Geometric Phases, Noise and Non-adiabatic Effects in Multi-level Superconducting Systems
NASA Astrophysics Data System (ADS)
Berger, S.; Pechal, M.; Abdumalikov, A. A.; Steffen, L.; Fedorov, A.; Wallraff, A.; Filipp, S.
2012-02-01
Geometric phases depend neither on time nor on energy, but only on the trajectory of the quantum system in state space. In previous studies [1], we have observed them in a Cooper pair box qubit, a system with large anharmonicity. We now make use of a superconducting transmon-type qubit with low anharmonicity to study geometric phases in a multi-level system. We measure the contribution of the second excited state to the geometric phase and find very good agreement with theory treating higher levels perturbatively. Furthermore, we quantify non-adiabatic corrections by decreasing the manipulation time in order to optimize our geometric gate. Geometric phases have also been shown to be resilient against adiabatic field fluctuations [2]. Here, we analyze the effect of artificially added noise on the geometric phase for different system trajectories. [1] P. J. Leek et al., Science 318, 1889 (2007) [2] S. Filipp et al., Phys. Rev. Lett. 102, 030404 (2009)
Wang, Li; Tu, Tao; Gong, Bo; Zhou, Cheng; Guo, Guang-Can
2016-01-01
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. PMID:26738875
NASA Astrophysics Data System (ADS)
Wang, Li; Tu, Tao; Gong, Bo; Zhou, Cheng; Guo, Guang-Can
2016-01-01
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.
Wang, Li; Tu, Tao; Gong, Bo; Zhou, Cheng; Guo, Guang-Can
2016-01-01
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. PMID:26738875
Non-adiabatic effect on quantum pumping
NASA Astrophysics Data System (ADS)
Uchiyama, Chikako
2014-03-01
We study quantum pumping for an anharmonic junction model which interacts with two kinds of bosonic environments. We provide an expression for the quantum pumping under a piecewise modulation of environmental temperatures with including non-adiabatic effect under Markovian approximation. The obtained formula is an extension of the one expressed with the geometrical phase(Phys. Rev. Lett. 104,170601 (2010)). This extension shows that the quantum pumping depends on the initial condition of the anharmonic junction just before the modulation, as well as the characteristic environmental parameters such as interaction strength and cut-off frequencies of spectral density other than the conditions of modulation. We clarify that the pumping current including non-adiabatic effect can be larger than that under the adiabatic condition. This means that we can find the optimal condition of the current by adjusting these parameters. (The article has been submitted as http://arxiv.org/submit/848201 and will be appeared soon.) This work is supported by a Grant-in-Aid for Scientific Research (B) (KAKENHI 25287098).
Geometric phase shifting digital holography.
Jackin, Boaz Jessie; Narayanamurthy, C S; Yatagai, Toyohiko
2016-06-01
A new phase shifting digital holographic technique using a purely geometric phase in Michelson interferometric geometry is proposed. The geometric phase in the system does not depend upon either optical path length or wavelength, unlike dynamic phase. The amount of geometric phase generated is controllable through a rotating wave plate. The new approach has unique features and major advantages in holographic measurement of transparent and reflecting three-dimensional (3D) objects. Experimental results on surface shape measurement and imaging of 3D objects are presented using the proposed method. PMID:27244436
Geometrical Phases in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
NASA Astrophysics Data System (ADS)
Alijah, Alexander; Kokoouline, Viatcheslav
2015-10-01
Vibrational energies and wave functions of the triplet state of the H3+ ion have been determined. In the calculations, the ground and first excited triplet electronic states are included as well as the most important part of the non-Born-Oppenheimer coupling between them. The diabatization procedure proposed by Longuet-Higgins is then applied to transform the two adiabatic ab initio potential energy surfaces of the triplet-H3+ state into a 2 × 2 diabatic matrix. The diabatization takes into account the effect of the geometrical phase due to the conical intersection between the two adiabatic potential surfaces. The results are compared to the calculation involving only the lowest adiabatic potential energy surface of the triplet-H3+ ion and neglecting the geometrical phase. The energy difference between results with and without the non-adiabatic coupling and the geometrical phase is about one wave number for the lowest vibrational levels.
Nonlinear effects generation in non-adiabatically tapered fibres
NASA Astrophysics Data System (ADS)
Palací, Jesús; Mas, Sara; Monzón-Hernández, David; Martí, Javier
2015-12-01
Nonlinear effects are observed in a non-adiabatically tapered optical fibre. The designed structure allows for the introduction of self-phase modulation, which is observed through pulse breaking and spectral broadening, in approximately a centimetre of propagation using a commercial telecom laser. These devices are simple to fabricate and suitable to generate and control a variety of nonlinear effects in practical applications because they do not experience short-term degradation as previously reported approaches. Experimental and theoretical results are obtained, showing a good agreement.
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
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.
The geometric phase in quantum physics
Bohm, A.
1993-03-01
After an explanatory introduction, a quantum system in a classical time-dependent environment is discussed; an example is a magnetic moment in a classical magnetic field. At first, the general abelian case is discussed in the adiabatic approximation. Then the geometric phase for nonadiabatic change of the environment (Anandan--Aharonov phase) is introduced, and after that general cyclic (nonadiabatic) evolution is discussed. The mathematics of fiber bundles is introduced, and some of its results are used to describe the relation between the adiabatic Berry phase and the geometric phase for general cyclic evolution of a pure state. The discussion is restricted to the abelian, U(1) phase.
Geometric phase in vacuum condensates, application to Unruh effect and to quantum thermometer
NASA Astrophysics Data System (ADS)
Capolupo, Antonio
2015-07-01
We report on the recent results revealing the presence of the geometric phase in all the systems characterized by particle creation from vacuum and vacuum condensates. This fact makes the geometric phase a useful tool in the study and the understanding of disparate phenomena. Its possible application ranges from the dynamical Casimir effect to the Hawking effect, from quantum field theory in curved space to the study of CP and CPT symmetries, from the graphen physics to superconductivity and to the Bose Einstein condensate. Here, we consider the possibility of the detection of the Unruh effect and of the fabrication of a very precise quantum thermometer. We analyze the Mukunda-Simon phase for a two level atom system and consider two case: 1) atoms accelerated in electromagnetic field, and 2) atoms interacting with thermal states. The Mukunda-Simon phase generalizes the Berry phase to the case of non-cyclic and non-adiabatic evolutions; therefore it represents a more useful instrument in experimental implementations with respect to the Berry phase.
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 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
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.
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.
Detection of geometric phases in superconducting nanocircuits
NASA Astrophysics Data System (ADS)
Falci, Giuseppe; Fazio, Rosario; Palma, G. Massimo; Siewert, Jens; Vedral, Vlatko
2000-09-01
When a quantum-mechanical system undergoes an adiabatic cyclic evolution, it acquires a geometrical phase factor in addition to the dynamical one; this effect has been demonstrated in a variety of microscopic systems. Advances in nanotechnology should enable the laws of quantum dynamics to be tested at the macroscopic level, by providing controllable artificial two-level systems (for example, in quantum dots and superconducting devices). Here we propose an experimental method to detect geometric phases in a superconducting device. The setup is a Josephson junction nanocircuit consisting of a superconducting electron box. We discuss how interferometry based on geometrical phases may be realized, and show how the effect may be applied to the design of gates for quantum computation.
Non-adiabatic perturbations in Ricci dark energy model
Karwan, Khamphee; Thitapura, Thiti E-mail: nanodsci2523@hotmail.com
2012-01-01
We show that the non-adiabatic perturbations between Ricci dark energy and matter can grow both on superhorizon and subhorizon scales, and these non-adiabatic perturbations on subhorizon scales can lead to instability in this dark energy model. The rapidly growing non-adiabatic modes on subhorizon scales always occur when the equation of state parameter of dark energy starts to drop towards -1 near the end of matter era, except that the parameter α of Ricci dark energy equals to 1/2. In the case where α = 1/2, the rapidly growing non-adiabatic modes disappear when the perturbations in dark energy and matter are adiabatic initially. However, an adiabaticity between dark energy and matter perturbations at early time implies a non-adiabaticity between matter and radiation, this can influence the ordinary Sachs-Wolfe (OSW) effect. Since the amount of Ricci dark energy is not small during matter domination, the integrated Sachs-Wolfe (ISW) effect is greatly modified by density perturbations of dark energy, leading to a wrong shape of CMB power spectrum. The instability in Ricci dark energy is difficult to be alleviated if the effects of coupling between baryon and photon on dark energy perturbations are included.
Genuine vacuum-induced geometric phases
NASA Astrophysics Data System (ADS)
Wang, Minghao; Wei, L. F.; Liang, J. Q.
2015-04-01
Since a pioneer work on vacuum-induced Berry phase (VIBP) was done by Fuentes-Guridi et al. [Phys. Rev. Lett. 89 (2002) 220404], much attention has been paid to the geometric phase effects of vacuum field. However, all the so-called VIBPs investigated previously are not purely vacuum-induced (i.e. the nonvacuum components of the field are also involved). In this paper, we discuss how to deliver geometric phases from the evolution of a genuine vacuum field in a standard cavity quantum electrodynamics (QED) system. First, we design a cyclic evolution of an atom-field system with the atom being initially prepared at the excited state and the field at the genuine vacuum. Then, we calculate the geometric phases acquired during such a cyclic evolution. It is found that such geometric phases are really induced by an evolution of the genuine vacuum field. Specifically, our generic proposal is demonstrated with both the one- and two-mode Jaynes-Cummings model interactions (JCM).
Classical nuclear motion coupled to electronic non-adiabatic transitions
NASA Astrophysics Data System (ADS)
Agostini, Federica; Abedi, Ali; Gross, E. K. U.
2014-12-01
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.
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.
Geometric-phase atom optics and interferometry
NASA Astrophysics Data System (ADS)
Zygelman, B.
2015-10-01
We illustrate how geometric gauge forces and topological phase effects emerge in atomic and molecular systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices including a velocity sieve, a component in mass spectrometers, for neutral atoms. We introduce and outline a possible experimental setup that demonstrates topological interferometry for neutral spin-1/2 systems. For that two-level system, we study the transition from Abelian to non-Abelian behavior and explore its relation to the molecular Aharonov-Bohm effect.
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.
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.).
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
Kinetically constrained ring-polymer molecular dynamics for non-adiabatic chemical reactions.
Menzeleev, Artur R; Bell, Franziska; Miller, Thomas F
2014-02-14
We extend ring-polymer molecular dynamics (RPMD) to allow for the direct simulation of general, electronically non-adiabatic chemical processes. The kinetically constrained (KC) RPMD method uses the imaginary-time path-integral representation in the set of nuclear coordinates and electronic states to provide continuous equations of motion that describe the quantized, electronically non-adiabatic dynamics of the system. KC-RPMD preserves the favorable properties of the usual RPMD formulation in the position representation, including rigorous detailed balance, time-reversal symmetry, and invariance of reaction rate calculations to the choice of dividing surface. However, the new method overcomes significant shortcomings of position-representation RPMD by enabling the description of non-adiabatic transitions between states associated with general, many-electron wavefunctions and by accurately describing deep-tunneling processes across asymmetric barriers. We demonstrate that KC-RPMD yields excellent numerical results for a range of model systems, including a simple avoided-crossing reaction and condensed-phase electron-transfer reactions across multiple regimes for the electronic coupling and thermodynamic driving force. PMID:24527896
Kinetically constrained ring-polymer molecular dynamics for non-adiabatic chemical reactions
Menzeleev, Artur R.; Bell, Franziska; Miller, Thomas F.
2014-02-14
We extend ring-polymer molecular dynamics (RPMD) to allow for the direct simulation of general, electronically non-adiabatic chemical processes. The kinetically constrained (KC) RPMD method uses the imaginary-time path-integral representation in the set of nuclear coordinates and electronic states to provide continuous equations of motion that describe the quantized, electronically non-adiabatic dynamics of the system. KC-RPMD preserves the favorable properties of the usual RPMD formulation in the position representation, including rigorous detailed balance, time-reversal symmetry, and invariance of reaction rate calculations to the choice of dividing surface. However, the new method overcomes significant shortcomings of position-representation RPMD by enabling the description of non-adiabatic transitions between states associated with general, many-electron wavefunctions and by accurately describing deep-tunneling processes across asymmetric barriers. We demonstrate that KC-RPMD yields excellent numerical results for a range of model systems, including a simple avoided-crossing reaction and condensed-phase electron-transfer reactions across multiple regimes for the electronic coupling and thermodynamic driving force.
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
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.
Analysis of geometric phase effects in the quantum-classical Liouville formalism
Ryabinkin, Ilya G.; Izmaylov, Artur F.; Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 ; 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.
Nonadiabatic fluctuation in the measured geometric phase
NASA Astrophysics Data System (ADS)
Ai, Qing; Huo, Wenyi; Long, Gui Lu; Sun, C. P.
2009-08-01
We study how the nonadiabatic effect causes the observable fluctuation in the “geometric phase” for a two-level system, which is defined as the experimentally measurable quantity in the adiabatic limit. From the Rabi exact solution to this model, we give a reasonable explanation to the experimental discovery of phase fluctuation in the superconducting circuit system [P. J. Leek, J. M. Fink, A. Blais, R. Bianchetti, M. Göppl, J. M. Gambetta, D. I. Schuster, L. Frunzio, R. J. Schoelkopf, and A. Wallraf, Science 318, 1889 (2007)], which seemed to be regarded as the conventional experimental error.
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 Dynamics of Molecules in Optical Cavities
NASA Astrophysics Data System (ADS)
Kowalewski, Markus; Bennett, Kochise; Mukamel, Shaul
Molecular systems coupled to optical cavities are promising candidates for a novel kind of photo chemistry. Strong coupling to the vacuum field of the cavity can modify the potential energy surfaces opening up new reaction pathways. We present a derivation of the non-adiabatic couplings for single molecules in the strong coupling regime. The possibilities for photo chemistry are demonstrated for a set of model systems representing typical situations found in molecules. Supported by the Alexander von Humboldt Foundation.
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.
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.
Design of geometric phase measurement in EAST Tokamak
NASA Astrophysics Data System (ADS)
Lan, T.; Liu, H. Q.; Liu, J.; Jie, Y. X.; Wang, Y. L.; Gao, X.; Qin, H.
2016-07-01
The optimum scheme for geometric phase measurement in EAST Tokamak is proposed in this paper. The theoretical values of geometric phase for the probe beams of EAST Polarimeter-Interferometer (POINT) system are calculated by path integration in parameter space. Meanwhile, the influences of some controllable parameters on geometric phase are evaluated. The feasibility and challenge of distinguishing geometric effect in the POINT signal are also assessed in detail.
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, Li-Hong; Fang, Wei-Hai; Xie, Zhi-Zhong; Zhang, Yong
2013-04-01
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 CH3OH 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 S1 relaxation of the photo-induced E → Z process is only mildly affected by the solvent effect, the relatively slower S1 relaxation of the reverse reaction becomes even slower in the solution compared to the gas phase. The subsequent S0 dynamics from the conical intersection between S1 and S0 (CI_E) to Z is accelerated in solution compared to the gas phase because of avoided re-crossing to the S1 state, while the S0 dynamics from the conical intersection between S1 and S0 (CI_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. PMID:23574226
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.
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
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.
Geometric phases for mixed states of the Kitaev chain.
Andersson, Ole; Bengtsson, Ingemar; Ericsson, Marie; Sjöqvist, Erik
2016-05-28
The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyse the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyse the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation. PMID:27091168
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
Quantum phases and dynamics of geometric phase in a quantum spin chain under linear quench
NASA Astrophysics Data System (ADS)
Sarkar, S.; Basu, B.
2012-12-01
We study the quantum phases of anisotropic XY spin chain in presence and absence of adiabatic quench. A connection between geometric phase and criticality is established from the dynamical behavior of the geometric phase for a quench induced quantum phase transition in a quantum spin chain. We predict XX criticality associated with a sequence of non-contractible geometric phases.
Spatial Non-Cyclic Geometric Phase in Neutron Interferometry
Filipp, Stefan; Hasegawa, Yuji; Loidl, Rudolf; Rauch, Helmut
2005-01-01
We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by some of the authors to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism. The extension to non-cyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the non-cyclic geometric phase in terms of paths on the Bloch-sphere. The theoretical treatment comprises the cyclic geometric phase as a special case, which is confirmed by experiment. PMID:27308131
Geometric phase in a flat space for electromagnetic scalar waves.
Luis, Alfredo
2006-08-15
We show the existence of a fundamental geometric phase for classical electromagnetic fields arising after cyclic paths in a plane instead of a sphere. This phase is dispersive, is not related to polarization, distinguishes geometrical from wave optics, and can be easily measured in an interferometric arrangement. PMID:16880859
Non-adiabatic dynamics of molecules in optical cavities
NASA Astrophysics Data System (ADS)
Kowalewski, Markus; Bennett, Kochise; Mukamel, Shaul
2016-02-01
Strong coupling of molecules to the vacuum field of micro cavities can modify the potential energy surfaces thereby opening new photophysical and photochemical reaction pathways. While the influence of laser fields is usually described in terms of classical field, coupling to the vacuum state of a cavity has to be described in terms of dressed photon-matter states (polaritons) which require quantized fields. We present a derivation of the non-adiabatic couplings for single molecules in the strong coupling regime suitable for the calculation of the dressed state dynamics. The formalism allows to use quantities readily accessible from quantum chemistry codes like the adiabatic potential energy surfaces and dipole moments to carry out wave packet simulations in the dressed basis. The implications for photochemistry are demonstrated for a set of model systems representing typical situations found in molecules.
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.
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.
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.
Information flow, non-Markovianity, and geometric phases
Wu, S. L.; Wang, L. C.; Yi, X. X.; Huang, X. L.
2010-11-15
Geometric phases and information flows of a two-level system coupled to its environment are calculated and analyzed. The information flow is defined as a cumulant of changes in trace distance between two quantum states, which is similar to the measure for non-Markovianity given by Breuer. We obtain an analytic relation between the geometric phase and the information flow for pure initial states, and a numerical result for mixed initial states. The geometric phase behaves differently depending on whether there are information flows back to the two-level system from its environment.
Voltage Controlled Geometric Phase Rotation in ^{208}Pb^{19}F.
NASA Astrophysics Data System (ADS)
Furneaux, J. E.; Shafer-Ray, Neil; Coker, J.; Rupasinghe, P. M.; McRaven, C. P.
2013-06-01
Many theoretical publications have investigated the impact of the geometric phase on measurements of the e-EDM. However, there has been surprisingly little quantitative comparison of these models with experiment. Here we create a quantum beat experiment that starts with an optical pump and ends with an optical probe of ^{208}Pb^{19}F. This measurement includes the ability to control a geometric phase variation of the molecular alignment by applying an appropriate bias voltage. These experiments will then used to test the accuracy of our model calculations of geometric phase rotation.
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.
Non-adiabatic resonant conversion of solar neutrinos in three generations
NASA Astrophysics Data System (ADS)
Kim, C. W.; Nussinov, S.; Sze, W. K.
1987-02-01
The survival probability of solar electron neutrinos after non-adiabatic passage through the resonance-oscillation region in the Sun is discussed for the case of three generations. A method to calculate three-generation Landau-Zener transition probabilities between adiabatic states is described. We also discuss how the Landua-Zener probability is modified in the extreme non-adiabatic case.
Non-Adiabatic MHD Modes in Periodic Magnetic Medium
NASA Astrophysics Data System (ADS)
Kumar, Nagendra; Kumar, Anil
High-resolution satellite observations reveal that many solar features such as penumbra and plume regions possess the structures with alternating properties. So we study the joint effect of periodic alternation of magnetic slabs and thermal mechanisms on the propagation of MHD waves. We consider a perfectly conducting fluid permeated by a magnetic field having the peri-odicity along x-axis and constant direction along z-axis. We suppose that the medium consists of alternating slabs of strong and weak homogeneous magnetic field with a sharp discontinuity at the boundary. The inclusion of non-adiabatic effects modifies the energy equation in which the thermal mechanisms (radiation, heating and thermal conduction) are added. The gravi-tational effects are negligible because wavelengths are assumed to be much smaller than the gravitational scale height. The dispersion relations for the surface and body modes are derived and analyzed in the limiting cases of thin and thick slabs. The dispersion curves depend upon the Bloch's wavenumber due to the periodicity in magnetic field. We have examined the be-havior of dispersion curves for different values of slab width ratio and Bloch's wavenumber as a function of dimensionless wavelength. It is shown that the width of structures influences the propagation speed of waves. Our results might be useful in understanding the wave propagation in plume regions, photosphere and spaghetti structures in solar wind.
Highly parallel implementation of non-adiabatic Ehrenfest molecular dynamics
NASA Astrophysics Data System (ADS)
Kanai, Yosuke; Schleife, Andre; Draeger, Erik; Anisimov, Victor; Correa, Alfredo
2014-03-01
While the adiabatic Born-Oppenheimer approximation tremendously lowers computational effort, many questions in modern physics, chemistry, and materials science require an explicit description of coupled non-adiabatic electron-ion dynamics. Electronic stopping, i.e. the energy transfer of a fast projectile atom to the electronic system of the target material, is a notorious example. We recently implemented real-time time-dependent density functional theory based on the plane-wave pseudopotential formalism in the Qbox/qb@ll codes. We demonstrate that explicit integration using a fourth-order Runge-Kutta scheme is very suitable for modern highly parallelized supercomputers. Applying the new implementation to systems with hundreds of atoms and thousands of electrons, we achieved excellent performance and scalability on a large number of nodes both on the BlueGene based ``Sequoia'' system at LLNL as well as the Cray architecture of ``Blue Waters'' at NCSA. As an example, we discuss our work on computing the electronic stopping power of aluminum and gold for hydrogen projectiles, showing an excellent agreement with experiment. These first-principles calculations allow us to gain important insight into the the fundamental physics of electronic stopping.
