948 research outputs found
On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk
Dirac hamiltonian on the Poincare disk in the presence of an Aharonov-Bohm
flux and a uniform magnetic field admits a one-parameter family of self-adjoint
extensions. We determine the spectrum and calculate the resolvent for each
element of this family. Explicit expressions for Green functions are then used
to find Fredholm determinant representations for the tau function of the Dirac
operator with two branch points on the Poincare disk. Isomonodromic deformation
theory for the Dirac equation relates this tau function to a one-parameter
class of solutions of the Painleve VI equation with . We analyze long
distance behaviour of the tau function, as well as the asymptotics of the
corresponding Painleve VI transcendents as . Considering the limit of
flat space, we also obtain a class of solutions of the Painleve V equation with
.Comment: 38 pages, 5 figure
Ising Field Theory on a Pseudosphere
We show how the symmetries of the Ising field theory on a pseudosphere can be
exploited to derive the form factors of the spin fields as well as the
non-linear differential equations satisfied by the corresponding two-point
correlation functions. The latter are studied in detail and, in particular, we
present a solution to the so-called connection problem relating two of the
singular points of the associated Painleve VI equation. A brief discussion of
the thermodynamic properties is also presented.Comment: 39 pages, 6 eps figures, uses harvma
Form factors of twist fields in the lattice Dirac theory
We study U(1) twist fields in a two-dimensional lattice theory of massive
Dirac fermions. Factorized formulas for finite-lattice form factors of these
fields are derived using elliptic parametrization of the spectral curve of the
model, elliptic determinant identities and theta functional interpolation. We
also investigate the thermodynamic and the infinite-volume scaling limit, where
the corresponding expressions reduce to form factors of the exponential fields
of the sine-Gordon model at the free-fermion point.Comment: 20 pages, 2 figure
Non-Equilibrium Conformal Field Theories with Impurities
We present a construction of non-equilibrium steady states within conformal
field theory. These states sustain energy flows between two quantum systems,
initially prepared at different temperatures, whose dynamical properties are
represented by two, possibly different, conformal field theories connected
through an impurity. This construction relies on a real time formulation of
conformal defect dynamics based on a field scattering picture parallelizing -
but yet different from - the Euclidean formulation. We present the basic
characteristics of this formulation and give an algebraic construction of the
real time scattering maps that we illustrate in the case of SU(2)-based
conformal field theories.Comment: 12 pages + references, 1 figure. Published versio
Tricritical point of J1-J2 Ising model on hyperbolic lattice
A ferromagnetic-paramagnetic phase transition of the two-dimensional
frustrated Ising model on a hyperbolic lattice is investigated by use of the
corner transfer matrix renormalization group method. The model contains
ferromagnetic nearest-neighbor interaction J_1 and the competing
antiferromagnetic interaction J_2. A mean-field like second-order phase
transition is observed when the ratio \kappa = J_2 / J_1 is less than 0.203. In
the region 0.203 < \kappa < 1/4, the spontaneous magnetization is discontinuous
at the transition temperature. Such tricritical behavior suggests that the
phase transitions on hyperbolic lattices need not always be mean-field like.Comment: 7 pages, 13 figures, submitted to Phys. Rev.
Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories
We consider the finite-temperature frequency and momentum dependent two-point
functions of local operators in integrable quantum field theories. We focus on
the case where the zero temperature correlation function is dominated by a
delta-function line arising from the coherent propagation of single particle
modes. Our specific examples are the two-point function of spin fields in the
disordered phase of the quantum Ising and the O(3) nonlinear sigma models. We
employ a Lehmann representation in terms of the known exact zero-temperature
form factors to carry out a low-temperature expansion of two-point functions.
We present two different but equivalent methods of regularizing the divergences
present in the Lehmann expansion: one directly regulates the integral
expressions of the squares of matrix elements in the infinite volume whereas
the other operates through subtracting divergences in a large, finite volume.
Our central results are that the temperature broadening of the line shape
exhibits a pronounced asymmetry and a shift of the maximum upwards in energy
("temperature dependent gap"). The field theory results presented here describe
the scaling limits of the dynamical structure factor in the quantum Ising and
integer spin Heisenberg chains. We discuss the relevance of our results for the
analysis of inelastic neutron scattering experiments on gapped spin chain
systems such as CsNiCl3 and YBaNiO5.Comment: 54 pages, 10 figure
Direct Imaging of Multiple Planets Orbiting the Star HR 8799
Direct imaging of exoplanetary systems is a powerful technique that can
reveal Jupiter-like planets in wide orbits, can enable detailed
characterization of planetary atmospheres, and is a key step towards imaging
Earth-like planets. Imaging detections are challenging due to the combined
effect of small angular separation and large luminosity contrast between a
planet and its host star. High-contrast observations with the Keck and Gemini
telescopes have revealed three planets orbiting the star HR 8799, with
projected separations of 24, 38, and 68 astronomical units. Multi-epoch data
show counter-clockwise orbital motion for all three imaged planets. The low
luminosity of the companions and the estimated age of the system imply
planetary masses between 5 and 13 times that of Jupiter. This system resembles
a scaled-up version of the outer portion of our Solar System.Comment: 30 pages, 5 figures, Research Article published online in Science
Express Nov 13th, 200
Phase transition of clock models on hyperbolic lattice studied by corner transfer matrix renormalization group method
Two-dimensional ferromagnetic N-state clock models are studied on a
hyperbolic lattice represented by tessellation of pentagons. The lattice lies
on the hyperbolic plane with a constant negative scalar curvature. We observe
the spontaneous magnetization, the internal energy, and the specific heat at
the center of sufficiently large systems, where the fixed boundary conditions
are imposed, for the cases N>=3 up to N=30. The model with N=3, which is
equivalent to the 3-state Potts model on the hyperbolic lattice, exhibits the
first order phase transition. A mean-field like phase transition of the second
order is observed for the cases N>=4. When N>=5 we observe the Schottky type
specific heat below the transition temperature, where its peak hight at low
temperatures scales as N^{-2}. From these facts we conclude that the phase
transition of classical XY-model deep inside the hyperbolic lattices is not of
the Berezinskii-Kosterlitz-Thouless type.Comment: REVTeX style, 4 pages, 6 figures, submitted to Phys. Rev.
Non-equilibrium quantum spin dynamics from classical stochastic processes
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide exact formulae of broad applicability for the time-dependence of expectation values and correlation functions following a quantum quench in terms of averages over classical stochastic processes. We further explore the behavior of the classical stochastic variables in the presence of dynamical quantum phase transitions, including results for their distributions and correlation functions. We provide details on the numerical solution of the associated stochastic differential equations, and examine the growth of fluctuations in the classical description. We discuss the strengths and limitations of the current implementation of the stochastic approach and the potential for further development
Stochastic Approach to Non-Equilibrium Quantum Spin Systems
We investigate a stochastic approach to non-equilibrium quantum spin systems
based on recent insights linking quantum and classical dynamics. Exploiting a
sequence of exact transformations, quantum expectation values can be recast as
averages over classical stochastic processes. We illustrate this approach for
the quantum Ising model by extracting the Loschmidt amplitude and the
magnetization dynamics from the numerical solution of stochastic differential
equations. We show that dynamical quantum phase transitions are accompanied by
clear signatures in the associated classical distribution functions, including
the presence of enhanced fluctuations. We demonstrate that the method is
capable of handling integrable and non-integrable problems in a unified
framework, including those in higher dimensions.Comment: 5 pages, 5 figure
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