Bi Qiao

Master equation for a quantum system driven by a strong periodic field in the quasienergy representation

The evolution of a quantum system weakly coupled with a thermal reservoir and influenced by an external periodic field is formulated in the quasienergy representation where the strong external periodic field disappears and the original model is transformed to a time-dependent system weakly coupled with thermal reservoir. Based on this time-dependent subdynamics, we derive a master equation of the reduced density operator for the driven quantum system. This equation is valid in the weak-coupling limit. Our method can be useful for obtaining the master equation of any system coupled with a thermal reservoir and driven by strong external periodic fields.

Spectral decomposition of the tent maps and the isomorphism of dynamical systems

We construct a generalized spectral decomposition of the family of tent maps. Comparison with the Renyi maps shows that isomorphic systems may have different rates of approach to equilibrium. We propose therefore a natural isomorphism of dynamical systems on the basis of the identity of spectra in rigged Hilbert space.

Kinetic equation, non-perturbative approach and decoherence free subspace for quantum open system

A Schrodinger (Liouville) type of equation for an quantum open system is presented. The equation has a correlated part and many Master equations can be derived from it as special cases. Most significantly, it can be applied to construct a decoherence-free subspace for quantum computing. The original Schrodinger (Liouville) equation for the total system is related to it by a non-unitary similarity transformation, which enables us to propose a non-perturbative method for solving the eigenvalue problem for the total Hamiltonian. In addition, it also enables one to uncover a simple procedure to treat the eigenvalue problem of an open system under strong interaction. The correlated part of the equation is not necessarily self-adjoint, so that there exists a complex spectrum for the corresponding Hamiltonian (Liouvillian) which enables the time evolution of states to be asymmetric. This then exposes just the correlation required to produce evolution, which coincides with the second law of thermodynamics.

Two-qubit quantum computing in a projected subspace

A formulation for performing quantum computing in a projected subspace is presented, based on the subdynamical kinetic equation (SKE) for an open quantum system. The eigenvectors of the kinetic equation are shown to remain invariant before and after interaction with the environment. However, the eigenvalues in the projected subspace exhibit a type of phase shift to the evolutionary states. This phase shift does not destroy the decoherence-free (DF) property of the subspace because the associated fidelity is 1. This permits a universal formalism to be presented-the eigenprojectors of the free part of the Hamiltonian for the system and bath may be used to construct a DF projected subspace based on the SKE. To eliminate possible phase or unitary errors induced by the change in the eigenvalues, a cancellation technique is proposed, using the adjustment of the coupling time, and applied to a two-qubit computing system. A general criteria for constructing a DF-projected subspace from the SKE is discussed. Finally, a proposal for using triangulation to realize a decoherence-free subsystem based on SKE is presented. The concrete formulation for a two-qubit model is given exactly. Our approach is general and appears to be applicable to any type of decoherence.

Sensitivity of Exponents of Three-Power Laws to Hybrid Ratio in Weighted HUHPM

The sensitivity of exponents of three-power laws for node degree, node strength and edged weight to hybrid ratio are studied analytically and numerically in the weighted harmonious unifying hybrid preferential model (HUHPM), which is extended from un-weighted hybrid preferential attachment model we proposed previously [Chin. Phys. Lett. 22 (2005) 719]. Our weighted HUHPMs plus the Barrat–Barthelemy–Vespignani model and the traffic-driven evolution model, respectively, are taken as two typical examples for demonstration and application of the HUHPM.

Advances in theoretical models of network science

In this review article, we will summarize the main advances in network science investigated by the CIAE Group of Complex Network in this field. Several theoretical models of network science were proposed and their topological and dynamical properties are reviewed and compared with the other models. Our models mainly include a harmonious unifying hybrid preferential model, a large unifying hybrid network model, a quantum interference network, a hexagonal nanowire network, and a small-world network with the same degree. The models above reveal some new phenomena and findings, which are useful for deeply understanding and investigating complex networks and their applications.

Generalized spectral decomposition and intrinsic irreversibility of the Arnold Cat Map

Abstract We construct a generalized spectral decomposition of the Frobenius-Perron and Koopman operators of the Arnold Cat map. We define a suitable dual pair or rigged Hubert space which provides mathematical meaning to the spectral decomposition. The eigenvalues in the decomposition are the resonances of the power spectrum which determine the decay rates of the correlation functions and the rate of approach to equilibrium. The extended unitary evolution splits into two distinct semigroups which express the intrinsic irreversibility of the Cat map resulting from the strong chaotic properties.

Evolution of a two-dimensional quantum cellular neural network driven by an external field

A model of a two-dimensional quantum cellular neural network (QCNN) is presented in this article. The eigenvalues and eigenvectors for the Hamiltonian of a cell (neuron) are obtained, and we confirm that the ground or memory states are approximately two polarization states of 16 possible states in a cell (neuron) only when electron tunneling is relatively weak compared with the Coulomb repulsion. The evolution of the QCNN driven by a local external magnetic field is studied by solving the Liouville equation of the corresponding two-dimensional Ising model. The formula for the evolution of the density operator is given by using a subdynamics approach. We show that the local external magnetic field can drive the system to a global polarization state and induce a dynamical response in the original QCNN. This dynamical response can be interpreted as a computable function and measured by the system output.

Using sequences of pulses to control coherence in an open quantum computing system

A method for quantum control of coherence in an open quantum computing system is presented. The approach was applied to finding a suitable control sequence for maintaining coherence in a silicon-based nuclear spin quantum computing system, subject to Bose-type environmental noise, and under the Born-Markovian and rotating wave approximations. It is shown that the evolution operator remains decoherence free while the three control pulses are being applied

Spectral decomposition of excitons confined in a quantum dot by a parabolic potential and under the influence of an external field

A general formulation of subdynamics is presented for constructing the spectral decomposition of the Hamiltonian of N excitons confined within a quantum dot and influenced by an external electromagnetic field. The formulation offers a simple means for calculating the spectrum of the N-exciton Hamiltonian using recurrence relations for the creation and destruction operators. The spectral decomposition of the Hamiltonian may therefore be constructed using the intertwining relation. This formulation also can be extended to construct the spectral decomposition of the N-exciton Hamiltonian in more complex or nonintegrable quantum box systems, even when such systems are subject to a strong external field. As a demonstration of the application of this formulation, we consider the calculation of the eigenvalues and eigenvectors of Hamiltonian of an exciton in the system.