For the TO1 mode we ﬁnd that the Slater- and Last-like displacements are in phase, whereas they are out of phase for the TO2 mode.
First-principles prediction of oxygen octahedral rotations in perovskite-structure EuTiO3
The eigenvector of this mode shows that this vibration originates from the out-of-phase displacements of Ti atoms in the neighboring sublattices.
First-principles prediction of oxygen octahedral rotations in perovskite-structure EuTiO3
The values of ZO k and ZO ⊥ refer to the Z ∗ of the oxygen ion when it is displaced along the Ti-O direction or perpendicular to it, respectively. A Berry-phase calculation of the polarization17 using the relaxed atomic positions in rhombohedral BaTiO3 yields a value of 30 µC/cm2 .
Bloch-type Domain Walls in Rhombohedral BaTiO3
This ﬁeld is phase shifted by 2k lm where k is the wave vector of light ﬁeld and lm is the displacement of the mirror from its equilibrium position.
Achieving the Quantum Ground State of a Mechanical Oscillator using a Bose-Einstein Condensate with Back-Action and Cold Damping feedback schemes
The displacement of the oscillator is measured through phase-sensitive homodyne detection of the cavity output which is fed back to the resonator using a force proportional to the oscillator velocity [10, 12].
Achieving the Quantum Ground State of a Mechanical Oscillator using a Bose-Einstein Condensate with Back-Action and Cold Damping feedback schemes
The case (1.2) corresponds to a situation where the average magnetic ﬂux over each elementary plaquette of the grain network is an integer multiple of Φ0 , but random displacement of superconducting grains from a perfect lattice structure yields quenched random phase shifts [7,11].
Vortex statistics in a disordered two-dimensional XY model
Two-phase displacements in porous media have received much attention during the last two decades.
A Numerical Study of Capillary and Viscous Drainage in Porous Media
CDW displacement phase and θ is the angle of the SU 2 spin rotation.
Topological Character of Excitations in Strongly Correlated Electronic Systems: Confinement and Dimensional Crossover
The experimenter deduces the phase shift (2ωo /c) ˆx(t) and thence the test-mass displacement ˆx(t) by measuring the electric ﬁeld’s phase quadrature ˆEφ (e.g., via interferometry or homodyne detection).
The noise in gravitational-wave detectors and other classical-force measurements is not influenced by test-mass quantization
Hence, the signal phase shift of the output optical beam depends linearly on the displacement.
The noise in gravitational-wave detectors and other classical-force measurements is not influenced by test-mass quantization
The time displacements of the time intervals for the existence of eddies on different scales are essentially irrelevant for the generation of gravitational radiation, leading only to some relative phase shift between the gravitational radiation at two different frequencies.
Gravitational Radiation From Cosmological Turbulence
The measurements follow displacement operations, that is, translations in the phase spaces of the modes.
D-outcome measurement for a nonlocality test
Contrary to the naive belief that ferroelectric domains develop from the PNR, these unusual local polar nanoregions appear to be displaced, or ”out-of-phase ” with respect to the surroun ding lattice.
The Persistence and Memory of Polar Nano-Regions in a Ferroelectric Relaxor Under an Electric Field
However, Alice’s technology is limited and we will tend to replace technologically demanding displacements by simple phase shifts given by the well known time evolution |α(t)i = exp(−iH t/) |αi with the Hamiltonian H = ω (n + 1 2 ).
Continuous variable private quantum channel
We equip Alice/Bob with mentioned phase shifts leading to (16) and just one displacement operator D(rmin ).
Continuous variable private quantum channel
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