Luttinger Liquid in Non-equilibrium Steady State

Mihail Mintchev; Paul Sorba

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Luttinger Liquid in Non-equilibrium Steady State

Mihail Mintchev, Paul Sorba

Mathematical Physics · Submitted 19 Oct 2012

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The authors' main claim The relative momentum distribution away from equilibrium turns out to be the convolution of equilibrium anyon distributions at different temperatures.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.05 · mentions code or data availability 0.02.

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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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We propose and investigate an exactly solvable model of non-equilibrium Luttinger liquid on a star graph, modeling a multi-terminal quantum wire junction.	contribution 0.99	0.94	0.10	asserted 0.91
s1	The boundary condition at the junction is fixed by an orthogonal matrix S, which describes the splitting of the electric current among the leads.	method 0.91	0.58	0.04	asserted 1.00
s2	The system is driven away from equilibrium by connecting the leads to heat baths at different temperatures and chemical potentials.	method 0.97	0.51	0.03	asserted 1.00
s3	The associated non-equilibrium steady state depends on S and is explicitly constructed.	contribution 0.56	0.89	0.16	asserted 1.00
s4	In this context we develop a non-equilibrium bosonization procedure and compute some basic correlation functions.	method 0.85	0.95	0.07	asserted 1.00
s5	Luttinger liquids with general anyon statistics are considered.	contribution 0.87	0.47	0.04	asserted 0.92
s6	The relative momentum distribution away from equilibrium turns out to be the convolution of equilibrium anyon distributions at different temperatures.	result 1.00	0.93	0.25	asserted 1.00
s7	Both the charge and heat transport are studied.	contribution 1.00	0.89	0.06	asserted 0.96
s8	The exact current-current correlation function is derived and the zero-frequency noise power is determined.	result 0.91	0.95	0.18	asserted 1.00

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Original abstract

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.

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2 arXiv papers cite this in 3 sentences

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For $τ≠τ^'$, the result is [equation] which, up to the overall normalization factor, exactly coincides with the chiral half of the two-point Wightman function for $(1+1)$-dimensional anyon field at finite temperature $T=a/(2π)$ [ref] , where the proper time $τ$ plays the role of the light-cone coordinates $x^±=x^0±x^1$ of two-dimensional Minkowski spacetime.

Emergent Anyon Distribution in the Unruh Effect · Statistics Interpolation: Emergent Anyon Distribution · 0.89

What it cites · 14 sentences without a confident label

Builds on 1 paper

Eq. ([ref]) confirms the result of [ref] for $c=1$ and extends this result in two directions: imperfect junction with transmission probability $sin^2(θ)$ and $μ_b≠0$.

Energy flow in non-equilibrium conformal field theory · Energy density and energy transport in $Ω_β,μ_b$ · 0.96

Uses the method or tool of 1 paper

The normalization of ([ref]) is fixed [ref] by the Ward identities associated with the electric charge$Q_+$and the helicity$Q_-$defined by [equation] The normalization of ([ref]) in turn is determined by the conservation law [equation] Plugging ([ref],[ref],[ref]) in the quantum equations of motion [equation] one finds [equation] Moreover, the exchange relation ([ref]) implies [equation] Eqs. ([ref],[ref],[ref]) provide a system for determining$v$and$ζ_±$(or equivalently$σ$and$τ$) in terms of$$̨ and $g_±$.

Junctions of anyonic Luttinger wires · Operator solution of the TL model on $Γ$ · 0.81

Compares with 2 papers

Non-linear effects are absent in the critical regime under consideration, which implies the conductance tensor [equation] We see that the NESS approach, adopted in this paper, confirms the result for $$, obtained previously for $=̨1$ by different methods, including renormalization group techniques [ref] , linear response theory [ref] and conformal field theory [ref] .

Quantum Field Theory on Star Graphs · Charge and heat transport · 0.98
Non-linear effects are absent in the critical regime under consideration, which implies the conductance tensor [equation] We see that the NESS approach, adopted in this paper, confirms the result for $$, obtained previously for $=̨1$ by different methods, including renormalization group techniques [ref] , linear response theory [ref] and conformal field theory [ref] .

Bosonization and Scale Invariance on Quantum Wires · Charge and heat transport · 0.98

Cites as background 3 papers

The above structure is very general and equations ([ref],[ref]) apply to any representation of the algebra $$, which is a simplified version of the so called reflection-transmission (RT) algebra [ref] - [ref] , describing factorized scattering in integrable models with point-like defects in one dimension.

Reflection-Transmission Algebras · The non-equilibrium steady state $Ω_β,μ__b$ · 0.83
The heath transport has been investigated recently in the framework of conformal field theory (CFT) for generic central charge $c$ in [ref] .

Energy flow in non-equilibrium conformal field theory · Energy density and energy transport in $Ω_β,μ_b$ · 0.93
This theory[For some more recent reviews we refer to [ref] - [ref] .] applies to various systems, including nanowire junctions and carbon nanotubes, which are available nowadays in experiment [ref] - [ref] .

A Glimpse into the Past: The Recent Evolution of Globular Clusters · Introduction · 0.98

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