Connections Between Microscopic and Macroscopic Laws by Abhishek Dhar

Explore the connections between microscopic and macroscopic laws in physics through this comprehensive colloquium talk. Delve into the fundamental principles of heat conduction, Fourier's law, and the heat diffusion equation. Examine various approaches to proving Fourier's law, including kinetic theory and direct nonequilibrium measurements. Investigate heat conduction in disordered harmonic crystals, Anderson localization, and one-dimensional systems with non-integrable interactions. Discover signatures of anomalous transport and explore phenomenological descriptions like the Levy walkers model. Gain insights into fluctuating hydrodynamics, equilibrium simulations, and hydrodynamic theory for one-dimensional interacting systems. Conclude with a discussion on fluctuating hydrodynamics for a one-dimensional fluid and participate in a Q&A session to deepen your understanding of these complex physical phenomena.

DATE: Mon, 20 December 2021, 15:30 to
Connections between microscopic and macroscopic laws
Outline
MICROSCOPIC LAWS
MACROSCOPIC LAWS - Thermodynamics
Microscopic to Macroscopic - Equilibrium Statistical Physics
Macroscopic laws to describe nonequilibrium phenomena
Part I - Heat CONDUCTION and Fourier's law
Fourier's law and the heat diffusion equation
Proving Fourier's law
Simplest theory of heat conduction: Kinetic theory
Kinetic theory for phonon gas
Other approaches
Direct computation of from nonequilibrium measurements.
Heat current and heat conductivity
Results so far
Experiments
Experiments: graphene
The simplest microscopic model: a harmonic crystal
Possible scattering mechanisms
Heat conduction in disordered harmonic crystals
Landauer formula for heat current
Disordered Harmonic systems: Anderson localization
Character of normal modes of a disordered crystal
ID disordered harmonic chain
Disordered harmonic crystal
One-dimensional systems with non-integrable interactions
Signatures of anomalous transport: OPEN SYSTEM STUDIES
Other signatures of anomalous energy transport
Propagation of pulses OR bEx, t SE0, 0
A phenomenological description: Levy walkers model
Levv walk
Steady state current
An exactly solvable stochastic model of anomalous transport
An analytic understanding
Predictions of fluctuating hydrodynamics
Equilibrium simulations of FPU
Hydrodynamic theory for other one-dimensional interacting systems
Fluctuating hydrodynamics for a one-dimensional fluid
Conclusions
Q&A