Mean spin direction and spin squeezing in superpositions of spin
... if Sy ≤ 0. |S| sin(θ) The above expression is valid for θ = 0, π. For θ = 0, π, the mean spin is along the ±z direction, and one possible choice of φ can be φ = 0, π. To illustrate the above finding, we plot in Fig. 1, the azimuth angle and the polar angle versus the relative phase γ for state 1. ...
... if Sy ≤ 0. |S| sin(θ) The above expression is valid for θ = 0, π. For θ = 0, π, the mean spin is along the ±z direction, and one possible choice of φ can be φ = 0, π. To illustrate the above finding, we plot in Fig. 1, the azimuth angle and the polar angle versus the relative phase γ for state 1. ...
JOURNAL OF MODERN OPTICS, 1987, VOL . 34, NO. 11, 1401
... This result is precisely analogous to the phase shift later predicted by Aharonov and Bohm [11, 12], according to which two electron beams develop a phase shift proportional to the magnetic flux they enclose . For polarized light the analogue of magnetic flux is the solid angle of the polygon on the ...
... This result is precisely analogous to the phase shift later predicted by Aharonov and Bohm [11, 12], according to which two electron beams develop a phase shift proportional to the magnetic flux they enclose . For polarized light the analogue of magnetic flux is the solid angle of the polygon on the ...
The death of Schrödinger`s cat and of consciousness
... When a measurement is made at a quantum level, the superposition of possible outcomes described by the quantum wave-function collapses into a definite, single state. The question of exactly what constitutes a measurement is unresolved, however, and represents the so-called “measurement ...
... When a measurement is made at a quantum level, the superposition of possible outcomes described by the quantum wave-function collapses into a definite, single state. The question of exactly what constitutes a measurement is unresolved, however, and represents the so-called “measurement ...
Slide 1
... All these have hidden SO(4,2) (note this is more than usual Killing vectors). All are dual transforms of each other as field theories. Duality transformations: Weyl rescaling of background metric and general coordinate reparametrizations taking one field theory with backgrounds to another. The duali ...
... All these have hidden SO(4,2) (note this is more than usual Killing vectors). All are dual transforms of each other as field theories. Duality transformations: Weyl rescaling of background metric and general coordinate reparametrizations taking one field theory with backgrounds to another. The duali ...
Spin-valley lifetimes in a silicon quantum dot with tunable valley
... j2i ¼ jv ; "i, j3i ¼ jv þ ; #i, j4i ¼ jv þ ; "i. These states are considered to be only very weakly affected by higher excitations, such as orbital levels that are at least 8 meV above the ground state in our device41. In Supplementary Note 3 we detail how mixing to a 2p-like orbital state leads t ...
... j2i ¼ jv ; "i, j3i ¼ jv þ ; #i, j4i ¼ jv þ ; "i. These states are considered to be only very weakly affected by higher excitations, such as orbital levels that are at least 8 meV above the ground state in our device41. In Supplementary Note 3 we detail how mixing to a 2p-like orbital state leads t ...
Conjugation coinvariants of quantum matrices
... The conjugation A → g −1 Ag of a complex N × N matrix A by an invertible matrix g induces an action of GL(N, C) on the coordinate algebra C[X ij ] of N × N matrices. The invariant functions with respect to this action are well-known, they are the elements in the C-subalgebra of C[Xij ] that is gener ...
... The conjugation A → g −1 Ag of a complex N × N matrix A by an invertible matrix g induces an action of GL(N, C) on the coordinate algebra C[X ij ] of N × N matrices. The invariant functions with respect to this action are well-known, they are the elements in the C-subalgebra of C[Xij ] that is gener ...
Locality of Gravitational Systems from Entanglement of
... The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the b ...
... The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the b ...
73 013601 (2006)
... that can be observed in experiments 关12兴. It is therefore important to understand the route to chaos with increasing interactions. This problem has recently been studied for the kicked BEC in a harmonic oscillator 关6兴. In Ref. 关13兴, we have investigated the quantum dynamics of a BEC with repulsive i ...
... that can be observed in experiments 关12兴. It is therefore important to understand the route to chaos with increasing interactions. This problem has recently been studied for the kicked BEC in a harmonic oscillator 关6兴. In Ref. 关13兴, we have investigated the quantum dynamics of a BEC with repulsive i ...
6 Wave equation in spherical polar coordinates
... Note that we have to include both positive and negative values of m. As φ is an angular coordinate, we expect our solutions to be single-valued, i.e. unchanged as we go right round the circle φ → φ + 2π: Φ(φ + 2π) = Φ(φ) ...
... Note that we have to include both positive and negative values of m. As φ is an angular coordinate, we expect our solutions to be single-valued, i.e. unchanged as we go right round the circle φ → φ + 2π: Φ(φ + 2π) = Φ(φ) ...
Could Inelastic Interactions Induce Quantum Probabilistic Transitions?
... physical properties of entities, on the one hand, and dynamical laws of the relevant theory, on the other hand.3 Thus, in speaking of the physical properties of physical entities - electric charge, mass, wavelength, and so on - we are, in effect speaking of dynamic laws that govern the way these ent ...
... physical properties of entities, on the one hand, and dynamical laws of the relevant theory, on the other hand.3 Thus, in speaking of the physical properties of physical entities - electric charge, mass, wavelength, and so on - we are, in effect speaking of dynamic laws that govern the way these ent ...
1 Gaussian elimination: LU
... As we shall see later, these two substitution processes are no more costly than computing A−1 b, given that A−1 is known, so in that sense knowing L and U is as good for solving systems as knowing the inverse. Once the factorization is obtained, it is very cheap to solve many systems with the same m ...
... As we shall see later, these two substitution processes are no more costly than computing A−1 b, given that A−1 is known, so in that sense knowing L and U is as good for solving systems as knowing the inverse. Once the factorization is obtained, it is very cheap to solve many systems with the same m ...
The Quantum World
... Chapter 7 we shall find that there is in quantum theory a radical inability to pin things down which goes beyond the simple considerations outlined here. The second perplexity relates to the act of measurement. It is notorious that there is an inescapable random element in quantum mechanical measure ...
... Chapter 7 we shall find that there is in quantum theory a radical inability to pin things down which goes beyond the simple considerations outlined here. The second perplexity relates to the act of measurement. It is notorious that there is an inescapable random element in quantum mechanical measure ...