NASA Astrophysics Data System (ADS)
Wu, Wei; Xu, Jing-Bo
2016-06-01
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.
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 in p -n junctions of helical edge states
NASA Astrophysics Data System (ADS)
Wadhawan, Disha; Mehta, Poonam; Das, Sourin
2016-02-01
The quantum spin Hall effect is endowed with topologically protected edge modes with a gapless Dirac spectrum. Applying a magnetic field locally along the edge leads to a gapped edge spectrum with the opposite parity for winding of spin texture for conduction and valence bands. Using Pancharatnam's prescription for the geometric phase it is shown that mismatch of this parity across a p -n junction, which could be engineered into the edge by electrical gate induced doping, leads to a phase dependence in the two-terminal conductance which is quantized to either zero or π . It is further shown that application of a nonuniform magnetic field across the junction could lead to a nonquantized value of this geometric phase which is tunable between zero and π . A current asymmetry measurement which is shown to be robust against electron-electron interactions is proposed to infer the appearance of this Pancharatnam's geometric phase in transport across such junctions.
Control of the spin geometric phase in semiconductor quantum rings
Nagasawa, Fumiya; Frustaglia, Diego; Saarikoski, Henri; Richter, Klaus; Nitta, Junsaku
2013-01-01
Since the formulation of the geometric phase by Berry, its relevance has been demonstrated in a large variety of physical systems. However, a geometric phase of the most fundamental spin-1/2 system, the electron spin, has not been observed directly and controlled independently from dynamical phases. Here we report experimental evidence on the manipulation of an electron spin through a purely geometric effect in an InGaAs-based quantum ring with Rashba spin-orbit coupling. By applying an in-plane magnetic field, a phase shift of the Aharonov–Casher interference pattern towards the small spin-orbit-coupling regions is observed. A perturbation theory for a one-dimensional Rashba ring under small in-plane fields reveals that the phase shift originates exclusively from the modulation of a pure geometric-phase component of the electron spin beyond the adiabatic limit, independently from dynamical phases. The phase shift is well reproduced by implementing two independent approaches, that is, perturbation theory and non-perturbative transport simulations. PMID:24067870
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.
Geometric Phase Appears in the Ultracold Hydrogen Exchange Reaction
NASA Astrophysics Data System (ADS)
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-10-01
Quantum reactive scattering calculations for the hydrogen exchange reaction H +H2 (v =4 ,j =0 )→H +H2 (v', j') and its isotopic analogues are reported for ultracold collision energies. Because of the unique properties associated with ultracold collisions, it is shown that the geometric phase effectively controls the reactivity. The rotationally resolved rate coefficients computed with and without the geometric phase are shown to differ by up to 4 orders of magnitude. The effect is also significant in the vibrationally resolved and total rate coefficients. The dynamical origin of the effect is discussed and the large geometric phase effect reported here might be exploited to control the reactivity through the application of external fields or by the selection of a particular nuclear spin state.
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. PMID:26613450
Geometric frustration phases of diblock copolymers in nanoparticles.
Li, Shiben; Chen, Peng; Zhang, Linxi; Liang, Haojun
2011-04-19
The geometric frustration phases are investigated for diblock copolymers in nanoparticles with neutral surfaces using real-space self-consistent field theory. First, a rich variety of geometric frustration phases with specific symmetries are observed in the polymer nanoparticles with invariable diameters by constructing the phase diagrams arranged as the volume fraction and Flory-Huggins interaction parameter. Most of the space in the phase diagram is filled with phases with strong symmetries, such as spherical or cubic symmetries, while a number of asymmetric or axisymmetric phases are located in a narrow space in the diagram. Then the geometric frustration phases are examined systematically for the diblock copolymers with special polymer parameters, and a rich variety of novel frustration phases with multilayered structures are observed by varying the diameters of the nanoparticles. Furthermore, the investigations on the free energies indicate that the transitions between these frustrated phases are first-order, and the formation mechanism of the frustration phases is reasonably elucidated. PMID:21417241
The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
NASA Astrophysics Data System (ADS)
Titum, Paraj; Berg, Erez; Rudner, Mark S.; Refael, Gil; Lindner, Netanel H.
Periodically driven quantum systems provide a novel and versatile platform for realizing topological phenomena. Among these are analogs of topological insulators and superconductors, attainable in static systems; however, some of these phenomena are unique to the periodically driven case. Here, we show that disordered, periodically driven systems admit an ``anomalous'' two dimensional phase, whose quasi-energy spectrum consists of chiral edge modes that coexist with a fully localized bulk - an impossibility for static Hamiltonians. This unique situation serves as the basis for a new topologically-protected non-equilibrium transport phenomenon: quantized non-adiabatic charge pumping. We identify the bulk topological invariant that characterizes the new phase (which we call the ``anomalous Floquet Anderson Insulator'', or AFAI). We provide explicit models which constitute a proof of principle for the existence of the new phase. Finally, we present evidence that the disorder-driven transition from the AFAI to a trivial, fully localized phase is in the same universality class as the quantum Hall plateau transition.
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.
Exploring percolative landscapes: Infinite cascades of geometric phase transitions.
Timonin, P N; Chitov, Gennady Y
2016-01-01
The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2D 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. PMID:26871019
Importance of Geometric Phase Effects in Ultracold Chemistry.
Hazra, Jisha; Kendrick, Brian K; Balakrishnan, Naduvalath
2015-12-17
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 + 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". PMID:26317912
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…
Geometric phases, evolution loops and generalized oscillator potentials
NASA Technical Reports Server (NTRS)
Fernandez, David J.
1995-01-01
The geometric phases for dynamical processes where the evolution operator becomes the identity (evolution loops) are studied. The case of time-independent Hamiltonians with equally spaced energy levels is considered; special emphasis is made on the potentials having the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and their recently found coherent states.
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. PMID:26094205
Molecular geometric phase from the exact electron-nuclear factorization
NASA Astrophysics Data System (ADS)
Requist, Ryan; Tandetzky, Falk; Gross, E. K. U.
2016-04-01
The Born-Oppenheimer electronic wave function ΦRBO(r ) picks up a topological phase factor ±1 , a special case of Berry phase, when it is transported around a conical intersection of two adiabatic potential energy surfaces in R space. We show that this topological quantity reverts to a geometric quantity ei γ if the geometric phase γ =∮Im <ΦR|∇μΦR> .d Rμ is evaluated with the conditional electronic wave function ΦR(r ) from the exact electron-nuclear factorization ΦR(r ) χ (R ) instead of the adiabatic function ΦRBO(r ) . A model of a pseudorotating triatomic molecule, also applicable to dynamical Jahn-Teller ions in bulk crystals, provides examples of nontrivial induced vector potentials and molecular geometric phase from the exact factorization. The induced vector potential gives a contribution to the circulating nuclear current that cannot be removed by a gauge transformation. The exact potential energy surface is calculated and found to contain a term depending on the Fubini-Study metric for the conditional electronic wave function.
Nonlinearity of Pancharatnam's geometric phase in polarizing interferometers.
Hils, B; Dultz, W; Martienssen, W
1999-08-01
Earlier investigations show a time-variable nonlinear shift of the fringe pattern in a polarizing interferometer while rotating a polarizer at the exit. This effect was identified as Pancharatnam's geometrical phase and proposed for applications in interferometry and fast optical switching devices. A heterodyne analysis attributes moving fringes to a frequency difference between the interfering beams; thus changing fringe velocities point to a dynamic frequency development within the period of the uniformly rotating analyzer. This explanation offends the intuition and we undertake an experimental and theoretical investigation of the effect to solve the paradox. We determine, e.g., the complete frequency and mode spectrum of an arbitrary state of polarization P0 behind a rotating linear analyzer and behind a rotating arbitrary linear birefringent plate. We find that, in spite of a fast changing phase in the interferometer, no other (higher) frequency components appear in the spectral distribution of the intensity at the exit than the double of the rotary frequency of the analyzer: phase nonlinearities are compensated for by intensity changes. Only a phase-sensitive detector like an array of photodetectors is able to observe the nonlinearity of Pancharatnam's geometrical phase. A single detector only finds a sinusoidal intensity variation. Our insight into these relations leads us to two new applications of Pancharatnam's phase: supersensitivity of a polarizing double beam interferometer with a video camera acting as a phase detector and external tuning of a Fizeau interferometer. PMID:11970029
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 in Stückelberg interferometry
NASA Astrophysics Data System (ADS)
Lim, Lih-King; Fuchs, Jean-Noël; Montambaux, Gilles
2015-04-01
We study the time evolution of a two-dimensional quantum particle exhibiting a two-band energy spectrum with two Dirac cones as, for example, in the honeycomb lattice. A force is applied such that the particle experiences two Landau-Zener transitions in succession in the vicinity of the Dirac cones. The adiabatic evolution between the two transitions leads to Stückelberg interferences, due to two possible trajectories in energy-momentum space. In addition to well-known dynamical and Stokes phases, the interference pattern reveals a geometric phase which depends on the chirality (winding number) and the mass sign associated with each Dirac cone, as well as on the type of trajectory (parallel or diagonal with respect to the two cones) in parameter space. This geometric phase reveals the coupling between the bands encoded in the structure of the wave functions. Stückelberg interferometry therefore appears as a way to access both intra- and interband geometric information.
Some geometric properties of quantum phases and calculation of phase formulas
NASA Astrophysics Data System (ADS)
Bracken, Paul
An introduction to several geometrical ideas which are of use to quantum mechanics is presented. The Aharonov-Anandan phase is introduced and without reference to any dynamical equation, this phase is formulated by defining an appropriate connection on a specific fiber bundle. The holonomy element gives the phase. By introducing another connection, the Pancharatnam phase formula is derived following a different procedure.
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.
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.
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.
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.
Measuring the Aharonov–Anandan phase in multiport photonic systems
NASA Astrophysics Data System (ADS)
Wang, Kai; Weimann, Steffen; Nolte, Stefan; Perez-Leija, Armando; Szameit, Alexander
2016-04-01
The Aharonov-Anandan phase is a description of the geometric nature in non-adiabatic cyclic evolutions of quantum states. Here we report on a measurement of the Aharonov-Anandan phase in photonics. We consider a time-independent quantum driven harmonic oscillator that is initially prepared at the vacuum state. We utilize evanescently coupled waveguides to realize this physical model and achieve a measurement of the Aharonov-Anandan phase via integrated interferometry.
NASA Astrophysics Data System (ADS)
Dupret, M.-A.; De Ridder, J.; De Cat, P.; Aerts, C.; Scuflaire, R.; Noels, A.; Thoul, A.
2003-02-01
We present an improved version of the method of photometric mode identification of Heynderickx et al. (\\cite{hey}). Our new version is based on the inclusion of precise non-adiabatic eigenfunctions determined in the outer stellar atmosphere according to the formalism recently proposed by Dupret et al. (\\cite{dup}). Our improved photometric mode identification technique is therefore no longer dependent on ad hoc parameters for the non-adiabatic effects. It contains the complete physical conditions of the outer atmosphere of the star, provided that rotation does not play a key role. We apply our method to the two slowly pulsating B stars HD 74560 and HD 138764 and to the beta Cephei star EN (16) Lac. Besides identifying the degree l of the pulsating stars, our method is also a tool for improving the knowledge of stellar interiors and atmospheres, by imposing constraints on parameters such as the metallicity and the mixing-length parameter alpha (a procedure we label non-adiabatic asteroseismology). The non-adiabatic eigenfunctions needed for the mode identification are available upon request from the authors.
Non-adiabatic spin-transfer torque independent of the spin relaxation rate
NASA Astrophysics Data System (ADS)
Kim, Kyoung-Whan; Lee, Kyung-Jin; Lee, Hyun-Woo; Stiles, Mark
Non-adiabatic spin-transfer torques play an important role in magnetization dynamics. For example, they determine current-induced magnetic domain wall velocity. A well-known mechanism for non-adiabatic spin-transfer torques arises from spin relaxation and is directly proportional to the spin relaxation rate. Here we report mechanism that is independent of the spin relaxation rate. This mechanism is related to the recently reported intrinsic damping-like spin-orbit torque, which is proportional to an electric field but is independent of the conductivity, and hence the scattering rate. Likewise, the mechanism we report is independent of the scattering rate. It originates from the effective spin-orbit coupling that arises in systems with magnetic textures as we previously reported for related processes. In this work, we demonstrate the existence of such a spin-transfer torque, which is a contribution to the non-adiabatic spin-transfer torque and is independent of scattering rates. We also demonstrate that the magnitude of this torque can be much larger than other mechanisms for non-adiabatic spin-transfer torques, and may be the dominant contribution in some systems.
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
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.
Classification theorem for principal fibre bundles, Berry's phase, and exact cycle evolution
Bohm, A.; Boya, L.J.; Mostafazadeh, A. . Center for Particle Physics); Rudolph, G. . Fachbereich Physik)
1993-03-01
The relation between the two mathematical interpretations of the geometric (Berry) phase is discussed, using either the fibre bundle over parameter space or over projective Hilbert space. It turns out that these two geometric constructions are linked by the classification theorem for vector bundles. The classification theorem provides the means to classify the parameter space bundles for adiabatic evolution and for non-adiabatic cyclic evolution of the statevectors.
Classification theorem for principal fibre bundles, Berry`s phase, and exact cycle evolution
Bohm, A.; Boya, L.J.; Mostafazadeh, A.; Rudolph, G.
1993-03-01
The relation between the two mathematical interpretations of the geometric (Berry) phase is discussed, using either the fibre bundle over parameter space or over projective Hilbert space. It turns out that these two geometric constructions are linked by the classification theorem for vector bundles. The classification theorem provides the means to classify the parameter space bundles for adiabatic evolution and for non-adiabatic cyclic evolution of the statevectors.
Geometric phase-shifting for low-coherence interference microscopy
NASA Astrophysics Data System (ADS)
Roy, M.; Svahn, P.; Cherel, L.; Sheppard, C. J. R.
2002-06-01
A low-coherence Linnik interference microscope using high numerical aperture optics has been constructed. The system uses a tungsten halogen lamp and Köhler illumination, with separate control over field and aperture stops, so that experiments can be conducted with a range of different operating conditions. The novel feature of the system is the use of an achromatic phase-shifter operating on the principle of the geometric phase, achieved by using a polarising beam splitter, a quarter wave plate and a rotating polariser. Image information is extracted from the visibility of the fringes, the position of the visibility peak along the scanning axis yielding the height of the test surface at the corresponding point.
Quantum and classical non-adiabatic dynamics of Li_{2}^{+}Ne photodissociation
NASA Astrophysics Data System (ADS)
Pouilly, Brigitte; Monnerville, Maurice; Zanuttini, David; Gervais, Benoît
2015-01-01
The 3D photodissociation dynamics of Li2+Ne system is investigated by quantum calculations using the multi-configuration time-dependent Hartree (MCTDH) method and by classical simulations with the trajectory surface hopping (TSH) approach. Six electronic states of A’ symmetry and two states of A” symmetry are involved in the process. Couplings in the excitation region and two conical intersections in the vicinity of the Franck-Condon zone control the non-adiabatic nuclear dynamics. A diabatic representation including all the states and the couplings is determined. Diabatic and adiabatic populations calculated for initial excitation to pure diabatic and adiabatic states lead to a clear understanding of the mechanisms governing the non-adiabatic photodissociation process. The classical and quantum photodissociation cross-sections for absorption in two adiabatic states of the A’ symmetry are calculated. A remarkable agreement between quantum and classical results is obtained regarding the populations and the absorption cross-sections.
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.
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
Non-adiabatic molecular dynamics with complex quantum trajectories. I. The diabatic representation
NASA Astrophysics Data System (ADS)
Zamstein, Noa; Tannor, David J.
2012-12-01
We extend a recently developed quantum trajectory method [Y. Goldfarb, I. Degani, and D. J. Tannor, J. Chem. Phys. 125, 231103 (2006)], 10.1063/1.2400851 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)], 10.1063/1.459170. 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.
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.
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. PMID:23249054
Non-adiabatic response of relativistic radiation belt electrons to GEM magnetic storms
NASA Astrophysics Data System (ADS)
McAdams, K. L.; Reeves, G. D.
The importance of fully adiabatic effects in the relativistic radiation belt electron response to magnetic storms is poorly characterized due to many difficulties in calculating adiabatic flux response. Using the adiabatic flux model of Kim and Chan [1997a] and Los Alamos National Laboratory geosynchronous satellite data, we examine the relative timing of the adiabatic and non-adiabatic flux responses. In the three storms identified by the GEM community for in depth study, the non-adiabatic energization occurs hours earlier than the adiabatic re-energization. The adiabatic energization can account for only 10-20% of the flux increases in the first recovery stages, and only 1% of the flux increase if there is continuing activity.
Ultrafast hydrogen migration in acetylene cation driven by non-adiabatic effects.
Madjet, Mohamed El-Amine; Li, Zheng; Vendrell, Oriol
2013-03-01
Non-adiabatic dynamics of the acetylene cation is investigated using mixed quantum-classical dynamics based on trajectory surface hopping. To describe the non-adiabatic effects, two surface hopping methods are used, namely, Tully's fewest switches and Landau-Zener surface hopping. Similarities and differences between the results based on those two methods are discussed. We find that the photoionization of acetylene into the first excited state A(2)Σg(+) drives the molecule from the linear structure to a trans-bent structure. Through a conical intersection the acetylene cation can relax back to either the ground state of acetylene or vinylidene. We conclude that hydrogen migration always takes place after non-radiative electronic relaxation to the ground state of the monocation. Based on the analysis of correlation functions we identify coherent oscillations between acetylene and vinylidene with a period of about 70 fs after the electronic relaxation. PMID:23485298
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
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
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 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.
Multiple coupled landscapes and non-adiabatic dynamics with applications to self-activating genes.
Chen, Cong; Zhang, Kun; Feng, Haidong; Sasai, Masaki; Wang, Jin
2015-11-21
Many physical, chemical and biochemical systems (e.g. electronic dynamics and gene regulatory networks) are governed by continuous stochastic processes (e.g. electron dynamics on a particular electronic energy surface and protein (gene product) synthesis) coupled with discrete processes (e.g. hopping among different electronic energy surfaces and on and off switching of genes). One can also think of the underlying dynamics as the continuous motion on a particular landscape and discrete hoppings among different landscapes. The main difference of such systems from the intra-landscape dynamics alone is the emergence of the timescale involved in transitions among different landscapes in addition to the timescale involved in a particular landscape. The adiabatic limit when inter-landscape hoppings are fast compared to continuous intra-landscape dynamics has been studied both analytically and numerically, but the analytical treatment of the non-adiabatic regime where the inter-landscape hoppings are slow or comparable to continuous intra-landscape dynamics remains challenging. In this study, we show that there exists mathematical mapping of the dynamics on 2(N) discretely coupled N continuous dimensional landscapes onto one single landscape in 2N dimensional extended continuous space. On this 2N dimensional landscape, eddy current emerges as a sign of non-equilibrium non-adiabatic dynamics and plays an important role in system evolution. Many interesting physical effects such as the enhancement of fluctuations, irreversibility, dissipation and optimal kinetics emerge due to non-adiabaticity manifested by the eddy current illustrated for an N = 1 self-activator. We further generalize our theory to the N-gene network with multiple binding sites and multiple synthesis rates for discretely coupled non-equilibrium stochastic physical and biological systems. PMID:26455835
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.
The molecular symmetry adapted non - adiabatic coupling terms and diabatic Hamiltonian matrix
NASA Astrophysics Data System (ADS)
Mukherjee, Saikat; Bandyopadhyay, Sudip; Paul, Amit Kumar; Adhikari, Satrajit
2013-04-01
We calculate the adiabatic Potential Energy Surfaces (PESs) and the Non - Adiabatic Coupling Terms (NACTs) for the excited electronic states (22 E' and 12 A'1) of Na3 cluster at the MRCI level by using ab initio quantum chemistry package (MOLPRO), where the NACTs are adapted with Molecular Symmetry (MS) by employing appropriate Irreducible Representations (IREPs). Such terms are incorporated into the Adiabatic to Diabatic Transformation (ADT) equations to obtain the ADT angles to construct the continuous, single - valued, symmetric and smooth 3 × 3 diabatic Hamiltonian matrix.
NASA Astrophysics Data System (ADS)
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Maitra, Neepa T.; Gross, E. K. U.
2015-03-01
The Born-Oppenheimer (BO) approximation allows to visualize the coupled electron-nuclear dynamics in molecular systems as a set of nuclei moving on a single potential energy surface representing the effect of the electrons in a given eigenstate. Many interesting phenomena, however, such as vision or charge separation in organic photovoltaic materials, take place in conditions beyond its range of validity. Nevertheless, the basic construct of the adiabatic treatment, the BO potential energy surfaces, is employed to describe non-adiabatic processes and the full problem is represented in terms of adiabatic states and transitions among them in regions of strong non-adiabatic coupling. But the concept of single potential energy is lost. The alternative point of view arising in the framework of the exact factorization of the electron-nuclear wave function will be presented. A single, time-dependent, potential energy provides the force driving the nuclear motion and is adopted as starting point for the development of quantum-classical approximations to the full quantum mechanical problem.
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.
A dynamical approach to non-adiabatic electron transfers at the bio-inorganic interface.
