Nonlinear modes in rotating double well potential with parity–time symmetry

We investigate the nonlinear modes in a rotating double well potential with 79T symmetry. Focus on the existence and stability of the nonlinear PT modes in this system, we found that five types of PT modes can stably exist by given certain parameter settings. The multistable area between these modes are studied numerically and the bistable and tristable areas are delimited. With different input trial wavefunctions, five types of solitary wave modes are identified. We found that the rotating of the potential can significantly affect the power flow of the fundamental harmonic mode, whose effect is absent for the other modes.

Analytical Solutions of a Model for Brownian Motion in the Double Well Potential

In this paper, the analytical solutions of Schrodinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker-P1anck equation known as the Klein-Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schr6dinger equation. The anaiytical results obtained from the two different methods agree with each other well The double well potentiai is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function.

An analysis of the rate of isomerization in molecules with an asymmetric double well potential

The classical theory of the rate of unimolecular isomerization developed by Gray and Rice as extended by Zhao and Rice is applied to the calculation of the rate of isomerization in model systems which have linear asymmetric double well potentials. We are interested in this system for two reasons. First, we are interested in the detailed dynamical processes for the mentioned system because it is widely related to practical chemical reactions. Second, the present model system has an asymmetric double well potential, which provides a different test of the accuracy of the approximations used in the Gray-Zhao-Rice theory than posed by previous applications. We have calculated relaxation rates and relaxation times for the model systems on different time scales. We find that for the systems under studies the Gray-Zhao-Rice version of the classical theory of isomerization rate yields values in good agreement with those generated from trajectory calculations and from the Reactive Island theory of De Leon et al.

Soliton dynamical properties of Bose Einstein condensates trapped in a double square well potential

We first present an analytical solution of the single and double solitions of Bose-Einstein condensates trapped in a double square well potential using the multiple-scale method. Then, we show by numerical calculation that a dark soliton can be transmitted through the square well potential. With increasing depth of the square well potential, the amplitude of the dark soliton becomes larger, and the soliton propagates faster. In particular, we treat the collision behaviour of the condensates trapped in either equal or different depths of the double square well potential. If we regard the double square well potential as the output source of the solitons, the collision locations （position and time） between two dark solitons can be controlled by its depth.