6,245 research outputs found

### Wigner operator's new transformation in phase space quantum mechanics and its applications

Using operators' Weyl ordering expansion formula (Hong-yi Fan,\emph{\}J.
Phys. A 25 (1992) 3443) we find new two-fold integration transformation about
the Wigner operator $\Delta(q',p')$ ($q$-number transform) in phase space
quantum mechanics, $\iint_{-\infty}^\infty dp' dq'/\pi \Delta (q',p')
e^{-2i(p-p') (q-q')} =\delta (p-P) \delta (q-Q),$ and its inverse
$\iint_{-\infty}^\infty dq dp \delta (p-P) \delta (q-Q) e^{2i(p-p')
(q-q')}=\Delta (q',p'),$ where $Q,$ $P$ are the coordinate and momentum
operators, respectively. We apply it to studying mutual converting formulas
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.Comment: 11 pages no figur

### New approach for solving master equation of open atomic system

We describe a new approach called Ket-Bra Entangled State (KBES) Method which
enables one convert master equations into Schr\"odinger-like equation. In
sharply contrast to the super-operator method, the KBES method is applicable
for any master equation of finite-level system in theory, and the calculation
can be completed by computer. With this method, we obtain the exact dynamic
evolution of a radioactivity damped 2-level atom in time-dependent external
field, and a 3-level atom coupled with bath; Moreover, the master equation of
N-qubits Heisenberg chain each qubit coupled with a reservoir is also resolved
in Sec.III; Besides, the paper briefly discuss the physical implications of the
solution.Comment: 7 pages, 5figure

### Dynamic Entanglement Evolution of Two-qubit XYZ Spin Chain in Markovian Environment

We propose a new approach called Ket-Bra Entangled State (KBES) Method for
converting master equation into Schr\"{o}dinger-like equation. With this
method, we investigate decoherence process and entanglement dynamics induced by
a $2$-qubit spin chain that each qubit coupled with reservoir. The spin chain
is an anisotropy $XYZ$ Heisenberg model in the external magnetic field $B$, the
corresponding master equation is solved concisely by KBES method; Furthermore,
the effects of anisotropy, temperature, external field and initial state on
concurrence dynamics is analyzed in detail for the case that initial state is
Extended Wenger-Like(EWL) state. Finally we research the coherence and
concurrence of the final state (namely the density operator for time tend to
infinite

### New approach for deriving operator identities by alternately using normally, antinormally, and Weyl ordered integration

Dirac's ket-bra formalism is the "language" of quantum mechanics and quantum
field theory. In Refs.(Fan et al, Ann. Phys. 321 (2006) 480; 323 (2008) 500) we
have reviewed how to apply Newton-Leibniz integration rules to Dirac's ket-bra
projectors. In this work by alternately using the technique of integration
within normal, antinormal, and Weyl ordering of operators we not only derive
some new operator ordering identities, but also deduce some useful integration
formulas regarding to Laguerre and Hermite polynomials. This opens a new route
of deriving mathematical integration formulas by virtue of the quantum
mechanical operator ordering technique.Comment: 6 figures, submitted to Am. J. Phy

### Husimi operator and Husimi function for describing electron's probability distribution in uniform magnetic field derived by virtue of the entangled state representation

For the first time we introduce the Husimi operator
Delta_h(gamma,varepsilon;kappa) for studying Husimi distribution in phase
space(gamma,varepsilon) for electron's states in uniform magnetic field, where
kappa is the Gaussian spatial width parameter. Using the Wigner operator in the
entangled state |lambda> representation [Hong-Yi Fan, Phys. Lett. A 301
(2002)153; A 126 (1987) 145) we find that Delta_h(gamma,varepsilon;kappa) is
just a pure squeezed coherent state density operator |gamma,varepsilon>_kappa
kappa<gamma,varepsilon|, which brings convenience for studying and calculating
the Husimi distribution. We in many ways demonstrate that the Husimi
distributions are Gaussian-broadened version of the Wigner distributions.
Throughout our calculation we have fully employed the technique of integration
within an ordered product of operators.Comment: 15page

### Eigenvectors of Z-tensors associated with least H-eigenvalue with application to hypergraphs

Unlike an irreducible $Z$-matrices, a weakly irreducible $Z$-tensor
$\mathcal{A}$ can have more than one eigenvector associated with the least
H-eigenvalue. We show that there are finitely many eigenvectors of
$\mathcal{A}$ associated with the least H-eigenvalue. If $\mathcal{A}$ is
further combinatorial symmetric, the number of such eigenvectors can be
obtained explicitly by the Smith normal form of the incidence matrix of
$\mathcal{A}$. When applying to a connected uniform hypergraph $G$, we prove
that the number of Laplacian eigenvectors of $G$ associated with the zero
eigenvalue is equal to the the number of adjacency eigenvectors of $G$
associated with the spectral radius, which is also equal to the number of
signless Laplacian eigenvectors of $G$ associated with the zero eigenvalue if
zero is an signless Laplacian eigenvalue

### Relation between Optical Fresnel transformation and quantum tomography in two-mode entangled case

Similar in spirit to the preceding work [Opt. Commun. 282 (2009) 3734] where
the relation between optical Fresnel transformation and quantum tomography is
revealed, we study this kind of relationship in the two-mode entangled case. We
show that under the two-mode Fresnel transformation the bipartite entangled
state density |eta><eta|F_2
^{dag}=|eta>_{r,s}<eta|, which is just the Radon transform of the two-mode
Wigner operator (sigma,gama) in entangled form, where F_2 is an two-mode
Fresnel operator in quantum optics, and s,r are the complex-value expression of
(A, B, C,D). So the probability distribution for the Fresnel quadrature phase
is the {tomography (Radon transform of the two-mode Wigner function),
correspondingly, {s,r}_=. Similarly, we find a
simial conclusion in the `frequency` domain.Comment: 10 page

### Remarks on the Bose description of the Pauli spin operators

Using both the fermionic-like and the bosonic-like properties of the Pauli
spin operators we discuss the Bose description of the Pauli spin operators
firstly proposed by Shigefumi Naka, and derive another new bosonic
representation of the Pauli spin operators. The eigenvector of $\sigma_{-}$ in
the bosonic representation is a nonlinear coherent state with the eigenvalues
being the Grassmann numbers.Comment: 6 page

### Collins diffraction formula and the Wigner function in entangled state representation

Based on the correspondence between Collins diffraction formula (optical
Fresnel transform) and the transformation matrix element of a three-parameters
two-mode squeezing operator in the entangled state representation (Opt. Lett.
31 (2006) 2622) we further explore the relationship between output field
intensity determined by the Collins formula and the input field's probability
distribution along an infinitely thin phase space strip both in spacial domain
and frequency domain. The entangled Wigner function is introduced for
recapitulating the result.Comment: 6 pages, no figur

### Density matrix of the superposition of excitation on coherent states with thermal light and its statistical properties

A beam's density matrix that is described by the superposition of excitation
on coherent states with thermal noise (SECST) is presented, and its matrix
elements in Fock space are calculated. The maximum information transmitted by
the SECST beam is derived. It is more than that by coherent light beam and
increases as the excitation photon number increases. In addition, the
nonclassicality of density matrix is demonstrated by calculating its Wigner
function.Comment: 7 pages, 9 figures, revtex

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