Wigner function of optical cumulant operator and its dissipation in thermo-entangled state representation

To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.

New operator identities with regard to the two-variable Hermite polynomial by virtue of entangled state representation

By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial （TVHP）. By them and the technique of integration within an ordered product （IWOP） of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.

Dynamical nonlocality of the entangled coherent state in the phase damping model

This paper studies the dynamics of nonlocality for a bosonic entangled coherent state in a phase damping model. The density operator of the system is solved by using a superoperator method. The dynamics of nonlocality for the bosonic entangled coherent state is uncovered by the Bell operator based on the pseudospin operator of a light field. The dynamics of the nonlocality for this state has also been studied by other Bell operators. The result of the numerical calculations of the Bell function shows that the quantum nonlocality heavily depends on the chosen Bell operator.

Application of Functional Operators with Shift to the Study of Renewable Systems When the Reproductive Process Is Described by Integrals with Degenerate Kernels

We continue studying systems whose state depends on time and whose resources are renewably based on functional operators with shift. In previous articles, we considered the term which described results of reproductive processes as a linear expression or as a shift summand. In this work, the reproductive term is represented using an integral with a degenerate kernel. A cyclic model of evolution of the system with a renewable resource is developed. We propose a method for solving the balance equation and we determine an equilibrium state of the system. Having applied this model, we can investigate problems of natural systems and their resource production.

Preparation of optimal entropy squeezing state of atomic qubit inside the cavity via two-photon process and manipulation of atomic qubit outside the cavity

Considering two atomic qubits initially in Bell states, we send one qubit into a vacuum cavity with two-photon resonance and leave the other one outside. Using quantum information entropy squeezing theory, the time evolutions of the entropy squeezing factor of the atomic qubit inside the cavity are discussed for two cases, i.e., before and after rotation and measurement of the atomic qubit outside the cavity. It is shown that the atomic qubit inside the cavity has no entropy squeezing phenomenon and is always in a decoherent state before the operating atomic qubit outside the cavity. However,the periodical entropy squeezing phenomenon emerges and the optimal entropy squeezing state can be prepared for the atomic qubit inside the cavity by adjusting the rotation angle, choosing the interaction time between the atomic qubit and the cavity, controlling the probability amplitudes of subsystem states. Its physical essence is cutting the entanglement between the atomic qubit and its environment, causing the atomic qubit inside the cavity to change from the initial decoherent state into maximum coherent superposition state, which is a possible way of recovering the coherence of a single atomic qubit in the noise environment.

The squeezing entangled state of two particles with unequal mass

For two unequal-mass particles,we construct the entangled state representation and then derive the corresponding squeezing operator.This squeezing operator has a natural realization in the entangled state representation,which exhibits the intrinsic relation between squeezing and quantum entanglement.This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings.The maximum squeezing occurs when the two particles possess equal mass.When the two particles＇ mass difference becomes large,the component of the two single-mode squeezings becomes dominant.

Solving nonlinear master equation describing quantum damping by virtue of the entangled state representation

This paper solves the newly constructed nonlinear master equation dρ/dt = κ[2f （N） aρ （1/f （N - 1））a^＋ -a^＋aρ- ρa^＋a], where f（N） is an operator-valued function of N = a^＋a, for describing amplitude damping channel, and derives the infinite operator sum representation of quasi-Kraus operators for the density operator. It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field （a mixed state） when f （N） = 1√N ＋ 1.

Wigner function of the thermo number states

Based on thermo field dynamics （TFD） and using the thermo Wigner operator in the thermo entangled state representation we derive the Wigner function of number states at finite temperature （named thermo number states）. The figure of Wigner function shows that its shape gets smoothed as the temperature rises, implying that the quantum noise becomes larger.

Explicit solution of diffusion master equation under the action of linear resonance force via the thermal entangled state representation

Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.

A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation

Based on the displacement-squeezing related squeezed coherent state representation ｜z〉g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula （Huygens-Fresnel integration transformation describing optical diffraction）. The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz -- rz^＊ in the ｜Z〉g representation, while ｜z〉g in phase space is graphically denoted by an ellipse.

Properties of Phase and Their Evolutions in Damped Odd and Even Coherent States

The properties of measured phase operators in damped odd and even coherent states have been studied. The fluctuations associated with measured phase and their squeezing in these states are investigated. The phase properties in damped superposition coherent states are considered too with the help of measured phase operators. These fluctuations and their squeezing are affected by damping and evolve with time elapsing.

Gazeau–Klauder coherent states examined from the viewpoint of diagonal ordering operation technique

In this paper we investigate the Gazeau–Klauder coherent states using a newly introduced diagonal ordering operation technique, in order to examine some of the properties of these coherent states. The results coincide with those obtained from other purely algebraic methods, but the calculations are greatly simplified. We apply the general theory to two cases of Gazeau–Klauder coherent states： pseudoharmonic as well as the Morse oscillators.

Analytical and numerical investigations of displaced thermal state evolutions in a laser process

We investigate how displaced thermal states （DTSs） evolve in a laser channel. Remarkably, the initial DTS, an example of a mixed state, still remains mixed and thermal. At long times, they finally decay to a highly classical thermal field only related to the laser parameters κ and g. The normal ordering product of density operator of the DTS in the laser channel leads to obtaining the analytical time-evolution expressions of the photon number, Wigner function, and von Neumann entropy. Also, some interesting results are presented via numerically investigating these explicit time-dependent expressions.

