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51.
New two-fold integration transformation for the Wigner operator in phase space quantum mechanics and its relation to operator ordering 下载免费PDF全文
Using the Weyl ordering of operators expansion formula (Hong-Yi
Fan, \emph{ J. Phys.} A {\bf 25} (1992) 3443) this paper finds a
kind of two-fold integration transformation about the Wigner
operator $\varDelta \left( q',p'\right) $
($\mathrm{q}$-number transform) in phase space quantum mechanics,
$\iint_{-\infty}^{\infty}\frac{{\rm d}p'{\rm d}q'}{\pi
}\varDelta \left( q',p'\right) \e^{-2\i\left(
p-p'\right) \left( q-q'\right) }=\delta \left(
p-P\right) \delta \left( q-Q\right),$
and its inverse%
$
\iint_{-\infty}^{\infty}{\rm d}q{\rm d}p\delta \left( p-P\right)
\delta \left( q-Q\right) \e^{2\i\left( p-p'\right) \left(
q-q'\right) }=\varDelta \left(
q',p'\right),$ where $Q,$ $P$ are the coordinate
and momentum operators, respectively. We apply it to study mutual
converting formulae among $Q$--$P$ ordering, $P$--$Q$ ordering and Weyl
ordering of operators. In this way, the contents of phase space
quantum mechanics can be enriched. The formula of the Weyl
ordering of operators expansion and the technique of integration within the Weyl
ordered product of operators are used in this discussion. 相似文献
52.
New equation for deriving pure state density operators by Weyl correspondence and Wigner operator 下载免费PDF全文
By virtue of the completeness of Wigner operator and Weyl
correspondence we construct a general equation for deriving pure
state density operators. Several important examples are considered
as the applications of this equation, which shows that our approach
is effective and convenient for deducing these entangled state
representations. 相似文献
53.
Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation 下载免费PDF全文
In a preceding letter (2007 Opt.Lett.32 554) we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family.In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation,which makes the complex continuous wavelet transform theory complete.A new orthogonal property of mother wavelet in parameter space is revealed. 相似文献
54.
A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation 下载免费PDF全文
Based on the displacement-squeezing related squeezed
coherent state representation ≤ft\vert z\right\rangle _{g} and
using the technique of integration within an ordered product of
operators, this paper finds a generalized Fresnel operator, whose
matrix element in the coordinate representation leads to a
generalized Collins formula (Huygens--Fresnel integration
transformation describing optical diffraction). The generalized
Fresnel operator is
derived by a quantum mechanical mapping from z to sz-rz^{\ast } in the %
≤ft\vert z\right\rangle _{g} representation, while ≤ft\vert
z\right\rangle _{g} in phase space is graphically denoted by an
ellipse. 相似文献
55.
Two mutually conjugated tripartite entangled states and their fractional Fourier transformation kernel 下载免费PDF全文
We newly construct two mutually-conjugate tripartite entangled state representations,based on which we propose the formulation of three-mode entangled fractional Fourier transformation(EFFT) and derive the transformation kernel.The EFFT’s additivity property is proved and the eigenmode of EFFT is derived.As an application,we calculate the EFFT of the three-mode squeezed vacuum state. 相似文献
56.
Based on the construction of supersymmetric generators, we
use the Lewis--Riesenfeld invariant method to deduce the exact and
explicit eigen-energy spectrum with the time-dependent thermo
Jaynes--Cummings model. One of the advantages of this approach is
that it can transform the hidden form, related to the chronological
product, of the time evolution operator into an explicit expression.
Moreover, the dynamical and statistics properties of physical
quantities are obtained for the given initial states in the thermo
Jaynes--Cummings system. 相似文献
57.
QUANTUM FLUCTUATIONS IN MESOSCOPIC RESISTANCE-INDUCTANCE-CAPACITANCE ELECTRIC CIRCUITS AT FINITE TEMPERATURE 总被引:9,自引:0,他引:9 下载免费PDF全文
By using the charge and current in a quantization resistance-inductance-capacitance (RLC) electric circuit, we construct a pair of canonical variables. Using this pair of variables and the thermal field dynamics, we obtain the fluctuations of charge and current in the RLC electric circuit at finite temperatures. It is shown that the fluctuations increase with increasing temperature and decrease with prolonging of time. 相似文献
58.
59.
We find a new complex integration-transform which can establish a new relationship between a two-mode operator's matrix element in the entangled state representation and its Wigner function. This integration keeps modulus invariant and therefore invertible. Based on this and the Weyl–Wigner correspondence theory, we find a two-mode operator which is responsible for complex fractional squeezing transformation. The entangled state representation and the Weyl ordering form of the two-mode Wigner operator are fully used in our derivation which brings convenience. 相似文献
60.