On the Spectrum of 1D Quantum Ising Quasicrystal

We consider one-dimensional quantum Ising spin-1/2 chains with two-valued nearest neighbor couplings arranged in a quasi-periodic sequence, with uniform, transverse magnetic field. By employing the Jordan–Wigner transformation of the spin operators to spinless fermions, the energy spectrum can be computed exactly on a finite lattice. By employing the transfer matrix technique and investigating the dynamics of the corresponding trace map, we show that in the thermodynamic limit the energy spectrum is a Cantor set of zero Lebesgue measure. Moreover, we show that local Hausdorff dimension is continuous and non-constant over the spectrum. This forms a rigorous counterpart of numerous numerical studies.     

Color Representations of Ising Models

Journal of Theoretical Probability - In Steif and Tykesson (J Prob 16:899–955, 2019), the authors introduced the so-called general divide and color models. One of the best-known...     

Computation of Quasiperiodic Normally Hyperbolic Invariant Tori: Rigorous Results

The development of efficient methods for detecting quasiperiodic oscillations and computing the corresponding invariant tori is a subject of great importance in dynamical systems and their applications in science and engineering. In this paper, we prove the convergence of a new Newton-like method for computing quasiperiodic normally hyperbolic invariant tori carrying quasiperiodic motion in smooth families of real-analytic dynamical systems. The main result is stated as an a posteriori KAM-like theorem that allows controlling the inner dynamics on the torus with appropriate detuning parameters, in order to obtain a prescribed quasiperiodic motion. The Newton-like method leads to several fast and efficient computational algorithms, which are discussed and tested in a companion paper (Canadell and Haro in J Nonlinear Sci, 2017. doi: 10.1007/s00332-017-9388-z), in which new mechanisms of breakdown are presented.     

Coupling 3D and 1D Skeletal Muscle Models

This work introduces a modelling framework towards a forward dynamics simulation of skeletal muscle mechanics that couples three-dimensional (3D) continuum-mechanical-based Finite Element (FE) simulations to rigid body simulations. In this regard, this is a methodological approach, which incorporates different methods to realise simulations of the musculoskeletal system. Such simulations are at present computationally not feasible. To set up such a modelling framework the upper limp is selected. Here, the upper limb consists of an antagonistic muscle pair, the elbow (a simple hinge joint) and an external load. The skeletal muscles are represented by a 3D continuum-mechanical model. The tendons are, for now, assumed to be rigid. The results demonstrate the ability of the system to converge to a physiological realistic position. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Models of thermodiffusion in 1D

The goal of the paper is to study the Cauchy problem for 1D models of thermodiffusion. We explain qualitative properties of solutions. In particular, we show which part of the model has a dominant influence on well‐posedness, propagation of singularities, L^p ? L^q decay estimates on the conjugate line, and on the diffusion phenomenon. Copyright © 2013 John Wiley & Sons, Ltd.     

Hitchin and Beauville-Mukai System: Classical and Quantum Correspondence

This is a brief review of my recent works with B. Enriquez on the relations between Hitchin and Beauville-Mukai algebraically completely integrable systems (ACIS) with emphasis on the quantization of their birational correspondence. The second part of the contribution gives an example of the construction specifying by its relation with Sklyanin-Feigin-Odesskii elliptic algebras and based on my works with A. Odesskii. This contribution is a content of two my talks presented at the Twente Conferences on Lie Groups in December 2004 and December 2005.      

Sparse 1D discrete Dirac operators I: Quantum transport

Some dynamical lower bounds for one-dimensional discrete Dirac operators with different classes of sparse potentials are presented, and the particular role of the particle mass is emphasized.     

Seminar on Classical and Quantum Integrable Systems

Theoretical and Mathematical Physics -     

On the Dynamics of the Classical Transverse Field Ising Chain

We investigate stationary and travelling wave solutions of a special lattice differential equation in one space dimension. Depending on a parameter λ, results are given on the existence, shape and stability for these kind of solutions. The analysis of travelling wave solutions leads us to a functional differential equation with both forward and backward shifts. The existence of solutions of this equation will be proved by use of the implicit function theorem. In particular, we consider kink solutions and periodic solutions.     

Diracs Equation in 1+1 D from a Classical Random Walk

This paper is an investigation of the class of real classical Markov processes without a birth process that will generate the Dirac equation in 1+1 dimensions. The Markov process is assumed to evolve in an extra (ordinal) time dimension. The derivation requires that occupation by the Dirac particle of a space-time lattice site is encoded in a 4 state classical probability vector. Disregarding the state occupancy, the resulting Markov process is an homogeneous and almost isotropic binary random walk in Dirac space and Dirac time (including Dirac time reversals). It then emerges that the Dirac wavefunction can be identified with a polarization induced by the walk on the Dirac space-time lattice. The model predicts that QM observation must happen in ordinal time and that wavefunction collapse is due not to a dynamical discontinuity, but to selection of a particular ordinal time. Consequently, the model is more relativistically equitable in its treatment of space and time in that the observer is attributed no special ability to specify the Dirac time of observation.     