Zanetti-Polzi, Laura; Corni, Stefano
2016-04-21
A methodology is proposed to investigate electron transfer reactions between redox-active biomolecular systems (e.g. a protein) and inorganic surfaces. The whole system is modelled at the atomistic level using classical molecular dynamics - making an extensive sampling of the system's configurations possible - and the energies associated with the redox-active complex reduction are calculated using a hybrid quantum/classical approach along the molecular dynamics trajectory. The non-adiabaticity is introduced a posteriori using a Monte Carlo approach based on the Landau-Zener theory extended to treat a metal surface. This approach thus allows us to investigate the role of the energy fluctuations, determined by the dynamical evolution of the system, as well as the role of non-adiabaticity in affecting the kinetic rate of the electron transfer reaction. Most notably, it allows us to investigate the two contributions separately, hence achieving a detailed picture of the mechanisms that determine the rate. The analysis of the system configurations also allows us to relate the estimated electronic coupling to the structural and dynamic properties of the system. As a test case, the methodology is here applied to study the electron transfer reaction between cytochrome c and a gold surface. The results obtained explain the different electron transfer rates experimentally measured for two different concentrations of proteins on the electrode surface. PMID:27031179
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
NASA Astrophysics Data System (ADS)
Rafayelyan, Mushegh; Tkachenko, Georgiy; Brasselet, Etienne
2016-06-01
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.
Investigation of spontaneous Brillouin scattering generation based on non-adiabatic microfibres
NASA Astrophysics Data System (ADS)
Zarei, A.; Jasim, A. A.; Harun, S. W.; Ahmad, H.
2014-12-01
Brillouin Stokes and anti-Stokes generation is successfully demonstrated in backward direction using a non-adiabatic microfibre as the gain medium. The Stokes light wavelength is up-shifted by 0.088 nm (10 GHz) from the BP wavelength as monitored by using an optical spectrum analyzer. The Brillouin scattering can also be enhanced by employing a microfibre based inline Mach-Zehnder interferometer (IMZI) as the gain medium due to its stronger multimode interference effect. It is shown that the microfibre geometry plays an important role in the spontaneous Brillouin scattering generation and gain bandwidth broadening due to its effect on irritation of the acoustic modes inside the microfibre.
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 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
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
Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation
NASA Astrophysics Data System (ADS)
Zamstein, Noa; Tannor, David J.
2012-12-01
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 Schrödinger 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)], 10.1063/1.4739845. We apply our method to two benchmark models introduced by John Tully [J. Chem. Phys. 93, 1061 (1990)], 10.1063/1.459170, 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.
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
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.
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.
Semiclassical analysis of the electron-nuclear coupling in electronic non-adiabatic processes
NASA Astrophysics Data System (ADS)
Agostini, Federica; Min, Seung Kyu; Gross, E. K. U.
2015-10-01
In the context of the exact factorization of the electron-nuclear wave function, the coupling between electrons and nuclei beyond the adiabatic regime is encoded (i) in the time-dependent vector and scalar potentials and (ii) in the electron-nuclear coupling operator. The former appear in the Schroedinger-like equation that drives the evolution of the nuclear degrees of freedom, whereas the latter is responsible for inducing non-adiabatic effects in the electronic evolution equation. As we have devoted previous studies to the analysis of the vector and scalar potentials, in this paper we focus on the properties of the electron-nuclear coupling operator, with the aim of describing a numerical procedure to approximate it within a semiclassical treatment of the nuclear dynamics.
The exact forces on classical nuclei in non-adiabatic charge transfer
NASA Astrophysics Data System (ADS)
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Maitra, Neepa T.; Gross, E. K. U.
2015-02-01
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.
Gidopoulos, Nikitas I.; Gross, E. K. U.
2014-01-01
A novel treatment of non-adiabatic couplings is proposed. The derivation is based on a theorem by Hunter stating that the wave function of the complete system of electrons and nuclei can be written, without approximation, as a Born–Oppenheimer (BO)-type product of a nuclear wave function, X(R), and an electronic one, ΦR(r), which depends parametrically on the nuclear configuration R. From the variational principle, we deduce formally exact equations for ΦR(r) and X(R). The algebraic structure of the exact nuclear equation coincides with the corresponding one in the adiabatic approximation. The electronic equation, however, contains terms not appearing in the adiabatic case, which couple the electronic and the nuclear wave functions and account for the electron–nuclear correlation beyond the BO level. It is proposed that these terms can be incorporated using an optimized local effective potential. PMID:24516183
Inflationary perturbation theory is geometrical optics in phase space
NASA Astrophysics Data System (ADS)
Seery, David; Mulryne, David J.; Frazer, Jonathan; Ribeiro, Raquel H.
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 ("transport equations"), 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 fNL in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.
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.
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.
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).
Dark-field electron holography for the measurement of geometric phase.
Hÿtch, M J; Houdellier, F; Hüe, F; Snoeck, E
2011-07-01
The genesis, theoretical basis and practical application of the new electron holographic dark-field technique for mapping strain in nanostructures are presented. The development places geometric phase within a unified theoretical framework for phase measurements by electron holography. The total phase of the transmitted and diffracted beams is described as a sum of four contributions: crystalline, electrostatic, magnetic and geometric. Each contribution is outlined briefly and leads to the proposal to measure geometric phase by dark-field electron holography (DFEH). The experimental conditions, phase reconstruction and analysis are detailed for off-axis electron holography using examples from the field of semiconductors. A method for correcting for thickness variations will be proposed and demonstrated using the phase from the corresponding bright-field electron hologram. PMID:21864773
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
Coherent cancellation of geometric phase for the OH molecule in external fields
NASA Astrophysics Data System (ADS)
Bhattacharya, M.; Marin, S.; Kleinert, M.
2014-05-01
The OH molecule in its ground state presents a versatile platform for precision measurement and quantum information processing. These applications vitally depend on the accurate measurement of transition energies between the OH levels. Significant sources of systematic errors in these measurements are shifts based on the geometric phase arising from the magnetic and electric fields used for manipulating OH. In this article, we present these geometric phases for fields that vary harmonically in time, as in the Ramsey technique. Our calculation of the phases is exact within the description provided by our recent analytic solution of an effective Stark-Zeeman Hamiltonian for the OH ground state. This Hamiltonian has been shown to model experimental data accurately. We find that the OH geometric phases exhibit rich structure as a function of the field rotation rate. Remarkably, we find rotation rates where the geometric phase accumulated by a specific state is zero, or where the relative geometric phase between two states vanishes. We expect these findings to be of importance to precision experiments on OH involving time-varying fields. More specifically, our analysis quantitatively characterizes an important item in the error budget for precision spectroscopy of ground-state OH.
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.
Two-phase fluid flow in geometric packing.
Paiva, Aureliano Sancho S; Oliveira, Rafael S; Andrade, Roberto F S
2015-12-13
We investigate how a plug of obstacles inside a two-dimensional channel affects the drainage of high viscous fluid (oil) when the channel is invaded by a less viscous fluid (water). The plug consists of an Apollonian packing with, at most, 17 circles of different sizes, which is intended to model an inhomogeneous porous region. The work aims to quantify the amount of retained oil in the region where the flow is influenced by the packing. The investigation, carried out with the help of the computational fluid dynamics package ANSYS-FLUENT, is based on the integration of the complete set of equations of motion. The study considers the effect of both the injection speed and the number and size of obstacles, which directly affects the porosity of the system. The results indicate a complex dependence in the fraction of retained oil on the velocity and geometric parameters. The regions where the oil remains trapped is very sensitive to the number of circles and their size, which influence in different ways the porosity of the system. Nevertheless, at low values of Reynolds and capillary numbers Re<4 and n(c)≃10(-5), the overall expected result that the volume fraction of oil retained decreases with increasing porosity is recovered. A direct relationship between the injection speed and the fraction of oil is also obtained. PMID:26527816
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.
Between ethylene and polyenes--the non-adiabatic dynamics of cis-dienes.
Kuhlman, Thomas S; Glover, William J; Mori, Toshifumi; Møller, Klaus B; Martínez, Todd J
2012-01-01
Using Ab Initio Multiple Spawning (AIMS) with a Multi-State Multi-Reference Perturbation theory (MS-MR-CASPT2) treatment of the electronic structure, we have simulated the non-adiabatic excited state dynamics of cyclopentadiene (CPD) and 1,2,3,4-tetramethyl-cyclopentadiene (Me4-CPD) following excitation to S1. It is observed that torsion around the carbon-carbon double bonds is essential in reaching a conical intersection seam connecting S1 and S0. We identify two timescales; the induction time from excitation to the onset of population transfer back to S0 (CPD: -25 fs, Me4-CPD: -71 fs) and the half-life of the subsequent population transfer (CPD: -28 fs, Me4-CPD: -48 fs). The longer timescales for Me4-CPD are a kinematic consequence of the inertia of the substituents impeding the essential out-of-plane motion that leads to the conical intersection seam. A bifurcation is observed on S1 leading to population transfer being attributable, in a 5 : 2 ratio for CPD and 7 : 2 ratio for Me4-CPD, to two closely related conical intersections. Calculated time-resolved photoelectron spectra are in excellent agreement with experimental spectra validating the simulation results. PMID:23230770
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.
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.
2014-01-01
Non Adiabatic Rapid Sweep (NARS) EPR spectroscopy has been introduced for application to nitroxide-labeled biological samples (AW 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 4 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. PMID:24036469
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.
Suzuki-Trotter Formula for Real Time Dependent LDA II: Non-adiabatic MD
NASA Astrophysics Data System (ADS)
Miyamoto, Yoshiyuki; Sugino, Osamu
1998-03-01
In order to investigate ultrafast chemical reactions strongly coupled with electron dynamics, we must go beyond Born-Oppenheimer scheme. An ab-initio approach on this regime is quite challenging and applicable for many phenomena stimulated by electronic excitations. We have developed computational methods for a non-adiabatic molecular dynamics (MD) within the framework of the local density approximation (LDA) and pseudopotentials. The higher order Suziki-Trotter formula(M. Suzuki, J. Phys. Soc. Jpn. 61), L3015 (1992). for the time-evolution operator (e^fracihbarHΔ t) is found to be applicable even with use of separable non-local pseudopotentials(L. Kleinman, and D. M. Bylander, Phys. Rev. Lett. 48), 1425 (1982).. This formula enables us to perform numerically stable simulation for a long-time scale, during which orthonormality of wavefunctions is automatically conserved. At every time step, the Hellmann-Feynman force(J. Ihm, A. Zunger, and M. L. Cohen, J. Phys. C 12), 4409 (1979). on each atom is calculated to treat atomic motion within the classical Newton's equation. In this talk, a motion of an electronically excited K3 cluster is demonstrated as an example. During the simulation, sudden decrease of an expectation values of an excited electron is observed which can be attributed to non-radiative decay.
Vibrational coherences in charge-transfer dyes: A non-adiabatic picture
NASA Astrophysics Data System (ADS)
Sissa, Cristina; Delchiaro, Francesca; Di Maiolo, Francesco; Terenziani, Francesca; Painelli, Anna
2014-10-01
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.
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.
Minimal surfaces, incompressible flows and the geometric phase
NASA Astrophysics Data System (ADS)
Martinez, J. C.
1995-02-01
We show that the Berry phase may be associated with an incompressible flow issuing through a minimal surface. An example based on the linear Jahn-Teller effect is given and found to be related to a Clifford torus rather than the usual magnetic monopole in S 3.
Twisted geometries: A geometric parametrization of SU(2) phase space
Freidel, Laurent; Speziale, Simone
2010-10-15
A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase space in terms of quantities describing the intrinsic and extrinsic geometry of the triangulation dual to the graph. These are defined by the assignment to each face of its area, the two unit normals as seen from the two polyhedra sharing it, and an additional angle related to the extrinsic curvature. These quantities do not define a Regge geometry, since they include extrinsic data, but a looser notion of discrete geometry which is twisted in the sense that it is locally well-defined, but the local patches lack a consistent gluing among each other. We give the Poisson brackets among the new variables, and exhibit a symplectomorphism which maps them into the Poisson brackets of loop gravity. The new parametrization has the advantage of a simple description of the gauge-invariant reduced phase space, which is given by a product of phase spaces associated to edges and vertices, and it also provides an Abelianization of the SU(2) connection. The results are relevant for the construction of coherent states and, as a byproduct, contribute to clarify the connection between loop gravity and its subset corresponding to Regge geometries.
Geometric phase and gravitational precession of D-branes
NASA Astrophysics Data System (ADS)
Pedder, Chris; Sonner, Julian; Tong, David
2007-12-01
We study Berry’s phase in the D0-D4-brane system. When a D0-brane moves in the background of D4-branes, the first excited states undergo a holonomy described by a non-Abelian Berry connection. At weak coupling this is an SU(2) connection over R5, known as the Yang monopole. At strong coupling, the holonomy is recast as the classical gravitational precession of a spinning particle. The Berry connection is the spin connection of the near-horizon limit of the D4-branes, which is a continuous deformation of the Yang and anti-Yang monopole.
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.
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.
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.
Demonstration of Geometric Landau-Zener Interferometry in a Superconducting Phase Qubit
NASA Astrophysics Data System (ADS)
Yu, Yang; Tan, Xinsheng; Zhang, Zhentao; Zhu, Shiliang; Zhang, Danwei; Han, Siyuan
2014-03-01
Geometric quantum manipulation and Landau-Zener interferometry have been separately explored in many quantum systems. Here we fill this gap by combining these two approaches in the study of the dynamics of a superconducting phase qubit. We propose and then experimentally demonstrate Landau-Zener interferometry based on pure geometric phases in this solid-state qubit. We observe the interference due to geometric phases accumulated in the evolution between two consecutive Landau-Zener transitions, while the dynamical phase is eliminated by a spin-echo pulse. Our numerical simulation results using measured energy relaxation and dephasing times agree well with the experimental results. The full controllability of the qubit population as a function of intrinsically fault-tolerant geometric phases provides a promising approach to fault-tolerant quantum computation. This work is partially supported by the SKPBR of China (2011CB922104, 2011CBA00200), NSFC (91021003, 11274156,11125417), PAPD, and the PCSIRT. Han is supported in part by NSF of United States (PHY-1314861).
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.
Geometric phase in cavity QED containing a nonlinear optical medium and a quantum well
NASA Astrophysics Data System (ADS)
Mohamed, A.-B. A.; Eleuch, H.
2015-11-01
The geometric phase (GP) in cavity QED filled with a nonlinear medium and containing a quantum well is analyzed. We observe collapses and revivals. The optical nonlinearity leads to high frequency oscillations of the GP. The GP is very sensitive not only to the dissipation rates but also to the amplitude of the laser pump.
Dynamic and geometric phase accumulation by Gaussian-type modes in first-order optical systems.
Alieva, Tatiana; Bastiaans, Martin J
2008-08-01
Based on the ray transformation matrix formalism, we propose a simple method for the identification of the dynamic and geometric parts of the Gouy phase, acquired by an appropriate Gaussian-type beam while propagating through a first-order optical system. PMID:18670494
Geometric phase of two-level atoms and thermal nature of de Sitter spacetime
NASA Astrophysics Data System (ADS)
Tian, Zehua; Jing, Jiliang
2013-04-01
In the framework of open quantum systems, we study the geometric phase acquired by freely falling and static two-level atoms interacting with quantized conformally coupled massless scalar fields in de Sitter-invariant vacuum. We find that, for the freely falling atom, the geometric phase gets a correction resulting from a thermal bath with the Gibbons-Hawking temperature, thus it clearly reveals the intrinsic thermal nature of de Sitter spacetime from a different physical context. For the static atom, there is a correction to the geometric phase coming from both the intrinsic thermal nature of de Sitter spacetime and the Unruh effect associated with the proper acceleration of the atom. Furthermore, in a gedanken experiment, we estimate the magnitude of the correction to the geometric phase as opposed to that in a flat spacetime. We find that the correction for the freely falling atom is too tiny to be measured, and that for the static atom achieves an observable magnitude only when the atom almost locates at the horizon.
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.
Fishman, Randy Scott; Haraldsen, Jason T
2011-01-01
While a magnetic phase may be both locally stable and globally unstable, global stability always implies local stability. The distinction between local and global stability is studied on a geometrically-frustrated triangular lattice antiferromagnet with easy axis, single-ion anisotropy D along the z axis. Whereas the critical value Dloc c for local stability may be discontinuous across a phase boundary, the critical value Dglo c Dloc c for global stability must be continuous. We demonstrate this behavior across the phase boundary between collinear 3 and 4 sublattice phases that are stable for large D.
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
NASA Astrophysics Data System (ADS)
Zhang, J.; Kyaw, Thi Ha; Tong, D. M.; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-12-01
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.
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
Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models
NASA Astrophysics Data System (ADS)
Gomez, Hector; Reali, Alessandro; Sangalli, Giancarlo
2014-04-01
We propose new collocation methods for phase-field models. Our algorithms are based on isogeometric analysis, a new technology that makes use of functions from computational geometry, such as, for example, Non-Uniform Rational B-Splines (NURBS). NURBS exhibit excellent approximability and controllable global smoothness, and can represent exactly most geometries encapsulated in Computer Aided Design (CAD) models. These attributes permitted us to derive accurate, efficient, and geometrically flexible collocation methods for phase-field models. The performance of our method is demonstrated by several numerical examples of phase separation modeled by the Cahn-Hilliard equation. We feel that our method successfully combines the geometrical flexibility of finite elements with the accuracy and simplicity of pseudo-spectral collocation methods, and is a viable alternative to classical collocation methods.
Geometric analysis of phase bunching in the central region of cyclotron
NASA Astrophysics Data System (ADS)
Miyawaki, Nobumasa; Fukuda, Mitsuhiro; Kurashima, Satoshi; Kashiwagi, Hirotsugu; Okumura, Susumu; Arakawa, Kazuo; Kamiya, Tomihiro
2013-07-01
An optimum condition for realizing phase bunching in the central region of a cyclotron was quantitatively clarified by a simplified geometric trajectory analysis of charged particles from the first to the second acceleration gap. The phase bunching performance was evaluated for a general case of a cyclotron. The phase difference of incident particles at the second acceleration gap depends on the combination of four parameters: the acceleration harmonic number h, the span angle θD of the dee electrode, the span angle θF from the first to the second acceleration gap, the ratio RV of the peak acceleration voltage between the cyclotron and ion source. Optimum values of θF for phase bunching were limited by the relationship between h and θD, which is 90°/h+θD/2≤θF≤180°/h+θD/2, and sin θF>0. The phase difference with respect to the reference particle at the second acceleration gap is minimized for voltage-ratios between two and four for an initial phase difference within 40 RF degrees. Although the slope of the first acceleration gap contributes to the RF phase at which the particles reach the second acceleration gap, phase bunching was not affected. An orbit simulation of the AVF cyclotron at the Japan Atomic Energy Agency verifies the evaluation based on geometric analysis.
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)
Krix, David; Nienhaus, Hermann
2014-08-01
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 K2O2 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.
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 K2O2 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. PMID:25149810
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.
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.
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)
Mukherjee, Saikat; Adhikari, Satrajit
2014-08-01
We calculate the adiabatic potential energy surfaces (PESs) and the non-adiabatic coupling terms (NACTs) for the excited electronic states of K3 cluster by MRCI approach using MOLPRO. The NACTs are adapted with molecular symmetry to assign appropriate IREPs so that the elements of the Hamiltonian matrix are totally symmetric. We incorporate those NACTs into three-state adiabatic-to-diabatic transformation (ADT) equations to obtain ADT angles for constructing continuous, single-valued, smooth and symmetric diabatic Hamiltonian matrix, where its elements are fitted with analytic functions. Finally, we demonstrate that the dressed diabatic and adiabatic-via-dressed diabatic PECs show prominent topological effect over dressed adiabatic curves.
Orel, Ann E.; Miller, William H.
1980-11-01
A recently developed classical model for electronically nonadiabatic collision processes is applied to electronic-vibrational energy transfer in a collinear atom~diatom system, A + BC(v=1) + A*+ BC(v=0), which closely resembles Br-H{sub 2}. This classical model, which treats electronic as well as heavy particle (i.e., translation, rotation, and vibration) degrees of freedom by classical mechanics, is found to describe the resonance features in this process reasonably well. The usefulness of the approach is that it allows one to extend standard Monte Carlo classical trajectory methodology to include electronically non-adiabatic processes in a dynamically consistent way,
Quantum Entanglement and Geometric Phase of Two Moving Two-Level Atoms
NASA Astrophysics Data System (ADS)
Abdel-Khalek, S.
2015-09-01
An important kind of interaction between two moving two-level atoms and a field mode, where the coupling parameter is taken to be time-dependent, is presented in this paper. Nonlocal correlations between the atoms and the field have been investigated by means of concurrence and von Neumann entropy in terms of the involved parameters of the system. The results show that the atomic motion plays an essential role in the evolution of system dynamics, its nonlocal correlations and geometric phase. Moreover, an interesting correlation between the entanglement and the geometric phase during the evolution was observed. The presented system can be very useful for generating and maintaining high amount of entanglement by means of controlling the parameters of atomic motion.
Polarization conversion system with liquid-crystal geometric-phase-based cylindrical lens
NASA Astrophysics Data System (ADS)
Honma, Michinori; Nose, Toshiaki
2016-01-01
We demonstrate a polarization conversion system by utilizing the polarization-splitting function of a liquid-crystal (LC) geometric-phase-based cylindrical lens. The system was constructed by combining the LC lens with a partially rubbed cell. The operation principle includes the following two steps. (i) The incident light is first decomposed into right- and left-handed circularly polarized light (RCP and LCP, respectively) as an attribute of geometric-phase-based optical elements. (ii) Then, only the RCP light is transformed into LCP light by passing it through the partially rubbed cell; as a result, the incident unpolarized light is converted into LCP light. We experimentally reveal the feasibility of the system by evaluating the effects, on the polarization conversion capability, of the diffraction efficiency, focal length, and partially rubbed cell’s retardation. The polarization conversion efficiency was obtained to be 65% on average for 400-700 nm and a maximum of 79% at 610 nm.
NASA Astrophysics Data System (ADS)
Akopyan, M. E.; Baturo, V. V.; Lukashov, S. S.; Poretsky, S. A.; Pravilov, A. M.
