Non-Markovian finite-temperature two-time correlation functions of system operators: beyond the quantum regression theorem

An extremely useful evolution equation that allows systematically calculating the two-time correlation functions (CF's) of system operators for non-Markovian open (dissipative) quantum systems is derived. The derivation is based on perturbative quantum master equation approach, so non-Markovian open quantum system models that are not exactly solvable can use our derived evolution equation to easily obtain their two-time CF's of system operators, valid to second order in the system-environment interaction. Since the form and nature of the Hamiltonian are not specified in our derived evolution equation, our evolution equation is applicable for bosonic and/or fermionic environments and can be applied to a wide range of system-environment models with any factorized (separable) system-environment initial states (pure or mixed). When applied to a general model of a system coupled to a finite-temperature bosonic environment with a system coupling operator L in the system-environment interaction Hamiltonian, the resultant evolution equation is valid for both L = L(?) and L ≠ L(?) cases, in contrast to those evolution equations valid only for L = L(?) case in the literature. The derived equation that generalizes the quantum regression theorem (QRT) to the non-Markovian case will have broad applications in many different branches of physics. We then give conditions on which the QRT holds in the weak system-environment coupling case and apply the derived evolution equation to a problem of a two-level system (atom) coupled to the finite-temperature bosonic environment (electromagnetic fields) with L ≠ L(?).     

Communication: Partial linearized density matrix dynamics for dissipative, non-adiabatic quantum evolution

An approach for treating dissipative, non-adiabatic quantum dynamics in general model systems at finite temperature based on linearizing the density matrix evolution in the forward-backward path difference for the environment degrees of freedom is presented. We demonstrate that the approach can capture both short time coherent quantum dynamics and long time thermal equilibration in an application to excitation energy transfer in a model photosynthetic light harvesting complex. Results are also presented for some nonadiabatic scattering models which indicate that, even though the method is based on a "mean trajectory" like scheme, it can accurately capture electronic population branching through multiple avoided crossing regions and that the approach offers a robust and reliable way to treat quantum dynamical phenomena in a wide range of condensed phase applications.     

Some aspects of approach to equilibrium in classical and quantum systems

Investigations of general properties of time evolution of both classical and quantum systems show that the evolution (on a microscopic level) is reversible, and, if there is an approach to equilibrium, it exists only in the sense of weak convergence and necessarily in both directions of time. In this connection attempts to derive irreversibility and the approach to equilibrium in the sense of strong convergence and without any loss of information (using the so-called Lyapunov converters) are discussed. After demonstrating their drawbacks, an alternative approach is proposed based on the spectral properties of the generator of the group. The relevant spectral criteria for the approach of both classical and quantum ensembles to equilibrium are given, and the decisive role of loss of information in obtaining stronger variants of convergence is emphasized. The asymmetry between initial and any other state —consisting of different levels of information needed to prepare the states—is proposed as an adequate explanation of irreversibility. The importance of the method of complex scaling in this context is discussed, and its application in proving some spectral properties in the quantal Hamiltonian formulation is stressed.     

In vitro evolution of molecular cooperation in CATCH, a cooperatively coupled amplification system

Background: One of the key issues in the investigation of evolution is how complex systems evolved from simple chemical replicators. Theoretical work proposed several models in which complex replicating systems are kinetically stabilized. The development of powerful isothermal amplification technique allows complex nucleic acid based evolving in vitro systems to be set up, which may then serve to verify experimentally current theories of evolution. Recently such a system based on the 3SR (self-sustained sequence replication) reaction has been established to investigate the evolution of cooperation: the trans-cooperatively coupled CATCH (cooperative amplification by cross hybridization).Results: Over four rounds of serial transfer, the cooperatively coupled two species CATCH system evolved into a more complex cooperative four species system, which then was overgrown by CATCH-derived RNA-Z-like hairpin species. In contrast to the classical RNA-Z species, these molecules have complementary loop sequences and self-amplify using a dual mechanism that includes concentration-dependent phases of noncooperative and cooperative amplification.Conclusions: The evolution of a cooperative system, under conditions that were alternately unfavorable and favorable for cooperative amplification, led to a system showing facultative cooperation. This principle of facultative cooperation preserves the complexity of the system investigated and could have general implications for the evolution and stabilization of cooperation under oscillating reaction conditions.     

