Fluctuations in heat current and scaling dimension

Abstract

In this work, we theoretically study the heat flow between two $1+1$d chiral gapless systems connected by a point contact. With a small temperature gradient between the two, we find that the ratio between fluctuations of the heat current and the heat current itself is proportional to the scaling dimension -- a universal number that characterizes the distribution of the particles tunneling through the point contact. We adopt two different approaches, scattering theory and conformal field theory, to calculate this ratio and see that their results agree. Our findings are useful for probing not only fractional charge excitations in fractional quantum Hall states but also neutral ones in non-Abelian phases.

arXiv comment24 pages, 3 figures

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• Observation of the scaling dimension of fractional quantum Hall anyons
• Anyon statistics through conductance measurements of time-domain interferometry
• Delta-T noise for fractional quantum Hall states at different filling factor
• Impact of potential and temperature fluctuations on charge and heat transport in quantum Hall edges in the heat Coulomb blockade regime
• Role of scaling dimensions in generalized noises in fractional quantum Hall tunneling due to a temperature bias
• Landscapes of an out-of-equilibrium anyonic sea
• Anyon braiding on the single edge of a fractional quantum Hall state
• Universal relations between thermoelectrics and noise in mesoscopic transport across a tunnel junction
• Probing anyon statistics on a single-edge loop in the fractional quantum Hall regime
• Heating Dynamics of Mesoscopic Electron Baths at High Magnetic Field