Dynamics of non-Markovianity in the presence of a driving field

We investigate a two-level system in a cavity QED by considering the effects of amplitude damping, phase damping and driving field. We have studied the non-Markovianity in resonance and non-resonance limits in the presence of these effects using Breuer–Laine–Piilo (BLP) non-Markovianity measure (N_BLP). The evolution of the system is derived using the time convolutionless (TCL) master equation. In some conditions, it is shown that in the presence of a driving field, the N_BLP increases in the resonance and non-resonance limits. We have also found the exact solution of the master equation in order to investigate the effect of temperature- and environment-excited states. We have shown that the behaviour of non-Markovianity is very different from what one can see from the TCL approach. We have also presented some explanation about the behaviour of non-Markovianity in the exact solution using quantum discord (QD).     

Non-Markovian Process in the Interaction Between a Four-Level N-Type Atom with a Cavity Field Surrounded by a Kerr Medium

We have investigated the dynamics of a four-level N-type atom in cavity QED with consideration to the Kerr effect. The non-Markovianity of the system has been studied using the Breuer-Laine-Piilo (BLP) measure (N _{B L P} ). Moreover the effects of system parameters like temperature and atom-field coupling have also been discussed. The evolution equation of the system has been derived using the time convolution-less(TCL) master equation. Some interesting behaviour of the system and their reasons are discussed.

     

Delineating incoherent non-Markovian dynamics using quantum coherence

We introduce a method of characterization of non-Markovianity using coherence of a system interacting with the environment. We show that under the allowed incoherent operations, monotonicity of a valid coherence measure is affected due to non-Markovian features of the system–environment evolution. We also define a measure to quantify non-Markovianity of the underlying dynamics based on the non-monotonic behavior of the coherence measure. We investigate our proposed non-Markovianity marker in the behavior of dephasing and dissipative dynamics for one and two qubit cases. We also show that our proposed measure captures the back-flow of information from the environment to the system and compatible with well known distinguishability criteria of non-Markovianity.     

不同滤波方法在去趋势波动分析中去噪的应用比较

研究了连续噪声和尖峰噪声对去趋势波动分析的影响,发现噪声的存在使得双对数曲线在尺度较小时发生了"转折"现象.针对这一问题,文中采用三种不同滤波方法对理想时间序列进行了实验,结果表明,多级Vondrak滤波得到的高频序列与真实噪声序列无论是在强度还是在演变趋势上都展现出惊人的一致性,低频滤波序列的去趋势波动分析结果与真实信号十分接近,多级Vondrak滤波基本上能够消除由于噪声所引起的"转折"现象,而且这一研究结果对于滤波周期阈值的依赖性并不太大.多点滑动加权平均滤波虽然能够在一定程度上减轻噪声对于去趋势波动的影响,但不能从根本上消除由于噪声所引起的"转折"现象.快速傅里叶滤波在选择合适的滤波周期阈值时,能够基本消除噪声对去趋势波动分析的影响,但是由于其滤波结果对于滤波周期阈值的依赖较大,在实际应用中滤波周期阈值的选取比较困难.因此,多级Vondrak滤波是消除噪声对去趋势波动分析结果影响的一种有效的途径. 关键词： 多级Vondrak滤波 去趋势波动分析 多点滑动加权平均滤波 快速傅里叶滤波     

Non-Markovianity and initial correlations for the generalized Lindblad master equation

Taking a two-level system interacting with a two-band environment as an example, we discuss the non-Markovianity and initial system-environment correlations for the generalized Lindblad master equation by using a recently introduced measure given by Breuer et al. Our results show that the initial states of the environment and initial system-environment correlations have strong effects on the non-Markovianity of the reduced system. Moreover, we also show that information and energy can flow in different directions, i.e., energy flows to the system while information flows from the system, which is quite different from previous results.     

On the Ground State Energy of the¶Fractional Quantum Hall Effect

Let I(N,R) be the ground state energy of N electrons confined to a disc of radius R with a constant magnetic field B in the perpendicular direction. We show that, in the limit and , where ν is the Landau level filling factor, we have with . The factor is obtained through the solution of an extreme-value problem in measure theory. Received: 10 November 1998 / Accepted: 27 January 1999     

Non-Markovianity in the presence of multiple thermal environments via collision model

By means of the collision model, we study the non-Markovianity of an open quantum system S being coupled to M thermal reservoirs. In our model, each reservoir is modeled as a chain of ancillas whose intracollisions account for the occurrence of non-Markovian dynamics. We show that by incorporating M reservoir ancillas into the system, the non-Markovian dynamics of S can be embedded in the extended system that experiences a completely Markovian dynamics. The number M of involved reservoirs can thus be identified as the memory depth and determines the degree of the non-Markovianity. In the equilibrium case with identical temperatures for all the reservoirs, we show that though the non-Markovianity is proportional to M in the zero and relatively low temperature regimes, in the relatively high temperature regime such proportional relation holds only for the weak intracollisions of the reservoir ancillas. In the nonequilibrium situation, we examine the effect of temperature difference of reservoirs on the non-Markovianity. Focusing on a simple situation with two reservoirs, we observe that the nonzero temperature difference has a significant impact on the non-Markovianity.     

