32,587 research outputs found
Quantum invariants of motion in a generic many-body system
Dynamical Lie-algebraic method for the construction of local quantum
invariants of motion in non-integrable many-body systems is proposed and
applied to a simple but generic toy model, namely an infinite kicked
chain of spinless fermions. Transition from integrable via {pseudo-integrable
(\em intermediate}) to quantum ergodic (quantum mixing) regime in parameter
space is investigated. Dynamical phase transition between ergodic and
intermediate (neither ergodic nor completely integrable) regime in
thermodynamic limit is proposed. Existence or non-existence of local
conservation laws corresponds to intermediate or ergodic regime, respectively.
The computation of time-correlation functions of typical observables by means
of local conservation laws is found fully consistent with direct calculations
on finite systems.Comment: 4 pages in REVTeX with 5 eps figures include
Quantum transfer-matrices for the sausage model
In this work we revisit the problem of the quantization of the
two-dimensional O(3) non-linear sigma model and its one-parameter integrable
deformation -- the sausage model. Our consideration is based on the so-called
ODE/IQFT correspondence, a variant of the Quantum Inverse Scattering Method.The
approach allowed us to explore the integrable structures underlying the quantum
O(3)/sausage model. Among the obtained results is a system of non-linear
integral equations for the computation of the vacuum eigenvalues of the quantum
transfer-matrices.Comment: 89 pages, 10 figures, v2: misprints corrected, some comments added,
v3, v4: minor corrections, references adde
Correlation Functions in 2-Dimensional Integrable Quantum Field Theories
In this talk I discuss the form factor approach used to compute correlation
functions of integrable models in two dimensions. The Sinh-Gordon model is our
basic example. Using Watson's and the recursive equations satisfied by matrix
elements of local operators, I present the computation of the form factors of
the elementary field and the stress-energy tensor of
the theory.Comment: 19pp, LATEX version, (talk at Como Conference on ``Integrable Quantum
Field Theories''
Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
The integrable quantum models, associated to the transfer matrices of the
6-vertex reflection algebra for spin 1/2 representations, are studied in this
paper. In the framework of Sklyanin's quantum separation of variables (SOV), we
provide the complete characterization of the eigenvalues and eigenstates of the
transfer matrix and the proof of the simplicity of the transfer matrix
spectrum. Moreover, we use these integrable quantum models as further key
examples for which to develop a method in the SOV framework to compute matrix
elements of local operators. This method has been introduced first in [1] and
then used also in [2], it is based on the resolution of the quantum inverse
problem (i.e. the reconstruction of all local operators in terms of the quantum
separate variables) plus the computation of the action of separate covectors on
separate vectors. In particular, for these integrable quantum models, which in
the homogeneous limit reproduce the open spin-1/2 XXZ quantum chains with
non-diagonal boundary conditions, we have obtained the SOV-reconstructions for
a class of quasi-local operators and determinant formulae for the
covector-vector actions. As consequence of these findings we provide one
determinant formulae for the matrix elements of this class of reconstructed
quasi-local operators on transfer matrix eigenstates.Comment: 40 pages. Minor modifications in the text and some notations and some
more reference adde
Hamiltonian Dynamics, Classical R-matrices and Isomonodromic Deformations
The Hamiltonian approach to the theory of dual isomonodromic deformations is
developed within the framework of rational classical R-matrix structures on
loop algebras. Particular solutions to the isomonodromic deformation equations
appearing in the computation of correlation functions in integrable quantum
field theory models are constructed through the Riemann-Hilbert problem method.
The corresponding -functions are shown to be given by the Fredholm
determinant of a special class of integral operators.Comment: LaTeX 13pgs (requires lamuphys.sty). Text of talk given at workshop:
Supersymmetric and Integrable Systems, University of Illinois, Chicago
Circle, June 12-14, 1997. To appear in: Springer Lecture notes in Physic
Measurement and Information Extraction in Complex Dynamics Quantum Computation
We address the problem related to the extraction of the information in the
simulation of complex dynamics quantum computation. Here we present an example
where important information can be extracted efficiently by means of quantum
simulations. We show how to extract efficiently the localization length, the
mean square deviation and the system characteristic frequency. We show how this
methods work on a dynamical model, the Sawtooth Map, that is characterized by
very different dynamical regimes: from near integrable to fully developed
chaos; it also exhibits quantum dynamical localization.Comment: 8 pages, 4 figures, Proceeding of "First International Workshop
DICE2002 - Piombino (Tuscany), (2002)
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