The Quantum Correlation Function as the ז Function of Classical Differential Equations

1993 ◽  
pp. 407-417 ◽  
Author(s):  
A. R. Its ◽  
A. G. Izergin ◽  
V. E. Korepin ◽  
N. A. Slavnov
Keyword(s):  
Correlation Function ◽  
Differential Equations ◽  
Quantum Correlation ◽  
Quantum Correlation Function

DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS

1990 ◽  
Vol 04 (05) ◽  
pp. 1003-1037 ◽  
Author(s):  
A.R. Its ◽  
A.G. Izergin ◽  
V.E. Korepin ◽  
N.A. Slavnov
Keyword(s):  
Correlation Function ◽  
Integral Operator ◽  
Schrödinger Equation ◽  
Differential Equations ◽  
Nonlinear Schrödinger Equation ◽  
Correlation Functions ◽  
Quantum Correlation ◽  
Schrodinger Equation ◽  
Bose Gas ◽  
Nonlinear Schrodinger Equation

The quantum nonlinear Schrödinger equation (one dimensional Bose gas) is considered. Classification of representations of Yangians with highest weight vector permits us to represent correlation function as a determinant of a Fredholm integral operator. This integral operator can be treated as the Gelfand-Levitan operator for some new differential equation. These differential equations are written down in the paper. They generalize the fifth Painlève transcendent, which describe equal time, zero temperature correlation function of an impenetrable Bose gas. These differential equations drive the quantum correlation functions of the Bose gas. The Riemann problem, associated with these differential equations permits us to calculate asymp-totics of quantum correlation functions. Quantum correlation function (Fredholm determinant) plays the role of τ functions of these new differential equations. For the impenetrable Bose gas space and time dependent correlation function is equal to τ function of the nonlinear Schrödinger equation itself, For a penetrable Bose gas (finite coupling constant c) the correlator is τ-function of an integro-differentiation equation.

scholarly journals Determinant representation for a quantum correlation function of the lattice sine - Gordon model

1997 ◽  
Vol 30 (1) ◽  
pp. 219-244 ◽  
Author(s):  
Fabian H L Eßler ◽  
Holger Frahm ◽  
Alexander R Its ◽  
Vladimir E Korepin
Keyword(s):  
Correlation Function ◽  
Quantum Correlation ◽  
Determinant Representation ◽  
Quantum Correlation Function ◽  
Sine Gordon Model

Steady-state quantum correlation measurement in hybrid optomechanical systems

2020 ◽  
pp. 2050046
Author(s):  
Tesfay Gebremariam Tesfahannes ◽  
Merkebu Dereje Getahune
Keyword(s):  
Correlation Function ◽  
Steady State ◽  
Quantum Entanglement ◽  
Quantum Correlation ◽  
Optical Cavity ◽  
Quantum Correlations ◽  
Correlation Measurement ◽  
Atomic Ensemble ◽  
Optomechanical System ◽  
Optomechanical Systems

In this paper, we investigate the steady-state of quantum correlation measurement of hybrid optomechanical systems. The first system consists of a single optomechanical system simultaneously coupled to a mechanical oscillator. While the second system is a hybrid optomechanical system consisting of an atomic ensemble placed in between the optical cavity and mirror. For both optomechanical systems, we formulate the Hamiltonian and the explicit expression of the covariance matrix leading to the dynamic of the system. Under the linearization approximation, we investigate the steady-state quantum correlations which are quantified through the correlation function of non-Hermitian operators, while the logarithmic negativity is used to quantify the amount of quantum entanglement between the subsystems. Furthermore, our proposed quantum correlation function can be used to quantify the entangled bipartite states that are correlative and transfer information. It is found that the transfer of quantum correlations between the subsystem is related to the detuning and coupling strength. Our results provide a realistic route toward remote quantum entanglement detection and a framework of future realistic fiber-optic quantum network operating applications.

scholarly journals High-Visibility Pseudothermal Light Source Based on a Cr4+ : YAG Passively Q-Switched Single-Longitudinal-Mode Laser

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Can Cui ◽  
Yulei Wang ◽  
Zhiwei Lu ◽  
Zhenxu Bai ◽  
Hang Yuan ◽  
...  
Keyword(s):  
Light Source ◽  
Quantum Correlation ◽  
Peak Power ◽  
Laser System ◽  
Longitudinal Mode ◽  
High Peak Power ◽  
Ghost Imaging ◽  
Long Distance ◽  
Mode Laser ◽  
Quantum Correlation Function

High-visibility pseudothermal light source is required by the long-distance ghost imaging technology. In this article, the pulsed pseudothermal light based on a compact and Q-switched laser system with high peak power and intensity is reported. The passively Q-switched technique advances the performance of the pseudothermal light, where the second-order quantum correlation function g 2 value increased from 1.452 to 1.963.

On the Origin of the Electric Field of Polarization in a Gravitational Plasma

1973 ◽  
Vol 51 (5) ◽  
pp. 587-591
Author(s):  
M. Fridman
Keyword(s):  
Correlation Function ◽  
External Field ◽  
Differential Equations ◽  
Electric Field ◽  
Charge Separation ◽  
Charged Particles ◽  
Ion Plasma ◽  
Polarization Electric Field ◽  
Induced Changes

The theories developed to explain the expansion of charged particles from the atmosphere always involve an electric field of charge separation of gravitational origin. A theory is proposed replacing the quasi-neutral sources by a plasma polarization due to the external field of gravity.Assuming that the penetrated Debye clouds are distorted by gravity and hence provide the sources, the induced changes in the correlation function are evaluated. The formalism giving the polarization electric field is verified by using the solution of the differential equations for gravitation correlation in the simplest case of an electron and single ion plasma.

scholarly journals Conservation Laws in Quantum-Correlation-Function Dynamics

2010 ◽  
Vol 2010 ◽  
pp. 1-8
Author(s):  
Wei Wang ◽  
Mitsuo Takeda
Keyword(s):  
Conservation Laws ◽  
Quantum Correlation ◽  
Linear Combinations ◽  
First Order ◽  
New Concepts ◽  
Quantized Fields ◽  
Wave Particle Duality ◽  
Quantum Correlation Function ◽  
Quantum Optical ◽  
Tensor Densities

For a complete and lucid discussion of quantum correlation, we introduced two new first-order correlation tensors defined as linear combinations of the general coherence tensors of the quantized fields and derived the associated coherence potentials governing the propagation of quantum correlation. On the basis of these quantum optical coherence tensors, we further introduced new concepts of scalar, vector and tensor densities and presented some related properties, such as conservation laws and the wave-particle duality for quantum correlation, which provide new insights into photon statistics and quantum correlation.

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