scholarly journals Mesoscopic fluctuations of off-diagonal matrix elements of the angular momentum and orbital magnetism of free electrons in a rectangular box

2007 ◽  
Vol 75 (22) ◽  
Author(s):  
M. X. Lou ◽  
J. M. A. S. P. Wickramasinghe ◽  
R. A. Serota
Keyword(s):  
Angular Momentum ◽  
Diagonal Matrix ◽  
Matrix Elements ◽  
Free Electrons ◽  
Orbital Magnetism

INVESTIGATION COMPARISON ON THE GATE SPEED OF THREE-LEVEL AND TWO-LEVEL QUANTUM NOT GATES WITH ASYMMETRIC POTENTIAL OF rf-SQUID

2007 ◽  
Vol 21 (19) ◽  
pp. 1261-1270 ◽  
Author(s):  
YING-HUA JI ◽  
JU-JU HU ◽  
SHI-HUA CAI
Keyword(s):  
Microwave Pulse ◽  
Diagonal Matrix ◽  
Matrix Elements ◽  
The Asymmetry ◽  
Rf Squid ◽  
Double Well Potential

We investigate the relation between the speed of quantum NOT gate and the asymmetry or detuning of the potential in system of the interaction of a two-level rf-SQUID qubit with a classical microwave pulse. The rf-SQUID is characterized by an asymmetric double well potential that gives rise to diagonal matrix elements. Then in resonance, we compare the gate speeds for three-level and two-level quantum NOT gates. We show that in general, a three-level gate is much faster than the conventional two-level gate.

Broadband EM radiation amplification by means of a monochromatically driven two-level system

2017 ◽  
Vol 31 (04) ◽  
pp. 1750027 ◽  
Author(s):  
Andrey V. Soldatov
Keyword(s):  
Dipole Moment ◽  
Quantum System ◽  
High Frequency ◽  
Laser Field ◽  
Diagonal Matrix ◽  
Matrix Elements ◽  
Level System ◽  
Dipole Moment Operator ◽  
Moment Operator ◽  
Radiation Amplification

It is shown that a two-level quantum system possessing dipole moment operator with permanent non-equal diagonal matrix elements and driven by external semiclassical monochromatic high-frequency electromagnetic (EM) (laser) field can amplify EM radiation waves of much lower frequency.

SYMMETRY DECOUPLING IN LINEAR ALGEBRAIC VARIATIONAL SCATTERING PROBLEMS

1995 ◽  
Vol 06 (01) ◽  
pp. 105-121
Author(s):  
MEISHAN ZHAO
Keyword(s):  
Angular Momentum ◽  
Variational Principle ◽  
Total Angular Momentum ◽  
Numerical Calculations ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Scattering Problems ◽  
Identical Particles ◽  
Generalized Newton

This paper discusses the symmetry decoupling in quantum mechanical algebraic variational scattering calculations by the generalized Newton variational principle. Symmetry decoupling for collisions involving identical particles is briefly discussed. Detailed discussion is given to decoupling from evaluation of matrix elements with nonzero total angular momentum. Example numerical calculations are presented for BrH2 and DH2 systems to illustrate accuracy and efficiency.

On Extending the Trace as a Linear Functional, II

1980 ◽  
Vol 32 (6) ◽  
pp. 1288-1298
Author(s):  
George A. Elliott
Keyword(s):  
Positive Operator ◽  
Selfadjoint Operator ◽  
Linear Functional ◽  
Orthonormal Basis ◽  
Unitary Operator ◽  
Trace Class ◽  
Diagonal Matrix ◽  
Matrix Elements ◽  
Von Neumann ◽  
The Difference

A positive bounded selfadjoint operator is in the trace class of von Neumann and Schatten ([4]) if the sum of its diagonal matrix elements with respect to some orthonormal basis is finite, and the trace is then defined to be this sum, which is independent of the basis. A bounded selfadjoint but not necessarily positive operator x is in the trace class if in the decomposition x = x+ – x−, with x+ and x− positive and x+x− = 0, both x+ and x−are in the trace class; the trace of x is then defined to be the difference of the finite traces of x+ and x−. The trace defined in this way is a linear functional on the trace class, and is unitarily invariant; if u is a unitary operator, the trace of uxu−1 is the same as the trace of x.

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