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1.
Francesco Fidaleo 《Proceedings of the American Mathematical Society》2002,130(1):121-127
A characterization of the quasi-split property for an inclusion of -algebras in terms of the metrically nuclear maps is established. This result extends the known characterization relative to inclusions of -factors. An application to type von Neumann algebras is also presented.
2.
We introduce a model suggested by disordered anharmonic quantum crystals. We then investigate in detail the ergodic properties
exhibited by such a model.
Received: 14 January 2002 / Accepted: 14 October 2002 Published online: 10 February 2003
Communicated by J. L. Lebowitz 相似文献
3.
We present a quantum system composed of infinitely many particles, subject to a nonquadratic Hamiltonian, for which it is possible to investigate the long time behavior of the dynamics and its ergodic properties. We do so both for the KMS states and for a large class of locally normal invariant states, whose very existence is already of some interest. 相似文献
4.
Since the grand partition function for the so-called q-particles (i.e., quons), , cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for , and its q-deformations for the remaining cases, we determine such grand partition functions in order to obtain the natural generalisation of the Plank distribution to . We also note the (non) surprising fact that the right grand partition function concerning the Boltzmann case (i.e., ) can be easily obtained by using the full Fock space 2nd quantisation, by considering the appropriate correction by the Gibbs factor in the n term of the power series expansion with respect to the fugacity z. As an application, we briefly discuss the equations of the state for a gas of free quons or the condensation phenomenon into the ground state, also occurring for the Bose-like quons . 相似文献
5.
Annali di Matematica Pura ed Applicata (1923 -) - We analyze general aspects of exchangeable quantum stochastic processes, as well as some concrete cases relevant for several applications to... 相似文献
6.
Francesco Fidaleo 《Journal of Functional Analysis》2012,262(10):4634-4637
Due to the boundary effects, the standard definition of the integrated density of the states (i.d.s. for short) used in [F. Fidaleo, Harmonic analysis on perturbed Cayley Trees, J. Funct. Anal. 261 (3) (2011) 604–634], does not work for nonamenable graphs like Cayley Trees and density zero perturbations of those. On the other hand, Proposition 2.3 in the previous mentioned paper works under the right definition we are going to describe, and which is useful for all the applications. For the sake of completeness and the convenience of the reader, we also show that both the definitions coincide in the amenable case. 相似文献
7.
We study some spectral properties of the adjacency operator of non-homogeneous networks. The graphs under investigation are obtained by adding density zero perturbations to the homogeneous Cayley Trees. Apart from the natural mathematical meaning, such spectral properties are relevant for the Bose Einstein Condensation for the pure hopping model describing arrays of Josephson junctions on non-homogeneous networks. The resulting topological model is described by a one particle Hamiltonian which is, up to an additive constant, the opposite of the adjacency operator on the graph. It is known that the Bose Einstein condensation already occurs for unperturbed homogeneous Cayley Trees. However, the particles condensate on the perturbed graph, even in the configuration space due to non-homogeneity. Even if the graphs under consideration are exponentially growing, we show that it is enough to perturb in a negligible way the original graph in order to obtain a new network whose mathematical and physical properties dramatically change. Among the results proved in the present paper, we mention the following ones. The appearance of the Hidden Spectrum near the zero of the Hamiltonian, or equivalently below the norm of the adjacency. The latter is related to the value of the critical density and then with the appearance of the condensation phenomena. The investigation of the recurrence/transience character of the adjacency, which is connected to the possibility to construct locally normal states exhibiting the Bose Einstein condensation. Finally, the study of the volume growth of the wave function of the ground state of the Hamiltonian, which is nothing but the generalized Perron Frobenius eigenvector of the adjacency. This Perron Frobenius weight describes the spatial distribution of the condensate and its shape is connected with the possibility to construct locally normal states exhibiting the Bose Einstein condensation at a fixed density greater than the critical one. 相似文献
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9.
The symmetric states on a quasi local C*–algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend the De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki–Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self–containing interest. 相似文献
10.
Stephen Dias?BarretoEmail author Francesco?Fidaleo 《Communications in Mathematical Physics》2004,250(1):1-21
We study the set of KMS states of spin systems with random interactions. This is done in the framework of operator algebras by investigating Connes and Borchers –invariants of W*–dynamical systems. In the case of KMS states exhibiting a property of invariance with respect to the spatial translations, some interesting properties emerge naturally. Such a situation covers KMS states obtained by infinite–volume limits of finite–volume Gibbs states, that is the quenched disorder. This analysis can be considered as a step towards fully understanding the very complicated structure of the set of temperature states of quantum spin glasses, and its connection with the breakdown of the symmetry for replicas. 相似文献