Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function C（ω） of the spin operator σz for the biased sub-Ohmic spin-boson model. The small-ω behavior C（ω） ∝ ω～s is found to be universal and independent of the bias ε and the coupling strength α（except at the quantum critical point α = αc and ε = 0）. Our NRG data also show C（ω） ∝ χ～2ω～s for a wide range of parameters, including the biased strong coupling regime（ε = 0 and α 〉 αc）, supporting the general validity of the Shiba relation. Close to the quantum critical point αc,the dependence of C（ω） on α and ε is understood in terms of the competition between ε and the crossover energy scale ω0^＊of the unbiased case. C（ω） is stable with respect to ε for ε《ε^＊. For ε 》ε^＊, it is suppressed by ε in the low frequency regime. We establish that ε^＊∝（ω0^＊）^1/θ holds for all sub-Ohmic regime 0≤s 〈 1, with θ = 2/（3s） for 0 〈 s≤1/2 and θ = 2/（1 ＋ s） for 1/2 〈 s 〈 1. The variation of C（ω） with α and ε is summarized into a crossover phase diagram on the α–ε plane.

Dynamical correlation functions of the quadratic coupling spin-Boson model

The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method.We focus on the dynamical auto-correlation functions CO（ω）, with the operator taken as σx, σz, and X, respectively. In the weak-coupling regime α 〈 αc, these functions show power law ω-dependence in the small frequency limit, with the powers 1 ＋ 2s, 1 ＋ 2s, and s, respectively. At the critical point α = αc of the boson-unstable quantum phase transition, the critical exponents yO of these correlation functions are obtained as yσx= yσz= 1-2s and yX=-s, respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of Cσx（ω） is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.

Quantum parameter estimation in a spin-boson dephasing quantum system by periodical projective measurements

In this paper,we explore how to estimate the phase damping parameter γ and the tunneling amplitude parameter ？from a spin-boson dephasing quantum model by periodical projective measurements.The preparation of initial states is accomplished by performing the period measurements in our scheme.The parameter γ can be always estimated when projective measurement bases are chosen as θ = π/2 and φ = 0.Based on the estimated value of γ and the interval information of ？,we can select another measurement bases（θ = π/4 and φ = π/2） to obtain the estimated value of ？.A coherent control is indispensable to estimate ？ if γ is in the interval of ？;whereas the control is not necessary if γ is out of the known interval of ？.We establish the relation between the optimal period time and the parameter γ or ？ in terms of Fisher information.Although the optimal measurement period cannot be selected beforehand,the aforementioned relation can be utilized to adjust the measurement period to approach the optimal one.

A note on localized transition in the spin-boson model by variational calculation

We present mathematical analyses of the evolution of solutions of the self-consistent equation derived from variational calculations based on the displaced-oscillator-state and the displaced-squeezed-state in spin-boson model at a zero temperature and a finite temperature. It is shown that, for a given spectral function defined as J（w） = π∑k Ck^2 = π/2αw^8w^1-s, there exists a universal sc for both kinds of variational schemes, the localized transition happens only for 2 s ≤ sc, moreover, the localized transition is discontinuous for s 〈 sc while a continuous transition always occurs when s = sc. At T = 0, we have sc = 1, while for T ≠ 0, sc = 2 which indicates that the localized transition in super-Ohmic case still exists, manifesting that the result is in discrepancy with the existing result.

Simulation of Decoherence by Averaged Semiquantum Method for Spin-Boson Model

We investigate the dynamics of a system coupled to an environment by averaged semiquantum method. The theory origins from the time-dependent variational principle （TDVP） formulation and contains nondiagonal matrix elements. So it can be applied to study dissipation, measurement, and decoherence problems in the model （H= hs＋hE＋ht ）. In the calculation, the influence of the environment govern by differential dynamical equation is incorporated through a mean field. We have performed averaged semiquantum method for a spin-boson model, which reproduce the results from stochastic Schrodinger equation method and Hierarchical approach quite accurately. The problems, dynamics in nonequilibrium environments, have also been studied by our method.

Equilibrium dynamics of the sub-ohmic spin-boson model at finite temperature

We use the full-density matrix numerical renormalization group method to calculate the equilibrium dynamical correlation function C(ω) of the spin operator σ_(z) at finite temperature for the sub-ohmic spin-boson model.A peak is observed at the frequency ω_(T)~T in the curve of C(ω).The curve merges with the zero-temperature C(ω) in ω>>ω_(T) and deviates significantly from the zero-temperature curve in ω<<ω_(T).

