Dynamical Entropy of Generalized Quantum Markov Chains on Gauge-invariant C *-algebras

We prove that the mean entropy and the dynamical entropy are equal for generalized quantum Markov chains on gauge-invariant C ^*-algebras.     

Conditional entropy in algebraic statistical physics

The notion of conditional entropy as entropy of conditional state on C^*-algebra with respect to its C^*-subalgebra ₁ is introduced. It is proved that for a compatible state σ on (which admits the conditional expectation of Umegaki-Takesaki) the mean conditional entropy in an a priori state σ₁ on ₁ is equal to the difference of the entropy of the state σ on and the entropy of the state σ₁ on ₁. The conditional entropy enables us to define the input-output information of a quantum communication channel in analogy to the classical Shannon formula.     

Topological entropy for endomorphisms of localC *-algebras

A notion of topological entropy for endomorphisms of localC ^*-algebras is introduced as a generalisation of the topological entropy of classical dynamical systems. The basic properties are derived and a series of calculations are presented.     

On a question of Bratteli and Robinson

We give a partial answer to a question raised by Bratteli and Robinson, by showing that the mean entropy equals the mean conditional entropy for a large class of translation invariant states. In the general case we show that equality holds if and only if the mean conditional entropy is upper semicontinuous in the w^*-topology.     

Dimension and Dynamical Entropy for Metrized <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">*</Emphasis></Superscript>-Algebras

 We introduce notions of dimension and dynamical entropy for unital C ^* -algebras ``metrized' by means of , which are complex-scalar versions of the Lip-norms constitutive of Rieffel's compact quantum metric spaces. Our examples involve the UHF algebras and noncommutative tori. In particular we show that the entropy of a noncommutative toral automorphism with respect to the canonical coincides with the topological entropy of its commutative analogue. Received: 13 February 2002 / Accepted: 20 August 2002 Published online: 22 November 2002     

Density correlation function and dynamic transient exponents for liquid helium at and aboveT λ

The critical dynamics of liquid helium are studied by means of renormalized field theory on the basis of the symmetric planar-spin model of Halperin, Hohenberg, and Siggia. The stability problem of the dynamic fixed point is discussed in detail. Two-loop results suggest, but do not establish, the stability of the dynamic scaling fixed point. The previously found small fixed point valuew ^*~O(0.15) is tentatively confirmed which implies a small ratio of relaxation rates of the order parameter and the entropy. The ensuing dynamic transient exponents are calculated. The density correlation function is determined toO(ε=4?d) at and aboveT _λ. Its properties in the casew ^*?1 provide quantitative support for the recently proposed explanation of the discrepancy between theory and light scattering experiments. A small value ofw ^* implies pronounced peaks of the frequency spectrum at finite frequencies at and aboveT _λ. It also suppresses the temperature dependence of finite-frequency properties over an enlarged critical region as found in light scattering measurements. The quantitative relation between the value ofw ^*>0 and observable properties of the frequency spectrum is computed.     

Convexity,unitary invariance and monotonicity under completely positive maps over injective vN-algebras

The action of dynamical maps over the normal state space of a properly infinite, injective vN-algebra is analyzed and shown to be equivalent to convec unitary mixing with respect to some suitably chosen C ^*-subalgebra. As an application, it is shown that the conditions usually imposed on (convex) relative state functionals (like the relative entropy etc.) necessarily imply their decrease under completely positive maps.     

Generalization of the Williams--Landel--Ferry equation

Based on the model of Gibbs-Di Marzio we write the logarithmic shift factor without explicit knowledge of the form for the entropy, an expression which enables us to write a generalization of the Williams--Landel--Ferry equation. Comparison with the empirical relation of Williams--Landel--Ferry and use of the fact that the model exhibits the existence of a isoentropic temperature T₀ for which the configurational entropy of the system vanishes, leads to a value of the isoentropic temperature for which the configurational entropy of the system vanishes. The form for the specific heat proposed by Dowell and Di Marzio based on the lattice model of Gibbs-Di Marzio for the glass transition of polymeric substances, has been used by García-Colín et al. to find the molar configurational entropy (MCE) of glass. Knowledge of the form of the MCE, allows us to find an expression for the critical configurational entropy (S^*_c) and a form for the potential energy hindering the cooperative rearrangement per monomer segment (Δμ).     

Non-Equilibrium Steady States of Finite¶Quantum Systems Coupled to Thermal Reservoirs

We study the non-equilibrium statistical mechanics of a 2-level quantum system, ?, coupled to two independent free Fermi reservoirs ?₁, ?₂, which are in thermal equilibrium at inverse temperatures β₁≠β₂. We prove that, at small coupling, the combined quantum system ?+?₁+?₂ has a unique non-equilibrium steady state (NESS) and that the approach to this NESS is exponentially fast. We show that the entropy production of the coupled system is strictly positive and relate this entropy production to the heat fluxes through the system. A part of our argument is general and deals with spectral theory of NESS. In the abstract setting of algebraic quantum statistical mechanics we introduce the new concept of the C-Liouvillean, L, and relate the NESS to zero resonance eigenfunctions of L ^*. In the specific model ?+?₁+?₂ we study the resonances of L ^* using the complex deformation technique developed previously by the authors in [JP1]. Dedicated to Jean Michel Combes on the occasion of his sixtieth birthday Received: 12 July 2001 / Accepted: 11 October 2001     

Operational Independence and Operational Separability in Algebraic Quantum Mechanics

Recently, new types of independence of a pair of C ^*- or W ^*-subalgebras $({\mathcal{A}}_{1},{\mathcal{A}}_{2})$ of a C ^*- or W ^*-algebra have been introduced: operational C ^*- and W ^*-independence (Rédei and Summers, http://arxiv.org/abs/0810.5294, 2008) and operational C ^*- and W ^*-separability (Rédei and Valente, How local are local operations in local quantum field theory? 2009). In this paper it is shown that operational C ^*-independence is equivalent to operational C ^*-separability and that operational W ^*-independence is equivalent to operational W ^*-separability. Specific further sub-types of both operational C ^*- and W ^*-separability and operational C ^*- and W ^*-independence are defined and the problem of characterization of the logical interdependencies of the independence notions is raised.     

