225 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
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
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
The Role of Initial Conditions in Presence of Extra Dimensions
Quantum field theory in 4+1 dimensional bulk space with boundary, representing a 3-brane, is considered. We study the impact of the initial conditions in the bulk on the field dynamics on the brane. We demonstrate that these conditions determine the Kaluza-Klein measure. We also establish the existence of a rich family of quantum fields on the brane, generated by the same bulk action, but corresponding to different initial conditions. A simple classification of these fields is proposed and it is shown that some of them lead to ultraviolet finite theories, which have some common features with strings
Quantum Fields on Star Graphs
We construct canonical quantum fields which propagate on a star graph
modeling a quantum wire. The construction uses a deformation of the algebra of
canonical commutation relations, encoding the interaction in the vertex of the
graph. We discuss in this framework the Casimir effect and derive the
correction to the Stefan-Boltzmann law induced by the vertex interaction. We
also generalize the algebraic setting for covering systems with integrable bulk
interactions and solve the quantum non-linear Schroedinger model on a star
graph.Comment: LaTex 23+1 pages, 4 figure
The quantum non-linear Schrodinger model with point-like defect
We establish a family of point-like impurities which preserve the quantum
integrability of the non-linear Schrodinger model in 1+1 space-time dimensions.
We briefly describe the construction of the exact second quantized solution of
this model in terms of an appropriate reflection-transmission algebra. The
basic physical properties of the solution, including the space-time symmetry of
the bulk scattering matrix, are also discussed.Comment: Comments on the integrability and the impurity free limit adde
Modular Hamiltonians for the massless Dirac field in the presence of a defect
We study the massless Dirac field on the line in the presence of a point-like defect characterised by a unitary scattering matrix, that allows both reflection and transmission. Considering this system in its ground state, we derive the modular Hamiltonians of the subregion given by the union of two disjoint equal intervals at the same distance from the defect. The absence of energy dissipation at the defect implies the existence of two phases, where either the vector or the axial symmetry is preserved. Besides a local term, the densities of the modular Hamiltonians contain also a sum of scattering dependent bi-local terms, which involve two conjugate points generated by the reflection and the transmission. The modular flows of each component of the Dirac field mix the trajectory passing through a given initial point with the ones passing through its reflected and transmitted conjugate points. We derive the two-point correlation functions along the modular flows in both phases and show that they satisfy the Kubo-Martin-Schwinger condition. The entanglement entropies are also computed, finding that they do not depend on the scattering matrix
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