The Quantum Mechanical Rotation Operators of Spins 5/2 to 7/2

With the creation of logic gates and algorithms for quantum computers and entering our lives, it is predicted that great developments will take place in this area and important efforts are made. Spin rotation processors are quantum mechanical rotation processors and have no classic counterparts. The rotation operators of spin 1/2 are well known and can be found in related textbooks. But rotation operators of other spins greater than 1/2 can be found numerically by evaluating the series expansions of exponential operator obtained from Schr?dinger equation, by evaluation of Wigner-d formula or by recently established expressions in polynomial forms discussed in the text. In a previous paper, rotation operators for spins 1/2 to 2 were published. In this work, explicit symbolic expressions of x, y and z components of rotation operators for spin 5/2, 3 and 7/2 are worked via exponential operator for each element of related spin operators and utilizing simple linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators.

Valence orbital method of calculating harmonic emission from diatomic molecule

We present a valence orbital method of calculating high-order harmonic generation from a diatomic molecule with arbitrary orientation by using a space rotation operator. We evaluate the effects of each valence orbital on harmonic emissions from N2 and O2 molecules in detail separately. The calculation results confirm the different properties of harmonic yields from N2 and O2 molecules which are well consistent with available experimental data. We observe that due to the orientation dependence of ／sigma and ／pi orbitals, the bonding orbital （π2pz）^2 of N2 determines the maximum of harmonic emission when the molecular axis of N2 is aligned parallel to the laser vector, and the magnitude of the high harmonic signal gradually weakens with the orientation angle of molecular axis increasing. But for O2 molecule the antibonding orbitals （π2pz）^1 and （π2pz）^1 contribute to the maximum of harmonic yield when O2 is aligned at 45° and bonding orbitals （π2pz）^2 and （π2pz）^2 slightly influence the orientation angle of maximum of harmonic radiation not exactly at 45°.

Preparation of optimal entropy squeezing state of atomic qubit inside the cavity via two-photon process and manipulation of atomic qubit outside the cavity

Considering two atomic qubits initially in Bell states, we send one qubit into a vacuum cavity with two-photon resonance and leave the other one outside. Using quantum information entropy squeezing theory, the time evolutions of the entropy squeezing factor of the atomic qubit inside the cavity are discussed for two cases, i.e., before and after rotation and measurement of the atomic qubit outside the cavity. It is shown that the atomic qubit inside the cavity has no entropy squeezing phenomenon and is always in a decoherent state before the operating atomic qubit outside the cavity. However,the periodical entropy squeezing phenomenon emerges and the optimal entropy squeezing state can be prepared for the atomic qubit inside the cavity by adjusting the rotation angle, choosing the interaction time between the atomic qubit and the cavity, controlling the probability amplitudes of subsystem states. Its physical essence is cutting the entanglement between the atomic qubit and its environment, causing the atomic qubit inside the cavity to change from the initial decoherent state into maximum coherent superposition state, which is a possible way of recovering the coherence of a single atomic qubit in the noise environment.

Dynamic behavior of a rotating gliding arc plasma in nitrogen:effects of gas flow rate and operating current

The effects of feed gas flow rate and operating current on the electrical characteristics and dynamic behavior of a rotating gliding arc （RGA） plasma codriven by a magnetic field and tangential flow were investigated.The operating current has been shown to significantly affect the time-resolved voltage waveforms of the discharge,particularly at flow rate =21 min^-1.When the current was lower than 140 mA,sinusoidal waveforms with regular variation periods of 13.5-17.0 ms can be observed （flow rate =21 min^-1）.The restrike mode characterized by serial sudden drops of voltage appeared under all studied conditions.Increasing the flow rate from 8 to 121 min^-1 （at the same current） led to a shift of arc rotation mode which would then result in a significant drop of discharge voltage （around 120-200 V）.For a given flow rate,the reduction of current resulted in a nearly linear increase of voltage.

