Glass-forming liquids,anomalous liquids,and polyamorphism in liquids and biopolymers

Summary Glass formation in nature and materials science is reviewed and the recent recognition of polymorphism within the glassy state, polyamorphism, is discussed. The process by which the glassy state originates during the continuous cooling or viscous slowdown process, is examined and the three canonical characteristics of relaxing liquids are correlated through the fragility. The conversion of strong liquids to fragile liquids by pressure-induced coordination number increases is discussed, and then it is shown that for the same type of system it is possible to have the same conversion accomplished via a first-order transition within the liquid state. The systems in which this can happen are of the same type which exhibit polyamorphism, and the whole phenomenology can be accounted for by a recent simple modification of the van der Waals model for tetrahedrally bonded liquids. The concept of complex amorphous systems which can lose a significant number of degrees of freedom through weak first-order transitions is then used to discuss the relation between native and denatured hydrated proteins, since the latter have much in common with plasticized chain polymer systems. Finally, we close the circle by taking a short-time-scale phenomenon given much attention by protein physicists,viz., the onset of an anomaly in the Debye-Waller factor with increasing temperature, and showing that for a wide variety of liquids, including computer-simulated strong and fragile ionic liquids, this phenomenon is closely correlated with the experimental glass transition temperature. This implies that the latter owes its origin to the onset of strong anharmonicity in certain components of the vibrational density of states (evidently related to the boson peak) which then permits the system to gain access to its configurational degrees of freedom. The more anharmonic these vibrational components, the closer to the Kauzmann temperature will commence the exploration of configuration space and, for a given configurational microstate degeneracy, the more fragile the liquid will be. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Thermal vacuum state corresponding to squeezed chaotic light and its application

For the density operator(mixed state) describing squeezed chaotic light(SCL) we search for its thermal vacuum state(a pure state) in the real-fictitious space. Using the method of integration within ordered product(IWOP) of operators we find that it is a kind of one- and two-mode combinatorial squeezed state. Its application in evaluating the quantum fluctuation of photon number reveals: the stronger the squeezing is, the larger a fluctuation appears. The second-order degree of coherence of SCL is also deduced which shows that SCL is classic. The new thermal vacuum state also helps to derive the Wigner function of SCL.     

Phänomenologische Zustandsgrößen,Regressions-Schwankungs-Sätze und Transportkoeffizienten in linearen Onsager-Systemen

Starting from Onsager's assumption that the dynamical equilibrium correlations can be separated into a microscopic and a hydrodynamic part it is shown how to obtain phenomenological state variables in non-equilibrium, regression fluctuation theorems and (in some important cases) microscopic representations of thermal transport coefficients. The results are demonstrated for “pure” heat conduction, but most of them can be easily extended to systems which are described initially by the densities of dynamical constants.     

奇相干光源的测量设备无关量子密钥分配研究

刻画了奇相干光源的光子数分布特征,研究了奇相干光源下诱骗态测量设备无关量子密钥分配系统的密钥生成率与安全传输距离的关系,推导了奇相干光源下的计数率下界和误码率上界.仿真结果表明,奇相干光源光子数分布中多光子脉冲的比例低于弱相干光,可以有效提高诱骗态测量设备无关密钥分配系统的最大安全通信距离,为实用的量子密钥分配实验提供了重要的理论参数.     

Joint Extension of States of Subsystems for a CAR System

 The problem of existence and uniqueness of a state of a joint system with given restrictions to subsystems is studied for a Fermion system, where a novel feature is non-commutativity between algebras of subsystems. For an arbitrary (finite or infinite) number of given subsystems, a product state extension is shown to exist if and only if all states of subsystems except at most one are even (with respect to the Fermion number). If the states of all subsystems are pure, then the same condition is shown to be necessary and sufficient for the existence of any joint extension. If the condition holds, the unique product state extension is the only joint extension. For a pair of subsystems, with one of the given subsystem states pure, a necessary and sufficient condition for the existence of a joint extension and the form of all joint extensions (unique for almost all cases) are given. For a pair of subsystems with non-pure subsystem states, some classes of examples of joint extensions are given where non-uniqueness of joint extensions prevails. Received: 17 May 2002 / Accepted: 16 January 2003 Published online: 17 April 2003 Communicated by D. Buchholz and K.Fredenhagen     

Expectation Value Theorem for Thermo Vacuum States of Optical Chaotic Field and Negative-Binomial Field

For the density operator (mixed state) describing chaotic light and negative-binomial field there exist the corresponding thermal vacuum state (pure state) in the real-fictitious space. Using the method of integration within ordered product of operators we find the expectation value theorem in these two thermo vacuum states respectively. The thermal average theorem of translation operator is also deduced. Application of the new thermo vacuum state in calculating photon number disturibution and fluctuation and thermal average is presented.     