Structure of T Modules and Restricted Duals: The Classical and the Quantum Case

Abstract

A concrete realization of Enright's T modules is obtained. This is used to show their self-duality. As a consequence, the restricted duals of Verma modules are also identified.     

A Dynamic Simulation Comparing Classical and Emergent-Network Models: Organizational Design Implications

In the last decade, organizations have spent more on the creation, transformation, and communication of information than on the production of physical goods. The information age has been ushered in by the widespread assimilation of information and communication technologies. Many contemporary practitioners and organizational theorists predict the demise of the classical organizational design because of its inability to accommodate the sociological change engendered by the information age.The current study advances an emergent-network model of organizational design and compares it to the classical approach through a dynamic simulation of prototypical organizational activities. Organizational activities approximating one year were simulated in each of five organizations under constant baseline conditions and over one hundred experimental design conditions. The emergent network model manifested higher levels of goal attainment, resource utilization, and organizational capacity for accommodating change. These findings suggest that organizations will benefit from conformance to the design principals of the emergent-network model.Bernard D. Hill Jr. earned his Ph.D. in Public Policy and Administration from Virginia Commonwealth University. He also holds a Master of Science in Business and a Bachelor of Science in Education. Bernard is currently employed as a Chief Information Officer with the Commonwealth of Virginia. He has held a broad array of technology leadership positions in both the public and private sectors and the academic arena. Bernard was selected as one of Computerworld’s Premier 100 IT Leaders for 2002. As CIO for the Virginia Department of Transportation, he also brokered a public-private partnership that won a nationwide Government Technology Leadership Award. This partnership provides security awareness training for employees in Virginia State government, as well as cities, counties, and localities throughout Virginia.Heinz Roland Weistroffer is an Associate Professor of Information Systems in the School of Business at Virginia Commonwealth University. Roland holds a Doctor of Science degree from the Free University Berlin, Germany, and a Master of Arts degree from Duke University. Previous appointments include Chief Research Officer at the Council for Scientific and Industrial Research in Pretoria, South Africa, and Senior Lecturer at the University of Natal in Durban, South Africa. Roland’s current research interests include computer assisted decision support, computer simulation modeling, object oriented modeling, and software engineering. He has published in IEEE Transactions on Software Engineering, IEEE Transactions on Systems, Man and Cybernetics, the Journal of Multi-Criteria Decision Analysis, and Socio-Economic Planning Sciences, among other journals.Peter Aiken is Director of the Institute for Data Research and an Associate Professor of Information Systems at Virginia Commonwealth University. His research has widely explored the area of data engineering and its relationship to systems and business reengineering. He is the author of Data Reverse Engineering and Clive Finkelstein’s co-author of Corporate Information Portals (McGraw-Hill 1996/99). His sixth book is titled XML in Data Management and is co-authored with David Allen. He has held leadership positions with the US Department of Defense and consulted with more than 50 organizations in 14 different counties. His research publications have appeared in the Communications of the ACM, IBM Systems Journal, IEEE Software and many others. He is a member of ACM, and the IEEE (Senior Member). He has been a DAMA International Advisor since 1999 and received their 2001 International Achievement Award. He has lectured internationally on these and related topics.     

Existence of Classical Solutions to a Stationary Simplified Quantum Energy-Transport Model in 1-Dimensional Space

The existence of classical solutions to a stationary simplified quantum energytransport model for semiconductor devices in 1-dimensional space is proved.The model consists of a nonlinear elliptic third-order equation for the electron density,including a temperature derivative,an elliptic nonlinear heat equation for the electron temperature,and the Poisson equation for the electric potential.The proof is based on an exponential variable transformation and the Leray-Schauder fixed-point theorem.     

Characterization of Classical and Quantum Poisson Systems by Thinnings and Splittings

There exist several well–known characterizations of Poisson and mixed Poisson point processes (Cox processes) by thinning and splitting procedures. So a point process is necessarily a Cox process if for arbitrary small thinning parameter it can be obtained by a thinning of some other point process [30]. Poisson processes are characterized by the independence of the two random subconfigurations obtained by an independent splitting of the configuration into two parts [11]. For quantum mechanical particle systems beam splittings which are well–known in quantum optics provide analogous procedures. It is shown that coherent states respectively mixtures of them can be characterized in the same way as Poisson processes and Cox processes. Moreover, for the position distributions of these states which are “classical” point processes just the above mentioned characterizations are obtained. As example of mixed coherent states we consider Gaussian states which arise as equilibrium states of ideal Bose gases.