Roman Gielerak

Verification of the global Markov property in some class of strongly coupled exponential interactions

We verify the global Markov property in some class of strongly coupled exponential interactions in two‐dimensional space‐time. To obtain this result we apply the Albeverio and Ho/egh‐Krohn strategy. The basic ingredients we use in order to employ this strategy are the Fortuin–Kastelyn–Ginibre correlation inequalities.

Reconstruction of Kubo–Martin–Schwinger structure from Euclidean Green functions

The explicit form of the Poisson kernel for the strip Tβ={z∈C:0<Im z<β} is used to derive some conditions for a state ω on a given C*‐algebra dynamical system (A,αt) to be a Kubo–Martin–Schwinger (KMS) state. Reflection positivity and generalized periodicity of the Euclidean Green functions corresponding to ω are established and used for an analytic continuation to real time. Reflection positivity is also used for the construction of a cyclic and faithful representation of (A,αt) on some Hilbert space. A sufficient condition for the identification of the constructed dynamics with the modular group of a von Neumann algebra generated by the representation is formulated in terms of the Euclidean Green functions.

W*‐KMS structure from multi‐time Euclidean Green functions

An axiomatic approach to the problem of reconstruction of a dynamics from the Euclidean multi‐time Green functions is proposed. The existence of a W*‐algebra on which the reconstructed dynamics acts as the canonical group of modular automorphisms is shown. A condition under which the reconstruction from the one‐time and multi‐time Green functions are equivalent is formulated.

Gentle perturbations of the free Bose gas. I

It is demonstrated that the thermal structure of the noncritical free Bose gas is completely described by certain periodic generalized Gaussian stochastic process or equivalently by a certain periodic generalized Gaussian random field. Elementary properties of this Gaussian stochastic thermal structure are established. Gentle perturbations of several types of the free thermal stochastic structure are studied. In particular, new models of non-Gaussian thermal structures are constructed and a new functional integral representation of the corresponding Euclidean-time Green functions is obtained rigorously.

Bounded perturbations of the generalized random fields

Functional DLR equations corresponding to the bounded perturbations of sufficiently regular generalized Gaussian random fields are studied. Certain uniqueness theorems are proved. Some qualitative properties of the set of the corresponding Gibbs states are described.

From stochastic differential equation to quantum field theory

Abstract Covariant stochastic partial (pseudo)-differential equations are studied in arbitrary dimension. In particular, a large class of covariant interacting local quantum fields obeying the Morchio-Strocchi system of axioms for indefinite quantum field theory is constructed by solving the analysed equations. The associated random co-surface models are discussed and some of their elementary properties are outlined.

On the DLR equation for the (λ:φ4: + b :φ2: + μφ, μ ≠ 0)2 euclidean quantum field theory: The uniqueness theorem

The Dobrushin-Lanford-Ruelle (DLR) equation is studied in a certain space of measures in the case of 2-dimensional lambda:phi/sup 4/:+b:phi/sup 2/:+..mu..phi, ..mu..not =0, euclidean quantum field theory. The uniqueness theorem stating that for any ..mu..not =0 there exists unique, translationally invariant 8-regular solution of the corresponding DLR equation is proved. The theorem is proved by combining the Lee-Yang theorem with the general van Hove type theorem for infinite volume free energy densities. copyright 1989 Academic Press, Inc.

Transfer of Quantum Continuous Variable and Qudit States in Quantum Networks

The Bose lattice quantum gas based protocols for perfect coherent states transfer are discussed. Additionally, the perfect transfer of qudit states protocol based on Heisenberg-like interactions and in 1D-chains is discussed together with its computer implementation within Zielona Gora Quantum Computer Simulator.

Generalised quantum weakest preconditions

Generalisation of the quantum weakest precondition result of D’Hondt and Panangaden is presented. In particular the most general notion of quantum predicate as positive operator valued measure (termed POVM) is introduced. The previously known quantum weakest precondition result has been extended to cover the case of POVM playing the role of a quantum predicate. Additionally, our result is valid in infinite dimension case and also holds for a quantum programs defined as a positive but not necessary completely positive transformations of a quantum states.

GPGPU based simulations for one and two dimensional quantum walks

Simulations of standard 1D and 2D quantum walks have been performed within Quantum Computer Simulator (QCS system) environment and with the use of GPGPU (General Purpose Graphics Processor Unit) supported by CUDA (Compute Unified Device Architecture) technology. In particular, simulations of quantum walks may be seen as an appropriate benchmarks for testing computational power of the processors used. It was demonstrated by a series of tests that the use of CUDA based technology radically increases the computational power compared to the standard CPU based computations.