Exact calculation of thermodynamical quantities of the integrable t-J model

The specific heat and the compressibility for the integrable t-J model are calculated showing Luttinger liquid behavior for low temperatures. A Trotter-Suzuki mapping and the quantum transfer matrix approach are utilized. Using an algebraic Bethe ansatz this method permits the exact calculation of the free energy and related quantities. A set of just two non-linear integral equations determining these quantities is studied for various particle densities and temperatures. The structure of the specific heat is discussed in terms of the elementary charge as well as spin excitations.Comment: 4 pages, 5 Postscript figures, uses epsf.sty and revtex, tar'ed, gzip'ed and uuencode

Excited state TBA and functional relations in spinless Fermion model

The excited state thermodynamic Bethe ansatz (TBA) equations for the spinless Fermion model are presented by the quantum transfer matrix (QTM) approach. We introduce a more general family called T-functions and explore functional relations among them (T-system) and their certain combinations (Y-system). {}From their analytical property, we derive a closed set of non-linear integral equations which characterize the correlation length of $$ at any finite temperatures. Solving these equations numerically, we explicitly determine the correlation length, which coincides with earlier results with high accuracy.Comment: 4 page

Commuting quantum transfer matrix approach to intrinsic Fermion system: Correlation length of a spinless Fermion model

The quantum transfer matrix (QTM) approach to integrable lattice Fermion systems is presented. As a simple case we treat the spinless Fermion model with repulsive interaction in critical regime. We derive a set of non-linear integral equations which characterize the free energy and the correlation length of $$ for arbitrary particle density at any finite temperatures. The correlation length is determined by solving the integral equations numerically. Especially in low temperature limit this result agrees with the prediction from conformal field theory (CFT) with high accuracy.Comment: 17 page

Completeness of ``Good'' Bethe Ansatz Solutions of a Quantum Group Invariant Heisenberg Model

The $sl_q(2)$-quantum group invariant spin 1/2 XXZ-Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for $q$ equal to a root of unity possess a finite number of ``good'' representations with non-zero q-dimension and ``bad'' ones with vanishing q-dimension. Correspondingly, the state space of an invariant Heisenberg chain decomposes into ``good'' and ``bad'' states. A ``good'' state may be described by a path of only ``good'' representations. It is shown that the ``good'' states are given by all ``good'' Bethe ansatz solutions with roots restricted to the first periodicity strip, i.e. only positive parity strings (in the language of Takahashi) are allowed. Applying Bethe's string counting technique completeness of the ``good'' Bethe states is proven, i.e. the same number of states is found as the number of all restricted path's on the $sl_q(2)$-Bratteli diagram. It is the first time that a ``completeness" proof for an anisotropic quantum invariant reduced Heisenberg model is performed.Comment: LaTeX file with LaTeX figures, 24 pages, 1 PiCTeX figur

The Hubbard chain at finite temperatures: ab initio calculations of Tomonaga-Luttinger liquid properties

We present a novel treatment of finite temperature properties of the one-dimensional Hubbard model. Our approach is based on a Trotter-Suzuki mapping utilizing Shastry's classical model and a subsequent investigation of the quantum transfer matrix. We derive non-linear integral equations for three auxiliary functions which have a clear physical interpretation of elementary excitations of spin type and charge excitations in lower and upper Hubbard bands. This allows for a transparent analytical study of certain limiting cases as well as for precise numerical investigations. We present data for the specific heat, magnetic and charge susceptibilities for various particle densities and coupling strengths U. The structure exposed by these curves is discussed in terms of the elementary charge and spin excitations. Special emphasis is placed on the study of the low-temperature behavior within our ab initio approach confirming the scaling predictions by Tomonaga-Luttinger liquid theory. In addition we make contact with the ``dressed energy'' formalism established for the analysis of ground state properties.Comment: 33 pages including 24 Postscript figure

Relativistic diffusive motion in random electromagnetic fields

We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Juettner equilibrium at the inverse temperature \beta^{-1}=mc^{2}. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).Comment: the version published in JP

