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In multitype lattice gas models with hard-core interaction of Widom Rowlinson type, there is a competition between the entropy due to the large number of types, and the positional energy and geometry resulting from the exclusion rule and the activity of particles. We investigate this phenomenon in four different models on the square lattice: the multitype… (More)

We study the annealed site-diluted versions of the classical O(n) Heisenberg ferromagnets. It is shown that if the temperature is low enough, then at some value of the chemical potential there is phase coexistence between a magnetized, high-density state (liquid-crystal state) and a low-density state (gaseous state) with no magnetic order.

We discuss statistical mechanics on nonamenable graphs, and we study the features of the phase transition, which are due to nonamenability. For the Ising model on the usual lattice it is known that below the critical temperature fluctuations of magnetization are much less likely in the states with nonzero magnetic field than in the pure states with zero… (More)

We revise the notion of the quasi-sectorial contractions. Our main theorem establishes a relation between semigroups of quasi-sectorial contractions and a class of m−sectorial generators. We discuss a relevance of this kind of contractions to the theory of operator-norm approximations of strongly continuous semigroups.

(1.1) i∂tψ(t) = Hψ(t) . For all initial conditions ψ(0) ∈ H, the unique solution is given by ψ(t) = e−itHψ(0), for all t ∈ R. Due to Stone’s Theorem e−itH is a strongly continuous one-parameter group of unitary operators on H, and the self-adjointness of H is the necessary and sufficient condition for the existence of a unique continuous solution for all… (More)

- Francois Bentosela, Ricardo M. Cavalcanti, P . Exner, Valentin A . Zagrebnov
- 1999

a) Centre de Physique Théorique, C.N.R.S., 13288 Marseille Luminy b) Université de la Mediterranée (Aix–Marseille II), 13288 Marseille Luminy, France c) Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA d) Nuclear Physics Institute, Academy of Sciences, 25068 Řež e) Doppler Institute, Czech Technical University,… (More)

- Joseph V. Pulé, André F. Verbeure, Valentin A . Zagrebnov
- 2004

We study the effect of electromagnetic radiation on the condensate of a Bose gas. In an earlier paper we considered the problem for two simple models showing the cooperative effect between Bose-Einstein condensation and superradiance. In this paper we formalise the model suggested by Ketterle et al in which the Bose condensate particles have a two level… (More)

In this letter we discuss the relevance of the 3D Perfect Bose gas (PBG) condensation in extremely elongated vessels for the study of anisotropic condensate coherence and the “quasi-condensate”. To this end we analyze the case of exponentially anisotropic (van den Berg) boxes, when there are two critical densities ρc < ρm for a generalised Bose-Einstein… (More)

- Bruno Nachtergaele, Anna Vershynina, Valentin A . Zagrebnov, Valentin A.Zagrebnov
- 2011

We prove Lieb-Robinson bounds and the existence of the thermodynamic limit for a general class of irreversible dynamics for quantum lattice systems with time-dependent generators that satisfy a suitable decay condition in space.

We show that there is a family Schrödinger operators with scaled potentials which approximates the δ-interaction Hamiltonian in the normresolvent sense. This approximation, based on a formal scheme proposed by Cheon and Shigehara, has nontrivial convergence properties which are in several respects opposite to those of the Klauder phenomenon.