Dilations of quantum dynamical semigroups with classical Brownian motion

We show that any quantum dynamical semigroup can be written with the help of the solution of a vector-valued classical stochastic differential equation. Moreover this equation leads to a natural construction of a unitary dilation in term of Wiener spaces.On leave of absence from Institute of Theoretical Physics and Astrophysics, Gdansk, PolandBevoegdverklaard navorser N.F.W.O., Belgium     

Bi-representations and semi-groups

For a map of C ^*-algebra into itself arising formally in the study of bi-representations, it is proved that it can be spatially implemented and can generate a contraction semi-group, if certain plausible conditions are satisfied.     

Role of Dilations in Diffeomorphism-Covariant Algebraic Quantum Field Theory

A generalization of algebraic quantum field theory on differentiable manifoldsis given in terms of nets of *-algebras over open sets of the manifold. The presentinvestigations are motivated by diffeomorphism invariance and finite localizationas they appear, e.g., in quantum gravity. A possible generalization of Haag-Kastleraxioms for differentiable manifolds is discussed and a minimal framework basedon isotony, covariance, and a state-dependent GNS construction is presented.Possible adaptions of Haag's commutant duality are discussed in a specific settingof one-parameter families of finite and nondegenerate nested localization domainsof the net, with universal minimal and maximal algebras for the small and largelimits of the net, respectively. For von Neumann algebras the modular group isdiscussed. The geometric interpretation of a one-parameter subgroup of outerisomorphisms is related to dilations of the open sets of the net.     

Particle Systems Analysis by Using Skeletonization and Exact Dilations

This paper describes how the formation of particle systems can be investigated by using computer vision techniques, namely effective exact dilations and multiscale skeletonization. By assuming that all particles started to grow at the same time and had the same growth rate, a hypothesis that can be validated later, it becomes possible to infer the shape and distribution of the particles in the initial system configuration. Multiscale skeletons are obtained for each individual particle, and a suitable overall spatial scale, i.e. those best approximating the initial configuration, is determined as that immediately before the smallest particle fades. The thus obtained skeletons provide an estimate of the shape and position of the initial particles before uniform expansion. By using exact dilations, a generalized Dirichlet tessellation reconstruction of the particle system is obtained from these skeletons, and the similarity between this reconstruction and the original system can be used to validate the assumptions about the growth conditions. The proposed methodology is illustrated with respect to KC1 polycrystalline thin films.     

On the possible connection between renormalization-groups and nonlinear semi-groups

Some algebraic properties of the renormalization-group (RNG) are studied using the nonlinear semi-group theory. The RNG is defined in an axiomatic manner as a bounded nonlinear semi-group on an abstract Banach space. Perturbations of the fixed point of RNG and the problem of marginality are investigated using a hierarchy of nonlinear semi-groups.     

Topology of dynamical lattice configurations including results from dynamical overlap fermions

We investigate how the topological charge density in lattice QCD simulations is affected by violations of chiral symmetry caused by the fermion action. To this end we compare lattice configurations generated with a number of different actions including first configurations generated with exact dynamical overlap quarks. We visualize the topological profiles after mild smearing. In the topological charge correlator we measure the size of the positive core, which is known to shrink to zero extension in the continuum limit. To leading order we find the core size to scale linearly with the lattice spacing with the same coefficient for all actions, even including quenched simulations. In the subleading term the different actions vary over a range of about 10%. Our findings suggest that non-chiral lattice actions at current lattice spacings do not differ much for observables related to topology, both among themselves and compared to overlap fermions.     

Resynchronizing dynamical systems

Resynchronizing dynamical systems are important for certain chaotic signal masking methods. We demonstrate the dependence of the resynchronizing property of linear dynamical systems on choices of coordinate systems. Using these insights, we demonstrate how a nonlinear system not previously known to be synchronizable can be used for chaotic signal masking.     

