We study the non-resonant interaction of a moving four-level N-type atom with cavity fields in the presence of a nonlinear Kerr-like medium. The exact solutions of the considered models are obtained when the atom is initially in an upper state, while the field is in a coherent state. We derive an expression for the occupation numbers of the photon state. Also, the momentum increment of the atomic system is obtained. The influence of the detuning parameters or the Kerr medium on the evolution time of the momentum increment is examined numerically. The existence of the detuning parameters leads to the retraction of the revivals for the three atomic systems. On the other hand, the presence of the Kerr medium is conducive to increasing the regularity and periodicity of the collapse–revival phenomenon for the one- and two-mode systems, while chaotic behaviour occurs for the three-mode system.

https://iopscience.iop.org/article/10.1088/0953-4075/41/10/105502/pdf

A moving four-level N-type atom interacting with cavity fields

Critical Casimir effect: Exact results

کلون بیان پروتئین سطحی 31 کیلودالتونی بروسلا ملی تنسیس در اشریشیاکلی

We study the ageing properties of the semi-infinite kinetic spherical model at the critical point and in the ordered low-temperature phase for both Dirichlet and Neumann boundary conditions. The surface fluctuation–dissipation ratio and the scaling functions of two-time surface correlation and response functions are determined explicitly in the dynamical scaling regime. In the low-temperature phase, our results show that for the case of Dirichlet boundary conditions the value of the non-equilibrium surface exponent b1 differs from the usual bulk value of systems undergoing phase ordering.

Out-of-equilibrium properties of the semi-infinite kinetic spherical model

A detailed analysis of the finite-size effects on the bulk critical behaviour of the d-dimensional mean spherical model confined to a film geometry with finite thickness L is reported. Along the finite direction different kinds of boundary conditions are applied: periodic (p), antiperiodic (a) and free surfaces with Dirichlet (D), Neumann (N) and a combination of Neumann and Dirichlet (ND) on both surfaces. A systematic method for the evaluation of the finite-size corrections to the free energy for the different types of boundary conditions is proposed. The free energy density and the equation for the spherical field are computed for arbitrary d. It is found, for 2 < d < 4, that the singular part of the free energy has the required finite-size scaling form at the bulk critical temperature only for (p) and (a). For the remaining boundary conditions the standard finite-size scaling hypothesis is not valid. At d = 3, the critical amplitude of the singular part of the free energy (related to the so-called Casimir amplitude) is estimated. We obtain Δ(p) = −2ζ(3)/(5π) = −0.153 051..., Δ(a) = 0.274 543... and Δ(ND) = 0.019 22..., implying a fluctuation-induced attraction between the surfaces for (p) and repulsion in the other two cases. For (D) and (N) we find a logarithmic dependence on L.

Finite-size effects in the spherical model of finite thickness

In this paper, we investigate the entanglement degree in the interaction of a two-level atom prepared in a momentum eigenstate with an additional Stark-shift. We use the quantum entropy as a measure of the entanglement degree. The constants of motion and the density matrix of the system are obtained. The effect of the detuning and the Stark-shift parameters when the atom is prepared initially in the upper state are investigated. It is found that the detuning and the Stark shift affected on the entanglement of the atomic system, and the influence of the center-of-mass motion play an important role in the entanglement degree.

Influence of the Stark Shift and the Detuning Parameters on the Entanglement Degree in a Two-Mode Coupling System

A modified three-dimensional mean spherical model with a L-layer film geometry under Neumann-Neumann boundary conditions is considered. Two spherical fields are present in the model: a surface one fixes the mean square value of the spins at the boundaries at some $\rho > 0$, and a bulk one imposes the standard spherical constraint (the mean square value of the spins in the bulk equals one). The surface susceptibility $\chi_{1,1}$ has been evaluated exactly. For $\rho =1$ we find that $\chi_{1,1}$ is finite at the bulk critical temperature $T_c$, in contrast with the recently derived value $\gamma_{1,1}=1$ in the case of just one global spherical constraint. The result $\gamma_{1,1}=1$ is recovered only if $\rho =\rho_c= 2-(12 K_c)^{-1}$, where $K_c$ is the dimensionless critical coupling. When $\rho > \rho_c$, $\chi_{1,1}$ diverges exponentially as $T\to T_c^{+}$. An effective hamiltonian which leads to an exactly solvable model with $\gamma_{1,1}=2$, the value for the $n\to \infty $ limit of the corresponding O(n) model, is proposed too.

Surface critical exponents for a three-dimensional modified spherical model

On the Dynamics of Correlations in 2 ⊗ 3 Heisenberg Chains with Inhomogeneous Magnetic Field

We study the interaction between a four-level atom (ladder type) in a momentum eigenstate with a single mode cavity field in the presence of non-linearities of both the field and the intensity-dependent coupling. The constants of motion and the wave function for the atomic system have been obtained. Special attention is given to discuss some statistical aspects of the considered atomic system such as momentum increment, momentum diffusion and high-order squeezing. The influence of the Kerr-like medium and the intensity dependent coupling on the momentum increment and the high-order squeezing are investigated numerically. It is found that addition of these parameters has an important effect on both the momentum increment and the squeezing phenomenon.

One-mode interaction with a four-level atom in a momentum eigenstate

Abstract The one-dimensional Ising model with various boundary conditions is considered. Exact expressions for the thermodynamic and magnetic properties of the model using different kinds of boundary conditions [Dirichlet (D), Neumann (N), and a combination of Neumann–Dirichlet (ND)] are presented in the absence (presence) of a magnetic field. The finite-size scaling functions for internal energy, heat capacity, entropy, magnetisation, and magnetic susceptibility are derived and analysed as function of the temperature and the field. We show that the properties of the one-dimensional Ising model is affected by the finite size of the system and the imposed boundary conditions. The thermodynamic limit in which the finite-size functions approach the bulk case is also discussed.

Investigation of the Finite Size Properties of the Ising Model Under Various Boundary Conditions

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