scholarly journals Investigations on Dynamical Stability in 3D Quadrupole Ion Traps

2021 ◽  
Author(s):  
Bogdan Mihalcea ◽  
Stephen Lynch
Keyword(s):  
Quantum Dynamics ◽  
Hessian Matrix ◽  
Ion Traps ◽  
Quadrupole Ion Trap ◽  
Dynamical Stability ◽  
Phase Portraits ◽  
Ion Distribution ◽  
Hamilton Function ◽  
Coupling Condition ◽  
Equilibrium Configurations

We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. We obtain the solutions of the coupled system of equations that characterizes the associated dynamics. In addition, we supply the modes of oscillation and demonstrate the weak coupling condition is inappropriate in practice, while for collective modes of motion (and strong coupling) only a peak of the mass can be detected. Phase portraits and power spectra are employed to illustrate how the trajectory executes quasiperiodic motion on the surface of torus, namely a Kolmogorov-Arnold-Moser (KAM) torus. In an attempt to better describe dynamical stability of the system, we introduce a model that characterizes dynamical stability and the critical points based on the Hessian matrix approach. The model is then applied to investigate quantum dynamics for many-body systems consisting of identical ions, levitated in 2D and 3D ion traps. Finally, the same model is applied to the case of a combined 3D Quadrupole Ion Trap (QIT) with axial symmetry, for which we obtain the associated Hamilton function. The ion distribution can be described by means of numerical modeling, based on the Hamilton function we assign to the system. The approach we introduce is effective to infer the parameters of distinct types of traps by applying a unitary and coherent method, and especially for identifying equilibrium configurations, of large interest for ion crystals or quantum logic.

scholarly journals Investigations on Dynamical Stability in 3D Quadrupole Ion Traps

2021 ◽  
Vol 11 (7) ◽  
pp. 2938
Author(s):  
Bogdan M. Mihalcea ◽  
Stephen Lynch
Keyword(s):  
Quantum Dynamics ◽  
Hessian Matrix ◽  
Ion Traps ◽  
Quadrupole Ion Trap ◽  
Dynamical Stability ◽  
Phase Portraits ◽  
Ion Distribution ◽  
Hamilton Function ◽  
Coupling Condition ◽  
Equilibrium Configurations

We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. We obtain the solutions of the coupled system of equations that characterizes the associated dynamics. In addition, we supply the modes of oscillation and demonstrate the weak coupling condition is inappropriate in practice, while for collective modes of motion (and strong coupling) only a peak of the mass can be detected. Phase portraits and power spectra are employed to illustrate how the trajectory executes quasiperiodic motion on the surface of torus, namely a Kolmogorov–Arnold–Moser (KAM) torus. In an attempt to better describe dynamical stability of the system, we introduce a model that characterizes dynamical stability and the critical points based on the Hessian matrix approach. The model is then applied to investigate quantum dynamics for many-body systems consisting of identical ions, levitated in 2D and 3D ion traps. Finally, the same model is applied to the case of a combined 3D Quadrupole Ion Trap (QIT) with axial symmetry, for which we obtain the associated Hamilton function. The ion distribution can be described by means of numerical modeling, based on the Hamilton function we assign to the system. The approach we introduce is effective to infer the parameters of distinct types of traps by applying a unitary and coherent method, and especially for identifying equilibrium configurations, of large interest for ion crystals or quantum logic.

scholarly journals Investigations on Dynamical Stability in 3D Quadrupole Ion Traps

2021 ◽  
Author(s):  
Bogdan Mihalcea ◽  
Stephen Lynch
Keyword(s):  
Critical Points ◽  
Ion Trap ◽  
Hessian Matrix ◽  
Ion Traps ◽  
Quadrupole Ion Trap ◽  
Dynamical Stability ◽  
Many Body ◽  
Ion Distribution ◽  
Hamilton Function ◽  
Quantum Stability

We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. The system dynamics is characterized using a well established model that relies on two control parameters: the axial angular moment and the ratio between the radial and axial trap pseudo-oscillator characteristic frequencies. We augment this model and employ the Hessian matrix of the potential function in an attempt to better describe dynamical stability and the critical points. Our approach is then used to explore quantum stability in case of strongly coupled Coulomb many-body systems and establish a technique aimed at determining the critical points. Finally, we apply the model in case of a 3D Quadrupole Ion Trap (QIT) with axial symmetry, for which we obtain the associated Hamilton function. A different approach is used to better characterize many-body dynamics in combined (Paul and Penning) traps, with applications such as stable trapping of antimatter or fundamental tests of the Standard Model. The ion distribution can be described by means of numerical modeling, based on the Hamilton function we assign to the system. The approach we introduce is effective to infer the parameters of distinct types of traps by applying a cohesive method.

