrinos.
Translating cosmological special relativity into geometric algebra
NASA Astrophysics Data System (ADS)
Horn, Martin Erik
2012-11-01
Geometric algebra and Clifford algebra are important tools to describe and analyze the physics of the world we live in. Although there is enormous empirical evidence that we are living in four dimensional spacetime, mathematical worlds of higher dimensions can be used to present the physical laws of our world in an aesthetical and didactical more appealing way. In physics and mathematics education we are therefore confronted with the question how these high dimensional spaces should be taught. But as an immediate confrontation of students with high dimensional compactified spacetimes would expect too much from them at the beginning of their university studies, it seems reasonable to approach the mathematics and physics of higher dimensions step by step. The first step naturally is the step from four dimensional spacetime of special relativity to a five dimensional spacetime world. As a toy model for this artificial world cosmological special relativity, invented by Moshe Carmeli, can be used. This five dimensional non-compactified approach describes a spacetime which consists not only of one time dimension and three space dimensions. In addition velocity is regarded as a fifth dimension. This model very probably will not represent physics correctly. But it can be used to discuss and analyze the consequences of an additional dimension in a clear and simple way. Unfortunately Carmeli has formulated cosmological special relativity in standard vector notation. Therefore a translation of cosmological special relativity into the mathematical language of Grassmann and Clifford (Geometric algebra) is given and the physics of cosmological special relativity is discussed.
Nanoparticle fabrication by geometrically confined nanosphere lithography
NASA Astrophysics Data System (ADS)
Denomme, Ryan C.; Iyer, Krishna; Kreder, Michael; Smith, Brendan; Nieva, Patricia M.
2013-07-01
Arrays of metal nanoparticles, typically gold or silver, exhibit localized surface plasmon resonance, a phenomenon that has many applications, such as chemical and biological sensing. However, fabrication of metal nanoparticle arrays with high uniformity and repeatability, at a reasonable cost, is difficult. Nanosphere lithography (NSL) has been used before to produce inexpensive nanoparticle arrays through the use of monolayers of self-assembled microspheres as a deposition mask. However, control over the size and location of the arrays, as well as uniformity over large areas is poor, thus limiting its use to research purposes. In this paper, a new NSL method, called here geometrically confined NSL (GCNSL), is presented. In GCNSL, microsphere assembly is confined to geometric patterns defined in photoresist, allowing high-precision and large-scale nanoparticle patterning while still remaining low cost. Using this new method, it is demonstrated that 400 nm polystyrene microspheres can be assembled inside of large arrays of photoresist patterns. Results show that optimal microsphere assembly is achieved with long and narrow rectangular photoresist patterns. The combination of microsphere monolayers and photoresist patterns is then used as a deposition mask to produce silver nanoparticles at precise locations on the substrate with high uniformity, repeatability, and quality.
Geometric and Radiometric Evaluation of Rasat Images
NASA Astrophysics Data System (ADS)
Cam, Ali; Topan, Hüseyin; Oruç, Murat; Özendi, Mustafa; Bayık, Çağlar
2016-06-01
RASAT, the second remote sensing satellite of Turkey, was designed and assembled, and also is being operated by TÜBİTAK Uzay (Space) Technologies Research Institute (Ankara). RASAT images in various levels are available free-of-charge via Gezgin portal for Turkish citizens. In this paper, the images in panchromatic (7.5 m GSD) and RGB (15 m GSD) bands in various levels were investigated with respect to its geometric and radiometric characteristics. The first geometric analysis is the estimation of the effective GSD as less than 1 pixel for radiometrically processed level (L1R) of both panchromatic and RGB images. Secondly, 2D georeferencing accuracy is estimated by various non-physical transformation models (similarity, 2D affine, polynomial, affine projection, projective, DLT and GCP based RFM) reaching sub-pixel accuracy using minimum 39 and maximum 52 GCPs. The radiometric characteristics are also investigated for 8 bits, estimating SNR between 21.8-42.2, and noise 0.0-3.5 for panchromatic and MS images for L1R when the sea is masked to obtain the results for land areas. The analysis show that RASAT images satisfies requirements for various applications. The research is carried out in Zonguldak test site which is mountainous and partly covered by dense forest and urban areas.
Geometrical analysis of cytochrome c unfolding
NASA Astrophysics Data System (ADS)
Urie, Kristopher G.; Pletneva, Ekaterina; Gray, Harry B.; Winkler, Jay R.; Kozak, John J.
2011-01-01
A geometrical model has been developed to study the unfolding of iso-1 cytochrome c. The model draws on the crystallographic data reported for this protein. These data were used to calculate the distance between specific residues in the folded state, and in a sequence of extended states defined by n = 3, 5, 7, 9, 11, 13, and 15 residue units. Exact calculations carried out for each of the 103 residues in the polypeptide chain demonstrate that different regions of the chain have different unfolding histories. Regions where there is a persistence of compact structures can be identified, and this geometrical characterization is fully consistent with analyses of time-resolved fluorescence energy-transfer (TrFET) data using dansyl-derivatized cysteine side-chain probes at positions 39, 50, 66, 85, and 99. The calculations were carried out assuming that different regions of the polypeptide chain unfold synchronously. To test this assumption, lattice Monte Carlo simulations were performed to study systematically the possible importance of asynchronicity. Calculations show that small departures from synchronous dynamics can arise if displacements of residues in the main body of the chain are much more sluggish than near-terminal residues.
Processing geometric representations on SIMD computers
Hung, Y.
