Decay of correlations in spin systems

We investigate the decay of initial correlations in a spin system where each spin relaxes independently by an intramolecular mechanism. The equation of motion for the spin density matrix is assumed to be the Redfield equation, which is of the form of a quantum mechanical master equation. Our analysis of this problem is based on the techniques of Shuler, Oppenheim, and coworkers, who have studied the decay of correlations in systems which can be described by classical stochastic master equations. We find that the off-diagonal elements of the reduced spin density matrices approach their equilibrium values faster than the diagonal elements. The Ursell functions, which are a measure of the correlations in the system, decay to their zero equilibrium values faster than the spin density matrix except for the furthest off-diagonal elements. Far off-diagonal matrix elements of the spin density matrix approach equilibrium at the same rate as the Ursell functions, which is the important difference between the quantum mechanical model studied here and the classical models studied earlier.Supported in part by the National Science Foundation.     

Decoherence from a spin chain with Dzyaloshinskii—Moriya interaction

We study the dynamics of quantum discord and entanglement for two spin qubits coupled to a spin chain with Dzyaloshinsky-Moriya interaction.In the case of a two-qubit with an initial pure state,quantum correlations decay to zero at the critical point of the environment in a very short time.In the case of a two-qubit with initial mixed state,it is found that quantum discord may get maximized due to the quantum critical behavior of the environment,while entanglement vanishes under the same condition.Besides,we observed a sudden transition between classical and quantum decoherence when only a single qubit interacts with the environment.The effects of Dzyaloshinsky-Moriya interaction on quantum correlations are considered in the two cases.The decay of quantum correlations is always strengthened by Dzyaloshinsky-Moriya interaction.     

Application of the theory of open quantum systems to nuclear physics problems

Quantum diffusion equations with transport coefficients explicitly depending on time are derived from the generalized non-Markovian Langevin equations. The asymptotic behavior of the friction and diffusion coefficients is investigated in the case of the FC and RWA couplings between the collective and internal subsystems. An asymptotic expression is obtained for the propagator of the density matrix of the open quantum system with the general quadratic Hamiltonian, linearly coupled (in coordinate and momentum) to internal degrees of freedom. The effect of different sets of transport coefficients on the decoherence and decay rate of the metastable state is investigated using the master equation for the reduced density matrix of open quantum systems. The developed approach is used to study the capture of the projectile nucleus by the target nucleus at energies near the Coulomb barrier. Capture cross sections in asymmetric reactions are well described with allowance for the calculated capture probabilities. Particular cases where dissipation favors penetration through the potential barrier are found. The generalized Kramers formula for the quasi-stationary decay rate of the quantum metastable systems is analytically derived.     

Symmetric Telecloning and Entanglement Distribution of Spin Quantum States

We propose a physical realization of symmetric telecloning machine for spin quantum states. The concept of area average fidelity is introduced to describe the telecloning quality. It is indicated that for certain input states this quantity may come to an enough high level to satisfy the need of quantum information processing. We also study the properties of entanglement distribution via the spin chain for arbitrary two-qubit entangled pure states as inputs and find that the decay ratio of entanglement for the output states is only determined by the parameters of spin chain and waiting time, independent of the initial input states.     

Graviton propagator from background-independent quantum gravity

We study the graviton propagator in Euclidean loop quantum gravity. We use spin foam, boundary-amplitude, and group-field-theory techniques. We compute a component of the propagator to first order, under some approximations, obtaining the correct large-distance behavior. This indicates a way for deriving conventional spacetime quantities from a background-independent theory.     

Spin dynamics from majorana fermions

Using the Majorana fermion representation of spin-1/2 local moments, we show how the dynamic spin correlation and susceptibility are obtained directly from the one-particle Majorana propagator. We illustrate our method by applying it to the spin dynamics of a nonequilibrium quantum dot, computing the voltage-dependent spin relaxation rate and showing that, at weak coupling, the fluctuation-dissipation relation for the spin of a quantum dot is voltage dependent. We confirm the voltage-dependent Curie susceptibility recently found by Parcollet and Hooley [Phys. Rev. B 66, 085315 (2002)]].     

Feynman propagator for spin foam quantum gravity

We link the notion causality with the orientation of the spin foam 2-complex. We show that all current spin foam models are orientation independent. Using the technology of evolution kernels for quantum fields on Lie groups, we construct a generalized version of spin foam models, introducing an extra proper time variable. We prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of quantum field theory (QFT) or as inner products between quantum gravity states; and a new class of causal models, the quantum gravity analogue of the Feynman propagator in QFT, nontrivial function of the orientation data, and implying a notion of "timeless ordering".     

On comparison of classical and quantum kicked tops with dissipation

We analyze the influence of dissipation on dynamics of a quantum spin system. Properties of spectrum of the quantum propagator are discussed and it is shown how they imply strong damping of quantum mean values. Relations between an asymptotic density matrix and an invariant measure on attractor are discussed.     

Heat transport in quantum spin chains

We discuss the problem of heat conduction in quantum spin chain models. To investigate this problem it is necessary to consider the finite open system connected to heat baths. We describe two different procedures to couple the system with the reservoirs: a model of stochastic heat baths and the quantum trajectories solution of the quantum master equation. The stochastic heat bath procedure operates on the pure wave function of the isolated system, so that it is locally and periodically collapsed to a quantum state consistent with a boundary nonequilibrium state. In contrast, the quantum trajectories procedure evaluates ensemble averages in terms of the reduced density matrix operator of the system. We apply these procedures to different models of quantum spin chains and numerically show their applicability to study the heat flow.     

