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Quantum correlations play a fundamental role in quantum information science. Within bipartite mixed states, they can arise in different incarnations, i.e. Bell nonlocality, steering, and entanglement. Besides being of fundamental interest, they can all be exploited to attain enhancements in quantum information processing tasks over classical methods. Here, in a two-mode Gaussian state ${\varrho }_{m_1{m}_2}$, where the mode $m_1$($m_2$) is generated during the first(second) transition of a correlated-emission laser, we perform a comparative study between the three forms of quantum correlations in the presence of dissipation and thermal noise. We use the master equation of the state ${\varrho }_{m_1{m}_2}$ to obtain the first and second moments of the laser modes variables in the steady state regime. Under realistic experimental conditions, we show that Bell nonlocality could be exhibited by the state ${\varrho }_{m_1{m}_2}$ only when the two laser modes $m_1$ and $m_2$ are weakly entangled, in contrast, it disappears when they are strongly entangled. Especially, we find that Bell nonlocality is strongly sensitive to thermal noise. Also, we show that the state ${\varrho }_{m_1{m}_2}$ can display one-way and two-way steering in a wide range of operating parameters. In particular, we demonstrate that one-way steering can be detected solely in the direction $m_1\to m_2$. Against thermal noise, entanglement is found to be more robust than steering, which is in turn found to be more robust than Bell nonlocality. The obtained results are helpful in understanding the behavior of quantum nonlocality in dissipative-noisy environments, and may find potential applications for quantum information tasks.

In this paper, we establish a generalized version of Gibbons’ conjecture in the context of the master equation

We study the train aggregation behavior in a railway subsystem using the Markov approach. This approach is different from the queue theory, which is a main method to design some railway subsystems in the literature. With some simple assumptions, we solve the corresponding master equation describing the train aggregation behavior. Using the least square trigonometric approximation, we construct a continuous rate function for a real example, and show the evolution of the size of train cluster with time. Also the variance and relative error of the train aggregation are calculated.

We study the temporal evolution of quantum coherence and parameter estimation for two-mode coherent-state superposition by using the master equation. Analytic expressions are provided and numerically displayed, which can illustrate the reliance of the coherence and Fisher information during the dynamics. Generally, we find that the amount of the quantum measures has the same behavior during the time variation, and displays a different order that depends on the different strength regimes of the input radiation fields and then disappears at infinite times. We show that these measures start from maximal value at the initial instant and decrease the time goes on. Moreover, we can observe that these measures can be protected resisted from the environment effect during the dynamics, showing an important feature of coherence and Fisher information. The obtained results can be assumed more practical in the characterization of the behavior of the coherence and Fisher information under the effect of the environment. Our observations can provide significant implications in harnessing these phenomena in quantum optics and information.

In this paper, we introduce a quantum decomposition algorithm (QDA) that decomposes the problem $\frac{\partial \rho }{\partial t}={ℒ}\rho =\lambda \rho$ into a summation of eigenvalues times phase–space variables. One interesting feature of QDA stems from its ability to simulate damped spin systems by means of pure quantum harmonic oscillators adjusted with the eigenvalues of the original eigenvalue problem. We test the proposed algorithm in the case of undriven qubit with spontaneous emission and dephasing.

By explicit calculation of the effect of a ghost-dependent canonical transformation of BRST-charge, we derive the corresponding transformation law for structure coefficients of Hamiltonian gauge algebra under rotation of constraints. We show the transformation law to deviate from the behavior (expected naively) characteristic to a genuine connection.

The master equations in the Euclidean Schwarzschild–Tangherlini space–time of a small static perturbation are studied. For each harmonic mode on the sphere there are two solutions that behave differently at infinity. One solution goes like the power 2-l-n of the radial variable, the other solution goes like the power l. These solutions occur in power series.

The second main statement of the paper is that any eigentensor of the Lichnerowicz operator in a Euclidean Schwarzschild space–time with an eigenvalue different from zero is essentially singular at infinity. Possible applications of the stability of instantons are discussed.

