123,578 research outputs found
Pseudo-differential equations, and the Bethe ansatz for the classical Lie algebras
No full textThe correspondence between ordinary differential equations and Bethe ansatz equations for integrable lattice models in their continuum limits is generalised to vertex models related to classical simple Lie algebras. New families of pseudo-differential equations are proposed, and a link between specific generalised eigenvalue problems for these equations and the Bethe ansatz is deduced. The pseudo-differential operators resemble in form the Miura-transformed Lax operators studied in work on generalised KdV equations, classical W-algebras and, more recently, in the context of the geometric Langlands correspondence. Negative-dimension and boundary-condition dualities are also observe
Bethe Ansatz equations for the classical A^(1)_n affine Toda field theories
No full textWe establish a correspondence between classical A(1)n affine Toda field theories and An Bethe Ansatz systems. We show that the connection coefficients relating specific solutions of the associated classical linear problem satisfy functional relations of the type that appear in the context of the massive quantum integrable model.1751-812
Z(_N)-symmetric field theories and the thermodynamic Bethe ansatz
No full textThis thesis is concerned with perturbed conformal field theory, the thermodynamic Bethe ansatz technique and applications to statistical mechanics. In particular, the phase space of two dimensional Z(_N)-symmetric statistical models is examined using these techniques. The aim of the first two chapters is to review some general material concerning statistical mechanics, perturbed conformal field theory, integrable two-dimensional quantum field theory and the thermodynamic Bethe ansatz (TBA) technique. In the third chapter Z(_N)-symmetric statistical theories are discussed and the known features of the phase space of such models are surveyed. The field content of the conformal models in this space (called parafermionic models) is investigated in order to determine which perturbations can be used to investigate the phase space. In the fourth and fifth chapters TBA equations are proposed to describe massless and massive renormalisation flows from the Z(_N)-symmetric conformal theories under self-dual Z(_N)-symmetric perturbations. According to the sign of the perturbation parameter the infrared limits are shown to be either conformal c = 1 or massive theories. The ground state energies of these models can be discovered in all perturbative regimes via the TBA method and the results agree with perturbation theory in ultraviolet and infrared limits. Results from detailed studies of the N = 5, 6..10 models are presented throughout. It is also deduced that the parafermionic models lie exactly at the bifurcation point of the first-order transition region into the Kosterlitz-Thouless region of the Z(_N)-symmetric phase space. The sixth and seventh chapters deal solely with massive perturbations. In chapter six, results from the TBA equations are used to deduce the mass spectrum and the vacuum structure of the underlying scattering theory. In chapter seven, proposals for the massive S-matrices are made. For N odd the mass spectra proposed by the TBA method and that predicted by the S-matrix approach (using the minimality principle) differ. It is suggested therefore, that the N odd S-matrices contain zeroes in the physical strip, violating the minimality principle
Interview with Hans A. Bethe
No full textTwo interviews conducted at Caltech in 1982 and 1993 with theoretical physicist Hans Bethe. The recipient of the Nobel Prize in physics in 1967 for his work on nuclear reactions in stars, Bethe was born in Strasbourg and educated at the University of Frankfurt and at the University of Munich, where he earned a PhD in 1928 under A. Sommerfeld at the Institute for Theoretical Physics. From 1928 to 1933, Bethe held a variety of teaching positions in Germany, also visiting the Physics Institute of the University of Rome in Via Panisperna 89A in 1931 and 1932. Hitler's rise to power forced Bethe from the University of Tubingen in 1933. Two years later he became an assistant professor at Cornell University, garnering a full professorship there in 1937. In the 1982 interview Bethe speaks principally about his contacts at Caltech, including L. Pauling, R. Millikan, T. von Karman, F. Zwicky, C. C. Lauritsen, W. A. Fowler, R. Feynman and R. F. Bacher. He discusses his relations with other prominent physicists, including E. Teller, N. Bohr and J. R. Oppenheimer. He also describes his first impressions of nuclear physics, the political climate in Italy in the 1930s, and the Rome school of physics, including E. Fermi, F. Rasetti, and E. Segre. The 1993 interview concerns R. Bacher at Cornell and at work on the Manhattan Project at Los Alamos during World War II
Perturbed conformal field theory, nonlinear integral equations and spectral problems
No full textThis thesis is concerned with various aspects of perturbed conformal field theory and the methods used to calculate finite-size effects of integrable quantum field theories. Nonlinear integral equations are the main tools to find the exact ground-state energy of a quantum field theory. The thermodyamic Bethe ansatz (TBA) equations are a set of examples and are known for a large number of models. However, it is also an interesting question to find exact equations describing the excited states of integrable models. The first part of this thesis uses analytical continuation in a continuous parameter to find TBA like equations describing the spin-zero excited states of the sine-Gordon model at coupling β(^2) = 16π/3. Comparisons are then made with a further type of nonlinear integral equation which also predicts the excited state energies. Relations between the two types of equation are studied using a set of functional relations recently introduced in integrable quantum field