Entropy of Quantum Limits

 In this paper we show that any measure arising as a weak^* limit of microlocal lifts of eigenfunctions of the Laplacian on certain arithmetic manifolds have dimension at least 11/9, and in particular all ergodic components of this measure with respect to the geodesic flow have positive entropy. Received: 14 March 2002 / Accepted: 24 June 2002 Published online: 13 January 2003     

Damping of second sound in the critical dynamics of liquid helium belowT λ

We calculate toO(=4 –d) the effect of the small ratiow ^* of the relaxation rates of the order parameter and the entropy on the damping of second sound in the hydrodynamic regime of liquid helium belowT . Forw ^* 1 we find a partial reduction of the previous discrepancy between theory and experiment on the amplitude of second sound damping.On leave from Universität Linz, Austria     

Self-organization of N<Superscript>*</Superscript> inclusions in SmC<Superscript>*</Superscript> free-standing films

The behaviour of freely suspended smectic-C* ( SmC^*) films at the bulk SmC^*-cholesteric ( N^*) phase transition has been investigated using polarized-reflected-light microscopy. Our experimental observations show that above the bulk SmC^*- N^* phase transition the N^* order appears in different ways according to the film thickness. In thin films, the conventional layer-by-layer thinning occurs. In films of intermediate thickness N^* inclusions nucleate inside the SmC^* film. The distortions of the in-plane orientational order of the SmC^* host phase induce elastic interactions between the inclusions and lead to their self-organization in chain-like structures. Both the dynamic of the chaining and the parameters driving the equilibrium distance between the inclusions in the chain are investigated. In thick films, N^* fingers grow inside the film. The influence of the experimental conditions on the various processes is analysed. Received 1 July 2002 / Published online: 15 April 2003 RID="a" ID="a"e-mail: Philippe.cluzeau@univ-lille1.fr     

快放电激励下准分子ArF*和Ar2F*时间谱的研究

本文通过对快放电激励下He/Ar/F₂混合气体中ArF^*,Ar₂F^*时间分辨谱的研究,探讨了准分子ArF^*和Ar₂F^*的形成和猝灭动力学过程。分析表明,ArF^*的时间衰减过程由生成它的主要前态Ar^*的时间变化过程决定,而Ar₂F^*的时间衰减过程则取决于它自己的有效寿命 关键词：     

Spacetime dynamical entropy of quantum systems

The definition of the dynamical entropy for single automorphisms of nuclear C ^*-algebras is extended to groups of several commuting automorphisms. This entropy of a Z ^v-action is shown to be nonzero only if all the corresponding Z -subactions (0<<v) have infinite entropy. As a simple consequence, the spacetime entropy of quantum lattice spin systems, and of one-dimensional continuous systems with physically reasonable quasifree states, vanishes.     

He/Ar/Kr/F2混合气体中准分子KrF*和Kr2F*的动力学研究

本文用时间积分谱的方法研究了快放电激励下He/Ar/Kr/F₂混合气体中Kr₂F^*的动力学,探讨了Kr₂F^*形成的通道特性,理论分析和实验结果表明,在快放电激励下,三体碰撞过程KrF^*+Kr+M→Kr₂F^*+M是形成Kr₂F^*的主要通道,而置换反应ArF^*+Kr→KrF^*+Ar又能有效地产生KrF^*。实验测量了Kr₂F^*形成的有关速率常数。 关键词：     

Semantic alternatives in Brouwer-Zadeh logics

In this paper we investigate an algebraic semantics for a particular kind of Brouwer-Zadeh logic (BZL^*). We prove that this semantics and the orthopair semantics (based on certainly-yes and certainly-no domains) characterize BZL^*. Further, we prove that every BZ^* lattice can be embedded into a complete BZ^* lattice.     

Kinetic studies of Ar2F* in fast transverse-discharge-excited He-Ar-F2 mixtures

Time-resolved and time-integrated spectra for various He-Ar-F₂ mixtures excited by a fast transverse discharge were recorded. The fluorescence of ArF^* and Ar₂F^* was investigated and the radiative lifetime and emission characteristics of Ar₂F^* were determined. A mechanism for the formation of Ar₂F^* is suggested.     

密度泛函理论方法研究6H-SiC(0001)表面对氧分子和水分子的吸附

本文通过密度泛函方法计算6H-SiC(0001)表面对氧分子和水分子的吸附. 在6H-SiC(0001)表面上吸附的O₂分子自发地解离成O^*,并被吸收在C与Si原子之间的空位上. 吸附的H₂O自发地分解成OH^*和H^*,它们都被吸附在Si原子的顶部,OH^*进一步可逆地转化为O^*和H^*. H^*可以使Si悬键饱和并改变O^*的吸附类型,并进一步稳定6H-SiC(0001)表面并防止其转变为SiO₂.