QUANTIZATION SCHEME FOR FERMIONIC SYSTEM AND s-ORDERED OPERATOR EXPANSION FORMULA OF FERMIONIC DENSITY OPERATORS

2011 ◽  
Vol 26 (11) ◽  
pp. 833-842 ◽  
Author(s):  
YE-JUN XU ◽  
JUN SONG ◽  
HONG-CHUN YUAN ◽  
HONG-YI FAN ◽  
QIU-YU LIU
Keyword(s):  
Coherent State ◽  
Quantization Scheme ◽  
Expansion Formula ◽  
Wigner Operator ◽  
Fermionic System ◽  
Operator Expansion ◽  
Density Operators ◽  
S Parameter ◽  
Classical Correspondence ◽  
One To One

We introduce the generalized fermionic Wigner operator with an s parameter. Based on its remarkable properties, we establish one-to-one mapping between fermion operators and their s-parametrized pseudo-classical correspondence, which may involve fermionic Weyl pseudo-classical correspondence, P-representation and Q-representation in a unified way. Furthermore, starting with the projector of the fermionic coherent state, we obtain the s-ordered operator expansion formula of fermionic density operators, which includes normally ordered, antinormally ordered and Weyl ordered product of operators for different values of s. Applications in calculating some Fermi operators' s-ordered expansions are presented.

MUTUAL TRANSFORMATION BETWEEN DIFFERENT s-PARAMETRIZED QUANTIZATION SCHEMES BASED ON s-ORDERED WIGNER OPERATOR

2012 ◽  
Vol 27 (16) ◽  
pp. 1250089
Author(s):  
HONG-YI FAN ◽  
SHUAI WANG
Keyword(s):  
Hermite Polynomials ◽  
Delta Function ◽  
Mutual Transformation ◽  
Quantization Scheme ◽  
Wigner Operator ◽  
Dirac Delta ◽  
Classical Correspondence ◽  
Phase Space Theory ◽  
Transformation Relation ◽  
Thermal States

s-parametrized quantization is essential to phase space theory of quantum mechanical. Based on s-ordered Wigner operator, we examine the classical correspondence of the s2-parametrized Wigner operator through the s1-parametrized quantization scheme, and establish the mutual transformation relation between different s-parametrized quantization schemes. It turns out that the s-parametrized Wigner operator's s-ordering is just the Dirac delta function, which seems to be a new result. As applications, we derive the s-ordered form of the density operator of thermal states and some new generating function formula of Hermite polynomials.

NEW THREE-MODE COHERENT-ENTANGLED STATE DERIVED BY VIRTUE OF DECOMPOSING NORMALLY ORDERED GAUSSIAN OPERATOR INTEGRAND

2012 ◽  
Vol 10 (01) ◽  
pp. 1250017 ◽  
Author(s):  
GANG REN ◽  
HONG-YI FAN
Keyword(s):  
Coherent State ◽  
Entangled State ◽  
Wigner Operator ◽  
Squeezing Operator ◽  
Gaussian Operator ◽  
The Ideal

We introduce a new kind of three-mode coherent-entangled state (CES) |x,β1,β2〉, which has both properties of the coherent state and the entangled state. We derive it by virtue of decomposing normally ordered Gaussian operator integrand. An experiment setup to produce the ideal coherent-entangled state is presented. The corresponding Wigner operator and squeezing operator in terms of CES are also given.

scholarly journals GENERAL SOLUTION OF THE QUANTUM DAMPED HARMONIC OSCILLATOR II: SOME EXAMPLES

2009 ◽  
Vol 06 (02) ◽  
pp. 225-231 ◽  
Author(s):  
KAZUYUKI FUJII ◽  
TATSUO SUZUKI
Keyword(s):  
General Solution ◽  
Coherent State ◽  
Harmonic Oscillator ◽  
Infinite Series ◽  
Operator Algebra ◽  
Preceding Paper ◽  
Initial Value ◽  
Damped Harmonic Oscillator ◽  
Density Operators ◽  
Algebra Level

In the preceding paper (arXiv: 0710.2724 [quant-ph]) we have constructed the general solution for the master equation of quantum damped harmonic oscillator, which is given by the complicated infinite series in the operator algebra level. In this paper we give the explicit and compact forms to solutions (density operators) for some initial values. In particular, the compact one for the initial value based on a coherent state is given, which has not been given as far as we know. Moreover, some related problems are presented.

New s-parametrized quasiprobability distribution for fermion system and its application on fermion-counting

2014 ◽  
Vol 29 (05) ◽  
pp. 1450022
Author(s):  
Ye-Jun Xu ◽  
Hong-Chun Yuan ◽  
Xian-Cai Wang ◽  
Xue-Fen Xu
Keyword(s):  
Density Operator ◽  
The Other ◽  
Fermion System ◽  
Expansion Formula ◽  
Operator Expansion ◽  
Counting Formula ◽  
Multi Mode ◽  
Quasiprobability Distributions ◽  
Quasiprobability Distribution

Based on the fermion operators' s-ordered rule, we introduce a new kind of s-ordered quasiprobability distributions [Formula: see text], which is defined by the supertrace different from the other definition introduced by Cahill and Glauber [Phys. Rev. A59, 1538 (1999)]. We further obtain the s-parametrized operator expansion formula of fermion density operator for multi-mode case. At last, we apply it to deriving new multi-mode fermion-counting formula, which would be convenient to calculate the probability of counting n fermions.

A Support Program

1994 ◽  
Vol 25 (2) ◽  
pp. 112-114 ◽  
Author(s):  
Henna Grunblatt ◽  
Lisa Daar
Keyword(s):  
Hearing Aids ◽  
School Counselor ◽  
Support Program ◽  
Educational Audiology ◽  
Part Program ◽  
One To One

A program for providing information to children who are deaf about their deafness and addressing common concerns about deafness is detailed. Developed by a school audiologist and the school counselor, this two-part program is geared for children from 3 years to 15 years of age. The first part is an educational audiology program consisting of varied informational classes conducted by the audiologist. Five topics are addressed in this part of the program, including basic audiology, hearing aids, FM systems, audiograms, and student concerns. The second part of the program consists of individualized counseling. This involves both one-to-one counseling sessions between a student and the school counselor, as well as conjoint sessions conducted—with the student’s permission—by both the audiologist and the school counselor.

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