theory. A relevant perturbation of a conformal field theory results in either a massive quantum field theory such as the sine-Gordon model, or a different massless conformal field theory. The second part of this thesis investigates flows between conformal field theories using a nonlinear integral equation. New families of flows are found which exhibit a rather unexpected behaviour. The final part of this thesis begins with a review of a connection between integrable quantum field theory and properties of certain ordinary differential equations of second- and third-order. The connection is based on functional relations which appear on both sides of the correspondence; for the second-order case these are exactly the functional relations mentioned above. The results are extended to include a correspondence between n(^th) order differential equations and Bethe ansatz system of SU(n) type. A set of nonlinear integral equations are derived to check the results
On quantum phase crossovers in finite systems
No full textIn this work we define a formal notion of a quantum phase crossover for certain Bethe ansatz solvable models. The approach we adopt exploits an exact mapping of the spectrum of a many-body integrable system, which admits an exact Bethe ansatz solution, into the quasi-exactly solvable spectrum of a one-body Schrodinger operator. Bifurcations of the minima for the potential of the Schrodinger operator determine the crossover couplings. By considering the behaviour of particular ground state correlation functions, these may be identified as quantum phase crossovers in the many-body integrable system with finite particle number. In this approach the existence of the quantum phase crossover is not dependent on the existence of a thermodynamic limit, rendering applications to finite systems feasible. We study two examples of bosonic Hamiltonians which admit second-order crossovers
Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases
No full textAbstractThe modified algebraic Bethe ansatz, introduced by Crampé and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-12 chain on the segment with lower and upper triangular boundaries. The eigenvalues and the eigenvectors are conjectured. They are characterized by a set of Bethe roots with cardinality equal to N the length of the chain and which satisfies a set of Bethe equations with an additional term. The conjecture follows from exact results for small chains. We also present a factorized formula for the Bethe vectors of the Heisenberg XXZ spin-12 chain on the segment with two upper triangular boundaries
Efeitos de aperiodicidade no comportamento crítico de modelos magnéticos na rede de Bethe
No full textDissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas. Programa de Pós-graduação em FísicaDemonstramos neste trabalho que a modulação dos parâmetros de interação dos hamiltonianos de Ising e Blume-Capel, segundo seqüências aperiódicas, pode ocasionar uma mudança de classe de universalidade na rede de Bethe e oscilação log-periódica da magnetização. Observamos possível mudança do expoente crítico da magnetização ß em relação a seu valor em sistemas homogêneos ou periódicos. Esta mudança não ocorre quando a seqüência de Fibonacci é usada. Na seqüência de duplicação de período caracterizamos o expoente ß como uma função da razão JA/JB. Na seqüência de Rudin-Shapiro obtemos evidências de que esta aperiodicidade causa mudança na classe de universalidade do sistema
Perturbative and non-perturbative studies in low dimensional quantum field theory
No full textA relevant perturbation of a conformal field theory (CFT) on the half-plane, by both a bulk and boundary operator, often leads to a massive theory with a particle description in terms of the bulk S-matrix and boundary reflection factor R. The link between the particle basis and the CFT in the bulk is usually made with the thermodynamic Bethe ansatz effective central charge C(_eff). This allows a conjectured S-matrix to be identified with a specific perturbed CFT. Less is known about the links between the reflection factors and conformal boundary conditions, but it has been proposed that an exact, off-critical version of Affleck and Ludwig's g-function could be used, analogously to C(_eff), to identify the physically realised reflection factors and to match them with the corresponding boundary conditions. In the first part of this thesis, this exact g-function is tested for the purely elastic scattering theories related to the ADET Lie algebras. Minimal reflection factors are given, and a method to incorporate a boundary parameter is proposed. This enables the prediction of several new flows between conformal boundary conditions to be made. The second part of this thesis concerns the three-parameter family of PT-symmetric Hamiltonians H(M,o,1) = p(^2) – (ix) (^2M) – α(ix) The positions where the eigenvalues merge and become complex correspond to quadratic and cubic exceptional points. The quasi-exact solvability of the models for M = 3 is exploited to exploreaway from M = 3 is investigated using both numerical and perturbative approaches
Current presentation for the double super-Yangian DY(gl(m|n)) and Bethe vectors
No full textInternational audienceWe find Bethe vectors for quantum integrable models associated with thesupersymmetric Yangians in terms of the currentgenerators of the Yangian double . More specifically,we use the method of projections onto intersections of different type Borelsubalgebras in this infinite dimensional algebra to construct the Bethevectors. Calculating these projection the supersymmetric Bethe vectors can beexpressed through matrix elements of the universal monodromy matrix elements.Using two different but isomorphic current realizations of the Yangian double we obtain two different presentations for the Bethevectors. These Bethe vectors are also shown to obey some recursion relationswhich prove their equivalence
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