2012-06-01
The stepwise two-step two-color and three-step three-color laser excitation schemes are used for selective population of rovibronic levels of the first-tier ion-pair E0_g^ + and D0_u^ + states of molecular iodine and studies of non-adiabatic transitions to the D and E states induced by collisions with M = I2(X) and H2O. Collection and analysis of the luminescence after excitation of the vE = 8, 13 and vD = 13, 18 vibronic levels of the E and D states in the pure iodine vapor and the gas-phase mixtures with H2O provide rate constants for the non-adiabatic transitions to the D and E state induced by collisions with these molecules. Vibrational distributions for the I2(E,v_E {longleftrArr} limits^M D,v_D ) collision-induced non-adiabatic transitions (CINATs) are obtained. Rather strong λ _{lum}^{max } ≈ 3400 Å luminescence band is observed in the I2 + H2O mixtures, whereas its intensity is ˜100 times less in pure iodine vapor. Radiative lifetimes and quenching rate constants of the I2(E,vE = 8, 13 and D,vD = 13, 18) vibronic state are also determined. Rate constants of the I2(E,v_E stackrel {I_2 (X)} { to 30pt {rArrfill}} D,v_D ), vE = 8-54, CINATs are measured again and compared with those obtained earlier. New data confirm resonance characters of the CINATs found in our laboratory about 10 years ago. Possible reasons of differences between rate constant values obtained in this and earlier works are discussed. It is shown, in particular, that differences in rate constants of non-resonant CINATs are due to admixture of water vapor in iodine.
Geometric quantum gates in liquid-state NMR based on a cancellation of dynamical phases
NASA Astrophysics Data System (ADS)
Ota, Yukihiro; Goto, Yoshito; Kondo, Yasushi; Nakahara, Mikio
2009-11-01
A proposal for applying nonadiabatic geometric phases to quantum computing, called double-loop method [S.-L. Zhu and Z. D. Wang, Phys. Rev. A 67, 022319 (2003)], is demonstrated in a liquid-state nuclear magnetic-resonance quantum computer. Using a spin-echo technique, the original method is modified so that quantum gates are implemented in a standard high-precision nuclear magnetic-resonance system for chemical analysis. We show that a dynamical phase is successfully eliminated and a one-qubit quantum gate is realized although the gate fidelity is not high.
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. PMID:24387367
NASA Astrophysics Data System (ADS)
Pedrosa, Inácio A.; Melo, Jilvan L.; Salatiel, Sadoque
2014-11-01
We present an alternative quantum treatment for a generalized mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Taking advantage of the Lewis and Riesenfeld quantum invariant method and using quadratic invariants we obtain exact nonstationary Schrödinger states for this electromagnetic oscillation system. Afterwards, we construct coherent and squeezed states for the quantized RLC circuit and employ them to investigate some of the system's quantum properties, such as quantum fluctuations of the charge and the magnetic flux and the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary mesoscopic circuit. Finally we evaluate the dynamical and Berry phases for three special circuits. Surprisingly, we find identical expressions for the dynamical phase and the same formulae for the Berry's phase.
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
NASA Astrophysics Data System (ADS)
Liu, Tong; Cao, Xiao-Zhi; Su, Qi-Ping; Xiong, Shao-Jie; Yang, Chui-Ping
2016-02-01
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.
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
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.
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
A geometric entropy detecting the Erdös-Rényi phase transition
NASA Astrophysics Data System (ADS)
Franzosi, Roberto; Felice, Domenico; Mancini, Stefano; Pettini, Marco
2015-07-01
We propose a method to associate a differentiable Riemannian manifold to a generic many-degrees-of-freedom discrete system which is not described by a Hamiltonian function. Then, in analogy with classical statistical mechanics, we introduce an entropy as the logarithm of the volume of the manifold. The geometric entropy so defined is able to detect a paradigmatic phase transition occurring in random graphs theory: the appearance of the “giant component” according to the Erdös-Rényi theorem.
Geometric phase for a neutral particle in the presence of a topological defect
NASA Astrophysics Data System (ADS)
Bakke, K.; Nascimento, J. R.; Furtado, C.
2008-09-01
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.
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.
Phase Diagram of a Geometrically-Frustrated Triangular-Lattice Antiferromagnet in a Magnetic Field
Fishman, Randy Scott
2011-01-01
The magnetic phase diagram of a geometrically-frustrated triangular-lattice antiferromagnet is evaluated as a function of external magnetic field and anisotropy using a trial spin state built from harmonics of a fundamental ordering wavevector. A non-collinear incommensurate state, observed to be chiral and ferroelectric in CuFeO2, is sandwiched between a collinear state with 4 sublattices (SLs) and a 5-SL state. Chiral and non-collinear 5-SL states are predicted to appear at fields above and below the collinear 5-SL states.
Geometric phase low-coherence interference microscopy at high numerical apertures
NASA Astrophysics Data System (ADS)
Roy, Maitreyee; Svahn, Peter; Sheppard, Colin J. R.
2001-09-01
A low-coherence Linnik interference microscope using high numerical aperture optics has been constructed. The system uses a tungsten halogen lamp and a Koehler illumination, with separate control over field and aperture stops, so that experiments can be conducted with a range of different geometric phase which is achieved by using a polarizing beam splitter, a quarter wave plate and a rotating polarizer. Image information is extracted from the visibility of the fringes, and the position of the visibility peak along the scanning axis, yielding the height of the test surface at the corresponding points.
Piezoelectric control of the mobility of a domain wall driven by adiabatic and non-adiabatic torques
NASA Astrophysics Data System (ADS)
de Ranieri, E.; Roy, P. E.; Fang, D.; Vehsthedt, E. K.; Irvine, A. C.; Heiss, D.; Casiraghi, A.; Campion, R. P.; Gallagher, B. L.; Jungwirth, T.; Wunderlich, J.
2013-09-01
The rich internal degrees of freedom of magnetic domain walls make them an attractive complement to electron charge for exploring new concepts of storage, transport and processing of information. Here we use the tunable internal structure of a domain wall in a perpendicularly magnetized GaMnAsP/GaAs ferromagnetic semiconductor and demonstrate devices in which piezoelectrically controlled magnetic anisotropy yields up to 500% mobility variations for an electrical-current-driven domain wall. We observe current-induced domain wall motion over a wide range of current-pulse amplitudes and report a direct observation and the piezoelectric control of the Walker breakdown separating two regimes with different mobilities. Our work demonstrates that in spin-orbit-coupled ferromagnets with weak extrinsic domain wall pinning, the piezoelectric control allows one to experimentally assess the upper and lower boundaries of the characteristic ratio of adiabatic and non-adiabatic spin-transfer torques in the current-driven domain wall motion.
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.
Taioli, Simone; Garberoglio, Giovanni; Simonucci, Stefano; Beccara, Silvio a; Aversa, Lucrezia; Nardi, Marco; Verucchi, Roberto; Iannotta, Salvatore; Dapor, Maurizio; and others
2013-01-28
In this work, we investigate the processes leading to the room-temperature growth of silicon carbide thin films by supersonic molecular beam epitaxy technique. We present experimental data showing that the collision of fullerene on a silicon surface induces strong chemical-physical perturbations and, for sufficient velocity, disruption of molecular bonds, and cage breaking with formation of nanostructures with different stoichiometric character. We show that in these out-of-equilibrium conditions, it is necessary to go beyond the standard implementations of density functional theory, as ab initio methods based on the Born-Oppenheimer approximation fail to capture the excited-state dynamics. In particular, we analyse the Si-C{sub 60} collision within the non-adiabatic nuclear dynamics framework, where stochastic hops occur between adiabatic surfaces calculated with time-dependent density functional theory. This theoretical description of the C{sub 60} impact on the Si surface is in good agreement with our experimental findings.
Miller, William H.; Orel, Ann E.
1980-11-01
A classical interpretation of the Dirac-Van Vleck spin version of valence bond theory is used to obtain a classical model for electronic degrees of freedom within the valence bond framework. The approach is illustrated by deriving the explicit forms of the classical Hamiltonians, involving electronic and heavy particle degrees of freedom, for the H-H{sub 2}, F-H{sub 2} , and O-H{sub 2} systems. It is also shown how the initial conditions for both electronic and heavy particle degrees of freedom are chosen to carry out a classical trajectory simulation of collision processes. The attractive feature of this model is that it is as eaaily applicable to electronically non-adiabatic processes as it is to adiabatic ones.
Non-adiabatic and adiabatic transitions at level crossing with decay: two- and three-level systems
NASA Astrophysics Data System (ADS)
Kenmoe, M. B.; Mkam Tchouobiap, S. E.; Kenfack Sadem, C.; Tchapda, A. B.; Fai, L. C.
2015-03-01
We investigate the Landau-Zener (LZ) like dynamics of decaying two- and three-level systems with decay rates {{Γ }1} and {{Γ }2} for levels with minimum and maximum spin projection. Non-adiabatic and adiabatic transition probabilities are calculated from diabatic and adiabatic bases for two- and three-level systems. We extend the familiar two-level model of atoms with decay from the excited state out of the system into the hierarchy of three-level models which can be solved analytically or computationally in a non-perturbative manner. Exact analytical solutions are obtained within the framework of an extended form of the proposed procedure which enables to take into account all possible initial moments rather than large negative time {{t}0}=-∞ as in standard LZ problems. We elucidate the applications of our results from a unified theoretical basis that numerically analyzes the dynamics of a system as probed by experiments.
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
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.
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
Group theoretical Laws and Geometrical Phase for Paraxial Self-focusing and Solitons
NASA Astrophysics Data System (ADS)
Dantu, Subbarao; Uma, R.
1998-11-01
Group theoretical laws are formulated for the dynamics of paraxial self-focusing and soliton dynamics. The close similarity in the dynamical formulation of the theory of paraxial self-focusing of cylindrical laser beams of circular as well as elliptical cross-sections and paraxial solitons is exploited to state the group theoretical laws for the dynamics which in their limited form are known as ABCD laws in optics using our recent formulation of one of these phenomena^1. The dynamics of the laser beam is in terms of its evolution in the direction propagation while the soliton dynamics is along the actual time axis. (Conceiving soliton dynamics similar to a planar beam in the x-t plane, it can be analyzed using the paraxial approximation.) The group governing the dynamics is shown to be the Lorentz group, which gets reduced to the rotation group in the absorption-less case. Geometrical phase is evaluated for all these beams and solitons using our recent formulation of the geometric phase in projective space^2. 1. D. Subbarao, R. Uma and H. Singh, Phys. Plasmas, 5, Aug. (1998). 2. D.Subbarao Opt. Lett. 20, 2162 (1995) The authors acknowledge the financial support of CSIR(India) under the project 03(0815)/97/EMR-II for this work.
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
Viennot, David
2010-10-15
We show that the holonomy of a connection defined on a principal composite bundle is related by a non-Abelian Stokes theorem to the composition of the holonomies associated with the connections of the component bundles of the composite. We apply this formalism to describe the non-Abelian geometric phase (when the geometric phase generator does not commute with the dynamical phase generator). We find then an assumption to obtain a new kind of separation between the dynamical and the geometric phases. We also apply this formalism to the gauge theory of gravity in the presence of a Dirac spinor field in order to decompose the holonomy of the Lorentz connection into holonomies of the linear connection and of the Cartan connection.
Non-radial, non-adiabatic solar-like oscillations in RGB and HB stars
NASA Astrophysics Data System (ADS)
Grosjean, M.; Dupret, M. A.; Belkacem, K.; Montalbán, J.; Noels, A.; Samadi, R.
2013-03-01
CoRoT and Kepler observations of red giants reveal rich spectra of non-radial solar-like oscillations allowing to probe their internal structure. We compare the theoretical spectrum of two red giants in the same region of the HR diagram but in different evolutionary phases. We present here our first results on the inertia, lifetimes and amplitudes of the oscillations and discuss the differences between the two stars.
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.
Phase-space-region operators and the Wigner function: Geometric constructions and tomography
NASA Astrophysics Data System (ADS)
Ellinas, Demosthenes; Bracken, Anthony J.
2008-11-01
Quasiprobability measures on a canonical phase space give rise through the action of Weyl’s quantization map to operator-valued measures and, in particular, to region operators. Spectral properties, transformations, and general construction methods of such operators are investigated. Geometric trace-increasing maps of density operators are introduced for the construction of region operators associated with one-dimensional domains, as well as with two-dimensional shapes (segments, canonical polygons, lattices, etc.). Operational methods are developed that implement such maps in terms of unitary operations by introducing extensions of the original quantum system with ancillary spaces (qubits). Tomographic methods of reconstruction of the Wigner function based on the radon transform technique are derived by the construction methods for region operators. A Hamiltonian realization of the region operator associated with the radon transform is provided, together with physical interpretations.
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.
Kaestner, Bernd; Kashcheyevs, Vyacheslavs
2015-10-01
Precise manipulation of individual charge carriers in nanoelectronic circuits underpins practical applications of their most basic quantum property--the universality and invariance of the elementary charge. A charge pump generates a net current from periodic external modulation of parameters controlling a nanostructure connected to source and drain leads; in the regime of quantized pumping the current varies in steps of [Formula: see text] as function of control parameters, where [Formula: see text] is the electron charge and f is the frequency of modulation. In recent years, robust and accurate quantized charge pumps have been developed based on semiconductor quantum dots with tunable tunnel barriers. These devices allow modulation of charge exchange rates between the dot and the leads over many orders of magnitude and enable trapping of a precise number of electrons far away from equilibrium with the leads. The corresponding non-adiabatic pumping protocols focus on understanding of separate parts of the pumping cycle associated with charge loading, capture and release. In this report we review realizations, models and metrology applications of quantized charge pumps based on tunable-barrier quantum dots. PMID:26394066
De Ranieri, E; Roy, P E; Fang, D; Vehsthedt, E K; Irvine, A C; Heiss, D; Casiraghi, A; Campion, R P; Gallagher, B L; Jungwirth, T; Wunderlich, J
2013-09-01
The rich internal degrees of freedom of magnetic domain walls make them an attractive complement to electron charge for exploring new concepts of storage, transport and processing of information. Here we use the tunable internal structure of a domain wall in a perpendicularly magnetized GaMnAsP/GaAs ferromagnetic semiconductor and demonstrate devices in which piezoelectrically controlled magnetic anisotropy yields up to 500% mobility variations for an electrical-current-driven domain wall. We observe current-induced domain wall motion over a wide range of current-pulse amplitudes and report a direct observation and the piezoelectric control of the Walker breakdown separating two regimes with different mobilities. Our work demonstrates that in spin-orbit-coupled ferromagnets with weak extrinsic domain wall pinning, the piezoelectric control allows one to experimentally assess the upper and lower boundaries of the characteristic ratio of adiabatic and non-adiabatic spin-transfer torques in the current-driven domain wall motion. PMID:23749266
NASA Astrophysics Data System (ADS)
Kaestner, Bernd; Kashcheyevs, Vyacheslavs
2015-10-01
Precise manipulation of individual charge carriers in nanoelectronic circuits underpins practical applications of their most basic quantum property—the universality and invariance of the elementary charge. A charge pump generates a net current from periodic external modulation of parameters controlling a nanostructure connected to source and drain leads; in the regime of quantized pumping the current varies in steps of {{q}\\text{e}} f as function of control parameters, where {{q}\\text{e}} is the electron charge and f is the frequency of modulation. In recent years, robust and accurate quantized charge pumps have been developed based on semiconductor quantum dots with tunable tunnel barriers. These devices allow modulation of charge exchange rates between the dot and the leads over many orders of magnitude and enable trapping of a precise number of electrons far away from equilibrium with the leads. The corresponding non-adiabatic pumping protocols focus on understanding of separate parts of the pumping cycle associated with charge loading, capture and release. In this report we review realizations, models and metrology applications of quantized charge pumps based on tunable-barrier quantum dots.
Geometrical phase and inertial regime of the magnetization: Hannay angle and magnetic monopole
NASA Astrophysics Data System (ADS)
Wegrowe, J.-E.; Olive, E.
2015-09-01
It is well known that the Landau-Lifshitz-Gilbert (LLG) equation for a macroscopic magnetic moment find its limit of validity at very short time scales or equivalently at very high frequencies. The reason for this limit of validity is well understood in terms of separation of the characteristic times between slow (the magnetization) and fast (the environment) degrees of freedom, as pointed-out in the stochastic derivation of the LLG equation first proposed by W. F. Brown in 1963. Indeed, the ferromagnetic moment is a slow collective variable, but fast degrees of freedom are also playing a role in the dynamics, and especially the variation of the angular momentum responsible for inertia. In the last couple of years, the generalization of the LLG equation with inertia (ILLG) has been derived by different means (see list of references). The signature of the inertial regime of the magnetization is the nutation that can be measured by resonance experiments (but it has not been observed up to know). We developed an approach in terms of geometrical phase (defining the corresponding Hannay angle, which is the classical analog to the quantum Berry phase: see references), that has recently been used with success to analogous problems. We calculated the Hannay angle for the precession of the magnetization in the case of the inertial effect, and the corresponding magnetic monopole. This analysis allows the slow vs. fast variable expansion to be calculated in the specific case of pure precession.
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
Molecular level crossing and the geometric phase effect from the optical Hanle perspective
NASA Astrophysics Data System (ADS)
Glenn, R.; Dantus, M.
2016-04-01
Level-crossing spectroscopy involves lifting the degeneracy of an excited state and using the interference of two nearly degenerate levels to measure the excited-state lifetime. Here we use the idea of interference between different pathways to study the momentum-dependent wave-packet lifetime due an excited-state level crossing (conical intersection) in a molecule. Changes in population from the wave-packet propagation are reflected in the detected fluorescence. We use a chirped pulse to control the wave-packet momentum. Increasing the chirp rate increases the transition to the lower state through the conical intersection. It also increases the interference of different pathways in the upper electronic state due to the geometric phase acquired. Therefore, increasing the chirp rate decreases the population of the upper electronic state and its fluorescence yield. This suggests that there is a finite momentum-dependent lifetime of the wave packet through the level crossing as a function of chirp. We dub this lifetime the wave-packet-momentum lifetime.
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.
Complex defect in pyrite and its structure model derived from geometric phase analysis.
Németh, Péter; Dódony, István; Pósfai, Mihály; Buseck, Peter R
2013-10-01
New methods for defect analysis can lead to improved interpretation of experimental data and thus better understanding of material properties. Although transmission electronmicroscopy (TEM) has been used to study defects for many decades, interpretive ambiguities can arise for cases that seem simple or even trivial.Using geometric phase analysis (GPA), an image processing procedure, we show that an apparent simple line defect in pyrite has an entirely different character. It appears to be a b = ½[100] edge dislocation as viewed in a [001] high-resolution TEM (HRTEM) image, but the measured u(x) and u(y) displacements are asymmetric, which is inconsistent with a simple line dislocation. Instead, the defect is best understood as a terminating {101} marcasite slab in pyrite. The simulated HRTEM image based on this model reproduces the defect contrast and illustrates the power of GPA analysis for (1) avoiding potential pitfalls of misinterpreting apparently simple defects in HRTEM images, (2) detecting differences in elastic properties at the atomic scale, and (3) providing data for the positions of atom columns, thereby facilitating the construction of structure models for complex defects. PMID:23773546
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
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
NASA Astrophysics Data System (ADS)
Sanz-Sanz, Cristina; Aguado, Alfredo; Roncero, Octavio; Naumkin, Fedor
2015-12-01
Analytical derivatives and non-adiabatic coupling matrix elements are derived for H n+ systems (n = 3-5). The method uses a generalized Hellmann-Feynman theorem applied to a multi-state description based on diatomics-in-molecules (for H 3+ ) or triatomics-in-molecules (for H 4+ and H 5+ ) 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 H 2 ( 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 H 2+ are calculated and compared with the available experimental data, yielding an excellent agreement. The effect of vibrational excitation of H 2+ 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.
NASA Astrophysics Data System (ADS)
Zhai, Hua; Zhang, Jialin; Yu, Hongwei
2016-08-01
We study the geometric phase of a uniformly accelerated two-level atom coupled with vacuum fluctuations of electromagnetic fields in the presence of a perfectly reflecting plane. We find that the geometric phase difference between the accelerated and inertial atoms which can be observed by atom interferometry crucially depends on the polarizability of the atom and the distance to the boundary and it can be dramatically manipulated with anisotropically polarizable atoms. In particular, extremely close to the boundary, the phase difference can be increased by two times as compared to the case without any boundary. So, the detectability of the effects associated with acceleration using an atom interferometer can be significantly increased by the presence of a boundary using atoms with anisotropic polarizability.
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
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.
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. PMID:26637984
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)
Kobayashi, S.; Mitsuda, S.; Prokes, K.
2001-01-01
Low-temperature magnetic phase transitions of the geometrically frustrated isosceles triangular Ising antiferromagnet CoNb2O6 have been investigated by means of neutron diffraction down to T=0.2 K under applied fields up to H∥c=4.4 kOe. Below T~0.6 K, the relaxation time of the system becomes extremely long compared with our observation time, being responsible for all the anomalous low-temperature magnetic properties observed in the bulk measurements [T. Hanawa et al., J. Phys. Soc. Jpn. 63, 2706 (1994)]. In addition to confirmation of the triple point where the antiferromagnetic, field-induced ferrimagnetic, and incommensurate phases meet together in the H∥c-T magnetic phase diagram, we also found various ordered phases that are field induced between the ferrimagnetic and saturated paramagnetic phases.