The time evolution of fluctuation algebra in mean field theories

Fluctuation algebra is defined for equilibrium states of mean field theories. The time evolution is calculated; and, in contrast to interactions with finite range, the fluctuation algebra is not in a KMS state with respect to this time evolution though the underlying quasilocal state. If the system is coupled to an other system mimicking a laser then the evolution depends on the underlying mean field theory and shows varying large time behaviour, so that the fluctuations either rotate or increase linearly or exponentially in time, in correspondence to the stability of the underlying quasilocal state.     

Covariant Thermodynamics of Quantum Systems: Passivity, Semipassivity, and the Unruh Effect

According to the Second Law of Thermodynamics, cycles applied to thermodynamic equilibrium states cannot perform any work (passivity property of thermodynamic equilibrium states). In the presence of matter this can hold only in the rest frame of the matter, as moving matter drives, e.g., windmills and turbines. If, however, a homogeneous and stationary state has the property that no cycle can perform more work than an ideal windmill, then it can be shown that there is some inertial frame where the state is a thermodynamic equilibrium state. This provides a covariant characterization of thermodynamic equilibrium states. In the absence of matter, cycles should perform work only when driven by nonstationary inertial forces caused by the observer's motion. If a (pure) state of a relativistic quantum field theory behaves this way, it satisfies the spectrum condition and exhibits the Unruh effect.     

Fluctuations of quantum entanglement

It is emphasized that quantum entanglement determined in terms of the von Neumann entropy operator is a stochastic quantity and, therefore, can fluctuate. The rms fluctuations of the entanglement entropy of two-qubit systems in both pure and mixed states have been obtained. It has been found that entanglement fluctuations in the maximally entangled states are absent. Regions where the entanglement fluctuations are larger than the entanglement itself (strong fluctuation regions) have been revealed. It has been found that the magnitude of the relative entanglement fluctuations is divergent at the points of the transition of systems from an entangled state to a separable state. It has been shown that entanglement fluctuations vanish in the separable states.     

四粒子任意纠缠态的控制隐形传输

隐形传送体系的总量子态的实质是完备基展开与变换算符的线性叠加,若变换算符可逆,且为幺正算符,则进行相应的逆幺正变换操作即可实现量子态的隐形传送;若变换算符不可逆,则不能实现任意量子态的隐形传送.本文由变换算符给出四粒子任意纠缠态的控制隐形传输的理论分析,给出控制方对拥有的粒子进行Hadamard门变换与不进行.Hadamard门变换的解释.     

Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations

The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper. These equations, in particular, include the ones which are rigorously derived recently as the Saint-Venant system for the motion of shallow water, from the Navier-Stokes system for incompressible flows with a moving free surface [14]. These compressible systems are degenerate when vacuum state appears. We study initial-boundary-value problems for such systems for both bounded spatial domains or periodic domains. The dynamics of weak solutions and vacuum states are investigated rigorously. First, it is proved that the entropy weak solutions for general large initial data satisfying finite initial entropy exist globally in time. Next, for more regular initial data, there is a global entropy weak solution which is unique and regular with well-defined velocity field for short time, and the interface of initial vacuum propagates along the particle path during this time period. Then, it is shown that for any global entropy weak solution, any (possibly existing) vacuum state must vanish within finite time. The velocity (even if regular enough and well-defined) blows up in finite time as the vacuum states vanish. Furthermore, after the vanishing of vacuum states, the global entropy weak solution becomes a strong solution and tends to the non-vacuum equilibrium state exponentially in time.     

Quantum fluctuation in excited states of mesoscopic LC circuits at finite temperature

We discuss quantum fluctuation in excited states(named thermo number states) of mesoscopic LC circuits at a finite temperature.By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation.The result shows that the noise becomes larger when either temperature or the excitation number increases.     

Enhancing the capability of controlling quantum systems via ancillary systems

This paper explores the potential of controlling quantum systems by introducing ancillary systems and then performing unitary operation on the resulting composite systems. It generalizes the concept of pure state controllability for quantum systems and establishes the link between the operator controllability of the composite system and the generalized pure state controllability of its subsystem. It is constructively demonstrated that if a composite quantum system can be transferred between any pair of orthonormal pure vectors, then its subsystem is generalized pure-state controllable. Furthermore, the unitary operation and the coherent control can be concretely given to transfer the system from an initial state to the target state. Therefore, these properties may be potentially applied in quantum information, such as manipulating multiple quantum bits and creating entangled pure states. A concrete example has been given to illustrate that a maximally entangled pure state of a quantum system can be generated by introducing an ancillary system and performing open-loop coherent control on the resulting composite system.     