Exact Generator and its High Order Expansions in Time-Convolutionless Generalized Master Equation:Applications to Spin-Boson Model and Exictation Energy Transfer

The time-convolutionless （TCL） quantum master equation provides a powerful tool to simulate reduced dynanfics of a quantum system coupled to a bath. The key quantity ill the TCL master equation is the so-called kernel or generator, which describes eflhcts of the bath degrees of freedom. Since the exact TCL generators are usually hard to calculate analytically, most applications of the TCL generalized master equation have relied on approximate generators using second and fourth order perturbative expansions. By using the hierarchical equation of motion （HEOM） and extended HEOM methods, we present a new approach to calculating the exact TCL generator and its high order perturbative expansions. The new approach is applied to the spin-boson model with diflhrent sets of parameters, to investigate the convergence of the high order expansiolls of the TCL generator. We also discuss circumstances where the exact TCL generator becomes singular for the spin-boson model, and a model of excitation energy transfer in the Fenna-Matthews-Olson complex.

Spin-Boson and Spin-Fermion Topological Model of Consciousness

The authors propose a new approach to the theory of spin-boson and spin-fermion topological model of consciousness. The authors will offer a common mechanism of spin-boson and spin-fermion topological model of consciousness.

Simulation of the spin-boson model with superconducting phase qubit coupled to a transmission line

Based on the rapid experimental developments of circuit QED,we propose a feasible scheme to simulate the spin-boson model with superconducting circuits,which can be used to detect quantum Kosterlitz-Thouless(KT) phase transition.We design the spinboson model by using a superconducting phase qubit coupled to a semi-infinite transmission line,which is regarded as a bosonic reservoir with a continuum spectrum.By tuning the bias current or the coupling capacitance,the quantum KT transition can be directly detected through tomography measurement on the states of the phase qubit.We also estimate the experimental parameters using the numerical renormalization group method.

反旋转波相互作用对非平衡自旋玻色模型热输运性质的影响

随着实验技术的发展,量子系统中已经实现了强和超强自旋-腔、自旋-环境相互作用。很大一类光学腔和耗散环境可以用波色热库描述。在强系统-热库耦合条件下,之前适用于弱耦合条件下的旋波近似失效,需要考虑系统-热库的反旋转波相互作用对系统动力学演化和稳态行为的影响。使用正则变换和全计数统计方法,研究系统-热库反旋转波相互作用对热输运性质的影响。结果表明:在弱耦合情况下采用旋波近似时,稳态热流、噪声功率以及热力学不确定关系随温度单调增大。强耦合情况,反旋转波相互作用下,以上物理量呈非单调性:先增大后减小。在弱耦合情况下采用旋波近似时,热力学不确定关系与耦合强度无关。强耦合情况,反旋转波相互作用下,热力学不确定关系随着耦合强度的增大而减小,向热力学不确定关系的下限逼近。说明量子相干性有助于提高量子热机的性能,使其优于经典热机。

Numerical approach for the evolution of spin-boson systems and its application to the Buck–Sukumar model

We study the evolution properties of spin-boson systems by a systematic numerical iteration approach,which performs well in the whole coupling regime.This approach evaluates a set of coefficients in the formal expression of the time-dependent Schr?dinger equation by expanding the initial state in Fock space.This set of coefficients is unique for the spin-boson Hamiltonian studied,allowing one to calculate the time evolution from different initial states.To complement our numerical calculations,we apply the method to the Buck–Sukumar model.We find that when the ground-state energy of the model is unbounded and no ground state exists in a certain parameter space,the time evolution of the physical quantities is naturally unstable.

No Spin-Localization Phase Transition in the Spin-Boson Model without Local Field

We explore the spin-boson model in a special case, i.e., with zero local field. In contrast to previous studies, we find no possibility for quantum phase transition （QPT） happening between the localized and delocalized phases, and the behavior of the model can be fully characterized by the even or odd parity as well as the parity breaking, instead of the QPT, owned by the ground state of the system. The parity breaking mentioned in our case is completely different from the spontaneously broken symmetry relevant to the conventionally defined QPT in previous studies. Our analytical treatment about the eigensolution of the ground state of the model presents for the first time a rigorous proof of no- degeneracy for the ground state of the model, which is independent of the bath type, the degrees of freedom of the bath and the calculation precision. We argue that the QPT mentioned previously appears due to incorrect employment of the ground state of the model and/or unreasonable treatment of the infrared divergence existing in the spectral functions for Ohmic and sub-Ohmic dissipations.

