WEYL CORRESPONDENCE FORMALISM FOR DESCRIBING ELECTRON UNDER UNIFORM MAGNETIC FIELD STUDIED BY VIRTUE OF THE ENTANGLED STATE REPRESENTATION

2011 ◽  
Vol 25 (08) ◽  
pp. 1029-1036
Author(s):  
NAN-RUN ZHOU ◽  
LI-YUN HU ◽  
HONG-YI FAN
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Weyl Function ◽  
Quantum States ◽  
Entangled State ◽  
Entangled State Representation ◽  
State Representation ◽  
Wigner Operator ◽  
Weyl Correspondence ◽  
Quantum Hamiltonian

Based on the entangled state representation for describing electron's coordinates under uniform magnetic field, we establish a one-to-one correspondence between quantum Hamiltonian and its classical Weyl function through the introduction of Wigner operator. We also study some new important properties of Wigner function of electron's quantum states, such as its upper bound, and its relation with electron's wave function. These discussions demonstrate the beauty and elegance of the entangled state representation.

ATOMIC COHERENT STATES AS THE EIGENSTATES OF A TWO-DIMENSIONAL ANISOTROPIC HARMONIC OSCILLATOR IN A UNIFORM MAGNETIC FIELD

2009 ◽  
Vol 24 (38) ◽  
pp. 3129-3136 ◽  
Author(s):  
XIANG-GUO MENG ◽  
JI-SUO WANG ◽  
HONG-YI FAN
Keyword(s):  
Magnetic Field ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Uniform Magnetic Field ◽  
Hermite Polynomial ◽  
Entangled State ◽  
Two Dimensional ◽  
Entangled State Representation ◽  
Single Variable ◽  
State Representation

In the newly constructed entangled state representation embodying quantum entanglement of Einstein, Podolsky and Rosen, the usual wave function of atomic coherent state ∣τ〉 = exp (μJ+-μ*J-)∣j, -j〉 turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j, where j is the spin value. We then prove that a two-dimensional time-independent anisotropic harmonic oscillator in a uniform magnetic field possesses energy eigenstates which can be classified as the states ∣τ〉 in terms of the spin values j.

THEORY OF TOMOGRAPHY FOR THE WIGNER FUNCTION OF TRIPARTITE ENTANGLED SYSTEMS

2003 ◽  
Vol 17 (30) ◽  
pp. 5737-5747 ◽  
Author(s):  
HONG-YI FAN ◽  
NIAN-QUAN JIANG
Keyword(s):  
Distribution Function ◽  
Wigner Function ◽  
Physical Meaning ◽  
Wigner Distribution ◽  
Entangled State ◽  
Entangled State Representation ◽  
State Representation ◽  
Wigner Distribution Function ◽  
Wigner Operator ◽  
Tripartite Entangled State

Based on the observation that for an entangled-particles system, the physical meaning of the Wigner distribution function should lie in that its marginal distributions would give the probability of finding the particles in an entangled way, we establish a tomography theory for the Wigner function of tripartite entangled systems. The newly constructed tripartite entangled state representation of the three-mode Wigner operator plays a central role in realizing this goal.

RADON TRANSFORMATION OF THE WIGNER OPERATOR FOR TWO-MODE CORRELATED SYSTEM IN GENERALIZED ENTANGLED STATE REPRESENTATION

2000 ◽  
Vol 15 (07) ◽  
pp. 499-507 ◽  
Author(s):  
HONG-YI FAN ◽  
GUI-CHUAN YU
Keyword(s):  
Projection Operator ◽  
Entangled State ◽  
Entangled State Representation ◽  
State Representation ◽  
Wigner Operator ◽  
Radon Transformation ◽  
Inverse Radon

We introduce a generalized entangled state |η,λ1,λ2>, which spans a complete and orthonormal representation. Using the technique of integration within an ordered product of operators we prove that the projection operator |η,λ1,λ2><η,λ1,λ2| is just the Radon transformation of the entangled Wigner operator. The inverse Radon transformation is also derived and the tomography theory for two-mode correlated system is established.

scholarly journals Normal product form of two-mode Wigner operator

2022 ◽  
Author(s):  
Rui He ◽  
Xiangyuan Liu ◽  
Xiangfei Wei ◽  
Congbing Wu
Keyword(s):  
Degrees Of Freedom ◽  
Polar Coordinates ◽  
Entangled State ◽  
Entangled State Representation ◽  
State Representation ◽  
Wigner Operator ◽  
Normal Product ◽  
Coordinate Form ◽  
Natural Connection ◽  
Polar Coordinate

Abstract In the context of normal product, we use the method of the integration within an ordered product (IWOP) of operators to derive three representations of the two-mode Wigner operator: SU (2) symmetric description, SU (1, 1) symmetric description and polar coordinate form. We find that two-mode Wigner operator has multiple potential degrees of freedom. As the physical meaning of the selected integral variable changes, Wigner operator shows different symmetries. In particular, in the case of polar coordinates, we reveal the natural connection between the two-mode Wigner operator and the entangled state representation.

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