1988-01-01
This thesis contributes to designing parallel algorithms to process border and linear quadtree representations on mesh-connected computers (MCCs) and hypercubes. This thesis consists of two parts. The first part studies some primitive operations on mesh-connected computers and hypercubes. These include various routing tasks and several versions of the parallel prefix algorithms. It is shown how general routings can be done in O(n) time on an n {times} n mesh and O(d{sup 2}) on a d-dimensional hypercube (d-cube). Also presented are optimal routing algorithms for some classes of permutation routings. For the parallel prefix problem, the author describes how the initial prefixes can be computed efficiently when the data are mapped into the MCC or the hypercube in some specific manners. The second part deals with processing border codes and linear quadtrees. These include generating border codes and linear quadtrees from a given image, reconstructing the image from its geometric representations, computing various geometric properties, answering the point-in-region query, performing set operations, etc. For linear quadtrees, algorithms are also designed for finding neighbors of equal or larger size for all nodes simultaneously. A connected component-labeling algorithm is also presented.
A Geometric Theory of Growth Mechanics
NASA Astrophysics Data System (ADS)
Yavari, Arash
2010-12-01
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. The time dependence of the metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and “shape”. We show that the time dependency of the material metric will affect the energy balance and the entropy production inequality; both the energy balance and the entropy production inequality have to be modified. We then obtain the governing equations covariantly by postulating invariance of energy balance under time-dependent spatial diffeomorphisms. We use the principle of maximum entropy production in deriving an evolution equation for the material metric. In the case of isotropic growth, we find those growth distributions that do not result in residual stresses. We then look at Lagrangian field theory of growing elastic solids. We will use the Lagrange-d’Alembert principle with Rayleigh’s dissipation functions to derive the governing equations. We make an explicit connection between our geometric theory and the conventional multiplicative decomposition of the deformation gradient, F= F e F g, into growth and elastic parts. We linearize the nonlinear theory and derive a linearized theory of growth mechanics. Finally, we obtain the stress-free growth distributions in the linearized theory.
Geometrically nonlinear behavior of piezoelectric laminated plates
NASA Astrophysics Data System (ADS)
Rabinovitch, Oded
2005-08-01
The geometrically nonlinear behavior of piezo-laminated plates actuated with isotropic or anisotropic piezoelectric layers is analytically investigated. The analytical model is derived using the variational principle of virtual work along with the lamination and plate theories, the von Karman large displacement and moderate rotation kinematic relations, and the anisotropic piezoelectric constitutive laws. A solution strategy that combines the approach of the method of lines, the advantages of the finite element concept, and the variational formulation is developed. This approach yields a set of nonlinear ordinary differential equations with nonlinear boundary conditions, which are solved using the multiple-shooting method. Convergence and verification of the model are examined through comparison with linear and nonlinear results of other approximation methods. The nonlinear response of two active plate structures is investigated numerically. The first plate is actuated in bending using monolithic piezoceramic layers and the second one is actuated in twist using macro-fiber composites. The results quantitatively reveal the complicated in-plane stress state associated with the piezoelectric actuation and the geometrically nonlinear coupling of the in-plane and out-of-plane responses of the plate. The influence of the nonlinear effects ranges from significant stiffening in certain combinations of electrical loads and boundary conditions to amplifications of the induced deflections in others. The paper closes with a summary and conclusions.
Geometrical basis for the Standard Model
Potter, F. )
1994-02-01
The robust character of the Standard Model is confirmed. Examination of its geometrical basis in three equivalent internal symmetry spaces - the unitary plane C[sup 2], the quaternion space Q, and the real space R[sup 4] - as well as the real space R[sup 3] uncovers mathematical properties that predict the physical properties of leptons and quarks. The finite rotational subgroups of the gauge group SU(2)[sub L] [times] U(1)[sub Y] generate exactly three lepton families and four quark families and reveal how quarks and leptons are related. Among the physical properties explained are the mass ratios of the six leptons and eight quarks, the origin of the left-handed preference by the weak interaction, the geometrical source of color symmetry, and the zero neutrino masses. The (u,d) and (c,s) quark families team together to satisfy the triangle anomaly cancellation with the electron family, while the other families pair one-to-one for cancellation. The spontaneously broken symmetry is discrete and needs no Higgs mechanism. Predictions include all massless neutrinos, the top quark at 160 GeV/c[sup 2], the b[prime] quark at 80 GeV/c[sup 2], and the t[prime] quark at 2600 GeV/c[sup 2].
Geometric control of myogenic cell fate
de Juan-Pardo, Elena M; Hoang, Mike Bao-Trong; Conboy, Irina M
2006-01-01
This work combines expertise in stem cell biology and bioengineering to define the system for geometric control of proliferation and differentiation of myogenic progenitor cells. We have created an artificial niche of myogenic progenitor cells, namely, modified extracellular matrix (ECM) substrates with spatially embedded growth or differentiation factors (GF, DF) that predictably direct muscle cell fate in a geometric pattern. Embedded GF and DF signal progenitor cells from specifically defined areas on the ECM successfully competed against culture media for myogenic cell fate determination at a clearly defined boundary. Differentiation of myoblasts into myotubes is induced in growth-promoting medium, myotube formation is delayed in differentiation-promoting medium, and myogenic cells, at different stages of proliferation and differentiation, can be induced to coexist adjacently in identical culture media. This method can be used to identify molecular interactions between cells in different stages of myogenic differentiation, which are likely to be important determinants of tissue repair. The designed ECM niches can be further developed into a vehicle for transplantation of myogenic progenitor cells maintaining their regenerative potential. Additionally, this work may also serve as a general model to engineer synthetic cellular niches to harness the regenerative potential of organ stem cells. PMID:17722537