LYAPUNOV EXPONENT AND ROTATION NUMBER FOR STOCHASTIC DIRAC OPERATORS

In this paper, we consider the stochastic Dirac operatoron a polish space (Ω,β, P). The relation between the Lyapunov index, rotation number andthe spectrum of Lis discussed. The existence of the Lyapunov index and rotation number isshown. By using the W-T functions and W-function we prove the theorems for Las in Kotani[1], [2] for Schrodinger operatorB, and in Johnson [5] for Dirac operators on compact space.

General coarsened measurement references for revelation of a classical world

It has been found that for a fixed degree of fuzziness in the coarsened references of measurements,the quantum-toclassical transition can be observed independent of the macroscopicity of the quantum state.We explore a general situation that the degree of fuzziness can change with the rotation angle between two states（different rotation angles represent different references）.The fuzziness of reference comes from two kinds of fuzziness：the Hamiltonian（rotation frequency）and the timing（rotation time）.For the fuzziness of the Hamiltonian alone,the degree of fuzziness for the reference will change with the rotation angle between two states,and the quantum effects can still be observed with any degree of fuzziness of Hamiltonian.For the fuzziness of timing,the degree of the coarsening reference is unchanged with the rotation angle.During the rotation of the measurement axis,the decoherence environment can also help the classical-to-quantum transition due to changing the direction of the measurement axis.

A highly efficient reconfigurable rotation unit based on an inverse butterfly network

We propose a reeonfigurable control-bit generation algorithm for rotation and sub-word rotation operations. The algorithm uses a self-routing characteristic to configure an inverse butterfly network. In addition to being highly parallelized and inexpensive, the algorithm integrates the rotation-shift, bi-directional rotation-shift, and sub-word rotation-shift operations. To our best knowledge, this is the first scheme to accommodate a variety of rotation operations into the same architecture. We have developed the highly efficient reconfigurable rotation unit （HERRU） and synthesized it into the Semiconductor Manufacturing International Corporation （SMIC）＇s 65-nm process. The results show that the overall efficiency （relative areaxrelative latency） of our HERRU is higher by at least 23% than that of other designs with similar functions. When executing the bi-directional rotation operations alone, HERRU occupies a significantly smaller area with a lower latency than previously proposed designs.

Coverage analysis for sensor networks based on Clifford algebra

The coverage performance is the foundation of information acquisition in distributed sensor networks. The previously proposed coverage work was mostly based on unit disk coverage model or ball coverage model in 2D or 3D space, respectively. However, most methods cannot give a homogeneous coverage model for targets with hybrid types. This paper presents a coverage analysis approach for sensor networks based on Clifford algebra and establishes a homogeneous coverage model for sensor networks with hybrid types of targets. The effectiveness of the approach is demonstrated with examples.

Orthogonal transformation operation theorem of a spatial universal uniform rotating magnetic field and its application in capsule endoscopy

According to the anti-phase sine current superposition theorem, the orientation, the magnetic flux density, the angular speed and the rotational direction of the spatial universal rotating magnetic field (SURMF) can be controlled within the tri-axial orthogonal square Helmholtz coils (TOSHC). Nevertheless, three coupling direction angles of the normal vector of the SURMF in the Descartes coordinate system cannot be separately controlled, thus the adjustment of the orientation of the SURMF is difficult and the flexibility of the robotic posture control is restricted. For the dimension reduction and the decoupling of control variables, the orthogonal transformation operation theorem of the SURMF is proposed based on two independent rotation angular variables, which employs azimuth and altitude angles as two variables of the three-phase sine current superposition formula derived by the orthogonal rotation inverse transformation. Then the unique control rules of the orientation and the rotational direction of the SURMF are generalized in each spatial quadrant, thus the scanning of the normal vector of the SURMF along the horizontal or vertical direction can be achieved through changing only one variable, which simplifies the control process of the orientation of the SURMF greatly. To validate its feasibility and maneuverability, experiments were conducted in the animal intestine utilizing the innovative dual hemisphere capsule robot (DHCR) with active and passive modes. It was demonstrated that the posture adjustment and the steering rolling locomotion of the DHCR can be realized through single variable control, thus the orthogonal transformation operation theorem makes the control of the orientation of the SURMF convenient and flexible significantly. This breakthrough will lay a foundation for the human-machine interaction control of the SURMF.