Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids

Abstract

Using the Calogero model as an example, we show that the transport in interacting non-dissipative electronic systems is essentially non-linear. Non-linear effects are due to the curvature of the electronic spectrum near the Fermi energy. As is typical for non-linear systems, propagating wave packets are unstable. At finite time shock wave singularities develop, the wave packet collapses, and oscillatory features arise. They evolve into regularly structured localized pulses carrying a fractionally quantized charge - {\it soliton trains}. We briefly discuss perspectives of observation of Quantum Shock Waves in edge states of Fractional Quantum Hall Effect and a direct measurement of the fractional charge.

References in corpus (4)

• Collective fields, Calogero-Sutherland model and generalized matrix models
• Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model
• Waves and Solitons in the Continuum Limit of the Calogero-Sutherland Model
• Energetics of Quantum Antidot States in Quantum Hall Regime

Cited by in corpus (78)

• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Soliton gases and generalized hydrodynamics
• Large-scale description of interacting one-dimensional Bose gases: generalized hydrodynamics supersedes conventional hydrodynamics
• Conformal field theory out of equilibrium: a review
• Lecture notes on Generalised Hydrodynamics
• A note on generalized hydrodynamics: inhomogeneous fields and other concepts
• Dynamics of hard rods with initial domain wall state
• Observation of a gradient catastrophe generating solitons
• Formation of Quantum Shock Waves by Merging and Splitting Bose-Einstein Condensates
• Numerical simulations of time resolved quantum electronics
• Non-equilibrium steady states in the quantum XXZ spin chain
• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Non-Equilibrium Dynamics and Weakly Broken Integrability
• Observation of shock waves in a strongly interacting Fermi gas
• Resonant radiation shed by dispersive shock waves
• Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation
• Transport fluctuations in integrable models out of equilibrium
• Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas
• Quantum ripples over a semi-classical shock
• A hydrodynamic approach to non-equilibrium conformal field theories
• Non-Linear hydrodynamics and Fractionally Quantized Solitons at Fractional Quantum Hall Edge
• Hydrodynamics of Euler incompressible fluid and the Fractional Quantum Hall Effect
• Hydrodynamics of cold atomic gases in the limit of weak nonlinearity, dispersion and dissipation
• Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
• Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion
• Quantum Shock Waves and Population Inversion in Collisions of Ultracold Atomic Clouds
• What is a quantum shock wave?
• Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical lattices
• On the effective hydrodynamics of FQHE
• Temporal dynamics of tunneling. Hydrodynamic approach
• Non-chiral Intermediate Long Wave equation and inter-edge effects in narrow quantum Hall systems
• Real-time dynamics in the one-dimensional Hubbard model
• Dissipationless kinetics of one dimensional interacting fermions
• Hard-Wall Confinement of a Fractional Quantum Hall Liquid
• Optical Spatial Shock Waves in Nonlocal Nonlinear Media
• Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type
• Spin-charge separated quasiparticles in one dimensional quantum fluids
• Hydrodynamics and the eigenstate thermalization hypothesis
• Effective Edge State Dynamics in the Fractional Quantum Hall Effect
• The classical hydrodynamics of the Calogero-Sutherland model
• Spin generalizations of the Benjamin-Ono equation
• Lifshitz Scaling, Microstate Counting from Number Theory and Black Hole Entropy
• Crossover dynamics of dispersive shocks in Bose-Einstein condensates characterized by two and three-body interactions
• Hydrodynamics of local excitations after an interaction quench in 1D cold atomic gases
• Linear and nonlinear edge dynamics of trapped fractional quantum Hall droplets
• Quantum Hall Edges with Hard Confinement: Exact Solution beyond Luttinger Liquid
• Far-From-Equilibrium Physics: An Overview
• Anisotropic Optical Shock Waves in Isotropic Media with Giant Nonlocal Nonlinearity
• Riemann surface and quantization
• Platforms for the realization and characterization of Tomonaga-Luttinger liquids
• Cold Fermi-gas with long range interaction in a harmonic trap
• How Emergent is Gravity?
• Mobile impurity approach to the optical conductivity in the Hubbard chain
• Transition fronts and their universality classes
• $\Psi$ - model of micro- and macrosystems
• The Quantum Hydrodynamics of the Sutherland Model
• The fate of quantum shock waves at late times
• Accessing and Manipulating Dispersive Shock Waves in a Nonlinear and Nonlocal Rydberg Medium
• Solitons in a one-dimensional Wigner crystal
• Directed-polymer systems explored via their quantum analogs: Topological constraints and their consequences
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• Quantum nonlinear optics on the edge of a few-particle fractional quantum Hall fluid in a small lattice
• Exact Bohr-Sommerfeld Conditions for the Quantum Periodic Benjamin-Ono Equation
• The anisotropic chiral boson
• Connected correlations in partitioning protocols: a case study and beyond
• Non-linear edge dynamics of an Integer Quantum Hall fluid
• Phase space holography with no strings attached
• Quantum Generalized Hydrodynamics of the Tonks-Girardeau gas: density fluctuations and entanglement entropy
• Generalized Gibbs Ensemble of 2D CFTs with U(1) Charge from the AGT Correspondence
• Hydrodynamics of the Polyakov Line in SU$(N_c)$ Yang-Mills
• Berry Phases in the Bosonization of Nonlinear Edge Modes
• Dissipative Hot-spot Enabled Shock and Bounce Dynamics via Terahertz Quantum Quenches in Helical Edge States
• Refermionized theory of the edge modes of a fractional quantum Hall cloud
• Edge dynamics of an Integer Quantum Hall system