Geometric Phase, Zeeman, and Optical Effects in the Excitation of Lead Fluoride and Kryptonite
NASA Astrophysics Data System (ADS)
Rupasinghe, Priyanka Milinda
2011-12-01
This dissertation is motivated by two major challenges in modern Physics. One is related to precession measurement and other is related to atmospheric science. The amount of CP violation (equivalently time reversal (T) symmetry violation) that occurs in the Standard Model, the most successful theory in the particle physics today, is not sufficient to explain why we live in a matter (rather than anti-matter) dominated universe. A measurable electric dipole moment of the electron (e-EDM) proportional to its spin may help to unravel this matter anti-matter mystery and could point the way to physics beyond the Standard Model. As an e-EDM probe, both cold molecular trap and molecular beam techniques have been proposed. In this thesis we show that the geometric phase effect limits the viability of a cold molecular trap technique. Specifically we show the molecular trap method can not be employed for PbF until the technology is available to cool down molecules to ultra cold temperatures. This thesis also addresses two major difficulties that need to be overcome in order to carry out a molecular beam e-EDM measurement. One of these difficulties is that background magnetic fields mimic the e-EDM. For this reason, molecules with small magnetic g-factors greatly reduce the background due to this effect. In this dissertation investigation of the Zeeman structure of the PbF molecule including state dependent g-factor measurements are determined through extensive analysis of microwave spectroscopy. The other major difficulty addressed in this thesis is the requirement to create a highly uniform electric field that can be reversed in a precise and consistent manner. Specifically we describe a precise high voltage control and switching system that has been built. Isotopic detection of Krypton has many important applications including archaeological dating beyond that possible using ^{14}C and nuclear activitymonitoring all around the world. It has been shown that laser cooling and
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.
Imai, Hiromitsu; Otsubo, Yuki; Morinaga, Atsuo
2007-07-15
The geometric manipulation of the quantum states of two-level atoms with two laser-controlled resonant {pi} pulses with a relative phase difference was evaluated using a time-domain atom interferometer comprising a cold sodium atom ensemble and two copropagating two-photon Raman pulses. It was verified that the relative phase shift between two states is double the control phase difference and that the rotation around the axis 3 of the Bloch sphere can be controlled by geometric manipulation.
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. PMID:26651714
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.
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.
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
NASA Astrophysics Data System (ADS)
Benabbas, Abdelkrim; Salna, Bridget; Sage, J. Timothy; Champion, Paul M.
2015-03-01
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)
Joyes, P.; Tarento, R. J.; Van de Walle, J.
1997-06-01
The non-adiabatic time-dependent reaction of valence electrons in media submitted to a violent perturbation has important consequences in monoatomic fragmentation. We study these effects for various fullerenes: C20, C60, C70 and C110. The ionization probability P(K) of a monoatomic fragment with kinetic K energy is investigated for C20, C60, C70 and C110. Our results show that there is no important variation of P(K) with size but, for a given size, P(K) may depend on the initial position of the ejected atom. We give the variation with time of the population on the ejected atom and on various substrate levels. We also study the electronic currents appearing during the phenomenon.
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.
2015-01-01
Non-adiabatic rapid passage (NARS) electron paramagnetic resonance (EPR) spectroscopy was introduced by Kittell, A.W., Camenisch, T.G., Ratke, J.J. Sidabras, J.W., Hyde, J.S., 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, and enhance spectral resolution in copper (II) spectra. 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
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
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.
Geometric diffusion of quantum trajectories
Yang, Fan; Liu, Ren-Bao
2015-01-01
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. PMID:26178745
Geometric diffusion of quantum trajectories.
Yang, Fan; Liu, Ren-Bao
2015-01-01
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. PMID:26178745
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.
Femtosecond time-resolved ionization spectroscopy of Na 3(B) and the question of the geometric phase
NASA Astrophysics Data System (ADS)
Schön, J.; Köppel, H.
1994-12-01
The femtosecond time-resolved ionization spectrum of the B-state of Na 3 has been studied theoretically, taking two nuclear degrees of freedom into account (bending mode and pseudorotation). Special emphasis is put on a comparison between different approaches to the pseudorotational dynamics of Na 3(B) proposed earlier in the literature: a Jahn-Teller treatment invoked in the original work versus a pseudo-Jahn-Teller treatment advanced in later studies. The time-dependent wave-packet dynamics is found to differ drastically in the two cases although it proceeds on (virtually) the same potential energy surface. This is interpreted as a consequence of the geometric phase which is nontrivial only in the Jahn-Teller case. A low-energy peak in the Fourier transform of the pump-probe spectrum of Baumert et al. (Chem. Phys. Letters 209 (1993) 29) is tentatively interpreted as evidence in favour of the pseudo-Jahn-Teller mechanism.
NASA Astrophysics Data System (ADS)
Yan, H.; Plaster, B.
2011-06-01
Geometric-phase-induced false electric dipole moment (EDM) signals, resulting from interference between magnetic field gradients and particle motion in electric fields, have been studied extensively in the literature, especially for neutron EDM experiments utilizing stored ultracold neutrons and co-magnetometer atoms. Previous studies have considered particle motion in the transverse plane perpendicular to the direction of the applied electric and magnetic fields. We show, via Monte Carlo studies, that motion along the field direction can impact the magnitude of this false EDM signal if the wall surfaces are rough such that the wall collisions can be modeled as diffuse, with the results dependent on the size of the storage cell's dimension along the field direction.
NASA Astrophysics Data System (ADS)
Huang, Chun-Feng; Tsai, I.-H.
It is well-established how the quantum interference induces strong localization leading to quantum Hall effect at high enough magnetic fields. Decreasing the magnetic fields, however, the localization strength can be reduced and the semiclassical magneto-oscillations following Shubnikov-de Haas formula appear in most quantum Hall systems. To understand the transport properties as the localization strength becomes weak, our team has investigated the magneto-resistance in some quantum Hall systems at low magnetic fields. Under the semiclassical transport, the crossing points in Hall plateaus showed Landau-band quantization and microwave-induced heating demonstrated the band-edge equivalence important to Landau-level addition transformation. We note that such equivalence is consistent with the edge universality based on the random matrices of Wigner type, and the Landau-band quantization can be explained by considering geometric phase effects. From our study, some quantum Hall features can survive as the semiclassical transport reveals the insufficient localization.
Geometric relationships for homogenization in single-phase binary alloy systems
NASA Technical Reports Server (NTRS)
Unnam, J.; Tenney, D. R.; Stein, B. A.
1978-01-01
A semiempirical relationship is presented which describes the extent of interaction between constituents in single-phase binary alloy systems having planar, cylindrical, or spherical interfaces. This relationship makes possible a quick estimate of the extent of interaction without lengthy numerical calculations. It includes two parameters which are functions of mean concentration and interface geometry. Experimental data for the copper-nickel system are included to demonstrate the usefulness of this relationship.
Zhu, Li; Hsieh, Fushing; Li, Juan; Chi, Eric
2011-08-30
We address statistical issues regarding modeling a collection of longitudinal response trajectories characterized by the presence of subject-specific phase-dependent effects and variation. To accommodate these two time-varying individual characteristics, we employ a geometric stochastic differential equation for modeling based on a Brownian motion process and develop a two-step paradigm for statistical analysis. This paradigm reverses the order of statistical inference in random effects model. We first extract individual information about phase-dependent treatment effects and volatility parameters for all subjects. Then, we derive the association relationship between the parameters characterizing the individual longitudinal trajectories and the corresponding covariates by means of multiple regression analysis. The stochastic differential equation model and the two-step paradigm together provide significant advantages both in modeling flexibility and in computational efficiency. The modeling flexibility is due to the easy adaptation of temporal change points for subject-specific phase transition in treatment effects, whereas the computational efficiency benefits in part from the independent increment property of Brownian motion that avoids high-dimensional integration. We demonstrate our modeling approach and statistical analysis on a real data set of longitudinal measurements of disease activity scores from a rheumatoid arthritis study. PMID:21751228
NASA Astrophysics Data System (ADS)
Liu, Shuli; Liu, Zhanwei
2016-05-01
The accurate measurement for the surface profiles of transparent object is of significance for quality control in optical devices and precision instruments. Here, a double transmission-mediums based geometric phase analysis method has been developed to evaluate both the upper and lower surface profiles of transparent object. To do this, the tested transparent object is placed above a preprinted lattice pattern. When viewed from above with a CCD camera, any slope variations of the surfaces will lead to distortions of the transmission-lattice patterns. And when changing one side of object's contact medium, the lattice virtual image with modulated phase is distorted once again. Combined with the derived relationship between phase variations of transmission-lattice patterns and out-of-plane heights of two surfaces, the double-sided surface profiles of transparent object can be reconstructed successfully. With this, the technique, which is verified experimentally, is demonstrated to be a feasible and reliable method. The advantage of this method is that it simplifies the setup and allows a fast estimation of the geometry of a transparent specimen. The double-sided profiles can be decoupled easily according to the big difference of refractive indexes between contact mediums. And the calculation accuracy can be guaranteed by the weighted average from four directions.
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.
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).
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.
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)
Wu, Lian-Ao
1994-12-01
It is shown that the cyclic evolution posed by Aharonov and Anandan [Phys. Rev. Lett. 58, 1593 (1987)] universally exists in any quantum system: cyclic evolution occurs for special initial wave functions, whatever the concrete form of the Hamiltonian. The above results are illustrated and some specific geometric phases are given.
NASA Astrophysics Data System (ADS)
Kang, Shouxin; Zhang, Hao; Liu, Bo; Lin, Wei; Zhang, Ning; Miao, Yinping
2016-01-01
A dual-parameter sensor based on a fiber-optic interferometer consisting of a non-adiabatic fiber taper and a long-period fiber grating (LPFG) integrated with magnetic nanoparticle fluids has been proposed and experimentally demonstrated. Due to the Mach-Zehnder interference induced by the concatenation of the fiber taper and long-period grating, an interferometric spectrum could be acquired within the transmission resonance spectral envelope of the LPFG. Thanks to different magnetic field and temperature sensitivities of difference interference dips, simultaneous measurement of the magnetic field intensity and environmental temperature could be achieved. Moreover, due to the variation in coupling coefficients of the fiber taper and the LPFG in response to the change of the applied magnetic field intensity, some of the interference dips would exhibit opposite magnetic-field-intensity-dependent transmission loss variation behavior. Magnetic field intensity and temperature sensitivities of 0.017 31 dB Oe-1 and 0.0315 dB K-1, and -0.024 55 dB Oe-1 and -0.056 28 dB K-1 were experimentally acquired for the experimentally monitored interference dips.
Habershon, Scott
2013-09-14
We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency.
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)
Muravsky, Leonid I.; Kulynych, Yaroslav P.; Maksymenko, Olexander P.; Voronyak, Taras I.; Kostyukevych, Sergey A.
2002-04-01
The new method for identification of optical marks containing transformed phase masks (TPMs) is considered. A TPM placed in an optical correlator produces several sharp correlation peaks on its output. We choose the distances between peaks as basic geometrical features of a TPM. The increase of quantity of basic features leads to the increase of security level of documents and valuable papers. However, the amount of such features is limited and is depending from many factors. We picked the probability of false identification of the nearest feature as the criterion of separation of features on independent classes. The optical/digital device for identification of credit cards based on a joint transform correlator architecture was used for the study of TPMs. To estimate the law of distribution of basic features inherent to the same class, we carried out experiments with the series of TPMs. We have shown, that the additional features allow to increase the number of basic features, separated on different classes. These experiments also have allowed to estimate the error of features measurements
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
Complete state-resolved non-adiabatic dynamics of the O((3)P) + D2 → OD(X(2)Π) + D reaction.
Lahankar, Sridhar A; Zhang, Jianming; Minton, Timothy K; McKendrick, Kenneth G
2014-09-01
The first quantum-state-resolved distributions over the full range of available product levels are reported for any isotopic variant of the elementary reaction of O((3)P) with molecular hydrogen. A laser-detonation source was used to produce a hyperthermal oxygen-atom beam, which allowed for sufficient collision energy to surmount the reaction barrier. This beam was crossed by a supersonic beam of D2. The nascent OD products were detected by laser-induced fluorescence. OD rotational distributions in vibrational states v' = 0, 1, and 2 at a collision energy of 25 kcal mol(-1) are reported, together with distributions for the dominant product vibrational level, v'= 0, at lower collision energies of 20 and 15 kcal mol(-1). The OD product is highly rotationally excited, to a degree that declines as expected for the higher vibrational levels or for reductions in the collision energy. The measured rovibrational distributions at the highest collision energy are in excellent agreement with previous theoretical predictions based on quantum scattering calculations on the triplet potential energy surfaces developed by Rogers et al. (J. Phys. Chem. A 2000, 104, 2308-2325). However, no significant OD spin-orbit preference was observed, in contrast to the predictions of most existing theoretical models of the non-adiabatic dynamics based on the widely used reduced-dimensional four-state model of Hoffmann and Schatz (J. Chem. Phys. 2000, 113, 9456-9465). Furthermore, a clear observed preference for OD Π(A') Λ-doublet levels is not consistent with a simple extrapolation of the calculated relative reaction cross sections on intermediate surfaces of (3)A' and (3)A″ symmetry. PMID:25084139
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.
Nagarajan, Mahesh B; Coan, Paola; Huber, Markus B; Diemoz, Paul C; Glaser, Christian; Wismüller, Axel
2014-02-01
Phase-contrast computed tomography (PCI-CT) has shown tremendous potential as an imaging modality for visualizing human cartilage with high spatial resolution. Previous studies have demonstrated the ability of PCI-CT to visualize (1) structural details of the human patellar cartilage matrix and (2) changes to chondrocyte organization induced by osteoarthritis. This study investigates the use of high-dimensional geometric features in characterizing such chondrocyte patterns in the presence or absence of osteoarthritic damage. Geometrical features derived from the scaling index method (SIM) and statistical features derived from gray-level co-occurrence matrices were extracted from 842 regions of interest (ROI) annotated on PCI-CT images of ex vivo human patellar cartilage specimens. These features were subsequently used in a machine learning task with support vector regression to classify ROIs as healthy or osteoarthritic; classification performance was evaluated using the area under the receiver-operating characteristic curve (AUC). SIM-derived geometrical features exhibited the best classification performance (AUC, 0.95 ± 0.06) and were most robust to changes in ROI size. These results suggest that such geometrical features can provide a detailed characterization of the chondrocyte organization in the cartilage matrix in an automated and non-subjective manner, while also enabling classification of cartilage as healthy or osteoarthritic with high accuracy. Such features could potentially serve as imaging markers for evaluating osteoarthritis progression and its response to different therapeutic intervention strategies. PMID:24043594
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)
Neira Bueno, O. L.; Hincapié H, L.; García Madrid, C.
2016-02-01
The study of geometric, electronic properties and intrinsic chemical reactivity is presented for the case of Quinoline and three-derived molecules (4-Amino-Quinoline, 3- Phenyl-Quinoline, 4-Amino-3-phenylquinoline). The study was carried for the ground state in gas phase in the context of the functional theory density using B3LYP/6 31+G (d) model. The purpose of the study is aimed for identifying a compound derived from quinoline, on based to mono- or bi-substitution, using the amino fragment and the phenyl group.
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.
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)
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; Guo, Hua
2015-03-28
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(X̃/Ã) 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(X̃, v = 0) exhibit very different characteristics. The A' states, produced mostly via the B̃→X̃ conical intersection pathway, have significantly higher populations than the A″ counterparts, which are primarily from the B̃→Ã 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(X̃) 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 B̃→X̃ non-adiabatic pathway. On the other hand, the experiment-theory agreement for the OH(Ã) fragment is also satisfactory, although some small quantitative differences suggest remaining imperfections of the ab initio based potential energy surfaces. PMID:25833589
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)
Chuang, K. H.; Hwang, K. S.
2011-07-01
The powder injection molded SKD11 tool steels often manifest shape retention problems during supersolidus liquid phase sintering due to the difficulties in controlling the amount of liquid phase. The typical temperature range for the sintering of SKD11 is only 10 K, between 1503 and 1513 K (1230 and 1240 °C), and this narrow sintering range demands a special furnace with very uniform temperature distribution. Through the addition of carbides, in particular TiC, this problem is resolved by enlarging the liquid + γ + carbide region in the phase diagram and by impeding the grain growth with the carbides. The resulting sintering window is broadened to 40 K, between 1513 and 1553 K (1240 and 1280 °C). The relevant mechanisms on the improvement of shape retention are discussed with a focus on the effect of carbide addition on the changes in the phase diagram and the microstructure. A guideline for the selection of effective carbides is also proposed based on the experimental results and the phase diagram analyses.
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.
Akai, Nobuyuki; Parazs, David; Kawai, Akio; Shibuya, Kazuhiko
2009-04-01
Low-temperature infrared spectra of thermally evaporated ionic liquids, 1-ethyl- and 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide and bis(trifluoromethanesulfonyl)amide have been measured in a cryogenic Ne matrix. The experimental IR spectrum of bis(trifluoromethanesulfonyl)amide can be reproduced theoretically by not B3LYP/6-31G* but MP2/6-31G* calculation, which suggests that the vibrational analysis for ionic liquids composed of bis(trifluoromethanesulfonyl)imide anion would be more successfully performed using the MP2 calculation. By comparison of the matrix-isolation spectra of the ionic liquids with the MP2 calculation, their geometrical structures in the gas phase are determined to be of C(2-position)-H(+)...N(-) interaction structure, which corresponds to the geometry of the energetically second-lowest ion-pair structure. The present study may provide a valuable clue to understand a vaporization mechanism of ionic liquid. PMID:19281187
NASA Astrophysics Data System (ADS)
Steyerl, A.; Kaufman, C.; Müller, G.; Malik, S. S.; Desai, A. M.; Golub, R.
2014-05-01
Pendlebury etal . [Phys. Rev. A 70, 032102 (2004), 10.1103/PhysRevA.70.032102] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schrödinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.
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 Astrophysics Data System (ADS)
van Gorp, Jetse S.; Bakker, Chris J. G.; Bouwman, Job G.; Smink, Jouke; Zijlstra, Frank; Seevinck, Peter R.
2015-01-01
In this study, we explore the potential of compressed sensing (CS) accelerated broadband 3D phase-encoded turbo spin-echo (3D-PE-TSE) for the purpose of geometrically undistorted imaging in the presence of field inhomogeneities. To achieve this goal 3D-PE-SE and 3D-PE-TSE sequences with broadband rf pulses and dedicated undersampling patterns were implemented on a clinical scanner. Additionally, a 3D multi-spectral spin-echo (ms3D-SE) sequence was implemented for reference purposes. First, we demonstrated the influence of susceptibility induced off-resonance effects on the spatial encoding of broadband 3D-SE, ms3D-SE, 3D-PE-SE and 3D-PE-TSE using a grid phantom containing a titanium implant (Δχ = 182 ppm) with x-ray CT as a gold standard. These experiments showed that the spatial encoding of 3D-PE-(T)SE was unaffected by susceptibility induced off-resonance effects, which caused geometrical distortions and/or signal hyper-intensities in broadband 3D-SE and, to a lesser extent, in ms3D-SE frequency encoded methods. Additionally, an SNR analysis was performed and the temporally resolved signal of 3D-PE-(T)SE sequences was exploited to retrospectively decrease the acquisition bandwidth and obtain field offset maps. The feasibility of CS acceleration was studied retrospectively and prospectively for the 3D-PE-SE sequence using an existing CS algorithm adapted for the reconstruction of 3D data with undersampling in all three phase encoded dimensions. CS was combined with turbo-acceleration by variable density undersampling and spherical stepwise T2 weighting by randomly sorting consecutive echoes in predefined spherical k-space layers. The CS-TSE combination resulted in an overall acceleration factor of 60, decreasing the original 3D-PE-SE scan time from 7 h to 7 min. Finally, CS accelerated 3D-PE-TSE in vivo images of a titanium screw were obtained within 10 min using a micro-coil demonstrating the feasibility of geometrically undistorted MRI near severe
van Gorp, Jetse S; Bakker, Chris J G; Bouwman, Job G; Smink, Jouke; Zijlstra, Frank; Seevinck, Peter R
2015-01-21
In this study, we explore the potential of compressed sensing (CS) accelerated broadband 3D phase-encoded turbo spin-echo (3D-PE-TSE) for the purpose of geometrically undistorted imaging in the presence of field inhomogeneities. To achieve this goal 3D-PE-SE and 3D-PE-TSE sequences with broadband rf pulses and dedicated undersampling patterns were implemented on a clinical scanner. Additionally, a 3D multi-spectral spin-echo (ms3D-SE) sequence was implemented for reference purposes. First, we demonstrated the influence of susceptibility induced off-resonance effects on the spatial encoding of broadband 3D-SE, ms3D-SE, 3D-PE-SE and 3D-PE-TSE using a grid phantom containing a titanium implant (Δχ = 182 ppm) with x-ray CT as a gold standard. These experiments showed that the spatial encoding of 3D-PE-(T)SE was unaffected by susceptibility induced off-resonance effects, which caused geometrical distortions and/or signal hyper-intensities in broadband 3D-SE and, to a lesser extent, in ms3D-SE frequency encoded methods. Additionally, an SNR analysis was performed and the temporally resolved signal of 3D-PE-(T)SE sequences was exploited to retrospectively decrease the acquisition bandwidth and obtain field offset maps. The feasibility of CS acceleration was studied retrospectively and prospectively for the 3D-PE-SE sequence using an existing CS algorithm adapted for the reconstruction of 3D data with undersampling in all three phase encoded dimensions. CS was combined with turbo-acceleration by variable density undersampling and spherical stepwise T2 weighting by randomly sorting consecutive echoes in predefined spherical k-space layers. The CS-TSE combination resulted in an overall acceleration factor of 60, decreasing the original 3D-PE-SE scan time from 7 h to 7 min. Finally, CS accelerated 3D-PE-TSE in vivo images of a titanium screw were obtained within 10 min using a micro-coil demonstrating the feasibility of geometrically undistorted MRI near severe
NASA Astrophysics Data System (ADS)
Cockburn, Bernardo; Kao, Chiu-Yen; Reitich, Fernando
2014-02-01
We present an adaptive spectral/discontinuous Galerkin (DG) method on curved elements to simulate high-frequency wavefronts within a reduced phase-space formulation of geometrical optics. Following recent work, the approach is based on the use of level sets defined by functions satisfying the Liouville equations in reduced phase-space and, in particular, it relies on the smoothness of these functions to represent them by rapidly convergent spectral expansions in the phase variables. The resulting (hyperbolic) system of equations for the coefficients in these expansions are then amenable to a high-order accurate treatment via DG approximations. In the present work, we significantly expand on the applicability and efficiency of the approach by incorporating mechanisms that allow for its use in scattering simulations and for a reduced overall computational cost. With regards to the former we demonstrate that the incorporation of curved elements is necessary to attain any kind of accuracy in calculations that involve scattering off non-flat interfaces. With regards to efficiency, on the other hand, we also show that the level-set formulation allows for a space p-adaptive scheme that under-resolves the level-set functions away from the wavefront without incurring in a loss of accuracy in the approximation of its location. As we show, these improvements enable simulations that are beyond the capabilities of previous implementations of these numerical procedures.
