Eigenkets of the q-deformed creation operator

2010 ◽  
Vol 51 (9) ◽  
pp. 092107 ◽  
Author(s):  
Ye-jun Xu ◽  
Jun Song ◽  
Hong-yi Fan ◽  
Qiu-yu Liu
Keyword(s):  
Creation Operator

How To Recognize The Creation Operator

2007 ◽  
Vol 59 (3) ◽  
pp. 401-408 ◽  
Author(s):  
Franciszek Hugon Szafraniec
Keyword(s):  
Creation Operator ◽  
The Creation

scholarly journals Monopole and instanton effects in QCD

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Masayasu Hasegawa
Keyword(s):  
Dirac Operator ◽  
Matrix Theory ◽  
Charged Pion ◽  
Lattice Gauge Theory ◽  
Pion Mass ◽  
Magnetic Monopoles ◽  
Chiral Condensate ◽  
Creation Operator ◽  
Experimental Result ◽  
Qcd Vacuum

Abstract We aim to show the effects of the magnetic monopoles and instantons in quantum chromodynamics (QCD) on observables; therefore, we introduce a monopole and anti-monopole pair in the QCD vacuum of a quenched SU(3) by applying the monopole creation operator to the vacuum. We calculate the eigenvalues and eigenvectors of the overlap Dirac operator that preserves the exact chiral symmetry in lattice gauge theory using these QCD vacua. We then investigate the effects of magnetic monopoles and instantons. First, we confirm the monopole effects as follows: (i) the monopole creation operator makes the monopoles and anti-monopoles in the QCD vacuum. (ii) A monopole and anti-monopole pair creates an instanton or anti-instanton without changing the structure of the QCD vacuum. (iii) The monopole and anti-monopole pairs change only the scale of the spectrum distribution without affecting the spectra of the Dirac operator by comparing the spectra with random matrix theory. Next, we find the instanton effects by increasing the number density of the instantons and anti-instantons as follows: (iv) the decay constants of the pseudoscalar increase. (v) The values of the chiral condensate, which are defined as negative numbers, decrease. (vi) The light quarks and the pseudoscalar mesons become heavy. The catalytic effect on the charged pion is estimated using the numerical results of the pion decay constant and the pion mass. (vii) The decay width of the charged pion becomes wider than the experimental result, and the lifetime of the charged pion becomes shorter than the experimental result. These are the effects of the monopoles and instantons in QCD.

ON THE COMMON EIGENVECTORS OF TWO-MODE CREATION OPERATORS AND THE CHARGE OPERATOR

1994 ◽  
Vol 09 (14) ◽  
pp. 1291-1297 ◽  
Author(s):  
FAN HONG-YI ◽  
JOHN R. KLAUDER
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Contour Integration ◽  
Creation Operator ◽  
Charge Operator ◽  
The Common ◽  
Creation Operators

Some comments are presented on the equivalence between Dirac’s ξ-representation of a harmonic oscillator (Ref. 5) and the eigenvectors of a creation operator derived by Fan et al. using Heitler’s contour integration form of δ-function. On the basis of this analysis the common eigenvectors of a†b† and Q=a†a−b†b, which are dual vectors of the charged coherent states of Bhaumik et al., are constructed.

THE EIGENVECTORS OF q-DEFORMED CREATION OPERATOR $a_q^+$ AND THEIR PROPERTIES

1995 ◽  
Vol 10 (08) ◽  
pp. 669-675
Author(s):  
GUOXIN JU ◽  
JINHE TAO ◽  
ZIXIN LIU ◽  
MIAN WANG
Keyword(s):  
Integral Representation ◽  
Creation Operator ◽  
Contour Integral ◽  
Root Of Unity

The eigenvectors of q-deformed creation operator [Formula: see text] are discussed for q being real or a root of unity by using the contour integral representation of δ function. The properties for the eigenvectors are also discussed. In the case of qp = 1, the eigenvectors may be normalizable.

scholarly journals UNIFIED TREATMENT OF HETERODYNE DETECTION: THE SHAPIRO–WAGNER AND CAVES FRAMEWORKS

2005 ◽  
Vol 19 (14) ◽  
pp. 2287-2310 ◽  
Author(s):  
GIULIO LANDOLFI ◽  
GIOVANNA RUGGERI ◽  
GIULIO SOLIANI
Keyword(s):  
Comparative Study ◽  
Annihilation Operator ◽  
Relative Number ◽  
Creation Operator ◽  
Quantum Phase ◽  
Heterodyne Detection ◽  
Photon Detectors ◽  
Simultaneous Measurements ◽  
Number State ◽  
Image Band

A comparative study is performed on two heterodyne systems of photon detectors expressed in terms of a signal annihilation operator and an image band creation operator called Shapiro–Wagner and Caves' frame, respectively. This approach is based on the introduction of a convenient operator [Formula: see text] which allows a unified formulation of both cases. For the Shapiro–Wagner scheme, where [Formula: see text], quantum phase and amplitude are exactly defined in the context of relative number state (RNS) representation, while a procedure is devised to handle suitably and in a consistent way Caves' framework, characterized by [Formula: see text], within the approximate simultaneous measurements of noncommuting variables. In such a case RNS phase and amplitude make sense only approximately.

scholarly journals A peculiarity of the creation operator

2002 ◽  
Vol 44 (01) ◽  
pp. 137 ◽  
Author(s):  
Jan Stochel ◽  
Franciszek Hugon Szafraniec
Keyword(s):  
Creation Operator ◽  
The Creation

NEW NONCLASSICAL SOLUTION ON GENERALIZED PAUL TRAP TYPE: NONCLASSICAL STUDY

2000 ◽  
Vol 15 (16) ◽  
pp. 1071-1078
Author(s):  
BISWANATH RATH
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Annihilation Operator ◽  
Paul Trap ◽  
Simple Expression ◽  
Creation Operator ◽  
Time Dependent ◽  
Dependent Frequency ◽  
Generalized Time

New nonclassical solutions for the harmonic oscillator with generalized time-dependent frequency have been found. Simple expression on energy level, creation operator a†(t) and annihilation operator a(t) have been obtained. Using new solutions we want to show how to study squeezing.

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