다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

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Convex Analysisの二,三の進展について

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

We review and further develop a mathematical framework for non-equilibrium quantum statistical mechanics recently proposed in refs 1–7 In the algebraic formalism of quantum statistical mechanics we introduce notions of non-equilibrium steady states, entropy production and heat fluxes, and study their properties Our basic paradigm is a model of a small (finite) quantum system coupled to several independent thermal reservoirs We exhibit examples of such systems which have strictly positive entropy production

/pdf/mathematical-theory-of-non-equilibrium-quantum-statistical-4kp54h5xaw.pdf

Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics

We investigate the dynamics of anN-level system linearly coupled to a field of mass-less bosons at positive temperature. Using complex deformation techniques, we develop time-dependent perturbation theory and study spectral properties of the total Hamiltonian. We also calculate the lifetime of resonances to second order in the coupling.

/pdf/on-a-model-for-quantum-friction-ii-fermi-s-golden-rule-and-3ozoxjh2p3.pdf

On a model for quantum friction. II. Fermi's golden rule and dynamics at positive temperature

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.

/pdf/non-equilibrium-steady-states-of-finite-quantum-systems-4io70cfgy5.pdf

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

Spectral Theory of Pauli–Fierz Operators

We investigate the dynamics of a 2-level atom (or spin 1/2) coupled to a mass-less bosonic field at positive temperature. We prove that, at small coupling, the combined quantum system approaches thermal equilibrium. Moreover we establish that this approach is exponentially fast in time. We first reduce the question to a spectral problem for the Liouvillean, a self-adjoint operator naturally associated with the system. To compute this operator, we invoke Tomita-Takesaki theory. Once this is done we use complex deformation techniques to study its spectrum. The corresponding zero temperature model is also reviewed and compared. From a more philosophical point of view our results show that, contrary to the conventional wisdom, quantum dynamics can be simpler at positive than at zero temperature.

/pdf/on-a-model-for-quantum-friction-iii-ergodic-properties-of-41adhdiguu.pdf

Vojkan Jaksic

Papers

Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics

On a model for quantum friction. II. Fermi's golden rule and dynamics at positive temperature

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

Spectral Theory of Pauli–Fierz Operators

On a model for quantum friction III. Ergodic properties of the spin-boson system