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)
Ahmed, Hilal; Khan, Shakeel; Khan, Wasi; Nongjai, Razia; Khan, Imran
2014-11-01
We have systematically investigated structural, electrical and magnetic properties of Fe doped La0.33Sr0.67MnO3 manganites synthesized through solid-state reaction-route. All the samples are found to have rhombohedral crystal structure. The crystallite sizes obtained by XRD data are much smaller than the average grain size obtained by scanning electron microscope (SEM). Temperature dependent resistivity data were fitted using Mott's variable-range hopping (VRH) and small polaron hopping (SPH) models for obtaining different parameters. The adiabatic SPH conduction mechanism is followed almost for both samples in the absence of magnetic field but a switching from adiabatic to non-adiabatic SPH conduction mechanism is found in the presence of magnetic field. Temperature dependent magnetization (M-T) measurements confirm the decrease in Curie-temperature (TC) with Fe doping. Both the samples exhibited ferromagnetic behavior at 10 K and 300 K with a small hysteresis loop and low coercivity.
Lehmpfuhl, Monika Carola; Hess, Andreas; Gaudnek, M André; Sibila, Michael
2011-07-01
The exact knowledge of the blood vessel geometry plays an important role, not only in clinical applications (stroke diagnosis, detection of stenosis), but also for deeper analysis of hemodynamic functional data, such as fMRI. Such vessel geometries can be obtained by different MR angiographic measurements. It is shown that simulations using computational fluid dynamics (CFD) can be used to validate the vessel geometry, automatically reconstructed from time of flight (TOF) angiograms or phase contrast angiography (PC-MRA) data. CFD simulations are based on PC-MRA data, since these data contain additionally rheological information (phases) besides merely amplitudes as is the case for TOF measurements. Parts of the rat brain vessel system are carefully modeled consisting of a main tube and second order branches. By analyzing velocity changes up and downstream of bifurcations, it is shown that CFD can be used to help detecting missing vessels in the TOF based reconstruction. It is demonstrated by artificially deleting a branch from the reconstruction and compared the flow in both resulting CFD simulations. Finally the simulations help to understand the effects of secondary branches on the flow in the main tube. The aim of this study is to compare the measured (PCA) flow data with the CFD simulation results, based on the vessel geometry gained from the PCA image using an in house reconstruction algorithm. If a more accurate simulation method is found and if in principal the simulation matches the PCA data, it might be possible to deduct that in cases where the measured data varies from the CFD simulation, the reconstruction is not complete, i.e. branches are missing or wrong branches were reconstructed. PMID:20696607
Hinker, P.; Hansen, C.
1993-09-01
An algorithm is presented which describes an application independent method for reducing the number of polygonal primitives required to faithfully represent an object. Reducing polygon count without a corresponding reduction in object detail is important for: achieving interactive frame rates in scientific visualization, reducing mass storage requirements, and facilitating the transmission of large, multi-timestep geometric data sets. This paper shows how coplanar and nearly coplanar polygons can be merged into larger complex polygons and re-triangulated into fewer simple polygons than originally required. The notable contributions of this paper are: (1) a method for quickly grouping polygons into nearly coplanar sets, (2) a fast approach for merging coplanar polygon sets and, (3) a simple, robust triangulation method for polygons created by 1 and 2. The central idea of the algorithm is the notion of treating polygonal data as a collection of segments and removing redundant segments to quickly form polygon hulls which represent the merged coplanar sets.
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)
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.
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
Geometric Quantum Noise of Spin
NASA Astrophysics Data System (ADS)
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.
Effect of noise on geometric logic gates for quantum computation
Blais, A.; Tremblay, A.-M.S.
2003-01-01
We introduce the nonadiabatic, or Aharonov-Anandan, geometric phase as a tool for quantum computation and show how this phase on one qubit can be monitored by a second qubit without any dynamical contribution. We also discuss how this geometric phase could be implemented with superconducting charge qubits. While the nonadiabatic geometric phase may circumvent many of the drawbacks related to the adiabatic (Berry) version of geometric gates, we show that the effect of fluctuations of the control parameters on nonadiabatic phase gates is more severe than for the standard dynamic gates. Similarly, fluctuations also affect to a greater extent quantum gates that use the Berry phase instead of the dynamic phase.
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 Landau-Zener interferometry.
Gasparinetti, S; Solinas, P; Pekola, J P
2011-11-11
We propose a new type of interferometry, based on geometric phases accumulated by a periodically driven two-level system undergoing multiple Landau-Zener transitions. As a specific example, we study its implementation in a superconducting charge pump. We find that interference patterns appear as a function of the pumping frequency and the phase bias, and clearly manifest themselves in the pumped charge. We also show that the effects described should persist in the presence of realistic decoherence. PMID:22181761
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.
Geometric Gyrokinetic Theory for Edge Plasma
Qin, H; Cohen, R H; Nevins, W M; Xu, X Q
2007-01-18
It turns out that gyrokinetic theory can be geometrically formulated as special cases of a geometrically generalized Vlasov-Maxwell system. It is proposed that the phase space of the spacetime is a 7-dimensional fiber bundle P over the 4-dimensional spacetime M, and that a Poincare-Cartan-Einstein 1-form {gamma} on the 7-dimensional phase space determines particles worldlines in the phase space. Through Liouville 6-form {Omega} and fiber integral, the 1-form {gamma} also uniquely defines a geometrically generalized Vlasov-Maxwell system as a field theory for the collective electromagnetic field. The geometric gyrokinetic theory is then developed as a special case of the geometrically generalized Vlasov-Maxwell system. In its most general form, gyrokinetic theory is about a symmetry, called gyro-symmetry, for magnetized plasmas, and the 1-form {gamma} again uniquely defines the gyro-symmetry. The objective is to decouple the gyro-phase dynamics from the rest of particle dynamics by finding the gyro-symmetry in {gamma}. Compared with other methods of deriving the gyrokinetic equations, the advantage of the geometric approach is that it allows any approximation based on mathematical simplification or physical intuition to be made at the 1-form level, and yet the field theories still have the desirable exact conservation properties such as phase space volume conservation and energy-momentum conservation if the 1-form does not depend on the spacetime coordinate explicitly. A set of generalized gyrokinetic equations valid for the edge plasmas is then derived using this geometric method. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. The fact that we adopted the geometric method in the present study does not necessarily imply that the major results reported here can not be achieved using classical methods. What the
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.
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…
Bayro-Corrochano, E J
2001-01-01
This paper shows the analysis and design of feedforward neural networks using the coordinate-free system of Clifford or geometric algebra. It is shown that real-, complex-, and quaternion-valued neural networks are simply particular cases of the geometric algebra multidimensional neural networks and that some of them can also be generated using support multivector machines (SMVMs). Particularly, the generation of radial basis function for neurocomputing in geometric algebra is easier using the SMVM, which allows one to find automatically the optimal parameters. The use of support vector machines in the geometric algebra framework expands its sphere of applicability for multidimensional learning. Interesting examples of nonlinear problems show the effect of the use of an adequate Clifford geometric algebra which alleviate the training of neural networks and that of SMVMs. PMID:18249926
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. PMID:19548707
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
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.
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)
NASA Astrophysics Data System (ADS)
Rice, Stuart A.; Toda, Mikito; Komatsuzaki, Tamiki; Konishi, Tetsuro; Berry, R. Stephen
2005-01-01
Edited by Nobel Prize winner Ilya Prigogine and renowned authority Stuart A. Rice, the Advances in Chemical Physics series provides a forum for critical, authoritative evaluations in every area of the discipline. In a format that encourages the expression of individual points of view, experts in the field present comprehensive analyses of subjects of interest. Advances in Chemical Physics remains the premier venue for presentations of new findings in its field. Volume 130 consists of three parts including: Part I: Phase Space Geometry of Multi-dimensional Dynamical Systems and Reaction Processes Part II Complex Dynamical Behavior in Clusters and Proteins, and Data Mining to Extract Information on Dynamics Part III New directions in Multi-Dimensional Chaos and Evolutionary Reactions
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.
NASA Technical Reports Server (NTRS)
Shahshahani, M.
1991-01-01
The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.
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.
ERIC Educational Resources Information Center
Burgess, Claudia R.
2014-01-01
Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…
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…
Levels of Geometric Understanding.
ERIC Educational Resources Information Center
Pegg, John; Davey, Geoff
1991-01-01
Three activities are presented to assess the level of students' geometric understanding according to van Hiele learning model. The activities--Descriptions, Minimum Properties, and Class Inclusion--are applied to the example of classifying quadrilaterals as squares, rectangles, rhombi, or parallelograms. Implications of this assessment are…
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
Geometrical deuteron stripping revisited
Neoh, Y. S.; Yap, S. L.
2014-03-05
We investigate the reality of the idea of geometrical deuteron stripping originally envisioned by Serber. By taking into account of realistic deuteron wavefunction, nuclear density, and nucleon stopping mean free path, we are able to estimate inclusive deuteron stripping cross section for deuteron energy up to before pion production. Our semiclassical model contains only one global parameter constant for all nuclei which can be approximated by Woods-Saxon or any other spherically symmetric density distribution.
Geometric measures of entanglement
Uyanik, K.; Turgut, S.
2010-03-15
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
Demonstration of Geometric Landau-Zener Interferometry in a Superconducting Qubit
NASA Astrophysics Data System (ADS)
Tan, Xinsheng; Zhang, Dan-Wei; Zhang, Zhentao; Yu, Yang; Han, Siyuan; Zhu, Shi-Liang
2014-01-01
Geometric quantum manipulation and Landau-Zener interferometry have been separately explored in many quantum systems. In this Letter, we combine these two approaches to study the dynamics of a superconducting phase qubit. We experimentally demonstrate Landau-Zener interferometry based on the pure geometric phases in this solid-state qubit. We observe the interference caused by a pure geometric phase accumulated in the evolution between two consecutive Landau-Zener transitions, while the dynamical phase is canceled out by a spin-echo pulse. The full controllability of the qubit state as a function of the intrinsically robust geometric phase provides a promising approach for quantum state manipulation.
Demonstration of geometric Landau-Zener interferometry in a superconducting qubit.
Tan, Xinsheng; Zhang, Dan-Wei; Zhang, Zhentao; Yu, Yang; Han, Siyuan; Zhu, Shi-Liang
2014-01-17
Geometric quantum manipulation and Landau-Zener interferometry have been separately explored in many quantum systems. In this Letter, we combine these two approaches to study the dynamics of a superconducting phase qubit. We experimentally demonstrate Landau-Zener interferometry based on the pure geometric phases in this solid-state qubit. We observe the interference caused by a pure geometric phase accumulated in the evolution between two consecutive Landau-Zener transitions, while the dynamical phase is canceled out by a spin-echo pulse. The full controllability of the qubit state as a function of the intrinsically robust geometric phase provides a promising approach for quantum state manipulation. PMID:24484040
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.
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.
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.
Information geometric nonlinear filtering
NASA Astrophysics Data System (ADS)
Newton, Nigel J.
2015-06-01
This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on a Hilbert information manifold. This supports the Fisher metric as a pseudo-Riemannian metric. Flows of Shannon information are shown to be connected with the quadratic variation of the process of posterior distributions in this metric. Apart from providing a suitable setting in which to study such information-theoretic properties, the Hilbert manifold has an appropriate topology from the point of view of multi-objective filter approximations. A general class of finite-dimensional exponential filters is shown to fit within this framework, and an intrinsic evolution equation, involving Amari's -1-covariant derivative, is developed for such filters. Three example systems, one of infinite dimension, are developed in detail.
Universal Superadiabatic Geometric Quantum Gates in Nitrogen-Vacancy Centers
NASA Astrophysics Data System (ADS)
Yan, Hui; Liang, Zhengtao; Zhu, Shiliang
We propose a scheme to implement a universal set of quantum gates based on geometric phases and superadiabatic quantum control. The proposed quantum gates consolidate the advantages of both strategies for robust and fast. The diamond nitrogen-vacancy center system is adopted as a typical example to illustrate the scheme. We show those gates can be realized in a simple two-level configuration by appropriately controlling the amplitude, phase and frequency of just one microwave field. The robust and fast features are confirmed by comparing the fidelities of the proposed superadiabatic geometric phase gate with three other kinds of phase gates.
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
Enhancing geometric reasoning.
Mistretta, R M
2000-01-01
Geometry is an important part of the mathematics curriculum. However, students are not demonstrating strong conceptual knowledge of this subject. The research of Van Hiele and Van Hiele-Geldof has focused on the concept of thinking levels in geometry and the role of instruction in raising levels of thinking. This paper describes a field trial of a supplemental geometry unit intended to raise Van Hiele thinking levels in a group of 23 eighth-grade students by having them become more adept at using higher order thinking skills. Sample questions assessing particular Van Hiele thinking levels and attitudes toward geometry, as well as field-tested activities yielding the most positive results, are presented. Educators can benefit from this application of the Van Hiele model of geometric thinking, since the thought processes involved in learning geometry are explained, along with teaching techniques and tools for assessment. By having teachers become more aware of their students' cognitive skills, attitudes, and misconceptions, teaching practices and student achievement can be enhanced. PMID:11019778
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.
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
Realization of geometric Landau-Zener-Stückelberg interferometry
NASA Astrophysics Data System (ADS)
Zhang, Junhua; Zhang, Jingning; Zhang, Xiang; Kim, Kihwan
2014-01-01
We report an experimental realization of the geometric Landau-Zener-Stückelberg (LZS) interferometry proposed by Gasparinetti et al. [Phys. Rev. Lett. 107, 207002 (2011), 10.1103/PhysRevLett.107.207002] in a single-trapped-ion system. Unlike those in a conventional LZS interferometer, the interference fringes of our geometric interferometer originate solely from a geometric phase. We also observe the robustness of the interference contrast against noise or fluctuations in the experimental parameters. Our scheme can be applied to other complex systems subject to relatively large errors in system control.
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
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
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.
Fast Ion Non-adiabaticity in Spherical Tokamaks
V.A. Yavorskij; D. Darrow; V.Ya. Goloborod'ko; S.N. Reznik; U. Holzmueller-Steinacker; N. Gorelenkov; K. Schoepf
2002-08-01
Transport processes of fast ions in axisymmetric low-aspect-ratio spherical torus (ST) plasmas are investigated, which are induced by the non-conservation of the magnetic moment {mu}. The reason for non-conservation of {mu} of fast ions in ST's is the relatively large adiabaticity parameter epsilon typically exceeding the value 0.1 (epsilon = ratio of ion gyroradius to the gradient scale length of the magnetic field). Both analytical and numerical evaluations of the magnitude of nonadiabatic variations of {mu} are performed. Nonadiabaticity effects are shown to be most significant for fast ions for which the bounce oscillations are in resonance with the gyromotion, i.e., for ions with omega(subscript)B - lomega(subscript)b = 0, where omega(subscript)B and omega(subscript)b represent the bounce-averaged gyrofrequency and the bounce frequency, respectively, and l is an integer. The critical threshold of the adiabaticity parameter, epsilon(subscript)cr, to be exceeded for the transition to stochastic behavior of fast ions in axisymmetric ST's is inspected. Nonadiabatic variations of {mu} are shown to lead to collisionless transformation of trapped orbits into circulating ones and vice versa. For the case of strong nonadiabaticity, epsilon > epsilon(subscript)cr, we assess the transport coefficients describing intense collisionless pitch-angle diffusion, whereas, in the case of weak nonadiabaticity, epsilon > epsilon(subscript)cr, the more substantial coefficients of enhanced collisional radial diffusion and convection of fast ions gyrating resonantly with the bounce oscillations are estimated.
Non Adiabatic Evolution of Elliptical Galaxies by Dynamical Friction
NASA Astrophysics Data System (ADS)
Arena, S. E.; Bertin, G.; Liseikina, T.; Pegoraro, F.
2007-05-01
Many astrophysical problems, ranging from structure formation in cosmology to dynamics of elliptical galaxies, refer to slow processes of evolution of essentially collisionless self-gravitating systems. In order to determine the relevant quasi-equilibrium configuration at time t from given initial conditions, it is often argued that such slow evolution may be approximated in terms of adiabatic evolution, for the calculation of which efficient semi--analytical techniques are available. Here we focus on the slow process of evolution, induced by dynamical friction of a host stellar system on a minority component of "satellites", to determine to what extent an adiabatic description might be applied. The study is realized by means of N--body simulations of the evolution of the total system (the stellar system plus the minority component), in a controlled numerical environment. In particular, we compare the evolution from initial to final configurations of the system subject to dynamical friction with that of the same system evolved adiabatically (in the absence of dynamical friction). We consider two classes of galaxy models characterized by significantly different density and pressure anisotropy profiles. We demonstrate that, for the examined process, the evolution driven by dynamical friction is significantly different from the adiabatic case, not only quantitatively, but also qualitatively. The two classes of galaxy models considered in this investigation exhibit generally similar trends in evolution, with one exception: concentrated models reach a final total density profile, in the internal region, shallower than the initial one, while galaxy models with a broad core show the opposite behaviour. The evolution of elliptical galaxies induced by dynamical friction is a slow process but it is not adiabatic. The results of our investigation should be taken as a warning against the indiscriminate use of adiabatic growth prescriptions in studies of the structure of galaxies.
Understanding electronically non-adiabatic relaxation dynamics in singlet fission.
Tao, Guohua
2015-01-13
Nonadiabatic relaxation of one singlet state into two triplet states is the key step in singlet fission dynamics, the understandings of which may help design next generation solar cells. In this work we perform the symmetrical quasi-classical (SQC) nonadiabatic molecular dynamics (MD) simulation [Cotton and Miller, J. Phys. Chem. A, 2013, 117, 7190; Meyer and Miller, J. Chem. Phys. 1979, 70, 3214] for a model system to study the real-time fission dynamics. The dependence of the nonadiabatic relaxation dynamics on energy levels, electronic couplings, and electronic-phonon couplings has been examined, in comparison with other analytical approximations, such as Förster theory and Marcus theory. Unlike many other methods, the SQC nondiabatic MD simulation approach is able to describe fission dynamics efficiently and accurately enough to provide microscopic insights into singlet fission. PMID:26574200
The Non-Adiabatic dynamics of Singlet Fission in Polyacenes
NASA Astrophysics Data System (ADS)
Bradforth, Stephen
2015-03-01
Singlet fission involves the splitting of a single excitation into two coupled triplet excitations and is manifested in an increasing range of aromatic crystals and amorphous thin films. If the energy of the lowest triplet state is one half (or less) of the first singlet excited state, as it is for tetracene or pentacene and their derivatives, singlet fission may occur between two adjacent chromophores. Since there is no change in the overall spin state of the system, singlet fission can be exceptionally fast, occuring on the fs - ps range. If the triplets can diffuse away from the fission site they are available for harvesting as a dissociated carriers with up to two charge carrier pairs per absorbed photon. The possibility of recovering excess energy above the material band gap (in this case determined by the triplet energy) when a higher energy photon is absorbed has led to great recent interest in exploiting this process for increased efficiency solar energy harvesting. The nature of the electronic couplings between the chromophores, intermediate electronic configurations, and the role of entropy in the spin-allowed primary fission event have all come under great scrutiny. Results from a series of femtosecond spectroscopy experiments on a variety of amorphous thin films, nanoparticles and isolated acene dimer compounds will be presented that shed light on the electronic intermediate states key to the efficiency and speed of this process. Work supported as part of the Center for Energy Nanoscience, an Energy Frontier Research Center funded by the U.S. Department of Energy (DE-SC0001013).
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.
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
Electronically non-adiabatic influences in surface chemistry and dynamics.
Wodtke, Alec M
2016-07-01
Electronically nonadiabatic interactions between molecules and metal surfaces are now well known. Evidence is particularly clear from studies of diatomic molecules that molecular vibration can be strongly coupled to electrons of the metal leading to efficient energy transfer between these two kinds of motion. Since molecular vibration is the same motion needed for bond breaking, it is logical to postulate that electronically nonadiabatic influences on surface chemical reaction probabilities would be strong. Still there are few if any examples where such influences have been clearly investigated. This review recounts the evidence for and against the aforementioned postulate emphasizing reacting systems that have yet to receive full attention and where electronically nonadiabatic influence of reaction probabilities might be clearly demonstrated. PMID:27152489
The geometric resistivity correction factor for several geometrical samples
NASA Astrophysics Data System (ADS)
Yilmaz, Serdar
2015-08-01
This paper reviews the geometric resistivity correction factor of the 4-point probe DC electrical conductivity measurement method using several geometrical samples. During the review of the literature, only the articles that include the effect of geometry on resistivity calculation were considered. Combinations of equations used for various geometries were also given. Mathematical equations were given in the text without details. Expressions for the most commonly used geometries were presented in a table for easy reference.
Geometric algorithms for sensor networks.
Gao, Jie; Guibas, Leonidas
2012-01-13
This paper surveys the use of geometric methods for wireless sensor networks. The close relationship of sensor nodes with their embedded physical space imposes a unique geometric character on such systems. The physical locations of the sensor nodes greatly impact on system design in all aspects, from low-level networking and organization to high-level information processing and applications. This paper reviews work in the past 10 years on topics such as network localization, geometric routing, information discovery, data-centric routing and topology discovery. PMID:22124080
Geometric approaches to mesh generation
Hoffmann, C.M.