scholarly journals DYNAMICAL STABILITY OF STRANGE QUARK STARS

2011 ◽  
Vol 20 (07) ◽  
pp. 1171-1182 ◽  
Author(s):  
P. S. NEGI
Keyword(s):  
Strange Quark ◽  
The State ◽  
Dynamical Stability ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Star Models ◽  
Quark Stars ◽  
Equilibrium Configurations ◽  
Necessary And Sufficient ◽  
R Relation

The necessary and sufficient condition for dynamical stability is worked out for the sequences of relativistic star models which correspond to the well-defined and causal values of adiabatic sound speed, [Formula: see text], at the center. On the basis of the conditions obtained in this study, we show that the mass–radius (M-R) relation corresponding to the MIT bag models of strange quark matter (SQM) and the models obtained by Dey et al. [Phys. Lett. B438 (1998) 123] does not provide the necessary and sufficient condition for dynamical stability for the equilibrium configurations. These findings will remain unaltered and can be extended to any other sequence of pure SQM. This study explicitly shows that though SQM may exist in the state of zero pressure and temperature, the models of pure strange quark "stars" cannot exist in the state of hydrostatic equilibrium. This study can affect the results which are claiming that various objects, like RX J1856.5-3754, SAX J1808.4-3658, 4U 1728-34 and PSR 0943+10, represent strange stars.

scholarly journals Thermodynamical and dynamical stability of a self-gravitating uncharged thin shell

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Santiago Esteban Perez Bergliaffa ◽  
Marcelo Chiapparini ◽  
Luz Marina Reyes
Keyword(s):  
Equation Of State ◽  
Energy Density ◽  
Thin Shell ◽  
Dynamical Stability ◽  
Thin Shells ◽  
Maximum Mass ◽  
Equilibrium Configurations

Abstract The dynamical stability of massive thin shells with a given equation of state (EOS) (both for the barotropic and non-barotropic case) is here compared with the results coming from thermodynamical stability. Our results show that the restrictions in the para-meter space of equilibrium configurations of the shell following from thermodynamical stability are much more stringent that those obtained from dynamical stability. As a byproduct, we furnish evidence that the link between the maximum mass along a sequence of equilibrium configurations and the onset of dynamical stability is valid for EOS relating the pressure P, the energy density $$\sigma $$σ of the matter on the shell, and its radius R, namely $$P=P(R, \sigma )$$P=P(R,σ).

Propagation of waves in high Brillouin zones: Chaotic branched flow and stable superwires

2021 ◽  
Vol 118 (40) ◽  
pp. e2110285118
Author(s):  
Alvar Daza ◽  
Eric J. Heller ◽  
Anton M. Graf ◽  
Esa Räsänen
Keyword(s):  
Periodic Structure ◽  
Potential Barrier ◽  
Quantum Dynamics ◽  
Periodic Potential ◽  
Dynamical Stability ◽  
Length Scale ◽  
Propagation Of Waves ◽  
Typical Length

We report unexpected classical and quantum dynamics of a wave propagating in a periodic potential in high Brillouin zones. Branched flow appears at wavelengths shorter than the typical length scale of the ordered periodic structure and for energies above the potential barrier. The strongest branches remain stable indefinitely and may create linear dynamical channels, wherein waves are not confined directly by potential walls as electrons in ordinary wires but rather, indirectly and more subtly by dynamical stability. We term these superwires since they are associated with a superlattice.

Determination and Stability Analysis of Equilibrium Configurations of Objects Suspended From Multiple Aerial Robots

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Qimi Jiang ◽  
Vijay Kumar
Keyword(s):  
Stability Analysis ◽  
Hessian Matrix ◽  
Polynomial Equation ◽  
Search Algorithms ◽  
Cable System ◽  
Aerial Robots ◽  
Equilibrium Configurations ◽  
Position And Orientation ◽  
The Stability ◽  
Direct Kinematics

This work addresses the problem for determining the position and orientation of objects suspended with n cables from n aerial robots. This is actually the direct kinematics problem of the 3D cable system. First, the problem is formulated based on the static equilibrium condition. Then, an analytic algorithm based on resultant elimination is proposed to determine all possible equilibrium configurations of the planar 4-bar linkage. As the nonlinear system can be reduced to a polynomial equation in one unknown with a degree 8, this algorithm is more efficient than numerical search algorithms. Considering that the motion of a 3D cable system in its vertical planes of symmetry can be regarded as the motion of an equivalent planar 4-bar linkage, the proposed algorithm is used to solve the direct kinematics problem of objects suspended from multiple aerial robots. Case studies with three to six robots are conducted for demonstration. Then, approaches for stability analysis based on Hessian matrix are developed, and the stability of obtained equilibrium configurations is analyzed. Finally, experiments are conducted for validation.

