KMS states for the Weyl algebra

We consider the possible automorphism groups for the Weyl algebra overR, resp.T, and classify those for which KMS states, unique or not unique, exist.     

Entropic dimension for completely positive maps

We extend the concept of quantum dynamical entropyh _φ (γ) to cover the case of a completely positive map γ. Forh _φ (γ) = 0 we examine the limit $$h_\phi (N,\gamma ,\beta ) = \mathop {\lim }\limits_n (1/n^\beta )H_\phi (N,\gamma {\rm N},...,\gamma ^{n -- 1} N)$$ calling the turning point β₀ between zero and infiniteh _φ (N, γ, β) the “entropic dimension”D _N (γ). The application of this theory to a solvable irreversible quantum dynamical semigroup on a one-dimensional fermion lattice provides any value ofD _N (γ) between 0 and 1.     

Quasi-particles at finite temperatures

We study the consequences of the KMS-condition on the properties of quasi-particles, assuming their existence. We establish

1. If the correlation functions decay sufficiently, we can create them by quasi-free field operators.
2. The outgoing and incoming quasi-free fields coincide, there is no scattering.
3. There are may age-operatorsT conjugate toH. For special forms of the dispersion law ε(k) of the quasi-particles there is aT commuting with the number of quasi-particles and its time-monotonicity describes how the quasi-particles travel to infinity.

     

Explicit Equivalence Bimodules for Rotation Algebras

The C*-algebras associated with irrational rotations are Morita equivalent if and only if the rotation parameters belong to the same orbit under the action of GL(2, Z). In this note, we suggest explicit type II representations such that the bimodule is dense in the corresponding Hilbert space. Bibliography: 4 titles. __________ Published in Zapiski Nauchnykh Seminarov POMI, Vol. 307, 2004, pp. 175–188.     

Thermodynamic functions for fermions with gravostatic and electrostatic interactions

The energy as function of entropy and the free energy as function of temperature is calculated rigorously for nonrelativistic fermions with interactions. It is shown that in the appropriate thermodynamic limit the corresponding Thomas-Fermi equation becomes exact.Work supported by Fonds zur Förderung der wissenschaftlichen Forschung, Projekt Nr. 1391.On leave of absence from the University of Heidelberg, Germany.     

Finite supersymmetry transformations

We investigate simple examples of supersymmetry algebras with real and Grassmann parameters. Special attention is paid to the finite supertransformations and their probability interpretation. Furthermore we look for combinations of bosons and fermions which are invariant under supertransformations. These combinations correspond to states that are highly entangled.Received: 30 January 2004, Published online: 23 April 2004N. Ilieva: On leave from Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Boul. Tzarigradsko Chaussee 72, 1784 Sofia, Bulgaria     

Entangled finitely correlated quantum spin chains

We study the multipartite entanglement properties of translation-invariant states of infinite quantum spin chains with a valence-bond structure.     

Comparison of dynamical entropies for the noncommutative shifts

It is shown that two definitions of dynamical entropy for noncommutative shifts give different results.On leave of absence from the Institute of Theoretical Physics and Astrophysics, University of Gdansk, PL-80-952 Gdansk, Poland     

Mixing properties of quantum systems

We generalize the classical notion of topological mixing for automorphisms ofC ^*-algebras in two ways. We show that for Galilean-invariant Fermi systems the weaker form of mixing is satisfied. With some additional requirement on the range of the interaction we can also demonstrate the stronger mixing property.