The Exact Solution of the Asymmetric Exclusion Problem With Particles of Arbitrary Size: Matrix Product Ansatz

The exact solution of the asymmetric exclusion problem and several of its generalizations is obtained by a matrix product {\it ansatz}. Due to the similarity of the master equation and the Schr\"odinger equation at imaginary times the solution of these problems reduces to the diagonalization of a one dimensional quantum Hamiltonian. We present initially the solution of the problem when an arbitrary mixture of molecules, each of then having an arbitrary size ($s=0,1,2, ...$) in units of lattice spacing, diffuses asymmetrically on the lattice. The solution of the more general problem where we have | the diffusion of particles belonging to $N$ distinct class of particles ($c=1, ..., N$), with hierarchical order, and arbitrary sizes is also solved. Our matrix product {\it ansatz} asserts that the amplitudes of an arbitrary eigenfunction of the associated quantum Hamiltonian can be expressed by a product of matrices. The algebraic properties of the matrices defining the {\it ansatz} depend on the particular associated Hamiltonian. The absence of contradictions in the algebraic relations defining the algebra ensures the exact integrability of the model. In the case of particles distributed in $N>2$ classes, the associativity of the above algebra implies the Yang-Baxter relations of the exact integrable model.Comment: 42 pages, 1 figur

Exact solutions of exactly integrable quantum chains by a matrix product ansatz

Most of the exact solutions of quantum one-dimensional Hamiltonians are obtained thanks to the success of the Bethe ansatz on its several formulations. According to this ansatz the amplitudes of the eigenfunctions of the Hamiltonian are given by a sum of permutations of appropriate plane waves. In this paper, alternatively, we present a matrix product ansatz that asserts that those amplitudes are given in terms of a matrix product. The eigenvalue equation for the Hamiltonian define the algebraic properties of the matrices defining the amplitudes. The existence of a consistent algebra imply the exact integrability of the model. The matrix product ansatz we propose allow an unified and simple formulation of several exact integrable Hamiltonians. In order to introduce and illustrate this ansatz we present the exact solutions of several quantum chains with one and two global conservation laws and periodic boundaries such as the XXZ chain, spin-1 Fateev-Zamolodchikov model, Izergin-Korepin model, Sutherland model, t-J model, Hubbard model, etc. Formulation of the matrix product ansatz for quantum chains with open ends is also possible. As an illustration we present the exact solution of an extended XXZ chain with $z$-magnetic fields at the surface and arbitrary hard-core exclusion among the spins.Comment: 57 pages, no figure

Organisational change and the computerisation of British and Spanish savings banks, 1965-1985

In this article we explore organisational changes associated with the automation of financial intermediaries in Spain and the UK. This international comparison looks at the evolution of the same organisational form in two distinct competitive environments. Changes in regulation and technological developments (particularly applications of information technology) are said to be responsible for enhancing competitiveness of retail finance. Archival research on the evolution of savings banks helps to ascertain how, prior to competitive changes taking place, participants in bank markets had to develop capabilities to compete

Organisational change and the computerisation of British and Spanish savings banks, circa 1965-1985

In this article we explore organisational changes associated with the computarization of British savings banks while making a running comparison with developments in Spain. This international comparison addresses the evolution of the same organisational form in two distinct competitive environments in the late 20th century. Changes in regulation and technological developments (particularly applications of information technology) are said to be responsible for enhancing competitiveness of retail finance. Archival research on the evolution of savings banks helps to ascertain how, prior to competitive changes taking place, participants in bank markets had to develop capabilities to compete. Moreover, assess the response of collaborative agreements to opportunities opened by technological change (in particular resolve apparent scale disadvantages to contest bank markets). Of particular interest are choices made between applications of computer technology to redefine the relation between head office and retail branches as well as between staff at retail branches and customers.comparative financial markets, United Kingdom, Spain, market structure, technological change, regulatory change, savings banks, banks, TSB, cajas de ahorro

Evidence from the Patent Record on the Development of Cash Dispensing Technology

There are but a handful of systematic studies on the history of automated teller machines (ATMs) yet all fail to address the issue of paternity while perpetrating ‘common wisdom’ beliefs. This article looks at the birth of currency dispensing equipment, the immediate predecessor to the ATM. At the simplest level, at least four separate instance of innovation can reasonably claim to be the origin of the concept. However, the question as to who invented it is less illuminating than an understanding of the process of innovation itself and how these competing families developed into the modern conception of an ATM. Our research supports the view of user-driven innovation as surviving business records and oral histories tell of close involvement of bank staff in establishing requirements and choosing amongst alternative solutions in the implementation of first generation technology. This case thus shows greater understanding in the user’s role in shaping and directing technological development.Cash dispensers (ATMs), History, Financial data processing, Patents, Research and development, User interfaces

Organisational change and the computerisation of British and Spanish savings banks, 1965-1985

In this article we explore organisational changes associated with the automation of financial intermediaries in Spain and the UK. This international comparison looks at the evolution of the same organisational form in two distinct competitive environments. Changes in regulation and technological developments (particularly applications of information technology) are said to be responsible for enhancing competitiveness of retail finance. Archival research on the evolution of savings banks helps to ascertain how, prior to competitive changes taking place, participants in bank markets had to develop capabilities to compete.comparative financial markets; United Kingdom; Spain; market structure; technological change; regulatory change; savings banks; banks

Design for Coworking in Honolulu.

D.Arch. Thesis. University of Hawaiʻi at Mānoa 2018