Waveboard Artifacts Generate Ghost Resonances Consistent with Equations for Predicting Ion Motion in Commercial Quadrupole Ion Traps

2005 ◽  
Vol 11 (1) ◽  
pp. 15-21 ◽  
Author(s):  
Kwenga F. Sichilongo ◽  
Bert C. Lynn
Keyword(s):  
Ion Trap ◽  
Ion Traps ◽  
Quadrupole Ion Trap ◽  
Stability Diagram ◽  
Two Dimensional ◽  
Quadrupole Field ◽  
Non Linear ◽  
Contour Plots ◽  
The Stability ◽  
Contour Surface

Real-time experiments involving fragmentation of the precursor molecular ion of n-butylbenzene ( m/z 134) to produce product ions C7H+7 ( m/z 91) and C7H+8 ( m/z 92), were used to observe the motion of ions in a commercial quadrupole ion trap. Initially, ghost resonance peaks were observed for excitation of the precursor ion at qz values of 0.4 and 0.5 on the qz axis of the stability diagram. Further experiments involving the generation of two-dimensional contour plots confirmed that these ghost peaks, which were in agreement with mathematical equations describing the motion of ions in a quadrupole field, arose due to waveboard artifacts. Two-dimensional contour surface plots showed non-linear secular frequency canyons from a qz value of 0.5 to higher values corresponding with higher drive radio frequency (rf) voltages on the stability diagram. This observation confirmed that ions are subjected to non-linear effects in this mass scan range. The octapole and hexapole field lines were observed at qz values of 0.65 and 0.78, respectively.

scholarly journals Control aspects of quantum computing using pure and mixed states

2012 ◽  
Vol 370 (1976) ◽  
pp. 4651-4670 ◽  
Author(s):  
Thomas Schulte-Herbrüggen ◽  
Raimund Marx ◽  
Amr Fahmy ◽  
Louis Kauffman ◽  
Samuel Lomonaco ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Quantum Control ◽  
Open Quantum Systems ◽  
Jones Polynomial ◽  
Ion Traps ◽  
Quantum States ◽  
Nitrogen Vacancy ◽  
Quantum Circuits ◽  
State Transfer ◽  
Hard Problems

Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.

scholarly journals NECESSARY AND SUFFICIENT CONDITION FOR HYDROSTATIC EQUILIBRIUM IN GENERAL RELATIVITY

2007 ◽  
Vol 16 (01) ◽  
pp. 35-52 ◽  
Author(s):  
P. S. NEGI
Keyword(s):  
General Relativity ◽  
Variational Method ◽  
Upper Bound ◽  
Trial Function ◽  
Hydrostatic Equilibrium ◽  
Dynamical Stability ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Equilibrium Configurations ◽  
Necessary And Sufficient

We present explicit examples to show that the "compatibility criterion" (recently obtained by us toward providing equilibrium configurations compatible with the structure of general relativity) which states that for a given value of σ[≡ (P0/E0) ≡ the ratio of central pressure to central energy-density], the compactness ratio u[≡ (M/R), where M is the total mass and R is the radius of the configuration] of any static configuration cannot exceed the compactness ratio, uh, of the homogeneous density sphere (i.e., u ≤ uh) is capable of providing a necessary and sufficient condition for any regular configuration to be compatible with the state of hydrostatic equilibrium. This conclusion is drawn on the basis of the finding that the M–R relation gives the necessary and sufficient condition for dynamical stability of equilibrium configurations only when the compatibility criterion for these configurations is appropriately satisfied. In this regard, we construct an appropriate sequence composed of core-envelope models on the basis of compatibility criterion such that each member of this sequence satisfies the extreme case of causality condition v = c = 1 at the center. The maximum stable value of u ≃ 0.3389 (which occurs for the model corresponding to the maximum value of mass in the mass–radius relation) and the corresponding central value of the local adiabatic index, (Γ1)0 ≃ 2.5911, of this model are found fully consistent with those of the corresponding absolute values, u max ≤ 0.3406 and (Γ1)0 ≤ 2.5946, which impose strong constraints on these parameters of such models. In addition to this example, we also study dynamical stability of pure adiabatic polytropic configurations on the basis of variational method for the choice of the "trial function," ξ = reν/4, as well as the mass–central density relation, since the compatibility criterion is appropriately satisfied for these models. The results of this example provide additional proof in favor of the statement regarding compatibility criterion mentioned above. Together with other results, this study also confirms the previous claim that just the choice of the "trial function," ξ = reν/4, is capable of providing the necessary and sufficient condition for dynamical stability of a mass on the basis of variational method. Obviously, the upper bound on the compactness ratio of neutron stars, u ≅ 0.3389, which belongs to two-density model studied here, turns out to be much stronger than the corresponding "absolute" upper bound mentioned in the literature.

Sign in / Sign up

Export Citation Format

Share Document