Eileen J. Cox: her journey with diatoms

Eileen already had a keen interest in science during her school years. She studied Botany at Bristol University from 1967–1970, and it was her University teacher, Professor Frank Round, who inspired her interest in diatoms. During her PhD at Bristol under Frank Round’s supervision (1970–1975) she investigated the biology of tube-dwelling diatoms. At the same time, she worked as Departmental Demonstrator in the Botany Department. She left Bristol University in 1976 and became a Claridge Druce Research Fellow at the University of Oxford (1977–1980). Her investigations focused on the genus Navicula and the ultrastructure of diatom cells more generally. From 1979–1980 Eileen took up a post as lecturer at Pembroke College, University of Oxford. In 1980 Eileen moved to Germany and worked as a Royal Society European Exchange Research Fellow at the Litoralstation, Biologische Anstalt Helgoland. Here her studies focused on living diatoms, in particular the genus Donkinia, and she explored the value of live-cell features as diagnostic characters. From 1982–1985 she worked as a Max Planck research fellow at the Max-Planck-Institute at Plön, and from 1985–1988 as a Fellow of the German Research Foundation at the Max-Planck-Institute of Limnology, River Station, in Schlitz. During these years Eileen’s research on Navicula continued, but she also worked on the genera Placoneis, Parlibellus and Pinnularia, and studied relationships between diatom distributions and the environment. In 1989 Eileen returned to the UK to join the University of Sheffield, first as Research Associate, then as NERC Advanced Research Fellow and Honorary Lecturer, and carried out ecotoxicological studies on zooplankton. In 1992 she joined the Natural History Museum as Research Botanist to continue her research on diatoms. Here Eileen made many important contributions to diatom taxonomy and systematics. She carried out important studies on the naviculoid diatoms, and on live diatoms including her novel research on valve morphogenesis. Eileen has been involved in the organisation of many scientific meetings. In 1987 she organized the first meeting of the German-speaking diatomists in Schlitz, Germany, a meeting that has subsequently developed to include a much larger group of scientists from across Europe and from 2020 onwards will be the European Diatom Meeting. Other meetings she has helped organize include those held by the British Phycological Society, British Diatom Meetings, a NorthWest and Midlands Freshwater Group meeting, the Van Heurck Symposium on Taxonomy, a SETAC Europe meeting, a Society for the History of Natural History Meeting, and several European and International Phycological Congresses. Eileen has taught extensively; hosted 7 post-doctoral fellows and many research visitors to the Natural History Museum; supervised 10 PhD students, 4 M.Sc./M.Phil. students, 1 M.Res. student, and 4 final year B.Sc. students; and examined 9 PhDs and 1 DSc. She is currently a member of six learned societies, has refereed manuscripts for 31 scientific journals, has been invited speaker at 32 scientific meetings, gave 28 invited lectures at universities and research institutes, and presented at 56 national and international conferences. Eileen has given great service to several scientific societies, as council member, secretary or president. These include the British Phycological Society (president 2001–2002), the International Society for Diatom Research (president 2000– 112 Pl. Ecol. Evol. 152 (2), 2019 2002), the Systematics Association, and the International Phycological Society. Since 2007 Eileen has been Head of Postgraduate Studies in the Science Directorate of the Natural History Museum. As part of her role she develops and implements the training programmes of students at NHM, is responsible for strategic planning, and coordinates with research and training partners at universities and research institutions across the UK. Eileen is currently Editor in Chief of Diatom Research, and was previously Associate Editor (2011–2014), she is a board member of Fottea (since 2010), was guest co-editor of the Journal of the North American Benthological Society (Special Issue on Ecology of Springs), guest co-editor of the Journal of Limnology (Special Issue on Spring Biodiversity and Conservation), and Co-Editor-in-Chief of the European Journal of Phycology (2004–2009). Private hobbies include gardening, crafts such as cross stitching and sewing, visiting art museums and travelling, especially river and ocean cruises that have taken Eileen and Elliot recently to Alaska, the Caribbean, Germany, the Czech Republic, France and Portugal. Readers may like to read Eileen’s own description of her journey in diatoms, written for the young diatomists’ blog (available at https://youngisdr.blogspot.com/p/blog-page_12. html or in this volume supplementary information).info:eu-repo/semantics/publishedVersio

Exact thermodynamics of an Extended Hubbard Model of single and paired carriers in competition

By exploiting the technique of Sutherland's species, introduced in \cite{DOMO-RC}, we derive the exact spectrum and partition function of a 1D extended Hubbard model. The model describes a competition between dynamics of single carriers and short-radius pairs, as a function of on-site Coulomb repulsion ($U$) and filling ($\rho$). We provide the temperature dependence of chemical potential, compressibility, local magnetic moment, and specific heat. In particular the latter turns out to exhibit two peaks, both related to `charge' degrees of freedom. Their origin and behavior are analyzed in terms of kinetic and potential energy, both across the metal-insulator transition point and in the strong coupling regime.Comment: 14 pages, 15 eps figure

Tribute to Eileen J. Cox - Editorial

This issue is dedicated to Dr. Eileen Joan Cox on the occasion of her 70th birthday. Eileen is a very well-known phycologist who has made a major contribution to diatom research, for instance in terms of scientific papers published and species described (all listed in pages 412–414 of this issue) but also in addressing different topics (e.g. taxonomy of particular groups, the ecology of streams and tube dwelling diatoms, life-history and morphogenesis, valve terminology, the chloroplasts of living diatoms, and many others). The photos on the issue’s cover were chosen to reflect some of these aspects of Eileen’s work: Navicula oblonga refers to her work and advocacy of research on living diatoms; Encyonema refers to her earliest work on diatoms that live inside polysaccharide tubes; and Navicula refers to Eileen’s principal taxonomic focus over many years – the diatoms that used to be classified in the catch-all genus Navicula, which have now been split off and placed into many different genera. However, perhaps the most important contribution of a scientist is one that cannot be so easily measured, and that is the positive impact and influence the scientist makes on her/his colleagues. In this respect, Eileen’s contribution has been huge: she has always facilitated collaborations, welcoming students and visitors and putting facilities at their disposal, always taking care of the person as well as the work. She has also volunteered her time and energy generously to scientific societies, editing journals and many other good causes. Not surprisingly we (editors) did not have to make any effort to convince researchers to contribute to this issue. In fact, we faced the opposite problem in having to restrict the number of papers quite severely to keep the issue manageable. We would like to take this opportunity to apologize to all those who would have liked to contribute but have been left out.info:eu-repo/semantics/publishedVersio

Integrability of quantum chains: theory and applications to the spin-1/2 XXZXXZ chain

In this contribution we review the theory of integrability of quantum systems in one spatial dimension. We introduce the basic concepts such as the Yang-Baxter equation, commuting currents, and the algebraic Bethe ansatz. Quite extensively we present the treatment of integrable quantum systems at finite temperature on the basis of a lattice path integral formulation and a suitable transfer matrix approach (quantum transfer matrix). The general method is carried out for the seminal model of the spin-1/2 $XXZ$ chain for which thermodynamic properties like specific heat, magnetic susceptibility and the finite temperature Drude weight of the thermal conductivity are derived