利用样本成分耗散物的非线性化学指纹图谱的检测方法、条件、特点和应用

分析了适用于测定样本非线性化学指纹图谱的热力学体系和动力学模型,结果表明,在远离平衡的封闭体系和无耗散物补充的敞开体系中,阻尼非线性化学反应对样本化学成分的群集表征和整体含量分析具有重要作用．以丙酮和葡萄糖等为耗散物的阻尼B—Z振荡非线性化学反应为例,研究了反应物种及其浓度、电极类型、温度、搅拌速率、样本种类及用量等影响非线性化学指纹图谱的因素,并对指纹图谱中样本化学成分的定量信息、指纹图谱的特点和应用等进行了研究．成功提出了用于鉴别和评价样本的非线性化学指纹图谱的检测条件和方法．     

Determining method, conditional factors, traits and applications of nonlinear chemical fingerprint by using dissipative components in samples

The thermodynamic systems and dynamic model suitable for determining the nonlinear chemical fingerprints of samples were analyzed.The results indicated that the damp nonlinear chemical reactions in close systems away from the equilibrium and open systems without the complementarity of the dissipation substances have important significance for the throng characterization and whole content analysis of chemical components in samples.Various factors influencing on nonlinear chemical fingerprint,such as reactant species and their concentrations,electrode types,temperature,stir rate,the sort,dosage and granularity of the sample,etc.were amply researched by a nonlinear chemistry reaction,namely,damp B-Z oscillation which used acetone and glucose as the main dissipative substances.In addition,the quantitative information on the whole of chemical components in samples and the traits and applications of the fingerprint were investigated.The method and its important conditions for determining nonlinear chemistry fingerprint used in distinguishing and evaluating complex samples were successfully put forward.     

Influence of environment induced correlated fluctuations in electronic coupling on coherent excitation energy transfer dynamics in model photosynthetic systems

Two-dimensional photon-echo experiments indicate that excitation energy transfer between chromophores near the reaction center of the photosynthetic purple bacterium Rhodobacter sphaeroides occurs coherently with decoherence times of hundreds of femtoseconds, comparable to the energy transfer time scale in these systems. The original explanation of this observation suggested that correlated fluctuations in chromophore excitation energies, driven by large scale protein motions could result in long lived coherent energy transfer dynamics. However, no significant site energy correlation has been found in recent molecular dynamics simulations of several model light harvesting systems. Instead, there is evidence of correlated fluctuations in site energy-electronic coupling and electronic coupling-electronic coupling. The roles of these different types of correlations in excitation energy transfer dynamics are not yet thoroughly understood, though the effects of site energy correlations have been well studied. In this paper, we introduce several general models that can realistically describe the effects of various types of correlated fluctuations in chromophore properties and systematically study the behavior of these models using general methods for treating dissipative quantum dynamics in complex multi-chromophore systems. The effects of correlation between site energy and inter-site electronic couplings are explored in a two state model of excitation energy transfer between the accessory bacteriochlorophyll and bacteriopheophytin in a reaction center system and we find that these types of correlated fluctuations can enhance or suppress coherence and transfer rate simultaneously. In contrast, models for correlated fluctuations in chromophore excitation energies show enhanced coherent dynamics but necessarily show decrease in excitation energy transfer rate accompanying such coherence enhancement. Finally, for a three state model of the Fenna-Matthews-Olsen light harvesting complex, we explore the influence of including correlations in inter-chromophore couplings between different chromophore dimers that share a common chromophore. We find that the relative sign of the different correlations can have profound influence on decoherence time and energy transfer rate and can provide sensitive control of relaxation in these complex quantum dynamical open systems.     

