Quantifying quantum discord and entanglement of formation via unified purifications

We propose a scheme to evaluate the amount of quantum discord and entanglement of formation for mixed states, and reveal their ordering relation via an intrinsic relationship between the two quantities distributed in different partners of the associated purification. This approach enables us to achieve analytical expressions of the two measures for a sort of quantum states, such as an arbitrary two-qubit density matrix reduced from pure three-qubit states and a class of rank-2 mixed states of 4\times 2 systems. Moreover, we apply the scheme to characterize fully the dynamical behavior of quantum correlations for the specified physical systems under decoherence.Comment: 4 pages, 2 figures, accepted for publication in Phys. Rev.

Quantum Transport from the Perspective of Quantum Open Systems

By viewing the non-equilibrium transport setup as a quantum open system, we propose a reduced-density-matrix based quantum transport formalism. At the level of self-consistent Born approximation, it can precisely account for the correlation between tunneling and the system internal many-body interaction, leading to certain novel behavior such as the non-equilibrium Kondo effect. It also opens a new way to construct time-dependent density functional theory for transport through large-scale complex systems.Comment: 4 pages, 2 figures; the TDDFT scheme is explained in more detail in this new versio

Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled and the master equation naturally comes out. Such an equation possesses the Lindblad form in which time dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.Comment: 24page

Kinetic-energy density functional for a special shape-invariant potential of a one-dimensional two-level system

By introducing the concept of supersymmetry to quantum mechanics, several authors have shown that exactly soluble potentials, including all those well known, are easily constructed. Is the kinetic-energy density functional corresponding to these potentials a simple form? We show that the answer is no, even to the simplest one, the harmonic potential, if one builds the kinetic-energy density functional from the reduced density matrix

Kinetic energy functional of noninteracting electrons: Functional integral method and gradient expansion

For a system of noninteracting electrons, the formulation and the gradient expansion of its kinetic energy functional are investigated. Studies are based on both the semiclassical theory and first principles. In the framework of the semiclassical theory, the traditional gradient expansion (to fourth order in the one-dimensional case and to second order in the general case) is derived by the Kirzhnits' operational calculus and by the Hodges' method. The newly derived gradient expansion for the one-dimensional system is applied to a model system. In this case the fourth-order term is divergent. For an even-dimensional system, it is shown that its kinetic energy functional and its density in the semiclassical sense are exactly solvable, namely, they can be expressed as finite series in #nabla# acting on the external potential. The full analysis is carried out through the Kirzhnits' approach. For instance, the semiclassical density of a two-dimensional system is shown to be the Thomas-Fermi density and the semiclassical kinetic energy functional is identical with the result from the traditional gradient expansion approximation. From first principles, an exact formulation of the kinetic energy functional, which has been sought for many years, is worked out by the functional integral method for the first time. Expressions of functional derivatives of the kinetic energy functional for the uniform system, which is contained in this formulation, are derived in terms of the response function. The exact kinetic energy functional is shown to be internally consistent by treating the uniform system. It is used to develop ab initio gradient expansion. To second order the ab initio gradient expansion yields the same result as the traditional one does. But, unlike the traditional or semiclassical counterpart, the ab initio gradient expansion is generally singular independent of the system under consideration. The conventional belief that the gradient expansion is asymptotically valid for the system with very slowly varying density is wrong. For certain nonlocal density functionals, it is shown that the gradient expansion yields singular higher-order terms, thus the gradient expansion is not a universally valid approximation method. Finally, a scheme for systematic approximations to the exact kinetic energy functional is proposed. (orig.)SIGLEAvailable from TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Reply to Comment on \u27Kinetic-energy density functional for a special shape-invariant potential of a one-dimensional two-level system\u27

For a harmonic potential, which is the special shape-invariant potential discussed in our paper [1], the relation between the ground state and the first-excited-state wave functions [Eq. (2)] should be . . . Therefore, we have shown that one cannot find a closed form of the kinetic-energy density for the harmonic oscillator