On the noisiness of steady state and intermittent noises

An experiment was designed to investigate the effects of sound level (L_A), number of single noises (N), level of total energy (L_T) and mean energy level ($\text{dB(A)}$) on the noisiness of steady state and intermittent noises. With the level and duration of pink noise controlled with a sound system called “Programmable Sound Control System”, 16 kinds of intermittent noises and 22 kinds of steady state noises were prepared. Seven subjects judged the noisiness of these stimuli by magnitude estimation. Their judgments were converted into the corresponding sound level (point of subjective equality, abbreviated PSE) by using the power function obtained between sound level and magnitude estimation for the seven kinds of steady state noises. As a result, the level of total energy and mean energy level were found inappropriate to evaluate the noisiness of intermittent noises though they showed high correlation with the noisiness of steady state noises. PSE's of the intermittent noises showed good correspondence with L_N, which is expressed by the equation $\text{L}{}_{\mathrm{N}}\text{=}\text{dB(A)}\text{+ 10}\text{log}\text{N}$. L_N could also be applied to steady state noises if it was assumed that a steady state noise with a duration of D_T is equal to a 2000 ms noise presented $\text{N (}\text{D}{}_{\mathrm{T}}\text{2000}\text{)}$ times. This result suggests that L_N is a good measure of the noisiness of both steady state and intermittent noises.     

Nonequilibrium stationary states of harmonic chains with bulk noises

We consider a chain composed of N coupled harmonic oscillators in contact with heat baths at temperature T _ℓ and T _r at sites 1 and N respectively. The oscillators are also subjected to non-momentum conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier’s law. Here we describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type.     

Memory Effects in High-Dimensional Systems Faithfully Identified by Hilbert–Schmidt Speed-Based Witness

A witness of non-Markovianity based on the Hilbert–Schmidt speed (HSS), a special type of quantum statistical speed, has been recently introduced for low-dimensional quantum systems. Such a non-Markovianity witness is particularly useful, being easily computable since no diagonalization of the system density matrix is required. We investigate the sensitivity of this HSS-based witness to detect non-Markovianity in various high-dimensional and multipartite open quantum systems with finite Hilbert spaces. We find that the time behaviors of the HSS-based witness are always in agreement with those of quantum negativity or quantum correlation measure. These results show that the HSS-based witness is a faithful identifier of the memory effects appearing in the quantum evolution of a high-dimensional system with a finite Hilbert space.     

On the (3, N) Maurer-Cartan equation

Abstract

Deformations of the 3-differential of 3-differential graded algebras are controlled by the (3, N) Maurer-Cartan equation. We find explicit formulae for the coefficients appearing in that equation, introduce new geometric examples of N-differential graded algebras, and use these results to study N Lie algebroids.     

IR Evidences for N-9 and N-7 Regioisomers of the Acyclic Purine Nucleoside Analogues

The IR spectra have been recorded in the solid state for the parent molecule, 6-(N-pyrrolyl)purine (1) and its N-9-and N-7-substituted derivatives: 9-and 7-(2-hydroxyprop-1-yl)-6-(N-pyrrol-1-yl)purine (2 and 3), 9-and 7-(2-acetoxyprop-1-yl)-6-(N-pyrrol-1-yl)purine (4 and 5), 9-and 7-(2,3-dihydroxyprop-1-yl)-6-(N-pyrrol-1-yl)purine (6 and 7) as well as 9-and 7-(2,3-diacetoxyprop-1-yl)-6-(N-pyrrol-1-yl)purine (8 and 9). Analysis of the characteristic bands has proved to be useful in differentiating between N-9 and N-7 regioisomers.     

The Newhouse set has a positive Hausdorff dimension

The Newhouse phenomenon of infinitely many coexisting periodic attractors is studied in its simplest form. One shows that the corresponding parameter set (the Newhouse set)J _N has a strictly positive Hausdorff dimension. This result is stronger than that of Tedeschini-Lalli and Yorke [Commun. Math. Phys.106, 635 (1986)] concerning the Lebesgue measure of the Newhouse set; and is complementary to our knowledge on the topological properties ofJ _N, namely it is a residual set, hence uncountable and everywhere dense in a parameter interval.     

