Kraus-Form Operator Solution to Nonlinear Master Equation by Virtue of the Nonlinear Thermo-Entangled State Representation* *The work is supported by the National Natural Science Foundation of China under grant 11175113 and Key Project of Natural Science Fund in Anhui Province KJ2013A261.

2014 ◽  
Vol 74 (2) ◽  
pp. 221-234
Author(s):  
Cheng Da ◽  
Qian-fan Chen
Keyword(s):  
Master Equation ◽  
Natural Science ◽  
Anhui Province ◽  
Entangled State ◽  
Entangled State Representation ◽  
State Representation ◽  
Operator Solution ◽  
Nonlinear Master Equation ◽  
Thermo Entangled State Representation ◽  
Thermo Entangled State

SOLVING MASTER EQUATION FOR CALDEIRA–LEGGETT MODEL BY VIRTUE OF THE THERMO ENTANGLED STATE REPRESENTATION AND THE IWOP TECHNIQUE

2012 ◽  
Vol 26 (14) ◽  
pp. 1250085 ◽  
Author(s):  
QIAN-FAN CHEN ◽  
QIAN YE ◽  
ZHI-HUA LI ◽  
HONG-YI FAN
Keyword(s):  
Master Equation ◽  
Formal Solution ◽  
Quantum Master Equation ◽  
Entangled State ◽  
Iwop Technique ◽  
Entangled State Representation ◽  
State Representation ◽  
Initial State ◽  
Thermo Entangled State Representation ◽  
Thermo Entangled State

In the present work, the exact formal solution of the Caldeira–Leggett quantum master equation for the reduced density matrix of an oscillator is obtained by virtue of the thermo entangled state representation and the technique of integration within an ordered product (IWOP) of operators. Also, the solution for high temperature approximation is derived. When the initial state is a coherent state, it will evolve into a displaced-squeezed chaotic state (a mixed state) which shows that decoherence is involved in the Caldeira–Leggett equation due to the interactions between the system and environment.

PHASE OPERATOR AND PHASE STATE IN THERMO FIELD DYNAMICS

2009 ◽  
Vol 24 (15) ◽  
pp. 1219-1226 ◽  
Author(s):  
HONG-YI FAN ◽  
NIAN-QUAN JIANG
Keyword(s):  
Coherent States ◽  
Phase State ◽  
Entangled State ◽  
Entangled State Representation ◽  
Phase Operator ◽  
State Representation ◽  
Thermo Field Dynamics ◽  
Limiting Case ◽  
Thermo Entangled State Representation ◽  
Thermo Entangled State

We extend the Susskind–Glogower phase operator and phase state in quantum optics to thermo field dynamics (TFD). Based on the thermo entangled state representation, we introduce thermo excitation and de-excitation operators with which the phase operator and phase state in TFD can be constructed. The phase state treated as a limiting case of a new SU(1, 1) coherent states is also exhibited.

Density operator for describing driven damped harmonic oscillator in the diffusion-limited channel

2014 ◽  
Vol 92 (10) ◽  
pp. 1069-1073 ◽  
Author(s):  
Hong-Yi Fan ◽  
Qian-Fan Chen
Keyword(s):  
Harmonic Oscillator ◽  
External Source ◽  
Quantum Decoherence ◽  
Entangled State ◽  
State Representation ◽  
Chaotic State ◽  
Kraus Operator ◽  
Diffusion Limited ◽  
Thermo Entangled State Representation ◽  
Thermo Entangled State

In the present work, the Kraus-operator sum representation of the exact solution to the master equation describing a harmonic oscillator (driven by an external source) damping in the diffusion-limited channel is obtained by virtue of the thermo-entangled state representation and the technique of integration within an ordered product of operators. According to this solution, the initial coherent state will evolve into a displaced chaotic state that manifestly exhibits quantum decoherence.

Evolution of the photon-added coherent state in a laser channel

2012 ◽  
Vol 90 (6) ◽  
pp. 593-598 ◽  
Author(s):  
Jun Zhou ◽  
Jun Song ◽  
Hao Yuan ◽  
Hong-Yi Fan
Keyword(s):  
Coherent State ◽  
Density Operator ◽  
Gain Coefficient ◽  
Entangled State ◽  
State Representation ◽  
New Approach ◽  
Laser Process ◽  
Laser Channel ◽  
Thermo Entangled State Representation ◽  
Thermo Entangled State

We investigate the time evolution of a quantum state in the laser channel with cavity gain coefficient g and loss coefficient κ by virtue of the thermo entangled state representation. This is a new approach for solving master equations. We exactly calculate the evolving result of the photon-added coherent state (PACS) governed by the master equation describing the laser process, and the normal ordered form of the density operator in the laser channel is derived, based on which we calculate the Wigner function analytically and graphically. The corresponding law of the PACS evolution in the laser channel is evaluated.

APPLICATION OF ENTANGLED STATE IN QUANTIZING SUPERCONDUCTING CAPACITOR MODEL IN THE PRESENCE OF A VOLTAGE BIAS AND A CURRENT BIAS

2004 ◽  
Vol 18 (02) ◽  
pp. 233-240 ◽  
Author(s):  
HONG-YI FAN
Keyword(s):  
Operator Theory ◽  
Hamiltonian Operator ◽  
Entangled State ◽  
Entangled State Representation ◽  
Phase Operator ◽  
State Representation ◽  
Voltage Bias ◽  
A Current

Based on the entangled state representation and the appropriate bosonic phase operator we develop the superconducting capacitor model in the presence of a voltage bias and a current bias. In so doing, the full Hamiltonian operator theory for a superconducting barrier is established.

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