新的规范玻色子和直线对撞机上顶夸克对产生的自旋修正

在非对角基下,研究了3-3-1模型所预言的中性规范玻色子Z′对顶夸克对产生的自旋相关过程的修正.结果表明Z′的改变可以对t↑t^-↓和t↓t^-↑散射截面产生主要修正,而且在非对角基下散射截面在相同自旋态下是不为零的.因此我们希望,Z′对顶夸克对产生的自旋结构的贡献可以在未来的ILC实验上探测到,并且可以区别不同的3-3-1模型.

^(104)Cd核子顺排特征的微观研究

应用微观相互作用玻色子-费米子模型的形式体系,构造出唯象核芯+两准粒子模型的一个微观实现,微观sdIBM-2+2q.p方案.基于唯象模型和实现方案,导出原子核的一个d玻色子从退耦、拆散、占据闯入轨道,直到参加顺排所需的最小能量值;据此讨论了核高自旋态的微观结构及其拆对顺排次序.对104Cd核的计算结果显示微观方案较满意地描述了该核的低自旋态和部分高自旋态;核的一个d玻色子的突然拆对不会引起前后状态的显著改变.最后,本方案指认:这些高自旋态是构建于ν(h11/2)2和π(g9/2)2上的顺排态;而实验上观测到的81+、82+和83+态则很可能分别属于两准质子顺排态、两准中质子顺排态和基态。

Effect of system-reservoir correlations on temperature estimation

In many previous temperature estimation schemes,the temperature of a sample is directly read out from the final steady state of a quantum probe,which i5 eoupled to the sample.However,in these studies,information of eorrelations between system(the probe) and reservoir(the sample) is usually eliminated,leading the steady state of the probe is a canonical equilibrium state with respect solely to system’s Hamiltonian.To explore the influence of system-reservoir correlations on the estimation precision,we investigate the equilibration dynamics of a spin interacting with a finite temperature bosonic reservoir.By incorporating an intermediate harmonic oscillator or a collective coordinate into the spin,the system-reservoir correlations can be correspondingly encoded in a Gibbs state of an effective Hamilton,which is size consistent with the original bare spin.Extracting information of temperature from this corrected steady state,we find the effect of the systemreservoir correlations on the estimation precision is highly sensitive to the details of the spectral density function of the measured reservoir.

光子气体普朗克理论的探讨

光子是玻色子,自旋量子数为1,达到平衡后遵从玻色分布,符合普朗克理论.本文从基本量子理论出发,结合玻色分布,推导出普朗克公式.并给出几个重要推论.

广义相干态表示的性质及其应用

本文讨论了广义相干态表示的性质和应用,其中包含玻色相干态和自旋相干态,在极限条件下,它们的形式趋于一致。

自旋-玻色系统中纠缠态的量子Fisher信息量演化

基于典型的自旋-玻色模型,研究了具有类欧姆频谱的玻色场环境对量子参数估计精度的影响。原子受外场驱动时,采用二阶含时量子主方程和超算符方法得到了N个独立原子系统量子Fisher信息量的演化结果。计算结果表明:随着纠缠的原子数目增多,量子Fisher信息量增大,量子Fisher信息量的衰减也大大加快。在某些特征时间内,可以获得比标准量子极限更好的测量精度。在频谱幂指数较大的超欧姆玻色环境中,量子纠缠态Fisher信息量的衰减可以在一定程度上被抑制。

三量子比特系统中单个谐振子诱导的量子关联（英文）

我们考虑初始无关联并且与由一个谐振子构成的环境之间互相耦合的三量子比特系统.研究了量子比特与环境的耦合强度以及量子比特的初态对量子关联的影响,我们发现环境可以诱导量子关联,提出并证明了四个命题阐述谐振子如何调控三个量子比特中量子关联的分布,并且给出了产生量子关联的条件.特别地,对于弱耦合,我们不但能够获得很多的量子关联,而且还使量子比特系统和环境始终处于分离态.一般地,量子关联动力学是很复杂的,这是由于环境起着两个互相竞争的作用:一方面诱导出各个比特之间的量子关联;另一方面又使它们发生消相干,从而破坏量子关联.

原子核相互作用玻色子模型中的若干问题

在原子核的代数模型中，讨论了集体回弯效应，较高自旋的Ｆ旋混和对称态。