1995-12-31
We review three approaches to mesh generation that axe based on analyzing and accounting for the geometric structure of the domain. In the first approach, due to Armstrong, the domain is partitioned into subdomains based on the medial-axis transform, a tool for analyzing spatial structures. In the second approach, due to Cox, the design history defines a geometric structure of the domain. The design primitives of that structure are meshed separately, and mesh overlap is accounted for by coupling equations. The third approach argues that mesh generation ought to be integrated into the shape design process, by meshing design features separately and resolving overlapping meshes by standard geometric computations.
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.
Current Concept of Geometrical Accuracy
NASA Astrophysics Data System (ADS)
Görög, Augustín; Görögová, Ingrid
2014-06-01
Within the solving VEGA 1/0615/12 research project "Influence of 5-axis grinding parameters on the shank cutteŕs geometric accuracy", the research team will measure and evaluate geometrical accuracy of the produced parts. They will use the contemporary measurement technology (for example the optical 3D scanners). During the past few years, significant changes have occurred in the field of geometrical accuracy. The objective of this contribution is to analyse the current standards in the field of geometric tolerance. It is necessary to bring an overview of the basic concepts and definitions in the field. It will prevent the use of outdated and invalidated terms and definitions in the field. The knowledge presented in the contribution will provide the new perspective of the measurement that will be evaluated according to the current standards.
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.)
Algorithms of NCG geometrical module
NASA Astrophysics Data System (ADS)
Gurevich, M. I.; Pryanichnikov, A. V.
2012-12-01
The methods and algorithms of the versatile NCG geometrical module used in the MCU code system are described. The NCG geometrical module is based on the Monte Carlo method and intended for solving equations of particle transport. The versatile combinatorial body method, the grid method, and methods of equalized cross sections and grain structures are used for description of the system geometry and calculation of trajectories.
Algorithms of NCG geometrical module
Gurevich, M. I.; Pryanichnikov, A. V.
2012-12-15
The methods and algorithms of the versatile NCG geometrical module used in the MCU code system are described. The NCG geometrical module is based on the Monte Carlo method and intended for solving equations of particle transport. The versatile combinatorial body method, the grid method, and methods of equalized cross sections and grain structures are used for description of the system geometry and calculation of trajectories.
Transition of Bery Phase and Pancharatnam Phase and Phase Change
NASA Astrophysics Data System (ADS)
Fu, Guolan; Pan, Hui; Wang, Zisheng
2016-07-01
Berry Phase and time-dependent Pancharatnam phase are investigated for nuclear spin polarization in a liquid by a rotation magnetic field, where two-state mixture effect is exactly included in the geometric phases. We find that when the system of nuclear spin polarization is in the unpolarized state, the transitive phenomena of both Berry phase and Pancharatnam phase are taken place. For the polarized system, in contrast, such a transition is not taken place. It is obvious that the transitions of geometric phase correspond to the phase change of physical system.
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.
Geometrical characterization of hard-sphere systems.
Richard, P; Oger, L; Troadec, J P; Gervois, A
1999-10-01
By using molecular dynamics simulations on a large number of hard spheres and the Voronoï tessellation we characterize hard-sphere systems geometrically at any packing fraction eta along the different branches of the phase diagram. Crystallization of disordered packings occurs only for a small range of packing fraction. For the other packing fractions the system behaves as either a fluid (stable or metastable) or a glass. We have studied the evolution of the statistics of the Voronoï tessellation during crystallization and characterized the apparition of order by an order parameter (Q(6)) built from spherical harmonics. PMID:11970312
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.
Current carriers in the near-earth cross-tail current sheet during substorm growth phase
NASA Technical Reports Server (NTRS)
Mitchell, D. G.; Williams, D. J.; Huang, C. Y.; Frank, L. A.; Russell, C. T.
1990-01-01
Throughout most of the growth phase of a substorm, the cross-tail current at x about -10 Re can be supplied by the curvature drift of a bi-directional field aligned distribution of 1 keV electrons. Just prior to its local disruption after substorm onset, the cross-tail current in the now thin (about 400 km) current sheet is carried by the cross-tail serpentine motion of non-adiabatic ions (Speiser, 1965). The instability of this latter current leads to the local disruption of the near-earth current sheet.
Interlay of Quantum Criticality and Geometric Frustration in Columbite
NASA Astrophysics Data System (ADS)
Kaul, Ribhu
2011-10-01
CoNb2O6 is a remarkable magnetic material. The interplay between two of the most exciting features of correlated quantum physics, quantum criticality and geometric frustration, results in a rich phase diagram which reflects the fundamental underlying quantum many-body physics in this complex oxide material. Many aspects of the theoretically calculated phase diagram and expectations for quantum criticality have already been observed in beautiful neutron scattering experiments on this material.[4pt] Ref: Interplay of Quantum Criticality and Geometric Frustration in Columbite, SungBin Lee, Ribhu K. Kaul, Leon Balents, Nature Physics 6, 702-706 (2010)
Electronic structure theory: Applications and geometrical aspects
NASA Astrophysics Data System (ADS)
Coh, Sinisa
This thesis contains several applications of the first-principles electronic-structure theory with special emphasis in parts of the thesis on the geometrical aspects of the theory. We start by reviewing the basics of the first-principles electronic-structure methods which are then used throughout the thesis. The first application of these methods is on the analysis of the stability and lattice dynamics of alpha- and beta-cristobalite phases of SiO2. We also map the complete low-energy landscape connecting these two structures and give implications on the phase transition in this compound. Next we study a family of Pbnm perovskites that are promising candidates for silicon-compatible high-K dielectrics. We calculate their structure and dielectric response, and compare with experimental results where available. The third application of these methods is to the large isosymmetric reorientation of oxygen octahedra rotation axes in epitaxially strained perovskites. We explain the origin of the peculiar energy landscape topology as a function of epitaxial strain. In the part of the thesis devoted to the geometrical aspects of electronic structure theory, we begin by extending the concept of electronic polarization to a Chern insulators. These insulators are characterized by a non-zero off-diagonal sigma_xy conductivity tensor component, quantized in units of e 2/h. Finally we discuss another geometrical quantity, the Chern-Simons orbital magnetoelectric coupling. We present a first-principles based calculation of this quantity in several compounds, and motivated by recent developments in the theory of topological insulators, we speculate about the existence of "large-theta materials," in which this kind of coupling could be unusually large.
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.
Color Image Magnification: Geometrical Pattern Classification Approach
NASA Astrophysics Data System (ADS)
Yong, Tien Fui; Choo, Wou Onn; Meian Kok, Hui
In an era where technology keeps advancing, it is vital that high-resolution images are available to produce high-quality displayed images and fine-quality prints. The problem is that it is quite impossible to produce high-resolution images with acceptable clarity even with the latest digital cameras. Therefore, there is a need to enlarge the original images using an effective and efficient algorithm. The main contribution of this paper is to produce an enlarge color image with high visual quality, up to four times the original size of 100x100 pixels image. In the classification phase, the basic idea is to separate the interpolation region in the form of geometrical shape. Then, in the intensity determination phase, the interpolator assigns a proper color intensity value to the undefined pixel inside the interpolation region. This paper will discuss about problem statement, literature review, research methodology, research outcome, initial results, and finally, the conclusion.
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 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.
Light scattering in porous materials: Geometrical optics and stereological approach
NASA Astrophysics Data System (ADS)
Malinka, Aleksey V.
2014-07-01
Porous material has been considered from the point of view of stereology (geometrical statistics), as a two-phase random mixture of solid material and air. Considered are the materials having the refractive index with the real part that differs notably from unit and the imaginary part much less than unit. Light scattering in such materials has been described using geometrical optics. These two - the geometrical optics laws and the stereological approach - allow one to obtain the inherent optical properties of such a porous material, which are basic in the radiative transfer theory: the photon survival probability, the scattering phase function, and the polarization properties (Mueller matrix). In this work these characteristics are expressed through the refractive index of the material and the random chord length distribution. The obtained results are compared with the traditional approach, modeling the porous material as a pack of particles of different shapes.
Geometric pumping in autophoretic channels.
Michelin, Sébastien; Montenegro-Johnson, Thomas D; De Canio, Gabriele; Lobato-Dauzier, Nicolas; Lauga, Eric
2015-08-01
Many microfluidic devices use macroscopic pressure differentials to overcome viscous friction and generate flows in microchannels. In this work, we investigate how the chemical and geometric properties of the channel walls can drive a net flow by exploiting the autophoretic slip flows induced along active walls by local concentration gradients of a solute species. We show that chemical patterning of the wall is not required to generate and control a net flux within the channel, rather channel geometry alone is sufficient. Using numerical simulations, we determine how geometric characteristics of the wall influence channel flow rate, and confirm our results analytically in the asymptotic limit of lubrication theory. PMID:26000567
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.
Geometric integration for particle accelerators
NASA Astrophysics Data System (ADS)
Forest, Étienne
2006-05-01
This paper is a very personal view of the field of geometric integration in accelerator physics—a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling—unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction.
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. __________________________________________________
A geometric approach to complexity.
Ay, Nihat; Olbrich, Eckehard; Bertschinger, Nils; Jost, Jürgen
2011-09-01
We develop a geometric approach to complexity based on the principle that complexity requires interactions at different scales of description. Complex systems are more than the sum of their parts of any size and not just more than the sum of their elements. Using information geometry, we therefore analyze the decomposition of a system in terms of an interaction hierarchy. In mathematical terms, we present a theory of complexity measures for finite random fields using the geometric framework of hierarchies of exponential families. Within our framework, previously proposed complexity measures find their natural place and gain a new interpretation. PMID:21974666
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.
Effect of geometrical frustration on inverse freezing
NASA Astrophysics Data System (ADS)
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 (J1) and second-neighbor (J2) 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 J1/J in two cases: the absence of J2 interaction and the isotropic limit J2=J1 , where GF takes place. An IF reentrant transition from the spin-glass (SG) to paramagnetic (PM) phase is found for a certain range of J1/J in both cases. The J1 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.
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.
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…
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.
Geometric effects in SeaWiFS lunar observations
NASA Astrophysics Data System (ADS)
Eplee, Robert E.; Patt, Frederick S.; Meister, Gerhard
2015-09-01
The radiometric stability requirements for ocean color climate data records place tight constraints on the onorbit calibration of ocean color instruments. A major component of the on-orbit calibration methodology for NASA ocean color sensors is the normalization of lunar observations for variations in observing geometry by the USGS ROLO photometric model of the Moon. SeaWiFS made 204 lunar observations over its 13-year mission. 145 radiometric trending observations were made at low phase angles (-8° to -6° and +5° to +10°). 59 additional observations were made at high phase angles (-49° to -27° and +27° to +66° degrees). The NASA Ocean Biology Processing Group has undertaken a reanalysis of residual geometric effects in the SeaWiFS lunar observations. Ratios of SeaWiFS observations to ROLO model predictions were fit with quadratic functions of phase angle and linear functions of sub-spacecraft point and sub-solar point libration longitude and latitude angles. The resulting phase and libration fit coefficients have been used as additional geometric corrections for the SeaWiFS lunar observations. For the low phase angle observations, the phase corrections are 0.16% and the libration corrections are 0.18%. For the low and high phase angle observations, the phase corrections are 1.8% and the libration corrections are 0.22%. These geometric corrections have reduced the overall scatter in the lunar observations, bringing the high phase angle data into family with the low phase angle measurements without impacting the radiometric response in the low phase angle observations.
Flexible geometrical calibration for fringe-reflection 3D measurement.
Xiao, Yong-Liang; Su, Xianyu; Chen, Wenjing
2012-02-15
System geometrical calibration is a challenging task in fringe-reflection 3D measurement because the fringe displayed on the LCD screen does not lie within the camera's field of view. Commonly, a flat mirror with markers can accomplish system geometrical calibration. However, the position of the markers must be precisely located by photogrammetry in advance. In this Letter, we introduce a calibration method by use of a markerless flat mirror. Experiments in phase measuring deflectometry demonstrate that the proposed method is simple and flexible. PMID:22344126
Geometrical approach to tumor growth.
Escudero, Carlos
2006-08-01
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells and particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former paper [C. Escudero, Phys. Rev. E 73, 020902(R) (2006)], and in the present work we extend our analysis and try to shed light on the possible geometrical principles that drive tumor growth. We present two-dimensional models that reproduce the experimental observations, and analyze the unexplored three-dimensional case, for which interesting conclusions on tumor growth are derived. PMID:17025466
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.
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.
Geometrical scaling for identified particles
NASA Astrophysics Data System (ADS)
Praszalowicz, Michal
2013-12-01
We show that recently measured transverse momentum spectra of identified particles exhibit geometrical scaling (GS) in scaling variable τ=(( where m=√{m2+pT2}-m. We explore consequences of GS and show that both mid rapidity multiplicity and mean transverse momenta grow as powers of scattering energy. Furthermore, assuming Tsallis-like parametrization of the spectra we calculate the coefficients of this growth. We also show that Tsallis temperature is related to the average saturation scale.
Geometrical interpretation of optical absorption
Monzon, J. J.; Barriuso, A. G.; Sanchez-Soto, L. L.; Montesinos-Amilibia, J. M.
2011-08-15
We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 + 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm of the Klein model of hyperbolic geometry. The effects of absorption appear then as a loxodromic transformation, that is, a rhumb line crossing all the meridians at the same angle.
Improved geometrical model of fringe projection profilometry.
Huang, Zhengrong; Xi, Jiangtao; Yu, Yanguang; Guo, Qinghua; Song, Limei
2014-12-29
The accuracy performance of fringe projection profilometry (FPP) depends on accurate phase-to-height (PTH) mapping and system calibration. The existing PTH mapping is derived based on the condition that the plane formed by axes of camera and projector is perpendicular to the reference plane, and measurement error occurs when the condition is not met. In this paper, a new geometric model for FPP is presented to lift the condition, resulting in a new PTH mapping relationship. The new model involves seven parameters, and a new system calibration method is proposed to determine their values. Experiments are conducted to verify the performance of the proposed technique, showing a noticeable improvement in the accuracy of 3D shape measurement. PMID:25607188
Geometric characterization of true quantum decoherence
NASA Astrophysics Data System (ADS)
Kayser, Julius; Luoma, Kimmo; Strunz, Walter T.
2015-11-01
Surprisingly often decoherence is due to classical fluctuations of ambient fields and may thus be described in terms of random unitary (RU) dynamics. However, there are decoherence channels where such a representation cannot exist. Based on a simple and intuitive geometric measure for the distance of an extremal channel to the convex set of RU channels we are able to characterize the set of true quantum phase-damping channels. Remarkably, using the Caley-Menger determinant, our measure may be assessed directly from the matrix representation of the channel. We find that the channel of maximum quantumness is closely related to a symmetric, informationally complete positive operator-valued measure on the environment. Our findings are in line with numerical results based on the entanglement of assistance.
Geometric signature of complex synchronisation scenarios
NASA Astrophysics Data System (ADS)
Feldhoff, J. H.; Donner, R. V.; Donges, J. F.; Marwan, N.; Kurths, J.
2013-05-01
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the coupling strength often leads to qualitative changes in the dynamics exhibiting different types of synchronisation. Here, we study the geometric signatures of coupling along with the onset of generalised synchronisation (GS) between two coupled chaotic oscillators by mapping the systems' individual as well as joint recurrences in phase space to a complex network. For a paradigmatic continuous-time model system, we show that the transitivity properties of the resulting joint recurrence networks display distinct variations associated with changes in the structural similarity between different parts of the considered trajectories. They therefore provide a useful new indicator for the emergence of GS. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots by Eckmann et al. (EPL, 4 (1987) 973).
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.
Seismic coherent states and ray geometrical spreading
NASA Astrophysics Data System (ADS)
Thomson, C. J.
2001-02-01
The coherent-state transform (CST) is essentially a Gaussian-windowed Fourier transform and it yields a combined slowness-position (p,x) domain representation of seismic wavefields. Several forms of the inverse CST exist and the set of `coherent states' form an overcomplete basis for wave analysis, in many ways similar to modern wavelets. The asymptotic or `ray' solution to the CST of the seismic wave equation involves a phase function S(p,x) that is complex due to the Gaussian decay. Hence one must consider complex rays, as well as a higher-dimensional phase space (p,x,∂pS,∂xS) corresponding to the extended configuration or base space (p,x). The initial conditions and geometrical spreading of these rays involve generalizations of standard procedures, exemplified by analysis of the coherent states excited by a ray theory incident wavefield. Surfaces of constant S are `tangential' to the standard ray theory wavefront T(x) and the Maslov phase fronts given by the Legendre transformation of T. Hence the real rays of T (and the Maslov phase) are particular rays of S. The geometrical spreading of an individual coherent-state (CS) wavefield requires careful consideration. Although the transport equation involves divergence in the higher-dimensional base space (p,x), Smirnov's Lemma applied in this space still gives the solution. The incorporation of initial conditions is correspondingly intricate, but the final spreading function is better behaved (`smoother') than either a standard ray or Maslov theory amplitude. This provides a solution to the problem of pseudo-caustics. The task of finding a `KMAH index' for each ray contributing to the inverse CST is simplified to choosing a complex square root that is smoothly connected between these rays (i.e. it does not fork). It is suggested that in practice only real rays are needed and then the method can be reduced to a smoothed form of the Maslov Snell wave sum representation. This is achieved by approximating the
Characteristic signatures of quantum criticality driven by geometrical frustration.
Tokiwa, Yoshifumi; Stingl, Christian; Kim, Moo-Sung; Takabatake, Toshiro; Gegenwart, Philipp
2015-04-01
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
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
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
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)…
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,…
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.
NASA Astrophysics Data System (ADS)
Cabrera, I.; Thompson, J. D.; Coldea, R.; Prabhakaran, D.; Bewley, R. I.; Guidi, T.; Rodriguez-Rivera, J. A.; Stock, C.
2014-07-01
The quasi-one-dimensional (1D) Ising ferromagnet CoNb2O6 has recently been driven via applied transverse magnetic fields through a continuous quantum phase transition from spontaneous magnetic order to a quantum paramagnet, and dramatic changes were observed in the spin dynamics, characteristic of weakly perturbed 1D Ising quantum criticality. We report here extensive single-crystal inelastic neutron scattering measurements of the magnetic excitations throughout the three-dimensional (3D) Brillouin zone in the quantum paramagnetic phase just above the critical field 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, and this effect is attributed to quantum renormalization of the dispersion beyond the spin-wave approximation in fields slightly above the critical field, where quantum fluctuations are still significant.
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.
Geometric reasoning and spatial understanding
Binford, T.O.
1982-01-01
Progress has been made on extensions to ACRONYM which include: representation and reasoning with time, events, and sequences; collaboration with MIT to develop geometric learning: representation of function, and reasoning between structure and function. A new ribbon finder for ACRONYM is under construction. Work in figure/ground separation is underway as a basis for the ribbon finder. Preliminary results are shown in grouping operations to determine regularities in images. A stereo system has been completed which combines edge-based stereo matching with surface interpolation utilizing correspondence of gray levels. Design of a new stereo vision system is underway.
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.
NPP VIIRS geometric performance status
NASA Astrophysics Data System (ADS)
Lin, Guoqing; Wolfe, Robert E.; Nishihama, Masahiro
2011-10-01
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.
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. PMID:27038025
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 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.
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.
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
Experimental realization of universal geometric quantum gates with solid-state spins.
Zu, C; Wang, W-B; He, L; Zhang, W-G; Dai, C-Y; Wang, F; Duan, L-M
2014-10-01
Experimental realization of a universal set of quantum logic gates is the central requirement for the implementation of a quantum computer. In an 'all-geometric' approach to quantum computation, the quantum gates are implemented using Berry phases and their non-Abelian extensions, holonomies, from geometric transformation of quantum states in the Hilbert space. Apart from its fundamental interest and rich mathematical structure, the geometric approach has some built-in noise-resilience features. On the experimental side, geometric phases and holonomies have been observed in thermal ensembles of liquid molecules using nuclear magnetic resonance; however, such systems are known to be non-scalable for the purposes of quantum computing. There are proposals to implement geometric quantum computation in scalable experimental platforms such as trapped ions, superconducting quantum bits and quantum dots, and a recent experiment has realized geometric single-bit gates in a superconducting system. Here we report the experimental realization of a universal set of geometric quantum gates using the solid-state spins of diamond nitrogen-vacancy centres. These diamond defects provide a scalable experimental platform with the potential for room-temperature quantum computing, which has attracted strong interest in recent years. Our experiment shows that all-geometric and potentially robust quantum computation can be realized with solid-state spin quantum bits, making use of recent advances in the coherent control of this system. PMID:25279920
Geometric analysis of transient bursts
NASA Astrophysics Data System (ADS)
Osinga, Hinke M.; Tsaneva-Atanasova, Krasimira T.
2013-12-01
We consider the effect of a brief stimulation from the rest state of a minimal neuronal model with multiple time scales. Such transient dynamics brings out the intrinsic bursting capabilities of the system. Our main goal is to show that a minimum of three dimensions is enough to generate spike-adding phenomena in transient responses, and that the onset of a new spike can be tracked using existing continuation packages. We take a geometric approach to illustrate how the underlying fast subsystem organises the spike adding in much the same way as for spike adding in periodic bursts, but the bifurcation analysis for spike onset is entirely different. By using a generic model, we further strengthen claims made in our earlier work that our numerical method for spike onset can be used for a broad class of systems.
Geometric Mean Neutrino Mass Relation
NASA Astrophysics Data System (ADS)
He, Xiao-Gang; Zee, A.