Remarks on Chern–Simons Invariants

The perturbative Chern–Simons theory is studied in a finite-dimensional version or assuming that the propagator satisfies certain properties (as is the case, e.g., with the propagator defined by Axelrod and Singer). It turns out that the effective BV action is a function on cohomology (with shifted degrees) that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely. Out of it one obtains invariants.     

与XY双自旋链耦合的双量子比特系统的关联性与相干性

研究了双量子比特系统中在具有Dzyaloshinsky-Moriya相互作用的独立XY自旋链环境下的相干性与关联性动力学.推导出相干性与关联性的演化规律.发现在自旋链的临界点附近,当tt_0时,系统相干性的演化与经典关联完全相同;而在tt_0时,则与量子关联完全相同;在t_0时刻,量子关联突变为经典关联.     

Square-Root Operator Quantization and Nonlocality: A Review

A square-root-operator formalism is developed for quantum systems described with nonrelativistic and relativistic equations of motion. Spectral representation for Green's functions are designed for particles with spin 0, with the implication of its generalization to other spin values. Nonlocal operators suggest that a duality exists between physical particles and dual partners, which are tachyonic mathematical particles. It is shown that nonlocal operators result naturally from square-root operators, with the implication that microcausality holds only asymptotically. Applications help enlighten the formalism in order to envisage realistic situations with Schrödinger equations, Higgs fields, vacuum fluctuations, extra-dimensional methods in the potential theory, and electromagnetic interactions of extended charges and their consequences. It turns out that the innermost structure of these extended charges is associated with nonlocal photon propagators. It is shown that the propagator arisen from the charged torus potential consists of two different parts: a nonlocal photon propagator and a propagator of neutrino-like particles, which is described by square-root-operator equation. We examine the potential of the torus and its propagator as the appearance of superfields in terms of the photon and the massless fermion (photino).     

Relativistic quantum theory without quantized fields

Peculiarities of symmetrical quantum systems are considered with the aid of the Mackey's induced representations theory. The four-dimensional coordinate representation of the relativistic quantum mechanics suggested by Stueckelberg in 1941 is rederived, reinterpreted and generalized for an arbitrary spin. Then it is applied to introduce the causal propagator as a particleantiparticle transition amplitude without consideration of a field equation. Finally the theory of relativistic quantum particles interaction is reformulated without an appeal to the concept of quantized fields.     

解析计算SM中电子混合链图传播下Compton 散射微分截面

采用电弱统一标准模型(SM), 对由参与电弱相互作用的各种混合圈构成的电子重整化链图传播子的构架方式作了详细分析, 并完成了有关解析计算, 进而获得了电子重整化链图传播子的解析计算结果. 作者又将此结果应用到Compton散射, 精确计算了电子混合链图传播下Compton散射微分截面的解析结果 . 此外, 作者还将计算结果与最低阶微分截面 和量子电动力学(QED)中电子链图传播下的Compton散射微分截面 做了具体的数值计算与对比分析, 发现 比 能更加精细的反应辐射修正效应.     

Sensitive chemical compass and quantum criticality at finite temperature

We investigate the influence of a flip operation of the central spin on the quantum criticality of a radical pair system by employing the spin echo and its product yield. It is found that with echo control on the central spin, the critical behavior can be described by the product yield at very high temperatures. Moreover, we also study the short and long time behavior of the spin echo, and show that the decay factor of the short time evolution scales linearly. The long time evolution shows different statistics for varying chain lengths, temperature and external parameters of the Hamiltonian.     

解析计算SM中电子混合链图传播下Compton散射微分截面(英文)

采用电弱统一标准模型（SM）,对由参与电弱相互作用的各种混合圈构成的电子重整化链图传播子的构架方式作了详细分析,并完成了有关解析计算,进而获得了电子重整化链图传播子的解析计算结果.作者又将此结果应用到Compton散射,精确计算了电子混合链图传播下Compton散射微分截面的解析结果dσ_SM^chain/dcosθ.此外,作者还将计算结果与最低阶微分截面dσ^trcc/dcosθ口和量子电动力学（QED）中电子链图传播下的Compton散射微分截面dσ_QED^chain/dcosθ做了具体的数值计算与对比分析,发现dσ_SM^chain/dcosθ比dσ_QED^chain/dcosθ能更加精细的反应辐射修正效应.     

Quantum Theory of Localized Crystal

A quantum crystal each particle of which is located to a proximity of one lattice point is considered. The causal Green functions at finite temperatures are used. The localized approximation for the iteration of propagator equations is formulated. New type conditions defining parameters of model propagator are proposed. The general method is illustrated with the example of a linear chain.     

Loschmidt Echo of a central spin coupled to an XY spin chain:The role of the Dzyaloshinsky-Moriya interaction

By introducing the Dzyaloshinsky-Moriya(DM) interaction, the Loschmidt Echo(LE) of a quantum system consisting of a central spin and its surrounding environment characterized by an XY spin chain was investigated analytically and numerically. At the critical points of the magnetic field, the LE presents an obvious decay. The decay amplitude can be tuned by the DM interaction. In some specific intervals the DM interaction can remarkably delay the decay of the LE. On the other hand, the DM interaction can change the effects of the anisotropy parameter on the LE.