Hong-Yi Fan

Infinite Operator-Sum Representation of Density Operator for a Dissipative Cavity with Kerr Medium Derived by Virtue of Entangled State Representation

By using the thermo entangled state representation we solve the master equation for a dissipative cavity with Kerr medium to obtain density operators’ infinite operator-sum representation ρ(t)=∑m,n,l=0∞Mm,n,lρ0ℳm,n,l†. It is noticeable that Mm,n,l is not Hermite conjugate to ℳm,n,l†, nevertheless the normalization ∑m,n,l=0∞ℳn,m,l†Mm,n,l=1 still holds, i.e., they are trace-preserving in a general sense. This example may stimulate further studying if general superoperator theory needs modification.

FLUCTUATIONS AT FINITE TEMPERATURE AND THERMODYNAMICS OF MESOSCOPIC RLC CIRCUIT CALCULATED BY USING GENERALIZED THERMAL VACUUM STATE

By using the partial trace method and the technique of integration within an ordered product of operators we obtain the explicit expression of the generalized thermal vacuum state (GTVS) for an RLC circuit instead of using the Takahashi–Umezawa approach. According to thermal field dynamics (TFD), namely, the expectation value of physical observables in this GTVS is equivalent to their ensemble average, based on GTVS we successfully derive the quantum fluctuations at nonzero temperature and the thermodynamical relations for the mesoscopic RLC circuit. Our results show that the higher the temperature is, the more quantum noise the RLC circuit exhibits.

New Parametrized Entangled State Representations and Their Applications

We construct two new kinds of parametrized entangled states in two-mode Fock space. Using the technique of integration within an ordered product of operators, we prove that they span the complete space. Their applications to solving dynamic problems and finding new generalized squeezing are addressed.

CALCULATION OF ENTROPY FOR SOME COUPLED OSCILLATORS BY USING THE GENERALIZED HELLMANN–FEYNMAN THEOREM

The entropies of several typical coupled bosonic oscillators are calculated by virtue of the generalized Hellmann–Feynman theorem (GHFT). The relation between GHFT and entropy-variation is construct by using von Neumann entropy, which provides us with a new approach for deriving entropy of some complicated systems.

NEW APPROACH TO DERIVING THE THERMO-MINIMUM UNCERTAINTY STATES AND ITS WIGNER FUNCTION

Based on our previous study [Mod. Phys. Lett. A18 (2003) 677] in which minimum uncertainty states for thermo-field dynamics were proposed, we use a new approach to derive the thermo-minimum uncertainty states via the relation of two-variable Hermite polynomial. In addition, the compact expression for its corresponding Wigner function is obtained analytically by using the Weyl-ordered invariance under the similar transformations, which seems a new result.

Solving Multiphoton Jaynes-Cummings Model with Field Nonlinearity by Supersymmetric Unitary Transformation

We introduce a supersymmetric unitary transformation, to diagonalize the multiphoton Jaynes–Cummings model Hamiltonian based on supersymmetric quantum mechanics theory, that includes any forms of intensity-dependent coupling and field nonlinearity. On doing so, we obtain its eigenvalue and eigenstates, and the time evolution of state vector.

Properties of the q-Analogue of a Squeezed Vacuum State

We constructed a normalizable q-analogue of squeezed vacuum state using the technique of integration within an ordered product (IWOP) of operators and the properties of the inverses of q-deformed creation and annihilation operatots. We also study its nonclassical properties and phase probability distribution.

FLUCTUATION OF MESOSCOPIC RLC CIRCUIT AT PHOTON-SUBTRACTED AND PHOTON-ADDED THERMO VACUUM STATES WITH FINITE TEMPERATURE

By using the Wigner function to evaluate expectation values of any symmetrically order of operator in a classical fashion, we study the quantum fluctuation and the uncertainty relation of mesoscopic RLC circuit at photon-subtracted and photon-added thermo vacuum states. It is found that the fluctuations and the uncertainty relation of both charge and current are linearly related to the photon-subtracted and photon-added number.

Time evolution of Wigner functions governed by bipartite Hamiltonian system with kinetic coupling

For the bipartite Hamiltonian system with kinetic coupling, we derive time evolution equation of Wigner functions by virtue of the bipartite entangled state representation and entangled Wigner operator, which just indicates that choosing a good representation indeed provides great convenience for us to deal with the dynamics problem.

OPERATOR JOSEPHSON EQUATION FOR A JOSEPHSON JUNCTION CONNECTED INTO A MESOSCOPIC LC CIRCUIT

We find that when a single Josephson junction is inserted into a mesoscopic LC circuit, the operator Josephson equation is modified accompanying with the modification of Farady equation describing the inductance. By virtue of the entangled state representation and using the appropriate phase operator in bosonic form we derive the modified equations.