Influence of the Electric Field on the Properties of the Bound Magnetopolaron in GaAs Semiconductor Quantum Wells

The influence of the electric field on the properties of the bound magnetopolaron in an infinite-depth GaAs semiconductor quantum well is investigated using the linear-combination operator and the unitary transformation method. The relationships between the polaron＇s ground state energy and the Coulomb bound potential, electric field, magnetic field, and well-width are derived and discussed. Our numerical results show that the absolute value of the polaron＇s ground state energy increases as the electric field and the Coulomb bound potential increase, and decreases as the well-width and the magnetic field strength increase. When the well-width is small,the quantum size effect is significant.

New approach for deriving the exact time evolution of the density operator for a diffusive anharmonic oscillator and its Wigner distribution function

Using thermal entangled state representation,we solve the master equation of a diffusive anharmonic oscillator（AHO） to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation.We present a new evolution formula of the Wigner function（WF） for any initial state of the diffusive AHO by converting the WF calculation into an overlap between two pure states in an enlarged Fock space.It is found that this formula is very convenient in investigating the WF＇s evolution of any known initial state.As applications,this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of diffusive AHOs.

Key Issues for Modelling, Operation, Management and Diagnosis of Lithium Batteries: Current States and Prospects

1 Introduction.With the continuous growth of the global population,the energy demand continues to increase.However,due to the dominance of fossil fuels in global energy and fossil fuels are non-renewable,it has led to the global energy crisis[1].Besides,the use of fossil fuels will generate a mass of air pollutants(e.g.,carbon dioxide,sulfur dioxide,etc.),which will cause serious environmental pollution,climate change[2],etc.To resolve the aforementioned issues,countries around the world have implemented a variety of measures hoping to fundamentally adjust the global energy structure and achieve sustainable development.Thereinto,“Paris Agreement”reached in 2015 under the framework of“United Nations Framework Convention on Climate Change”aims to control the increase in the average temperature of the globe to within 2°C below preindustrial levels,and thereafter to peak global greenhouse gas emissions as soon as possible,continuously decreasing thereafter[3].United Kingdom plans to reduce the average exhaust emissions of“new cars”to approximately 50–70 g/km by 20230,which is roughly half of what it is now[4].In addition,China proposed a plan at“United Nations General Assembly”in 2020 to peak carbon dioxide emissions by 2030 and strive to achieve carbon neutrality by 2060.It is a fact that the whole world is committed to changing the current energy structure,protecting the Earth’s ecology,and achieving global sustainable development[5].

Reducing eutrophication risk of a reservoir by water replacement： a case study of the Qingcaosha reservoir in the Changjiang Estuary

Eutrophication of freshwater systems in cities is a major concern worldwide. Physical, biological and chemical methods have been used in eutrophic lakes and reservoirs to reduce their eutrophic state and algal biomass, but these approaches are not effective without a substantial reduction in nutrients input, which could take decades to achieve in the developing countries. This study aims to assess the risk of eutrophication and algal bloom in a coastal reservoir with high nutrient inputs to confirm the feasibility of inhibiting the reservoir＇s eutrophic state by hydrodynamic operations. A variety of water quality indexes（e.g., water temperature, secchi depth, dissolved oxygen, total nitrogen, total phosphorus, phytoplankton chlorophyll a） at five observed sites were investigated in the Qingcaosha reservoir, which located in the Changjiang Estuary, during the construction, trial and normal operation periods from 2009 to 2012. No water exchange happened during the construction from April 2009 to October 2010, and the water exchange increased during the trial from October 2010 to January 2011, and during normal operation period from January 2011. The comprehensive nutrition state index（TLI） calculated by several representative water quality indexes was adopted to evaluate the variation of the trophic state in the reservoir. The peak values of TLI reached 51 in the summer of 2009, and 55 in the summer of 2011, higher than the eutrophication threshold value 50. The lowest TLI, about 32, appeared in the summer of 2010. The values of TLI in other observation periods could keep under 50. The results showed that the reservoir could easily deteriorate into the eutrophic state because of excess nutrients and algal blooms in the summer of 2009 and 2011, while the eutrophication and algal blooms could be reduced by the lack of nutrients in 2010 or adequate water replacement in 2012. The temporal and spatial variations of water quality indexes were presented based on observation data and analysis. The adequate water replacement in the reservoir driven by tides was tested to be an efficient and economical method for controlling eutrophication and algae blooms in the water environment with high nutrient inputs.

Reliability analysis of the gasification process of nuclear fuel manufacturing facilities based on the GO methodology

Uranium hexafluoride(UF6)leakage accidents represent one of the most serious classes of accidents in the gasification process in nuclear fuel manufacturing facilities.Common UF6 leakage accidents include various fault conditions,such as pipeline and valve breakages or ruptures and pipeline blockages.By establishing goal-oriented(GO)operators that can represent multi-fault states,this study estimates the probabilities of various fault states corresponding to UF6 leakage accidents in the gasification process using the GO methodology and analyzes the system reliability.This article expands the scope of the GO methodology and provides technical support for reliability analysis using the GO methodology in multi-fault systems.

New Bosonic Operator Ordering Identities Gained by the Entangled State Representation and Two－Variable Hermite Polynomials

Based on the technique of integration within an ordered product of operators, we derive new bosonic operators, ordering identities by using entangled state representation and the properties of two-variable Hermite polynomials , and vice versa. In doing so, some concise normally (antinormally) ordering operator identities, such as : are obtained.

Thermal Wigner Operator in Coherent Thermal State Representation and Its Application

In the coherent thermal state representation we introduce thermal Wigner operator and find that it is'squeezed' under the thermal transformation. The thermal Wigner operator provides us with a new direct and neatapproach for deriving Wigner functions of thermal states.