arXiv subjects

Chengshi Liu

Publications and source records attributed to Chengshi Liu.

8 recordsLinked to original sources

arXiv2015

Stationary states and quantum quench dynamics of Bose-Einstein condensates in a double-well potential

We consider the properties of stationary states and the dynamics of Bose-Einstein condensates (BECs) in a double-well (DW) potential with pair tunneling by using a full quantum-mechanical treatment. Furthermore, we study the quantum quench dynamics of the DW system subjected to a sudden change of the Peierls phase. It is shown that strong pair tunneling evidently influences the energy spectrum structure of the stationary states. For relatively weak repulsive interatomic interactions, the dynamics of the DW system with a maximal initial population difference evolves from Josephson oscillations to quantum self-trapping as one increases the pair tunneling strength, while for large repulsion the strong pair tunneling inhibits the quantum self-trapping. In the case of attractive interatomic interactions, strong pair tunneling tends to destroy the Josephson oscillations and quantum self-trapping, and the system eventually enters a symmetric regime of zero population difference. Finally, the effect of the Peierls phase on the quantum quench dynamics of the system is analyzed and discussed. These new features are remarkably different from the usual dynamical behaviors of a BEC in a DW potential.

cond-mat.quant-gas↗

arXiv2007

Description of spin transport and precession in spin-orbit coupling systems and a general equation of continuity

By generalizing the usual current density to a matrix with respect to spin variables, a general equation of continuity satisfied by the density matrix and current density matrix has been derived. This equation holds in arbitrary spin-orbit coupling systems as long as its Hamiltonian can be expressed in terms of a power series in momentum. Thereby, the expressions of the current density matrix and a torque density matrix are obtained. The current density matrix completely describes both the usual current and spin current as well; while the torque density matrix describes the spin precession caused by a total effective magnetic field, which may include a realistic and an effective one due to the spin-orbit coupling. In contrast to the conventional definition of spin current, this expression contains an additional term if the Hamiltonian includes nonlinear spin-orbit couplings. Moreover, if the degree of the full Hamiltonian $\geq3$, then the particle current must also be modified in order to satisfy the local conservation law of number.

cond-mat.mes-hall↗

arXiv2006

Nonsymmetric entropy I: basic concepts and results

A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally from maximal nonsymmetric entropy principle.

cs.IT↗

arXiv2006

Rational expansion method of exponent function for solving exact solutions to nonlinear differential-difference equations

A new method named rational expansion method of exponent function is presented to find exact traveling wave solutions of differential-difference equations. This method generalizes the so-called tanh-method and other similar methods. Some examples are dealt with and their abundant exact solutions which include solitary solutions and periodic solutions are obtained. Among them, many solutions are new.

nlin.SI↗

arXiv2006

The classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation

Under the travelling wave transformation, Calogero-Degasperis-Focas equation was reduced to an ordinary differential equation. Using a symmetry group of one-parameter, this ODE was reduced to a second order linear inhomogeneous ODE. Furthermore, we applied the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation.

nlin.SI↗

arXiv2006

Direct integral method, complete discrimination system for polynomial and applications to classifications of all single traveling wave solutions to nonlinear differential equations:a survey

Complete discrimination system for polynomial and direct integral method were discussed systematically. In particularly, we pointed out some mistaken viewpoints. Combining with complete discrimination system for polynomial, direct integral method was developed to become a powerful method and was applied to a lot of nonlinear mathematical physics equations. All single traveling wave solutions to theses equations can be obtained. As examples, we gave all traveling wave solutions to some equations such as mKdV equation, Sine-Gordon equation, Double Sine-Gordon equation, triple Sine-Gordon equation, Fujimoto-Watanabe equation, coupled Harry-Dym equation and coupled KdV equation and so on. At the end, we give the partial answers to Fan's a problem.

nlin.SI↗

arXiv2006

Maximal nonsymmetric entropy leads naturally to Zipf's law

As the most fundamental empirical law, Zipf's law has been studied from many aspects. But its meaning is still an open problem. Some models have been constructed to explain Zipf's law. In the letter, a new concept named nonsymmetric entropy was introduced, maximizing nonsymmetric entropy leads naturally to Zipf's law.

cond-mat.dis-nn↗

arXiv2006

The classification of traveling wave solutions and superposition of multi-solutions to Camassa-Holm equation with dispersion

Under the traveling wave transformation, Camassa-Holm equation with dispersion is reduced to an integrable ODE whose general solution can be obtained using the trick of one-parameter group. Furthermore combining complete discrimination system for polynomial, the classifications of all single traveling wave solutions to the Camassa-Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More general, an implicit linear structure in Camassa-Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa-Holm equation with dispersion.

nlin.SI↗