Connections between microscopic and macroscopic laws by Abhishek Dhar

COLLOQUIUM

CONNECTIONS BETWEEN MICROSCOPIC AND MACROSCOPIC LAWS

SPEAKER: Abhishek Dhar (ICTS - TIFR, Bengaluru)

DATE: Mon, 20 December 2021, 15:30 to 17:00

VENUE: Online and Ramanujan Lecture Hall


ABSTRACT
It is common to describe physical systems using two different approaches --- the microscopic one based on writing equations of motion for the constituent atoms (Newton's equations for classical system) and the macroscopic one based on hydrodynamic equations for coarse-grained observables. Restricting mostly to the case of one-dimensions, I will discuss the connections between these two approaches. In particular the talk will focus on macroscopic laws such as Fourier's law of heat conduction, fluctuating hydrodynamics and the Navier Stokes equations.

Table of Contents (powered by https://videoken.com)
0:00:00 Connections between microscopic and macroscopic laws
0:03:34 Outline
0:04:16 MICROSCOPIC LAWS
0:05:28 MACROSCOPIC LAWS - Thermodynamics
0:06:27 Microscopic to Macroscopic - Equilibrium Statistical Physics
0:08:17 Macroscopic laws to describe nonequilibrium phenomena
0:10:24 Part I - Heat CONDUCTION and Fourier's law
0:11:27 Fourier's law and the heat diffusion equation
0:14:57 Proving Fourier's law
0:15:47 Simplest theory of heat conduction: Kinetic theory
0:16:45 Kinetic theory for phonon gas
0:18:01 Other approaches
0:20:21 Direct computation of from nonequilibrium measurements.
0:23:28 Heat current and heat conductivity
0:25:14 Results so far
0:28:46 Experiments
0:29:24 Experiments: graphene
0:30:02 The simplest microscopic model: a harmonic crystal
0:31:06 Possible scattering mechanisms
0:31:46 Heat conduction in disordered harmonic crystals
0:32:43 Landauer formula for heat current
0:33:34 Disordered Harmonic systems: Anderson localization
0:34:28 Character of normal modes of a disordered crystal
0:35:21 ID disordered harmonic chain
0:36:29 Disordered harmonic crystal
0:37:01 One-dimensional systems with non-integrable interactions
0:39:26 Signatures of anomalous transport: OPEN SYSTEM STUDIES
0:43:14 Other signatures of anomalous energy transport
0:44:58 Propagation of pulses OR (bE(x, t) SE(0, 0)
0:45:43 A phenomenological description: Levy walkers model
0:46:54 Levv walk
0:47:58 Steady state current
0:48:26 An exactly solvable stochastic model of anomalous transport
0:50:19 An analytic understanding
0:53:38 Predictions of fluctuating hydrodynamics
0:54:27 Equilibrium simulations of FPU
0:55:43 Hydrodynamic theory for other one-dimensional interacting systems
0:59:37 Fluctuating hydrodynamics for a one-dimensional fluid
1:00:36 Conclusions
1:02:39 Q&A

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