Non-equilibrium steady states of quantum systems on star graphs

2011/06/29 by Mihail Mintchev · 36 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Charge (physics) #Context (archaeology) #Coupling (piping) #Dirac (video compression format) #Electromagnetic field #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum and electron transport phenomena #Quantum graph #Schrödinger's cat #Star (game theory) #Vertex (graph theory) #cond-mat.stat-mech #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/1751-8113/44/41/415201

published in Journal of Physics A Mathematical and Theoretical 44(41), 415201 (Institute of Physics) · LaTex, 1+28 pages, 5 figures

arxiv created 2011/06/29 · openalex publication_date 2011/09/19 · arxiv updated 2011/09/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Non-equilibrium steady states of quantum fields on star graphs are explicitly constructed.These states are parametrized by the temperature and the chemical potential, associated with each edge of the graph.Time reversal invariance is spontaneously broken.We study in this general framework the transport properties of the Schrödinger and the Dirac systems on a star graph, modeling a quantum wire junction.The interaction, which drives the system away from equilibrium, is localized in the vertex of the graph.All point-like vertex interactions, giving rise to self-adjoint Hamiltonians possibly involving the minimal coupling to a static electromagnetic field in the ambient space, are considered.In this context, we compute the exact electric steady current and the non-equilibrium charge density.We also investigate the heat transport and derive the Casimir energy density away from equilibrium.The appearance of Friedel-type oscillations of the charge and energy densities along the edges of the graph is established.We focus finally on the noise power and discuss the non-trivial impact of the point-like interactions on the noise.

Citations

• Spintronics with NSN junction of one-dimensional quantum wires: A study of pure spin current and magnetoresistance
• Oscillatory Nonlinear Conductance of an Interacting Quantum Wire with an Impurity
• Measuring fractional charge and statistics in fractional quantum Hall fluids through noise experiments
• Mathematical aspects of vacuum energy on quantum graphs
• Landauer-Type Transport Theory for Interacting Quantum Wires: Application to Carbon Nanotube Y Junctions
• The generalized star product and the factorization of scattering matrices on graphs
• Conductance of Tomonaga-Luttinger liquid wires and junctions with resistances
• An algebraic approach to multiple defects on the line and application to the Casimir force
• Quantum Wires with Magnetic Fluxes
• Interedge interactions and fixed points at a junction of quantum Hall line junctions
• Renormalization group study of transport through a superconducting junction of multiple one-dimensional quantum wires
• Impurity and correlation effects on transport in one-dimensional quantum wires
• Shot Noise in Mesoscopic Conductors
• Kirchhoff's Rule for Quantum Wires. II: The Inverse Problem with Possible Applications to Quantum Computers
• Quantum fields on star graphs
• Electrical resistance of disordered one-dimensional lattices
• Regular networks of Luttinger liquids

Cited by

• Locally quasi-stationary states in noninteracting spin chains
• Energy transmutation in nonequilibrium quantum systems
• Non-equilibrium current cumulants and moments with a point-like defect
• Quantum Transport in Presence of Bound States – Noise Power
• Networks of quantum wire junctions: A system with quantized integer Hall resistance without vanishing longitudinal resistivity