Topological dynamical decoupling

We show that topological equivalence classes of circles in a two-dimensional square lattice can be used to design dynamical decoupling procedures to protect qubits attached on the edges of the lattice. Based on the circles of the topologically trivial class in the original and the dual lattices, we devise a procedure which removes all kinds of local Hamiltonians from the dynamics of the qubits while keeping information stored in the homological degrees of freedom unchanged. If only the linearly independent interaction and nearest-neighbor two-qubit interactions are concerned, a much simpler procedure which involves the four equivalence classes of circles can be designed. This procedure is compatible with Eulerian and concatenated dynamical decouplings,which make it possible to implement the procedure with bounded-strength controls and for a long time period. As an application,it is shown that our method can be directly generalized to finite square lattices to suppress uncorrectable errors in surface codes.     

Non-Hamiltonian dynamical systems

The class of dynamical systems is considered, which are described by several mutually noncommuting Hamiltonian currents, in particular, relativistic bi-Hamiltonian systems, the evolution of which is described by a pair of 4-momenta p and p The examination is conducted in classical and quantum realizations. The evolution equations are derived of relativistic bi-Hamiltonian systems in the Heisenberg and Schrödinger pictures. It is shown that the quantum theory of relativistic bi-Hamiltonian systems is not compatible with the unitary condition and is nonunitary. A physical interpretation is given of nonunitary quantum theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 5–12, October, 1990.     

Topological dynamical decoupling

Science China Physics, Mechanics & Astronomy - Active galactic nuclei (AGNs) have been attracting research attention due to their special observable properties. Specifically, a majority of AGNs...     

Semi-classical dynamical triangulations

For non-critical string theory the partition function reduces to an integral over moduli space after integrating over matter fields. The moduli integrand is known analytically for genus one surfaces. The formalism of dynamical triangulations provides us with a regularization of non-critical string theory and we show that even for very small triangulations it reproduces very well the continuum integrand when the central charge c   of the matter fields is large negative, thus providing a striking example of how the quantum fluctuations of geometry disappear when c→−∞$c\to -\infty$.     

Partial dynamical symmetries

This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify interactions, of a given order, with such intermediate symmetry structure. Explicit bosonic and fermionic Hamiltonians with PDS are constructed in the framework of models based on spectrum generating algebras. PDSs of various types are shown to be relevant to nuclear spectroscopy, quantum phase transitions and systems with mixed chaotic and regular dynamics.     

Supersymmetric inflation of dynamical origin

Dynamical models of inflation are given with composite inflatons by means of massive supersymmetric gauge theory. Nearly flat directions and stable massive ones in the potential are identified and slow-roll during inflation is examined. This kind of dynamical inflations may be ubiquitous in fundamental unified theory with supersymmetry, which should contain gauge theories for interactions of elementary particles.     

Convergence of dynamical zeta functions

I study poles and zeros of zeta functions in one-dimensional maps. Numerical and analytical arguments are given to show that the first pole of one such zeta function is given by the first zero ofanother zeta function: this describes convergence of the calculations of the first zero, which is generally the physically interesting quantity. Some remarks on how these results should generalize to zeta functions of dynamical systems with pruned symbolic dynamics and in higher dimensions follow.     

Multivariate analysis of dynamical processes

The analysis of multi-dimensional biomedical systems requires analysis techniques, which are able to deal with multivariate data consisting of both time series as well as point processes. Univariate and bivariate analysis techniques in the frequency domain for time series and point processes are established and investigated, although the number of investigations is strongly biased towards time series. Actual multivariate techniques for time series or hybrids of time series and point processes are scarcely addressed. Here, we present spectral analysis techniques which are able to analyse point processes as well as time series. Thereby, univariate, bivariate as well as multivariate techniques are discussed. Applications to simulated as well as real-world data reveal the abilities of the proposed techniques.     

Analytic structure of dynamical systems

The study of the analytic structure of nonlinear ordinary and partial differential equations is shown to provide a unified approach to determining their properties and finding their solutions. A course of lectures delivered at the School on Chaos and Nonlinear Dynamics held at the Indian Institute of Science, Bangalore, India (June 24th–July 18th 1987)     

Lattice dynamical study of platinum

Acta physica Academiae Scientiarum Hungaricae - A modified angular force model which takes into account the effect of electron-ion interaction on the basis ofSharma andJoshi model along with the...     

Optimal dynamical characterization of entanglement

We show that, for experimentally relevant systems, there is an optimal measurement strategy to monitor the time evolution of entanglement under open system dynamics. This suggests an efficient, dynamical characterization of the entanglement of composite, open quantum systems.