类氢原子核质量对电子状态的影响

在孤立的两体复合系统中,讨论其中一体的变化如何影响另一体的状态,有助于了解单粒子混合态与纯态的关系.本文讨论5个孤立的一维类氢原子模型系统,原子核的质量互不相同.这5个两体(电子与原子核)复合系统的相对运动状态都处于纠缠态,其中电子状态都用约化密度矩阵表示的混合态描述.在原子核质量趋近无穷大的一维氢原子模型中,电子处于纯态.为比较这里的纯态和混合态,在位置表象中计算了这些混合态的纯度、它们分别与纯态的保真度、以及所有这些态的相干性.研究表明,原子核的质量越大,纯度和保真度越接近1,混合态的相干性与纯态的也越接近.这样的纯态及其相干性可以是这种混合态及其相干性的近似,并与原子核及库仑相互作用有关.     

Protection of Quantum Correlation Through the Quantum Erasing Effect

By taking into account the quantum erasing effect(QEE), the quantum discord (QD) behavior of a two-qubit system with different initial states are investigated in detail. We find that the quantum correlation can be saved under a scheme of two spatially separated atoms, each located in a leaky cavity through the quantum erasing method. It is shown that QEE can weaken the effects of decoherence, and preserve the maximum information of the coherent item. No matter whether the two atoms are in the mixted or pure state, one can robusty save their initial quantum correlation even the number of erasing events is finite. If one limit the erasing events N → ∞, the QEE can be used to protect the initial quantum correlation independently of the state in which it is stored, the values of QD is always nearly equal to the initial QD values, and it is nearly independent of the decoherence, which imply us more encourage strategy for protecting the quantum correlation properties in some quantum systems.     

On the algebra of symmetries of Laplace and Dirac operators

We consider a generalization of the classical Laplace operator, which includes the Laplace–Dunkl operator defined in terms of the differential-difference operators associated with finite reflection groups called Dunkl operators. For this Laplace-like operator, we determine a set of symmetries commuting with it, in the form of generalized angular momentum operators, and we present the algebraic relations for the symmetry algebra. In this context, the generalized Dirac operator is then defined as a square root of our Laplace-like operator. We explicitly determine a family of graded operators which commute or anticommute with our Dirac-like operator depending on their degree. The algebra generated by these symmetry operators is shown to be a generalization of the standard angular momentum algebra and the recently defined higher-rank Bannai–Ito algebra.     

Superposition, Entropy and Schmidt Decomposition of States

Superposition and entropy are compared using the language of the logic of quantum mechanics. It is pointed out that a finite value of the relative quantum entropy of states implies a superposition relation between the states themselves. The superposition relation is then studied by comparing the pure state of the compound system with the product of the reduced states and an intermediate Schmidt state. All the corresponding relative quantum entropies are evaluated in terms of the Schmidt coefficients of the global pure state. Some of the results are extended in case the compound system is in a state represented by a general density operator.     

Electron self-trapping at quantum and classical critical points

Using Feynman path integral technique estimations of the ground state energy have been found for a conduction electron interacting with order parameter fluctuations near quantum critical points. In some cases only singular perturbation theory in the coupling constant emerges for the electron ground state energy. It is shown that an autolocalized state (quantum fluctuon) can be formed and its characteristics have been calculated depending on critical exponents for both weak and strong coupling regimes. The concept of fluctuon is considered also for the classical critical point (at finite temperatures) and the difference between quantum and classical cases has been investigated. It is shown that, whereas the quantum fluctuon energy is connected with a true boundary of the energy spectrum, for classical fluctuon it is just a saddle-point solution for the chemical potential in the exponential density of states fluctuation tail.     

Thermo Vacuum State for Describing the Density Operator of Photon-subtracted Squeezed Chaotic Light

For the density operator describing s?photon-subtracted squeezed chaotic light (PSSCL) we search for its thermo vacuum state (a pure state) in the real-fictitious space. We find that it reduces to a thermo vacuum state of squeezed chaotic light when s = 0, and to a thermo vacuum state of the optical negative binomial field when no squeezing. The new thermo vacuum state simplifies calculating photon number average, quantum fluctuation and Mandel’s Q parameter of PSSCL. Using the method of integration within ordered product (IWOP) of operators we also derive the normalization coefficient and explicitly analytical expressions of Wigner function for PSSCL.