44 research outputs found
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
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
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
Off-critical Luttinger Junctions
We investigate Luttinger junctions of quantum wires away from criticality.
The one-body scattering matrix, corresponding to the off-critical boundary
conditions at the junction, admits in general antibound and/or bound states.
Their contribution to the theory is fixed by causality. The presence/absence of
bound states determines the existence of two different regimes with
inequivalent physical properties. A scattering matrix without bound states
defines an isolated equilibrium system. Bound states instead drive the system
away from equilibrium, giving raise to non-trivial incoming or outgoing energy
flows in the junction. We derive in both regimes and in explicit form the
electromagnetic conductance tensor, pointing out the different impact of bound
and antibound states.Comment: LaTex, 9 pages, 1 figur
Energy transmutation in nonequilibrium quantum systems
We investigate the particle and heat transport in quantum junctions with the
geometry of star graphs. The system is in a nonequilibrium steady state,
characterized by the different temperatures and chemical potentials of the heat
reservoirs connected to the edges of the graph. We explore the
Landauer-Buettiker state and its orbit under parity and time reversal
transformations. Both particle number and total energy are conserved in these
states. However the heat and chemical potential energy are in general not
separately conserved, which gives origin to a basic process of energy
transmutation among them. We study both directions of this process in detail,
introducing appropriate efficiency coefficients. For scale invariant
interactions in the junction our results are exact and explicit. They cover the
whole parameter space and take into account all nonlinear effects. The energy
transmutation depends on the particle statistics.Comment: Version to appear in Journal of Physics A: Mathematical and Genera
Thermoelectric efficiency of critical quantum junctions
We derive the efficiency at maximal power of a scale-invariant (critical)
quantum junction in exact form. Both Fermi and Bose statistics are considered.
We show that time-reversal invariance is spontaneously broken. For fermions we
implement a new mechanism for efficiency enhancement above the Curzon-Ahlborn
bound, based on a shift of the particle energy in each heat reservoir,
proportional to its temperature. In this setting fermionic junctions can even
reach at maximal power the Carnot efficiency. The bosonic junctions at maximal
power turn out to be less efficient then the fermionic ones.Comment: 4.5 pages, 4 figures, 2 references and some clarifying remarks adde
Modular conjugations in 2D conformal field theory and holographic bit threads
We study the geometric action of some modular conjugations in two dimensional
(2D) conformal field theories. We investigate the bipartition given by an
interval when the system is in the ground state, either on the line or on the
circle, and in the thermal Gibbs state on the line. We find that the
restriction of the corresponding inversion maps to a spatial slice is obtained
also in the gauge/gravity correspondence through the geodesic bit threads in a
constant time slice of the dual static asymptotically AdS background. For a CFT
in the thermal state on the line, the modular conjugation suggests the
occurrence of a second world which can be related through the geodesic bit
threads to the horizon of the BTZ black brane background. An inversion map is
constructed also for the massless Dirac fermion in the ground state and on the
line bipartite by the union of two disjoint intervals.Comment: 49 pages, 15 figure