546 research outputs found
Quantum group symmetry of integrable systems with or without boundary
We present a construction of integrable hierarchies without or with boundary,
starting from a single R-matrix, or equivalently from a ZF algebra. We give
explicit expressions for the Hamiltonians and the integrals of motion of the
hierarchy in term of the ZF algebra. In the case without boundary, the
integrals of motion form a quantum group, while in the case with boundary they
form a Hopf coideal subalgebra of the quantum group.Comment: 14 page
Remarks on the Letter of the Patriarch Theophylact to Tsar Peter in the Context of Certain Byzantine and Slavic Anti-heretic Texts
Translated by Marek MajerThe Letter of patriarch Theophylact to tsar Peter is the oldest, but seemingly not the most informative
Greek source for the history of Bogomilism. It is in essence a standard document, a typical
product of the patriarch’s chancery; it is not conceived as an in-depth investigation into the theological
minutiae pertaining to the cosmogony, dogmas and social doctrines of the heretics and the orthodox Church, but rather as a practical tutorial on how to thwart any given neo-Manichaean dualist heresy. It brings to light the fact that Bogomilism, the ‘new’ heresy was treated as an ‘old’ one – as a ‘reactivation’ of earlier gnostic-dualist and neo-Manichaean movements. The letter also features
a peculiar innovative feature, though not one directly related to the Bogomil heresy itself: the degree
of commitment to preaching the dogmas of the heresy is used for differentiating the situation of
the followers. The analysis of the Letter of patriarch Theophylact to tsar Peter raises the more general issue
concerning the detailed study of Byzantine and Slavic liturgical texts as a source of information
on neo-Manichaean doctrines
Quantum Fields on Star Graphs with Bound States at the Vertex
We investigate the propagation of a massless scalar field on a star graph,
modeling the junction of quantum wires. The vertex of the graph is
represented by a point-like impurity (defect), characterized by a one-body
scattering matrix. The general case of off-critical scattering matrix with
bound and/or antibound states is considered. We demonstrate that the
contribution of these states to the scalar field is fixed by causality (local
commutativity), which is the key point of our investigation. Two different
regimes of the theory emerge at this stage. If bound sates are absent, the
energy is conserved and the theory admits unitary time evolution. The behavior
changes if bound states are present, because each such state generates a kind
of damped harmonic oscillator in the spectrum of the field. These oscillators
lead to the breakdown of time translation invariance. We study in both regimes
the electromagnetic conductance of the Luttinger liquid on the quantum wire
junction. We derive an explicit expression for the conductance in terms of the
scattering matrix and show that antibound and bound states have a different
impact, giving raise to oscillations with exponentially damped and growing
amplitudes respectively.Comment: LaTex 1+29 pages, 2 figures: Expanded version with new title and
abstract; clarifying comments, fig.2 and references added; final version to
appear in J. Math. Phy
Bosonization and Vertex Algebras with Defects
The method of bosonization is extended to the case when a dissipationless
point-like defect is present in space-time. Introducing the chiral components
of a massless scalar field, interacting with the defect in two dimensions, we
construct the associated vertex operators. The main features of the
corresponding vertex algebra are established. As an application of this
framework we solve the massless Thirring model with defect. We also construct
the vertex representation of the sl(2) Kac-Moody algebra, describing the
complex interplay between the left and right sectors due to the interaction
with the defect. The Sugawara form of the energy-momentum tensor is also
explored.Comment: 23 pages, 1 figur
Luttinger Liquid in Non-equilibrium Steady State
We propose and investigate an exactly solvable model of non-equilibrium
Luttinger liquid on a star graph, modeling a multi-terminal quantum wire
junction. The boundary condition at the junction is fixed by an orthogonal
matrix S, which describes the splitting of the electric current among the
leads. The system is driven away from equilibrium by connecting the leads to
heat baths at different temperatures and chemical potentials. The associated
non-equilibrium steady state depends on S and is explicitly constructed. In
this context we develop a non-equilibrium bosonization procedure and compute
some basic correlation functions. Luttinger liquids with general anyon
statistics are considered. The relative momentum distribution away from
equilibrium turns out to be the convolution of equilibrium anyon distributions
at different temperatures. Both the charge and heat transport are studied. The
exact current-current correlation function is derived and the zero-frequency
noise power is determined.Comment: LaTex, 1+28 pages, 7 figure
Quantum Field Theories and Critical Phenomena on Defects
We construct and investigate quantum fields induced on a d-dimensional
dissipationless defect by bulk fields propagating in a (d+1)-dimensional space.
All interactions are localized on the defect. We derive a unitary non-canonical
quantum field theory on the defect, which is analyzed both in the continuum and
on the lattice. The universal critical behavior of the underlying system is
determined. It turns out that the O(N)-symmetric phi^4 theory, induced on the
defect by massless bulk fields, belongs to the universality class of particular
d-dimensional spin models with long-range interactions. On the other hand, in
the presence of bulk mass the critical behavior crossovers to the one of
d-dimensional spin models with short-range interactions.Comment: 20 pages, references adde
Correlation functions of one-dimensional anyonic fluids
A universal description of correlation functions of one-dimensional anyonic
gapless systems in the low-momentum regime is presented. We point out a number
of interesting features, including universal oscillating terms with frequency
proportional to the statistical parameter and beating effects close to the
fermion points. The results are applied to the one-dimensional anyonic
Lieb-Liniger model and checked against the exact results in the impenetrable
limit.Comment: 4 pages, 1 figur
Algebraic approach to multiple defects on the line and application to Casimir force
An algebraic framework for quantization in presence of arbitrary number of
point-like defects on the line is developed. We consider a scalar field which
interacts with the defects and freely propagates away of them. As an
application we compute the Casimir force both at zero and finite temperature.
We derive also the charge density in the Gibbs state of a complex scalar field
with defects. The example of two delta-defects is treated in detail.Comment: 24 pages, 10 figure
Non-linear quantum noise effects in scale invariant junctions
We study non-equilibrium steady state transport in scale invariant quantum
junctions with focus on the particle and heat fluctuations captured by the
two-point current correlation functions. We show that the non-linear behavior
of the particle current affects both the particle and heat noise. The existence
of domains of enhancement and reduction of the noise power with respect to the
linear regime are observed. The impact of the statistics is explored. We
demonstrate that in the scale invariant case the bosonic particle noise exceeds
the fermionic one in the common domain of heat bath parameters. Multi-lead
configurations are also investigated and the effect of probe terminals on the
noise is discussed.Comment: LaTex, 1+20 pages, 10 figure
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