从色谱分离到智慧医疗所涉及共同的数学物理本质:不可逆性

溶质带中的众多分子在固定相-流动相环境中的色谱分离过程能够类比成疾病高危人群在多种暴露因素的疾病严重程度排序。色谱过程和机器疾病诊断-医嘱的共性在于对成分或个体疾病状态的分离或分类，二者都表现出随时间演化的不可逆性，但前者属于线性非平衡热力学而后者属于耗散结构的非线性非平衡热力学。当将科学视野从药物检测和制备扩展到循证医学、离散数学（公理集合论、概率测度）、人工智能（AI）-云计算领域时，对流-扩散方程和非平衡热力学中的不可逆性就成了色谱分离和智慧医疗两个交叉领域的共同的、核心的数学物理本质。抓住不可逆性这一学科间的共性特征，构建和发展这两个领域统一的、全覆盖的数学构架，具有深远的科学和现实意义。     

Reversibility of electrode reactions involving organic compounds

A general empirical approach allowing one to describe the kinetics and evaluate the mechanism of the electrode electron transfer reactions is offered. The approach is based on the electrode potentials, the vertical ionization potentials (oxidation), and the affinity to electron (reduction). An equation linking kinetic and thermodynamic parameters is derived. Electrode reactions involving organic compounds are discussed in polarographic terms. The conclusion is drawn that most electron transfer reactions involving organic compounds are reversible, and that the irreversibility of the net electrode reaction is due to the irreversibility of subsequent chemical and electrochemical stages. An experimental observation of the slow electron transfer is possible in the cases of a substantial reorganization of molecules in the presence of fast subsequent chemical and electrochemical reactions.     

Dissipative geometric phase and decoherence in parity-violating chiral molecules

Within a generalized Langevin framework for open quantum systems, the cyclic evolution of a two-level system is analyzed in terms of the geometric phase extended to dissipative systems for Ohmic friction. This proposal is applied to the dynamics of chiral molecules where the tunneling and parity violating effects are competing. The effect of different system-bath coupling functions in the dissipated energy is shown to be crucial to understand the behavior of the geometric phase as well as the decoherence displayed by the corresponding interference patterns.     

A continuum thermodynamical approach to electrochemical systems

This work focuses on formulating constitutive models for the bulk and double layer regions of an electrochemical system based on the fundamentals of modern continuum thermodynamics. Particularly, the constitutive models proposed accounting for transport phenomena in electrochemical systems by emphasizing the possibility of cross-coupling between two or more phenomena. Upon deriving a set of thermodynamic restrictions from the Müller-Liu approach of the second law of thermodynamics and axioms of constitutive theory, non-equilibrium quantities are examined in detail, and constitutive answers of the bulk and double layer regions are discussed. Moreover, the conditions for the thermodynamic equilibrium are evaluated for each region as well as the occurrence of dissipative mechanisms. Besides offering a proper formulation for non-equilibrium electrochemical systems, the approach described in this work can be easily extended to more complex chemical systems.     

量子混沌在谱涨落统计特征上的表象

通过对Ｈｅｎｏｎ－Ｈｅｉｌｅｓ模型、Ｂａｒｂａｎｉｓ模型和刚环转球模型这两类三种守恒体系之对应量子体系的研究，具体地剖析了本征值谱涨落统计特征与体系动力学行为的联系，说明了量子混沌现象的两种表现形式。同时，通过将本质上属于经典耗散系范畴的Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ模型之演化方程哈密顿化，发现其量子对应系本征值谱的涨落统计特征超出了Ｐｏｉｓｓｏｎ－ＧＯＥ（Ｗｉｇｎｅｒ）或ＧＵＥ框架。揭示出经典耗散     

Nonresonant holeburning in the Terahertz range: Brownian oscillator model

The response to the field sequence of nonresonant hole burning, a pump-wait-probe experiment originally designed to investigate slow relaxation in complex systems, is calculated for a model of Brownian oscillators, thus including inertial effects. In the overdamped regime the model predictions are very similar to those of the purely dissipative stochastic models investigated earlier, including the possibility to discriminate between dynamic homogeneous and heterogeneous relaxation. The case of underdamped oscillations is of particular interest when low-frequency excitations in glassy systems are considered. We show that also in this situation a frequency selective modification of the response should be feasable. This means that it is possible to specifically address various parts of the spectrum. An experimental realization of nonresonant holeburning in the Terahertz regime therefore is expected to shed further light on the nature of the vibrations around the so-called boson peak.     