Monotonicity Properties of Certain Measures over the Two-Level Quantum Systems

We demonstrate – using the case of the two-dimensional quantum systems – that the 'natural measure in the space of density matrices describing N-dimensional quantum systems' proposed by yczkowski et al. [Phys. Rev. A 58 (1998), 883] does not belong to the class of normalized volume elements of monotone metrics on the quantum systems. Such metrics possess the statistically important property of being decreasing under stochastic mappings (coarse-grainings). We do note that the proposed natural measure (and certain evident variations upon it) exhibit quite specific monotonicity characteristics, but not of the form required for membership in that distinguished class.     

Realization ofU q (so(N)) within the differential algebra onR q N

We realize the Hopf algebraU _q–1 (so(N)) as an algebra of differential operators on the quantum Euclidean spaceR _q ^N . The generators are suitableq-deformed analogs of the angular momentum components on ordinaryR ^N . The algebra Fun(R _q ^N ) of functions onR _q ^N splits into a direct sum of irreducible vector representations ofU _q–1 (so(N)); the latter are explicitly constructed as highest weight representations.     

Two Mn(II) and Zn(II) Coordination Polymers: Aqueous-Phase Detection of Nitroaromatic Explosives and Protective Effect on Atherosclerosis

Via the solvothermal reaction between Zn(II) or Mn(II) salts and 5-(3,4-dicarboxylphenoxy)nicotinic acid (H₃L) ligand, a trifunctional N,O-building block having three diverse kinds of functional groups (O-ether, N-pyridyl and COOH), two new coordination polymers (CPs) could be generated, and their chemical formulae respectively are {[Mn₃(L)₂(H₂O)₂]·4H₂O} (1) and {[Zn(HL)]·NMP} (2). The complex 2 based on Zn(II) possesses high efficiency of fluorescence quenching for the nitrophenol (2,4,6-trinitrophenol, TNP; 4-nitrophenol, 4-NP; 3-nitrophenol, 3-NP; 2-nitrophenol, 2-NP) in the aqueous solution. Furthermore, the treatment activity of compounds on the atherosclerosis was assessed, and relevant mechanism was investigated. First of all, the ELISA assay was used to measure the content of the inflammatory cytokines released into the plasma. Besides, the levels of the NF-κb signaling pathway in the vascular endothelial cells were measured with real time RT-PCR. The hemolysis test was conducted in this research to measure the biocompatibility of the new compound.

     

A Note on the Third Family of N=2 Supersymmetric KdV Hierarchies

Abstract

We propose a hamiltonian formulation of the N = 2 supersymmetric KP type hierarchy recently studied by Krivonos and Sorin. We obtain a quadratic hamiltonian structure which allows for several reductions of the KP type hierarchy. In particular, the third family of N = 2 KdV hierarchies is recovered. We also give an easy construction of Wronskian solutions of the KP and KdV type equations.     

Superstring on pp-wave orbifold from large-N quiver gauge theory

We extend the proposal of Berenstein, Maldacena and Nastase to the Type IIB superstring propagating on a pp-wave over the R ⁴/Z _k orbifold. We show that first-quantized free string theory is described correctly by the large-N, fixed gauge coupling limit of [U(N)] ^k quiver gauge theory. We propose a precise map between gauge theory operators and string states for both untwisted and twisted sectors. We also compute leading-order perturbative correction to the anomalous dimensions of these operators. The result is in agreement with the value deduced from the string energy spectrum, thus substantiating our proposed operator-state map. Received: 14 March 2002 / Published online: 5 July 2002     

Complex Anti-Self-Dual Connections on a Product of Calabi–Yau Surfaces and Triholomorphic Curves

We study the adiabatic limit of a sequence of Ω-anti-self-dual connections on unitary bundles over a product of two compact Calabi–Yau surfaces M×N by scaling metrics to shrink N to a point. We show that after fixing gauge transformations, a subsequence of the N-components of these connections converges to a triholomorphic curve from M away from a Cayley cycle in M×N to the moduli space of instantons on M×N modulo gauge equivalence in the Hausdorff topology, and converges on the blow-up locus to a family, which is parameterized by the Cayley cycle, of triholomorphic curves from C ² to . Received: 22 May 1998 / Accepted: 26 August 1998     

Quantum Non-Markovianity via the Covariance Matrix

In this paper, we propose a new characterization of non-Markovian quantum evolution based on the covariance matrix. The fundamental properties of covariance matrices are elucidated. The measure captures quite directly the characteristics of non-Markovianity from the perspective of uncertainty. We consider several typical examples and compare the covariance matrix characterization of quantum non-Markovianity with Fisher-information matrix, divisibility and the Breuer-Laine-Piilo characterization of quantum non-Markovianity.