Golden-Thompson and Peierls-Bogolubov inequalities for a general von Neumann algebra

Some inequalities for a general von Neumann algebra, which reduces to Golden-Thomspon and Peierls-Bogolubov inequalities when the von Neumann algebra has a trace, are proved.     

Decomposable differential operators in a cosmological context

The integrability conditions for a certain second order ordinary differential equation in two variables are studied via the concept of decomposability of the associated differential operator. The results are applied to regain in a unified manner the known exact solutions for locally rotationally symmetric, spatially homogeneous cosmological models. In addition, new solutions are obtained.     

Sufficient subalgebras and the relative entropy of states of a von Neumann algebra

A subalgebraM ₀ of a von Neumann algebraM is called weakly sufficient with respect to a pair (,) of states if the relative entropy of and coincides with the relative entropy of their restrictions toM ₀. The main result says thatM ₀ is weakly sufficient for (,) if and only ifM ₀ contains the Radon-Nikodym cocycle [D,D] _t . Other conditions are formulated in terms of generalized conditional expectations and the relative Hamiltonian.     

A unified approach to classical and quantum K.M.S. theory

We study a generalized K.M.S. condition which includes the classical and quantum mechanical K.M.S. conditions as special cases. We consider also a generalized centre of the von Neumann algebra and prove that with respect to the above K.M.S. condition it has properties analogous to the properties of the centre with respect to the quantum mechanical K.M.S. condition.     

Extension of K.M.S. states with respect to some locally compact groups

Given a state ω on the C^*-system { , R×G, α} which is K.M.S. with respect to time on the sub-algebra of of fixed points under the action of some locally compact group G, we study its K.M.S.-extension to the whole algebra. In this work, we study more precisely the cases where G is a class of locally compact abelian groups (such that { , G, α|G} is almost periodic) or a product of these groups with a compact group.     

The Weil-B.R.S. algebra of a Lie algebra and the anomalous terms in gauge theory

In this paper, we explain the computation we made in collaboration with M. Talon and C.M. Viallet of anomalous terms in gauge theory [1], [2], [3]. We relate our constructions to standard mathematical constructions. The paper is self-contained in the sense that all mathematical concepts and results we use are explained.     

Constraints imposed upon a state of a system that satisfies the K.M.S. boundary condition

Using the uniqueness of the K.M.S. automorphism, we investigate the set of automorphisms that commutes with it. The results are applied to gauge invariant quasi-free states of a fermion system.Attaché de Recherche, C.N.R.S.On leave of absence from the Groningen University, the Netherlands.     

Generalization of the von Neumann theorem to nonreproducible measurements in quantum field theory. III

The consequences of a Theorem, which is a generalization of the fundamental von Neumann theorem on the reduction of a wave packet, and a Corollary of this theorem, which has a deep fundamental significance, are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 85–91, November, 1978.     

Generalization of the von Neumann theorems to irreproducible measurements within quantum field theory. IV

It is shown that the theorem of the first part of this cycle of papers necessarily, by virtue of only the fundamental principles of quantum theory, implies the existence of two fundamentally different types of evolution of isolated quantum macrosystems, i.e., the S and PS evolutions of pure states. As for isolated quantum microsystems, they can only S-evolve. The paper considers the fundamental specific singularities of PS evolution, which follow strictly from the theorem itself, as well as its corollary, proved in the first part [1] of this cycle of papers, also only on the basis of the fundamental principles of quantum theory. These singularities consist in the fact that, regardless of the commutativity of any observable of a system described by a vector in physical Hilbert space with the S-operator of this system, the probability distribution of this observable during measurement (with an appropriate instrument ), providing complete information about the characteristic of the system, is not conserved during the process of PS evolution. Nor is even the expectation of the result of measurement of the observable conserved with time.Paper presented at a session of the Department of Nuclear Physics, Academy of Sciences of the USSR (Moscow, February, 1978).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 63–72, June, 1979.The author is indebted to Prof. S. N. Sokolov (Institute of High-Energy Physics, Serpukhov) for his invaluable discussion of the Everett concept.     

Observation of a new resonance at 2000 MeV in the K S K S system

This article continues a series of publications devoted to previously unknown narrow resonances in the K _S K _S system that are observed in experimental data coming from the 6-m spectrometer of the Institute of Theoretical and Experimental Physics (ITEP, Moscow). The experimental data on the production of K _S pairs were obtained in π ^? p interactions at 40 GeV by using a neutral trigger. In the K _S K _S system, a maximum of width not exceeding 15 MeV is observed at a mass of about 2000 MeV, the statistical significance of this maximum being not less than five standard deviations. With a high degree of reliability, the spin-parity of this structure is J ^P = 4⁺. The observed phenomenon may be interpreted as a resonance whose parameters are equal to the above values.     

von Neumann entropy signatures of a transition in one-dimensional electron systems with long-range correlated disorder

We study the von Neumann entropy and related quantities in one-dimensional electron systems with on-site long-range correlated potentials. The potentials are characterized by a power-law power spectrum S(k) μ\propto 1/k ^α, where α is the correlation exponent. We find that the first-order derivative of spectrum-averaged von Neumann entropy is maximal at a certain correlation exponent α _m for a finite system, and has perfect finite-size scaling behaviors around α _m . It indicates that the first-order derivative of the spectrum-averaged von Neumann entropy has singular behavior, and α _m can be used as a signature for transition points. For the infinite system, the threshold value α _c = 1.465 is obtained by extrapolating α _m .     

An E.S.R. study of electron irradiated K3IrCl6 in a NaCl host lattice

Electron irradiation of the diamagnetic [Ir^IIICl₆]^3- ion in a NaCl host lattice produces two paramagnetic species. ESR studies indicate that these slightly different species can be assigned to a [Ir^IICl₆]^4- complex, with 5d ⁷ low spin configuration, arising from the capture of an electron in a d_z ² orbital. The almost zero value for the quadrupolar interaction and the negative value for the core polarization field per unpaired spin are discussed in terms of a ligand field theory and the group overlap integral for the A _1g molecular orbital is calculated from the experimental data.