We present the analysis of a small static perturbation of the Euclidean Schwarzschild–Tangherlini metric tensor. The higher order perturbations will appear later. We determine independently the static perturbations of the Schwarzschild quantum black hole in dimension 1+n≥4, where the system of equations is reduced to master equations — ordinary differential equations. The solutions are hypergeometric functions which in some cases can be reduced to polynomials.

In the same Schwarzschild background, we analyze static perturbations of the scalar mode and show that there does not exist any static perturbation that is regular everywhere outside the event horizon and is well-behaved at the spatial infinity. This confirms the uniqueness of the spherically symmetric static empty quantum black hole, within the perturbation framework.

Our strategy for treating the stability problem is also applicable to other symmetric quantum black holes with a nonzero cosmological constant.

Time evolution of quantum fluctuations is investigated for an over-damped mesoscopic circuit with the help of the quantum characteristic function. It is found that, for an initial squeezed state, the quantum fluctuations of charge and current evolve with time by hyperbolic functions, and relate not only with the circuit parameters, but also the squeezing parameter. It is also found that with other conditions invariant to reducing the quantum fluctuations of charge and current, we should reduce the squeezing amplitude parameter. The research will be helpful in miniaturizing integrated circuits and electric components. It will also be significant for the further study of quantum information.

In this presentation, we considered the atomic decay (but not for the cavity) for a two-level atom interacting with a single mode of electromagnetic field. The exact solution of the master equation in the case of a high-Q cavity with atomic decay is found. The effects of the atomic damping for a thermal reservoir on the temporal evolution of partial entropies of the atom or the field, and the total entropy as a quantitative entanglement, was measured. The degree of entanglement, through the sum of the negative eigenvalues of the partially transposed density matrix and the negative mutual information, has been studied and compared with other measures.

We approach the case of two coupled oscillators where the first one may correspond to a photonic field, while the second one is damped and driven. We model the oscillator's damping via a bath and consider the relevant master equation. We use perturbation theory to handle it. We then path integrate over the effective Hamiltonian of the two oscillators and derive the path integrated density matrix. We suppose that initially both of the oscillators are in coherent states and study the quadrature squeezing effect of the second oscillator.

A system of a two level atom interacting with a multi-photon single mode of electromagnetic field and damped with a phase reservoir is considered. The squeezed coherent state is taken as initial field state. The exact solution of the master equation in the case of a high-Q cavity is found. The effects of phase damping on the temporal evolution of some quantitative entanglement measures between the states of the system are investigated.

In this paper, we consider a particle (carrier) which is stochastically reset to its initial position at a constant rate r. It leads toward a non-equilibrium stationary state with non-Gaussian fluctuations for the particle position and enhance escape rate of particles through the ultrathin film.

Here we explore strongly-correlated random sequences. It is based on Master — nonlinear Fokker–Planck and chemical reaction equations. In that case compounding moments can set useful constraints to synchrotron radiation spectra of ultrathin film (SRSUTF). This mechanism is explained within a fitting process where both diffusion and reaction occur in discrete cells, and with both Si and O₂ treated as moving and reacting species for the very thin oxides.

Filamentous protein structures are of high relevance for the normal functioning of the cell, where they provide the structural component for the cytoskeleton, but are also implicated in the pathogenesis of many disease states. The self-assembly of these supra-molecular structures from monomeric proteins has been studied extensively in the past 50 years and much interest has focused on elucidating the microscopic events that drive linear growth phenomena in a biological setting. Master equations have proven to be particularly fruitful in this context, allowing specific assembly mechanisms to be linked directly to experimental observations of filamentous growth. Recently, these approaches have increasingly been applied to aberrant protein polymerization, elucidating potential implications for controlling or combating the formation of pathological filamentous structures. This article reviews recent theoretical advances in the field of filamentous growth phenomena through the use of the master-equation formalism. We use perturbation and self-consistent methods for obtaining analytical solutions to the rate equations describing fibrillar growth and show how the resulting closed-form expressions can be used to shed light on the general physical laws underlying this complex phenomenon. We also present a connection between the underlying ideas of the self-consistent analysis of filamentous growth and the perturbative renormalization group.

Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level quantum system with finite number N of quantum eigenstates interacting with arbitrary external classical fields and dissipative environment simultaneously. It was shown that the structure of these equations can be simplified significantly if the free Hamiltonian driven dynamics of an arbitrary quantum multi-level system under the influence of the external driving fields as well as its Markovian and non-Markovian evolution, stipulated by the interaction with the environment, are described in terms of the SU(N) algebra representation. As a consequence, efficient numerical methods can be developed and employed to analyze these master equations for real problems in various fields of theoretical and applied physics. It was also shown that literally the same master equations hold not only for the reduced density operator but also for arbitrary nonequilibrium multi-time correlation functions as well under the only assumption that the system and the environment are uncorrelated at some initial moment of time. A calculational scheme was proposed to account for these lost correlations in a regular perturbative way, thus providing additional computable terms to the correspondent master equations for the correlation functions.

Based on the theory of non-equilibrium statistics and density operator equation, the generalized master equation satisfied by characteristic function for the non-extensive reaction-diffusion systems affected by pressure is derived by calculating the time variation of probability distribution function, where the pressure of the non-extensive systems is given in the framework of Tsallis statistics. This new equation not only depends on the non-extensive parameter but also has more nonlinear terms as compared with the master equation in the phenomenological theory and thus has more generality.

In the framework of thermo-field dynamics, invented by Umezawa et al., we construct a mixed coherent state representation of density operator ρ. This new representation is useful because it provides an approach to retrieve ρ from its c-number solution of master equations in the entangled state representation.

We solve various master equations to obtain density operators' infinite operator-sum representation via a new approach, i.e., by virtue of the thermo-entangled state representation that has a fictitious mode as a counterpart mode of the system mode. The corresponding Kraus operators from the point of view of quantum channel are derived, whose normalization conditions are proved. Miscellaneous characters possessed by different quantum channels, such as decoherence, phase diffusion, damping, and amplification, can be shown explicitly in the entangled state representation of the density operators. Squeezing transformation is applied to the density operator for decoherence to generate a master equation for describing the phase sensitive process. Partial trace method for deriving new density operators is also introduced. Throughout our discussion, the technique of integration within an ordered product (IWOP) of operators is fully used.

In this paper, we establish a nanothermoelectric engine consisting of two discrete energy levels embedded between two reservoirs at different temperatures and chemical potentials. Based on master equation, the expressions for the power output and efficiency of the nanothermoelectric engine are derived. The characteristic curves between the power output and the efficiency are plotted. Moreover, the optimal performance parameters are obtained by the numerical calculation. The influence of the strength of variations in electron–electron interactions on the optimal performance parameters is analyzed in detail.

Bacterial flagellar motor (BFM) is one of the ion-driven molecular machines, which drives the rotation of flagellar filaments and enable bacteria to swim in viscous solutions. Understanding its mechanism is one challenge in biophysics. Based on previous models and inspired by the idea used in description of motor proteins, in this study one two-state model is provided. Meanwhile, according to corresponding experimental data, mathematical relationship between BFM membrane voltage and pH value of the environment, and relationship between internal and external sodium concentrations are given. Therefore, with model parameter values obtained by fitting theoretical results of torque-speed relation to recent experimental data, many biophysical properties of bacterial flagellar motor can be obtained for any pH values and any external sodium concentrations, including the rotation speed, stall torque (i.e. the torque generated by BFM), rotation dispersion, and rotation randomness. In this study, the single-stator BFM will be firstly analyzed, and then properties of multiple-stator BFM are addressed briefly.

Thermoelectric properties of organic materials have attracted much attention for the potential application in clean energy sources. In this work, we use the master equation method to calculate transport properties of the organic material when there is a temperature gradient in the material. The themoelectric property is analyzed with our model under different temperatures and different disorder strengths. It will be helpful to understand the thermoelectric property of organic materials and make good use of the heat energy.