Present experimental data from neutrino oscillations have provided much information about the neutrino mixing angles. Since neutrino oscillations only determine the mass squared differences Δ m2ij = m2i - m2j, the absolute values for neutrino masses mi, can not be determined using data just from oscillations. In this work we study implications on neutrino masses from a geometric mean mass relation m2 = √ {m1m_3} which enables one to determined the absolute masses of the neutrinos. We find that the central values of the three neutrino masses and their 2σ errors to be m1 = (1.58 ± 0.18)meV, m2 = (9.04 ± 0.42)meV, and m3 = (51.8 ± 3.5)meV. Implications for cosmological observation, beta decay and neutrinoless double beta decays are discussed.
Geometric asymmetry driven Janus micromotors.
Zhao, Guanjia; Pumera, Martin
2014-10-01
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. PMID:25122607
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
Optimizing the geometrical accuracy of curvilinear meshes
NASA Astrophysics Data System (ADS)
Toulorge, Thomas; Lambrechts, Jonathan; Remacle, Jean-François
2016-04-01
This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high order elements. An optimization procedure is then used to both untangle invalid elements and optimize the geometrical accuracy of the mesh. Standard measures of the distance between curves are considered to evaluate the geometrical accuracy in planar two-dimensional meshes, but they prove computationally too costly for optimization purposes. A fast estimate of the geometrical accuracy, based on Taylor expansions of the curves, is introduced. An unconstrained optimization procedure based on this estimate is shown to yield significant improvements in the geometrical accuracy of high order meshes, as measured by the standard Hausdorff distance between the geometrical model and the mesh. Several examples illustrate the beneficial impact of this method on CFD solutions, with a particular role of the enhanced mesh boundary smoothness.
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.
Geometric solitons of Hamiltonian flows on manifolds
NASA Astrophysics Data System (ADS)
Song, Chong; Sun, Xiaowei; Wang, Youde
2013-12-01
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.
Noncommutative Anandan quantum phase
NASA Astrophysics Data System (ADS)
Passos, E.; Ribeiro, L. R.; Furtado, C.; Nascimento, J. R.
2007-07-01
In this work, we study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses permanent magnetic and electric dipole moments, in the presence of external electric and magnetic fields. We use the Foldy-Wouthuysen transformation of the Dirac spinor with a nonminimal coupling to obtain the nonrelativistic limit. In this limit, we study the noncommutative quantum dynamics and obtain the noncommutative Anandan geometric phase. We analyze the situation where the magnetic dipole moment of the particle is zero, and we obtain the noncommutative version of the He-McKellar-Wilkens effect. We demonstrate that this phase in the noncommutative case is a geometric dispersive phase. We also investigate this geometric phase by considering the noncommutativity in the phase space, and the Anandan phase is obtained.
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 and Graphical Solutions of Quadratic Equations.
ERIC Educational Resources Information Center
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
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 reconstruction of biological orthogonal plywoods.
Aguilar Gutierrez, Oscar F; Rey, Alejandro D
2016-01-28
In this paper we focus on the structural determination of biological orthogonal plywoods, fiber-like composite analogues of liquid crystalline phases, where the fibrils of the building blocks show sharp 90° orientation jumps between fibers in adjacent domains. We present an original geometric and computational modelling that allows us to determine the fibrillary orientation in biological plywoods from periodic herringbone patterns commonly observed in cross-sections. Although herringbone patterns were long reported, the specific and quantitative relationships between herringbones and the orthogonal plywoods were absent or at best incomplete. Here we provide an efficient and new procedure to perform an inverse problem that connects two specific features of the herringbone patterns (aperture angle and wavelength) with the 3D morphology of the structure, whose accuracy and validity were ascertained through in silico simulations and also with real specimens ("Eremosphaera viridis"). This contribution extends significantly the better known characterization methods of 2D cross sections, such as the arced patterns observed in biological helicoidal plywoods, and with the present proposed methodology it adds another characterization tool for a variety of biological fibrous composites that form cornea-like tissues. PMID:26583687
Geometric Hall effects in topological insulator heterostructures
NASA Astrophysics Data System (ADS)
Yasuda, K.; Wakatsuki, R.; Morimoto, T.; Yoshimi, R.; Tsukazaki, A.; Takahashi, K. S.; Ezawa, M.; Kawasaki, M.; Nagaosa, N.; Tokura, Y.
2016-06-01
Geometry, both in momentum and in real space, plays an important role in the electronic dynamics of condensed matter systems. Among them, the Berry phase associated with nontrivial geometry can be an origin of the transverse motion of electrons, giving rise to various geometric effects such as the anomalous, spin and topological Hall effects. Here, we report two unconventional manifestations of Hall physics: a sign-reversal of the anomalous Hall effect, and the emergence of a topological Hall effect in magnetic/non-magnetic topological insulator heterostructures, Crx(Bi1-ySby)2-xTe3/(Bi1-ySby)2Te3. The sign-reversal in the anomalous Hall effect is driven by a Rashba splitting at the bulk bands, which is caused by the broken spatial inversion symmetry. Instead, the topological Hall effect arises in a wide temperature range below the Curie temperature, in a region where the magnetic-field dependence of the Hall resistance largely deviates from the magnetization. Its origin is assigned to the formation of a Néel-type skyrmion induced by the Dzyaloshinskii-Moriya interaction.
Generalized Geometric Quantum Speed Limits
NASA Astrophysics Data System (ADS)
Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.
2016-04-01
The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
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.
Geometrical aspects of quantum spaces
Ho, P.M.
1996-05-11
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S{sub 1}{sup 2} and the quantum complex projective space CP{sub q}(N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S{sub q}{sup 2} and CP{sub q}(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP{sub q}(N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given.
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.
Gaining Insights into Children's Geometric Knowledge
ERIC Educational Resources Information Center
Mack, Nancy K.
2007-01-01
This article describes how research on children's geometric thinking was used in conjunction with the picture book "The Greedy Triangle" to gain valuable insights into children's prior geometric knowledge of polygons. Exercises focused on the names, visual appearance, and properties of polygons, as well as real-world connections for each, are…
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.
Geometric Growing Patterns: What's the Rule?
ERIC Educational Resources Information Center
Hourigan, Mairéad; Leavy, Aisling
2015-01-01
While within a geometric repeating pattern, there is an identifiable core which is made up of objects that repeat in a predictable manner, a geometric growing pattern (also called visual or pictorial growing patterns in other curricula) "is a pattern that is made from a sequence of figures [or objects] that change from one term to the next in…
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. PMID:26124252
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…
Enhanced Geometric Metadata for Cassini Optical Remote Sensing Instruments
NASA Astrophysics Data System (ADS)
Gordon, Mitchell K.; Showalter, M. R.; Wells, B.; Ballard, L.; Heather, N.
2012-10-01
In the past few years, the PDS Rings Node developed the Outer Planets Unified Search (OPUS), along with preview images or footprint diagrams for all OPUS supported data, and enhanced geometric metadata for Cassini ISS Saturn system data. Typically, geometric metadata for outer planets remote sensing observations is available only for the center of the instrument field of view. In our first effort at generating enhanced metadata, we calculated values for a fine grid of points over the entire field of view of Cassini ISS images using the most current SPICE kernel files. That project produce enhanced metadata specific to the rings; consequently the metadata was tied to the ring plane of Saturn. The combination of OPUS and the data base of enhanced geometric metadata provided a powerful, well received tool, and resulted in additional funding to extend metadata generation. We are developing a set of tools to produce geometric metadata for Cassini ISS, VIMS, UVIS, and CIRS Saturn data. This metadata will not be restricted to ring plane calculations and will support searches based on latitude and longitude for the planet and satellites as well as parameters such as viewing and illumination geometry. We also identify all known bodies and rings in the field of view, so target based search results will be comprehensive rather providing a subset based on the designated primary target. This autumn we have begun the incremental inclusion of the new metadata in the OPUS data base. In a subsequent phase we intend to expand our web services to include on-the-fly production of user selected geometric backplanes for each product returned by OPUS. http://pds-rings.seti.org/search/ Acknowledgments: This development has been supported by the Planetary Data System, by JPL through a special grant from the Cassini Project, and by research grants from STScI and NASA.
Bora, B.; Bhuyan, H.; Favre, M.; Wyndham, E.; Chuaqui, H.
2012-02-27
Plasma series resonance (PSR) effect is well known in geometrically asymmetric capacitively couple radio frequency plasma. However, plasma series resonance effect in geometrically symmetric plasma has not been properly investigated. In this work, a theoretical approach is made to investigate the plasma series resonance effect and its influence on Ohmic and stochastic heating in geometrically symmetric discharge. Electrical asymmetry effect by means of dual frequency voltage waveform is applied to excite the plasma series resonance. The results show considerable variation in heating with phase difference between the voltage waveforms, which may be applicable in controlling the plasma parameters in such plasma.
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
2011-08-01
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.
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
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.
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 view of adaptive optics control.
Wiberg, Donald M; Max, Claire E; Gavel, Donald T
2005-05-01
The objective of an astronomical adaptive optics control system is to minimize the residual wave-front error remaining on the science-object wave fronts after being compensated for atmospheric turbulence and telescope aberrations. Minimizing the mean square wave-front residual maximizes the Strehl ratio and the encircled energy in pointlike images and maximizes the contrast and resolution of extended images. We prove the separation principle of optimal control for application to adaptive optics so as to minimize the mean square wave-front residual. This shows that the residual wave-front error attributable to the control system can be decomposed into three independent terms that can be treated separately in design. The first term depends on the geometry of the wave-front sensor(s), the second term depends on the geometry of the deformable mirror(s), and the third term is a stochastic term that depends on the signal-to-noise ratio. The geometric view comes from understanding that the underlying quantity of interest, the wave-front phase surface, is really an infinite-dimensional vector within a Hilbert space and that this vector space is projected into subspaces we can control and measure by the deformable mirrors and wave-front sensors, respectively. When the control and estimation algorithms are optimal, the residual wave front is in a subspace that is the union of subspaces orthogonal to both of these projections. The method is general in that it applies both to conventional (on-axis, ground-layer conjugate) adaptive optics architectures and to more complicated multi-guide-star- and multiconjugate-layer architectures envisaged for future giant telescopes. We illustrate the approach by using a simple example that has been worked out previously [J. Opt. Soc. Am. A 73, 1171 (1983)] for a single-conjugate, static atmosphere case and follow up with a discussion of how it is extendable to general adaptive optics architectures. PMID:15898546
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.
NASA Astrophysics Data System (ADS)
Aleksandrov, V. D.; Sobolev, A. Yu.; Sobol', O. V.; Frolova, S. A.; Shchebetovskaya, N. V.
2015-09-01
Geometrical thermodynamics is used to analyze the possible dependences of the Gibbs energy on temperature and component concentration in the two-phase region during nonequilibrium solidification of eutectic alloys.
Surgical correction of gynecomastia: a geometric approach.
Martin, Antony E; Olinger, Thomas A; Yu, Jack C
2015-05-01
Many techniques are available for surgical correction of gynecomastia. In this article, we describe a technique based on geometrical principles that is simple to execute, effective, highly reproducible, and relies less on intuition of the surgeon. PMID:25919255
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)
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.
Sentinel-2 geometric image quality commissioning: first results
NASA Astrophysics Data System (ADS)
Languille, F.; Déchoz, C.; Gaudel, A.; Greslou, D.; de Lussy, F.; Trémas, T.; Poulain, V.
2015-10-01
In the frame of the Copernicus program of the European Comission, Sentinel-2 will offer multispectral highspatial- resolution optical images over global terrestrial surfaces. In cooperation with ESA, the Centre National d'Etudes Spatiales (CNES) is in charge of the image quality of the project, and will so ensure the CAL/VAL commissioning phase during the months following the launch. Sentinel-2 is a constellation of 2 satellites on a polar sun-synchronous orbit with a revisit time of 5 days (with both satellites), a high field of view - 290km, 13 spectral bands in visible and shortwave infrared, and high spatial resolution - 10m, 20m and 60m. The Sentinel-2 mission offers a global coverage over terrestrial surfaces. The satellites acquire systematically terrestrial surfaces under the same viewing conditions in order to have temporal images stacks. The first satellite has been launched in June 2015. Following the launch, the CAL/VAL commissioning phase will then last during 6 months for geometrical calibration. This paper first provides explanations about Sentinel-2 products delivered with geometric corrections. Then this paper details calibration sites, and the methods used for geometrical parameters calibration and presents the first linked results. The following topics are presented: viewing frames orientation assessment, focal plane mapping for all spectral bands, first results on geolocation assessment, and multispectral registration. There is a systematic images recalibration over a same reference which will be a set of S2 images produced during the 6 months of CAL/VAL. As it takes time to have all needed images, the geolocation performance with ground control points and the multitemporal performance are only first results and will be improved during the last phase of the CAL/VAL. So this paper mainly shows the system performances, the preliminary product performances and the way to perform them.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Liang, Zhen-Tao; Yue, Xianxian; Lv, Qingxian; Du, Yan-Xiong; Huang, Wei; Yan, Hui; Zhu, Shi-Liang
2016-04-01
We propose a feasible scheme to implement a universal set of quantum gates based on geometric phases and superadiabatic quantum control. Consolidating the advantages of both strategies, the proposed quantum gates are robust and fast. The diamond nitrogen-vacancy center system is adopted as a typical example to illustrate the scheme. We show that these gates can be realized in a simple two-level configuration by appropriately controlling the amplitude, phase, and frequency of just one microwave field. The gate's robust and fast features are confirmed by comparing the fidelity of the proposed superadiabatic geometric phase (controlled-phase) gate with those of two other kinds of phase (controlled-phase) gates.
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.
Probabilistically Perfect Cloning of Two Pure States: Geometric Approach.
Yerokhin, V; Shehu, A; Feldman, E; Bagan, E; Bergou, J A
2016-05-20
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. PMID:27258856
Ratcheting fluid with geometric anisotropy
NASA Astrophysics Data System (ADS)
Thiria, Benjamin; Zhang, Jun
2015-02-01
We investigate a mechanism that effectively transports fluids using vibrational motion imposed onto fluid boundary with anisotropy. In our experiment, two asymmetric, sawtooth-like structures are placed facing each other and form a corrugated fluid channel. This channel is then forced to open and close periodically. Under reciprocal motion, fluid fills in the gap during the expansion phase of the channel and is then forced out during contraction. Since the fluid experiences different impedances when flowing in different directions, the stagnation point that separates flows of two directions changes within each driving period. As a result, fluid is transported unidirectionally. This ratcheting effect of fluid is demonstrated through our measurements and its working principle discussed in some detail.
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.
Huo, Pengfei; Miller, Thomas F. III; Coker, David F.
2013-10-21
A partial linearized path integral approach is used to calculate the condensed phase electron transfer (ET) rate by directly evaluating the flux-flux/flux-side quantum time correlation functions. We demonstrate for a simple ET model that this approach can reliably capture the transition between non-adiabatic and adiabatic regimes as the electronic coupling is varied, while other commonly used semi-classical methods are less accurate over the broad range of electronic couplings considered. Further, we show that the approach reliably recovers the Marcus turnover as a function of thermodynamic driving force, giving highly accurate rates over four orders of magnitude from the normal to the inverted regimes. We also demonstrate that the approach yields accurate rate estimates over five orders of magnitude of inverse temperature. Finally, the approach outlined here accurately captures the electronic coherence in the flux-flux correlation function that is responsible for the decreased rate in the inverted regime.
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.
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.
Quantification of Osteon Morphology Using Geometric Histomorphometrics.
Dillon, Scott; Cunningham, Craig; Felts, Paul
2016-03-01
Many histological methods in forensic anthropology utilize combinations of traditional histomorphometric parameters which may not accurately describe the morphology of microstructural features. Here, we report the novel application of a geometric morphometric method suitable when considering structures without anatomically homologous landmarks for the quantification of complete secondary osteon size and morphology. The method is tested for its suitability in the measurement of intact secondary osteons using osteons digitized from transverse femoral diaphyseal sections prepared from two human individuals. The results of methodological testing demonstrate the efficacy of the technique when applied to intact secondary osteons. In providing accurate characterization of micromorphology within the robust mathematical framework of geometric morphometrics, this method may surpass traditional histomorphometric variables currently employed in forensic research and practice. A preliminary study of the intersectional histomorphometric variation within the femoral diaphysis is made using this geometric histomorphometric method to demonstrate its potential. PMID:26478136
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. PMID:24634545
Geometric direct search algorithms for image registration.
Lee, Seok; Choi, Minseok; Kim, Hyungmin; Park, Frank Chongwoo
2007-09-01
A widely used approach to image registration involves finding the general linear transformation that maximizes the mutual information between two images, with the transformation being rigid-body [i.e., belonging to SE(3)] or volume-preserving [i.e., belonging to SL(3)]. In this paper, we present coordinate-invariant, geometric versions of the Nelder-Mead optimization algorithm on the groups SL(3), SE(3), and their various subgroups, that are applicable to a wide class of image registration problems. Because the algorithms respect the geometric structure of the underlying groups, they are numerically more stable, and exhibit better convergence properties than existing local coordinate-based algorithms. Experimental results demonstrate the improved convergence properties of our geometric algorithms. PMID:17784595
MM Algorithms for Geometric and Signomial Programming
Lange, Kenneth; Zhou, Hua
2013-01-01
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. PMID:24634545
New developments on the geometric nonholonomic integrator
NASA Astrophysics Data System (ADS)
Ferraro, Sebastián; Jiménez, Fernando; Martín de Diego, David
2015-04-01
In this paper, we will discuss new developments regarding the geometric nonholonomic integrator (GNI) (Ferraro et al 2008 Nonlinearity 21 1911-28 Ferraro et al 2009 Discrete Contin. Dyn. Syst. (Suppl.) 220-9). GNI is a discretization scheme adapted to nonholonomic mechanical systems through a discrete geometric approach. This method was designed to account for some of the special geometric structures associated to a nonholonomic motion, like preservation of energy, preservation of constraints or the nonholonomic momentum equation. First, we study the GNI versions of the symplectic-Euler methods, paying special attention to their convergence behaviour. Then, we construct an extension of the GNI in the case of affine constraints. Finally, we generalize the proposed method to nonholonomic reduced systems, an important subclass of examples in nonholonomic dynamics. We illustrate the behaviour of the proposed method with the example of the inhomogeneous sphere rolling without slipping on a table.
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
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.
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
Gender recognition based on face geometric features
NASA Astrophysics Data System (ADS)
Xiao, Jie; Guo, Zhaoli; Cai, Chao
2013-10-01
Automatic gender recognition based on face images plays an important role in computer vision and machine vision. In this paper, a novel and simple gender recognition method based on face geometric features is proposed. The method is divided in three steps. Firstly, Pre-processing step provides standard face images for feature extraction. Secondly, Active Shape Model (ASM) is used to extract geometric features in frontal face images. Thirdly, Adaboost classifier is chosen to separate the two classes (male and female). We tested it on 2570 pictures (1420 males and 1150 females) downloaded from the internet, and encouraging results were acquired. The comparison of the proposed geometric feature based method and the full facial image based method demonstrats its superiority.
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.
The effect of photometric and geometric context on photometric and geometric lightness effects
Lee, Thomas Y.; Brainard, David H.
2014-01-01
We measured the lightness of probe tabs embedded at different orientations in various contextual images presented on a computer-controlled stereo display. Two background context planes met along a horizontal roof-like ridge. Each plane was a graphic rendering of a set of achromatic surfaces with the simulated illumination for each plane controlled independently. Photometric context was varied by changing the difference in simulated illumination intensity between the two background planes. Geometric context was varied by changing the angle between them. We parsed the data into separate photometric effects and geometric effects. For fixed geometry, varying photometric context led to linear changes in both the photometric and geometric effects. Varying geometric context did not produce a statistically reliable change in either the photometric or geometric effects. PMID:24464163
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…
On the dynamical and geometrical symmetries of Keplerian motion
NASA Astrophysics Data System (ADS)
Wulfman, Carl E.
2009-05-01
The dynamical symmetries of classical, relativistic and quantum-mechanical Kepler systems are considered to arise from geometric symmetries in PQET phase space. To establish their interconnection, the symmetries are related with the aid of a Lie-algebraic extension of Dirac's correspondence principle, a canonical transformation containing a Cunningham-Bateman inversion, and a classical limit involving a preliminary canonical transformation in ET space. The Lie-algebraic extension establishes the conditions under which the uncertainty principle allows the local dynamical symmetry of a quantum-mechanical system to be the same as the geometrical phase-space symmetry of its classical counterpart. The canonical transformation converts Poincaré-invariant free-particle systems into ISO(3,1) invariant relativistic systems whose classical limit produces Keplerian systems. Locally Cartesian relativistic PQET coordinates are converted into a set of eight conjugate position and momentum coordinates whose classical limit contains Fock projective momentum coordinates and the components of Runge-Lenz vectors. The coordinate systems developed via the transformations are those in which the evolution and degeneracy groups of the classical system are generated by Poisson-bracket operators that produce ordinary rotation, translation and hyperbolic motions in phase space. The way in which these define classical Keplerian symmetries and symmetry coordinates is detailed. It is shown that for each value of the energy of a Keplerian system, the Poisson-bracket operators determine two invariant functions of positions and momenta, which together with its regularized Hamiltonian, define the manifold in six-dimensional phase space upon which motions evolve.
Scale-invariant geometric random graphs
NASA Astrophysics Data System (ADS)
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.
Geometric accuracy in airborne SAR images
NASA Technical Reports Server (NTRS)
Blacknell, D.; Quegan, S.; Ward, I. A.; Freeman, A.; Finley, I. P.
1989-01-01
Uncorrected across-track motions of a synthetic aperture radar (SAR) platform can cause both a severe loss of azimuthal positioning accuracy in, and defocusing of, the resultant SAR image. It is shown how the results of an autofocus procedure can be incorporated in the azimuth processing to produce a fully focused image that is geometrically accurate in azimuth. Range positioning accuracy is also discussed, leading to a comprehensive treatment of all aspects of geometric accuracy. The system considered is an X-band SAR.
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.
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.