scholarly journals Directional Elastic Pseudospin and Nonseparability of Directional and Spatial Degrees of Freedom in Parallel Arrays of Coupled Waveguides

2020 ◽  
Vol 10 (9) ◽  
pp. 3202
Author(s):  
M. Arif Hasan ◽  
Lazaro Calderin ◽  
Trevor Lata ◽  
Pierre Lucas ◽  
Keith Runge ◽  
...  
Keyword(s):  
Elastic Waves ◽  
Degrees Of Freedom ◽  
Bell State ◽  
Tensor Products ◽  
Quantum Spin ◽  
Linear Combinations ◽  
Acoustic Waveguides ◽  
Parallel Arrays ◽  
Spatial Degrees Of Freedom ◽  
Coupled Waveguides

We experimentally and numerically investigated elastic waves in parallel arrays of elastically coupled one-dimensional acoustic waveguides composed of aluminum rods coupled along their length with epoxy. The elastic waves in each waveguide take the form of superpositions of states in the space of direction of propagation. The direction of propagation degrees of freedom is analogous to the polarization of a quantum spin; hence, these elastic waves behave as pseudospins. The amplitude in the different rods of a coupled array of waveguides (i.e., the spatial mode of the waveguide array) refer to the spatial degrees of freedom. The elastic waves in a parallel array of coupled waveguides are subsequently represented as tensor products of the elastic pseudospin and spatial degrees of freedom. We demonstrate the existence of elastic waves that are nonseparable linear combinations of tensor products states of pseudospin/ spatial degrees of freedom. These elastic waves are analogous to the so-called Bell states of quantum mechanics. The amplitude coefficients of the nonseparable linear combination of states are complex due to the Lorentzian character of the elastic resonances associated with these waves. By tuning through the amplitudes, we are able to navigate both experimentally and numerically a portion of the Bell state Hilbert space.

scholarly journals Reconstruction of Relative Phase of Self-Transmitting Devices by Using Multiprobe Solutions and Non-Convex Optimization

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2459
Author(s):  
Rubén Tena Sánchez ◽  
Fernando Rodríguez Varela ◽  
Lars J. Foged ◽  
Manuel Sierra Castañer
Keyword(s):  
Iterative Algorithm ◽  
Degrees Of Freedom ◽  
Relative Phase ◽  
Low Cost ◽  
Initial Guess ◽  
Noise Model ◽  
Medium Size ◽  
Phase Reconstruction ◽  
Linear Combinations ◽  
Iterative Optimization Algorithm

Phase reconstruction is in general a non-trivial problem when it comes to devices where the reference is not accessible. A non-convex iterative optimization algorithm is proposed in this paper in order to reconstruct the phase in reference-less spherical multiprobe measurement systems based on a rotating arch of probes. The algorithm is based on the reconstruction of the phases of self-transmitting devices in multiprobe systems by taking advantage of the on-axis top probe of the arch. One of the limitations of the top probe solution is that when rotating the measurement system arch, the relative phase between probes is lost. This paper proposes a solution to this problem by developing an optimization iterative algorithm that uses partial knowledge of relative phase between probes. The iterative algorithm is based on linear combinations of signals when the relative phase is known. Phase substitution and modal filtering are implemented in order to avoid local minima and make the algorithm converge. Several noise-free examples are presented and the results of the iterative algorithm analyzed. The number of linear combinations used is far below the square of the degrees of freedom of the non-linear problem, which is compensated by a proper initial guess. With respect to noisy measurements, the top probe method will introduce uncertainties for different azimuth and elevation positions of the arch. This is modelled by considering the real noise model of a low-cost receiver and the results demonstrate the good accuracy of the method. Numerical results on antenna measurements are also presented. Due to the numerical complexity of the algorithm, it is limited to electrically small- or medium-size problems.

The Motion of the Human Center of Mass and its Relationship to Mechanical Impedance

1966 ◽  
Vol 8 (5) ◽  
pp. 399-405 ◽  
Author(s):  
Edmund B. Weis ◽  
Frank P. Primiano
Keyword(s):  
Transfer Function ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Mechanical Impedance ◽  
Second Order ◽  
Analysis Tool ◽  
Isotropic Theory ◽  
Spatial Degrees Of Freedom

This report concerns the development of a relationship between the human mechanical impedance and the coupling of the human center of mass to the environment. The mechanical impedance is a common analysis tool in biomechanics while the analysis of the coupling of the center of mass to the environment is technically more difficult, if not impossible. The development is based on linear, passive, isotropic theory and shows that the transfer function which expresses the relation between the motion of the center of mass and the motion of the source is similar to a linear second order mechanical system in each of the translational spatial degrees of freedom.

Dynamics of bell-nonlocality for two atoms interacting with a vacuum multi-mode noise field

2016 ◽  
Vol 14 (03) ◽  
pp. 1650011 ◽  
Author(s):  
Yu-Jie Liu ◽  
Li Zheng ◽  
Dong-Mei Han ◽  
Huan-Lin Lü ◽  
Tai-Yu Zheng
Keyword(s):  
Degrees Of Freedom ◽  
Internal State ◽  
Bell Inequality ◽  
Entanglement Dynamics ◽  
Noise Field ◽  
Chsh Inequality ◽  
Internal States ◽  
Bell Nonlocality ◽  
Multi Mode ◽  
Spatial Degrees Of Freedom

We investigate the internal-state Bell nonlocal entanglement dynamics, as measured by CHSH inequality of two atoms interacting with a vacuum multi-mode noise field by taking into account the spatial degrees of freedom of the two atoms. The dynamics of Bell nonlocality of the atoms with the atomic internal states being initially in a Werner-type state is studied, by deriving the analytical solutions of the Schrödinger equation, and tracing over the degrees of freedom of the field and the external motion of the two atoms. In addition, through comparison with entanglement as measured by concurrence, we find that the survival time of entanglement is much longer than that of the Bell-inequality violation. And the comparison of the quantum correlation time between two Werner-type states is discussed.

scholarly journals Energy coupling among the degrees of freedom in an electron–positron plasma

2010 ◽  
Vol 76 (3-4) ◽  
pp. 329-335 ◽  
Author(s):  
WENMIN ZHANG ◽  
M. Y. YU ◽  
A. R. KARIMOV ◽  
L. STENFLO
Keyword(s):  
Exact Solutions ◽  
Degrees Of Freedom ◽  
Energy Coupling ◽  
Nonlinear Coupling ◽  
Irrotational Flow ◽  
Flow Component ◽  
Electron Positron ◽  
Rotational Components ◽  
Flow Components ◽  
Spatial Degrees Of Freedom

AbstractNonlinear coupling of the motion in the three spatial degrees of freedom of a cold fluid electron–positron plasma is investigated. Exact solutions describing expanding flows with oscillations are obtained. It is found that the energy in the irrotational flow component is in general transferred to the rotational components, but not in the reversed direction. Furthermore, since the density evolution need not be related to all the three flow components, oscillations in one or two of the flow fields can be purely electromagnetic and are not accompanied by density oscillations.

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