Landau damping and frequency-shift of a quadrupole mode in a disc-shaped rubidium Bose–Einstein condensate

The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose–Einstein condensate are investigated by using the Hartree–Fock–Bogoliubov approximation. The practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain advisable calculation formula for damping as well as frequency-shift. The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the analytic three-mode coupling matrix elements.According to these methods, both Landau damping rate and frequency-shift of the quadrupole mode are analytically calculated. In addition, all the theoretical results agree with the experimental ones.     

Discrete energy transport in collagen molecules

The modulational instability in the three coupled α-polypeptide chains of a collagen molecule is investigated. Choosing symmetric and asymmetric solutions, and applying the so-called rotating-wave approximation, we describe the dynamics of the system by the discrete nonlinear Schrdinger(DNLS) equation. The linear stability analysis of the continuous wave solution is performed. The numerical simulations show the generation of trains of solitonic structures in the lattice with increasing amplitude as time progresses. The effect of damping and noise forces of the physiological temperature(T = 300 K) introduces an erratic behavior to the formed patterns, reinforcing the idea that the energy used in metabolic processes is confined to specific regions for efficiency.     

Normally-Ordered Time Evolution Operator for Mass-Varying Harmonic Oscillator and Wigner Function of Squeezed Number State

For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integration operator in coherent state representation and then perform this integral by virtue of the technique of integration within an ordered product of operators. The normally ordered time evolution operator is thus obtained. We then derive the Wigner function of u（t）｜n,〉, where ｜n〉 is a Fock state, which exhibits a generalized squeezing, the squeezing effect is related to the varying mass with time.     

Effects of Phase Damping on Controlled Teleportation of a Qubit by a GHZ State

We investigate controlled teleportation ofa qubit via a GHZ state with the influence of phase damping in the Bloch sphere representation. We use the average trace distance to describe how close the output state is to the input state to be teleported. Our results show that the average trace distance is a function of decoherence rates and angles of the analyzer performed by the controller in the single-particle projective measurement. Moreover, for a fixed value of the decoherence rate, one can adjust the analyzer angle to achieve the optimal average trace distance.     

Landau damping of collective mode in a quasi-two-dimensional repulsive Bose-Einstein condensate

We investigate the Landau damping of the collective mode in a quasi-two-dimension repulsive Bose-Einstein condensate by using the self-consistent time-dependent Hatree-Fock-Bogoliubov approximation and a complete and orthogonal eigenfunction set for the elementary excitation of the system.We calculate the three-mode coupling matrix element between the collective mode and the thermal excited quasi-particles and the Landau damping rate of the collective mode.We discuss the dependence of the Landau damping on temperature,on atom number in the condensate,on transverse trapping frequency and on the length of the condensate.The energy width of the collective mode is taken into account in our calculation.With little approximation,our theoretic calculation results agree well with the experimental ones and are helpful for deducing the damping mechanics and the inter-particle interaction.     

Noisy teleportation of qubit states via the Greenberger-Horne-Zeilinger state or the W state

The effects of distributing entanglement through the amplitude damping channel or the phase damping channel on the teleportation of a single-qubit state via the Greenberger--Horne--Zeilinger state and the W state are discussed. It is found that the average fidelity of teleportation depends on the type and rate of the damping in the channel. For the one-qubit affected case, the Greenberger--Horne--Zeilinger state is as robust as the W state, i.e., the same quantum information is preserved through teleportation. For the two-qubit affected case, the W state is more robust when the entanglement is distributed via the amplitude damping channel; if the entanglement is distributed via the phase damping channel, the W state is more robust when the noisy parameter is small while the Greenberger--Horne--Zeilinger state becomes more robust when it is large. For the three-qubit affected case, the Greenberger--Horne--Zeilinger state is more robust than the W state.     

Nonlinear Landau damping of high frequency waves in non-Maxwellian plasmas

Space plasmas often possess non-Maxwellian distribution functions which have a significant effect on the plasma waves.When a laser or electron beam passes through a dense plasma,hot low density electron populations can be generated to alter the wave damping/growth rate.In this paper,we present theoretical analysis of the nonlinear Landau damping for Langmuir waves in a plasma where two electron populations are found.The results show a marked difference between the Maxwellian and non-Maxwellian instantaneous damping rates when we employ a non-Maxwellian distribution function called the generalized(r,q)distribution function,which is the generalized form of the kappa and Maxwellian distribution functions.In the limiting case of r=0 and q→∞,it reduces to the classical Maxwellian distribution function,and when r=0 and q→κ+1,it reduces to the kappa distribution function.     

Evolution law of a negative binomial state in an amplitude dissipative channel

For the first time we derive the evolution law of the negative binomial state In） （nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into The decay law of theaverage photon number is also obtained.     

Average Fidelity of Teleportation in Quantum Noise Channel

The effects of amplitude damping in quantum noise channels on average fidelity of quantum teleportation are analyzed in Bloch sphere representation for every stage of teleportation. When the quantum channels are varied from maximally entangled states to non-maximally entangled states, it is found that the effects of noise channels on the fidelity are nearly equivalent to each other for strong quantum noise. The degree of damage on the fidelity of non-maximally entangled channels is smaller than that of maximally entangled channels. The average fidelity of values larger than 2/3 may be one representation indirectly showing how much the unavoidable quantum noise is.     

