Junpeng Cao

Exact solution of XXZ spin chain with unparallel boundary fields

By using a set of gauge transformations (face-vertex correspondence relations), the XXZ spin chain with both transverse and longitudinal magnetic boundary fields is studied. The corresponding reflection boundary matrices therefore have non-diagonal elements. The Bethe ansatz equations, the eigenvalues and the eigenstates of the transfer matrix and the Hamiltonian of the system are obtained in the framework of algebraic Bethe ansatz method. The ground states for different couplings are derived.

Chemically-speciated on-road PM2.5 motor vehicle emission factors in Hong Kong.

PM(2.5) (particle with an aerodynamic diameter less than 2.5microm) was measured in different microenvironments of Hong Kong (including one urban tunnel, one Hong Kong/Mainland boundary roadside site, two urban roadside sites, and one urban ambient site) in 2003. The concentrations of organic carbon (OC), elemental carbon (EC), water-soluble ions, and up to 40 elements (Na to U) were determined. The average PM(2.5) mass concentrations were 229+/-90, 129+/-95, 69+/-12, 49+/-18microg m(-3) in the urban tunnel, cross boundary roadside, urban roadside, and urban ambient environments, respectively. Carbonaceous particles (sum of organic material [OM] and EC) were the dominant constituents, on average, accounting for approximately 82% of PM(2.5) emissions in the tunnel, approximately 70% at the three roadside sites, and approximately 48% at the ambient site, respectively. The OC/EC ratios were 0.6+/-0.2 and 0.8+/-0.1 at the tunnel and roadside sites, respectively, suggesting carbonaceous aerosols were mainly from vehicle exhausts. Higher OC/EC ratio (1.9+/-0.7) occurred at the ambient site, indicating contributions from secondary organic aerosols. The PM(2.5) emission factor for on-road diesel-fueled vehicles in the urban area of Hong Kong was 257+/-31mg veh(-1) km(-1), with a composition of approximately 51% EC, approximately 26% OC, and approximately 9% SO(4)(=). The other inorganic ions and elements made up approximately 11% of the total PM(2.5) emissions. OC composed the largest fraction (approximately 51%) in gasoline and liquid petroleum gas (LPG) emissions, followed by EC (approximately 19%). Diesel engines showed higher emission rates than did gasoline and LPG engines for most pollutants, except for V, Br, Sb, and Ba.

Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions

Employing the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the XXX spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated T-Q relation and the Bethe ansatz equations are derived

Off-Diagonal Bethe Ansatz and Exact Solution of a Topological Spin Ring

A general method is proposed for constructing the Bethe ansatz equations of integrable models without U(1) symmetry. As an example, the exact spectrum of the XXZ spin ring with a Möbius-like topological boundary condition is derived by constructing a modified T-Q relation based on the functional connection between the eigenvalues of the transfer matrix and the quantum determinant of the monodromy matrix. With the exact solution, the elementary excitations of the topological XX spin ring are discussed in detail. It is found that the excitation spectrum indeed shows a nontrivial topological nature.

Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields

The anisotropic spin-1/2 chains with arbitrary boundary fields are diagonalized with the off-diagonal Bethe ansatz method. Based on the properties of the R-matrix and the K-matrices, an operator product identity of the transfer matrix is constructed at some special points of the spectral parameter. Combining with the asymptotic behavior (for XXZ case) or the quasi-periodicity properties (for XYZ case) of the transfer matrix, the extended T-Q ansatzes and the corresponding Bethe ansatz equations are derived

Off-Diagonal Bethe ansatz for exactly solvable models

Overview.- The algebraic Bethe ansatz.- The periodic anisotropic spin-1/2 chains.- The spin-1/2 torus.- The spin-1/2 chain with arbitrary boundary fields.- The one-dimensional Hubbard model.- The nested off-diagonal Bethe ansatz.- The hierarchical off-diagonal Bethe Ansatz.- The Izergin-Korepin model.

Quantum speed limit for arbitrary initial states

The minimal time a system needs to evolve from an initial state to its one orthogonal state is defined as the quantum speed limit time, which can be used to characterize the maximal speed of evolution of a quantum system. This is a fundamental question of quantum physics. We investigate the generic bound on the minimal evolution time of the open dynamical quantum system. This quantum speed limit time is applicable to both mixed and pure initial states. We then apply this result to the damped Jaynes-Cummings model and the Ohimc-like dephasing model starting from a general time-evolution state. The bound of this time-dependent state at any point in time can be found. For the damped Jaynes-Cummings model, when the system starts from the excited state, the corresponding bound first decreases and then increases in the Markovian dynamics. While in the non-Markovian regime, the speed limit time shows an interesting periodic oscillatory behavior. For the case of Ohimc-like dephasing model, this bound would be gradually trapped to a fixed value. In addition, the roles of the relativistic effects on the speed limit time for the observer in non-inertial frames are discussed.

Spin-1/2 XYZ model revisit: General solutions via off-diagonal Bethe ansatz

The spin-1/2 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the inhomogeneous T Q relations, which allow us to treat both the even N (the number of lattice sites) and odd N cases simultaneously in a unified approach

Classical-driving-assisted quantum speed-up

We propose a method of accelerating the speed of evolution of an open system by an external classical driving field for a qubit in a zero-temperature structured reservoir. It is shown that, with a judicious choice of the driving strength of the applied classical field, a speed-up evolution of an open system can be achieved in both the weak system-environment couplings and the strong system-environment couplings. By considering the relationship between non-Makovianity of environment and the classical field, we can drive the open system from the Markovian to the non-Markovian regime by manipulating the driving strength of classical field. That is the intrinsic physical reason that the classical field may induce the speed-up process. In addition, the roles of this classical field on the variation of quantum evolution speed in the whole decoherence process is discussed.

Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields

The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method