Optimal control of quantum non-Markovian dissipation: reduced Liouville-space theory

An optimal control theory for open quantum systems is constructed containing non-Markovian dissipation manipulated by an external control field. The control theory is developed based on a novel quantum dissipation formulation that treats both the initial canonical ensemble and the subsequent reduced control dynamics. An associated scheme of backward propagation is presented, allowing the efficient evaluation of general optimal control problems. As an illustration, the control theory is applied to the vibration of the hydrogen fluoride molecule embedded in a non-Markovian dissipative medium. The importance of control-dissipation correlation is evident in the results.     

Dissipative Synthetic DNA‐Based Receptors for the Transient Loading and Release of Molecular Cargo

Supramolecular chemistry is moving into a direction in which the composition of a chemical equilibrium is no longer determined by thermodynamics but by the efficiency with which kinetic states can be populated by energy consuming processes. Herein, we show that DNA is ideally suited for programming chemically fueled dissipative self‐assembly processes. Advantages of the DNA‐based systems presented in this study include a perfect control over the activation site for the chemical fuel in terms of selectivity and affinity, highly selective fuel consumption that occurs exclusively in the activated complex, and a high tolerance for the presence of waste products. Finally, it is shown that chemical fuels can be used to selectively activate different functions in a system of higher complexity embedded with multiple response pathways.     

Altlastsanierung mit Huminstoffsystemen. Prinzipien der Natur in der Umwelttechnologie

A former open‐cast pit was used as deposit for wastewater from lignite‐pyrolysis processes until 1990. The lake formed was filled with highly toxic and dark phenolic water. Traditional remediation methods were not applicable and it was therefore necessary to develop a new ecologically and economically acceptable remediation strategy. The full‐scale remediation of this lake was realized as the results of an interdisciplinary research by a team of chemists, microbiologists and hydrologists. The newly developed complex remediation strategy is mainly based on the knowledge of the chemistry of dissolved‐organic matter systems. We could show the similarity of dissolved natural humic substances to the industrially formed black phenolic macromolecules formed in the wastewater deposit lake. Transfer of the knowledge originating from research on humic substances, their chemical reactions and microbiological interactions and on the hydrological behaviour of natural lakes helped to create a successful mild remediation strategy. As a result of the full‐scale application, after 10 years now, a new ecosystem with clear water was formed without any danger for the environment.     

Introducing nonlinear,multivariate ‘Predictor Surfaces’ for quantitative modeling of chemical systems with higher-order,coupled predictor variables

Innovations in chemometrics are required for studies of chemical systems which are governed by nonlinear responses to chemical parameters and/or interdependencies (coupling) among these parameters. Conventional and linear multivariate models have limited use for quantitative and qualitative investigations of such systems because they are based on the assumption that the measured data are simple superpositions of several input parameters. ‘Predictor Surfaces’ were developed for studies of more chemically complex systems such as biological materials in order to ensure accurate quantitative analyses and proper chemical modeling for in-depth studies of such systems. Predictor Surfaces are based on approximating nonlinear multivariate model functions by multivariate Taylor expansions which inherently introduce the required coupled and higher-order predictor variables.     

Time-dependent density functional theory of open quantum systems in the linear-response regime

Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a noninteracting open Kohn-Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C(2 +) atom including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on the Go?rling-Levy perturbation theory is calculated.     

非平衡定态化学反应体系对细致平衡偏离的不可逆性之随机热力学量度

在随机描述的层次上,成功地构筑了非平衡定态化学反应体系对细致平衡偏离的不可逆性之随机热力学判据.基于Fokker-Planck方程建立了连续Markov过程系统的随机熵平衡方程,发现在随机态空间中随机熵的时间变率亦可分为源项和流项两部分贡献.对于化学反应体系,作为态空间源项的随机熵产生可作为偏离细致平衡不可逆性的合适度量,此泛函量的零值标志着细致平衡.进一步借助按系统广度量的Ω展开法,通过对随机力及共轭的随机流的分析揭示态空间中的随机熵产生仅源于状态对细致平衡的偏离,并主要来自非Poisson涨落的贡献,因而可作为随机热力学量去判别和量度化学反应体系对细致平衡的偏离.