Entanglement-enhanced classical communication through generalized amplitude damping channel

The problem of sending a single classical bit through a generalized amplitude damping channel is considered. When two transmissions through the channel are available as a resource, we find that two entangled transmissions can enhance the capability of receiver's judging information correctly under certain conditions compared with two product-state transmissions. In addition, we find a special case in which the two entangled transmissions can always make a classical bit more effectively disable the noise influence.     

Entanglement fidelity of channel adaptive quantum codes

We study the performances of quantum channel adaptive [4,1] code transmitting in a joint amplitude damping and dephasing channel, the [6,2] code transmitting in an amplitude damping channel by combining the encoding, noise process, and decoding as one effective channel. We explicitly obtain the entanglement fidelities. The recovery operators of the [6,2] code are given. The performance is nearly optimal compared with that of the optimal method of semidefinite programming.     

Electromagnetic Bloch oscillation in one-dimensional multiple microcavities composed of metamaterials

We propose a photonic structure stacked sequentially by one-dimensional photonic crystals and cavities. The whole structure is composed of single-negative and double-negative materials. The optical Wannier-Stark ladder （WSL） can be obtained in a low frequency region by modulating the widths of the cavities in order. We simulate the dynamical behavior of the electromagnetic wave passing through the proposed photonic structure. Due to the dispersive characteristics of the metamaterials, a very narrow WSL can be obtained. The long-period electromagnetic Bloch oscillation is demonstrated theoretically to have a period on a microsecond time scale.     

Sub-ODE＇s New Solutions and Their Applications to Two Nonlinear Partial Differential Equations with Higher-Order Nonlinear Terms

In the present paper, with the aid of symbolic computation, families of new nontrivial solutions of the first-order sub-ODE F12 = AF2 ＋ BF2＋p ＋ CF2＋2p （where F1= dF/dε, p 〉 0） are obtained. To our best knowledge, these nontrivial solutions have not been found in [X.Z. Li and M.L. Wang, Phys. Lett. A 361 （2007） 115] and IS. Zhang, W. Wang, and J.L. Tong, Phys. Lett. A 372 （2008） 3808] and other existent papers until now. Using these nontrivial solutions, the sub-ODE method is described to construct several kinds of exact travelling wave solutions for the generalized KdV-mKdV equation with higher-order nonlinear terms and the generalized ZK equation with higher-order nonlinear terms. By means of this method, many other physically important nonlinear partial differential equations with nonlinear terms of any order can be investigated and new nontrivial solutions can be explicitly obtained with the help of symbolic computation system Maple or Mathematics.     

Mutual transformations between the P–Q,Q–P,and generalized Weyl ordering of operators

Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （p, q） with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （p, q）, which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.     

Pseudo-differential Operators and Generalized Lax Equations in Symbolic Computation

In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given.     

Envelope Solitons Perturbed by Stochastic Noise

We perform langevin dynamics simulation for envelope solitons in an FPU-β lattice, with the nearest- neighbor interaction and quartic anharmonicity. We get the motion equations of our discrete system by adding noise and damping to the set of deterministic motion equations. We define ＂half-time＂ as the time when the amplitude of the envelope soliton decreases by half due to damping. And then the mass, center and half-time of the perturbed envelope soliton are numerically simulated, beginning with the discrete envelope soliton at rest. Results show successfully how noise affects behavior of the envelope soliton.     

α-decay half-lives of superheavy nuclei and general predictions

The generalized liquid drop model （GLDM） and the cluster model have been employed to calculate the α-decay half-lives of superheavy nuclei （SHN） using the experimental α-decay Q values. The results of the cluster model are slightly poorer than those from the GLDM if experimental Q values are used. The prediction powers of these two models with theoretical Q values from Audi et al. （QAudi） and Muntian et al. （QM） have been tested to find that the cluster model with QAudi and QM could provide reliable results for Z 〉 112 but the GLDM with QAudi for Z 112. The half-lives of some still unknown nuclei are predicted by these two models and these results may be useful for future experimental assignment and identification.     

Generalized Quantum Two-Qutrit-State Splitting

A three-party scheme for splitting an arbitrary unknown two-qutrit state is proposed, where two nonmaximally-entangled three-qutrit states are taken as the quantum channel among three parties. With the sender＇s help, if and only if both receivers collaborate together, they can securely share the quantum state in a probabilistic way by introducing an ancilla qutrit and performing appropriate unitary operations. The relation between the success probability and coefficients characterizing the quantum channel is revealed. The security of the present scheme is analyzed and confirmed. Moreover, the generalization of the three-party scheme to more-party case is also sketched.     

Lie Symmetry and Generalized Mei Conserved Quantity for Nonconservative Dynamical System

Based on the total time derivative along the trajectory of the system, for noneonservative dynamical system, the generalized Mei conserved quantity indirectly deduced from the Lie symmetry of the system is studied. Firstly, the Lie symmetry of the system is given. Then, the necessary and sumeient condition under which the Lie symmetry is a Mei symmetry is presented and the generalized Mei conserved quantity indirectly deduced from the Lie symmetry of the system is obtained. Lastly, an example is given to illustrate the application of the result.     

Scheme for Generalized Quantum State Sharing of a Single-Qubit State in Cavity QED

An experimentally feasible scheme for generalized quantum state sharing of an arbitrary unknown single- qubit state in cavity QED is presented. Using a generalized Greenberger-Horne-Zeilinger （GHZ） state as the quantum channel among the three parties, the quantum information （i.e. the single-qubit state） from the sender can be split in such a way that the information can be recovered if and only if both receivers collaborate. Moreover, the scheme is insensitive to both the effects of thermal field and cavity decay.