Quantum Shock Waves Hydrodynamic Singularities in Degenerate 1D quantum systems P. Wiegmann Together with Alexander Abanov.

Slides:



Advertisements
Similar presentations
The Schrödinger Wave Equation 2006 Quantum MechanicsProf. Y. F. Chen The Schrödinger Wave Equation.
Advertisements

Classical and Quantum Gases
Trapped ultracold atoms: Bosons Bose-Einstein condensation of a dilute bosonic gas Probe of superfluidity: vortices.
Statistical Mechanics
Engineering correlation and entanglement dynamics in spin chains T. S. CubittJ.I. Cirac.
Statistical Mechanics
QCD Dirac Spectra and Random Matrix Theory: Recent Applications, Niels Bohr Institute, May 8, 2007 Eugene Kanzieper Department of Applied Mathematics H.I.T.
Laplacian Growth: singularities of growing patterns Random Matrices and Asymptotes of Orthogonal polynomials, P. Wiegmann University of Chicago P. Wiegmann.
Wavepacket1 Reading: QM Course packet FREE PARTICLE GAUSSIAN WAVEPACKET.
Stanford University Department of Aeronautics and Astronautics Introduction to Symmetry Analysis Brian Cantwell Department of Aeronautics and Astronautics.
Singularities in hydrodynamics of degenerate 1D quantum systems P. Wiegmann Together with Abanov.
Fermi-Dirac distribution function
2. High-order harmonic generation in gases Attosecond pulse generation 1. Introduction to nonlinear optics.
Superbosonization for quantum billiards and random matrices. V.R. Kogan, G. Schwiete, K. Takahashi, J. Bunder, V.E. Kravtsov, O.M. Yevtushenko, M.R. Zirnbauer.
Waves, Fluctuations and Turbulence General concept of waves Landau damping Alfven waves Wave energy Collisions and fluctuations.
Or Can all laws of nature be reduced to one single system?
Quantum Mechanics Classical – non relativistic Quantum Mechanical : Schrodinger eq.
Quantum fermions from classical statistics. quantum mechanics can be described by classical statistics !
Hawking radiation in 1D quantum fluids Stefano Giovanazzi bosons fermionsvs Valencia 2009.
Introducing Some Basic Concepts Linear Theories of Waves (Vanishingly) small perturbations Particle orbits are not affected by waves. Dispersion.
+ } Relativistic quantum mechanics. Special relativity Space time pointnot invariant under translations Space-time vector Invariant under translations.
Correlated tunneling and the instability of the fractional quantum Hall edge Dror Orgad Oded Agam July 21, 2009 PRL 100, (2008)
Nonequilibrium dynamics of bosons in optical lattices $$ NSF, AFOSR MURI, DARPA, RFBR Harvard-MIT Eugene Demler Harvard University.
Quantum Mechanics from Classical Statistics. what is an atom ? quantum mechanics : isolated object quantum mechanics : isolated object quantum field theory.
Simulating Physical Systems by Quantum Computers J. E. Gubernatis Theoretical Division Los Alamos National Laboratory.
6. Second Quantization and Quantum Field Theory
System and definitions In harmonic trap (ideal): er.
Integrable hierarchies of
Tatiana Talipova in collaboration with Efim Pelinovsky, Oxana Kurkina, Roger Grimshaw, Anna Sergeeva, Kevin Lamb Institute of Applied Physics, Nizhny Novgorod,
LUTTINGER LIQUID Speaker Iryna Kulagina T. Giamarchi “Quantum Physics in One Dimension” (Oxford, 2003) J. Voit “One-Dimensional Fermi Liquids” arXiv:cond-mat/
Gravitational Physics: Quantum Gravity and Other Theoretical Aspects Luca BombelliTibor Torma Arif Caixia Gao Brian Mazur approaches to quantum gravity:
AMS 691 Special Topics in Applied Mathematics Lecture 3 James Glimm Department of Applied Mathematics and Statistics, Stony Brook University Brookhaven.
Specific Heat of Solids Quantum Size Effect on the Specific Heat Electrical and Thermal Conductivities of Solids Thermoelectricity Classical Size Effect.
Fermi-Luttinger Liquid Michael Pustilnik, Georgia Tech
Physics and Astronomy Dept. Kevin Strecker, Andrew Truscott, Guthrie Partridge, and Randy Hulet Observation of Fermi Pressure in Trapped Atoms: The Atomic.
Theory of interacting Bose and Fermi gases in traps Sandro Stringari University of Trento Crete, July 2007 Summer School on Bose-Einstein Condensation.
Lecture III Trapped gases in the classical regime Bilbao 2004.
Lecture IV Bose-Einstein condensate Superfluidity New trends.
Soliton for PDEs Math 6399 – Lec 2 Zhijun Qiao Department of Mathematics The University of Texas – Pan American Sept 2, 2008.
The review of modern physics has given us a description of nature. Waves are described with a wave equation. Particles are described with particle equations.
Exact results for transport properties of one-dimensional hamiltonian systems Henk van Beijeren Institute for Theoretical Physics Utrecht University.
1 Electrical Conductivity Measured Data Material  [1/(  m)] Copper, Silver 5×10 7 Iron 1×10 7 Manganese 2×10 5 Germanium 1×10 0 Silicon 1×10 -3 Gallium.
The inclusion of fermions – J=1/2 particles
Magnetized spinor quantum gases Magnetized spinor quantum gases Jürgen Bosse Freie Universität Berlin Panjab University, Chandigarh 3 rd February, 2012.
Exploring many-body physics with synthetic matter
Wednesday, April 1, 2015PHYS , Spring 2015 Dr. Jaehoon Yu 1 PHYS 3313 – Section 001 Lecture #16 Wednesday, April 1, 2015 Dr. Jaehoon Yu Probability.
An equation for matter waves Seem to need an equation that involves the first derivative in time, but the second derivative in space As before try solution.
Soliton-core filling in superfluid Fermi gases with spin imbalance Collaboration with: G. Lombardi, S.N. Klimin & J. Tempere Wout Van Alphen May 18, 2016.
A Review of Bose-Einstein Condensates MATTHEW BOHMAN UNIVERSITY OF WASHINGTON MARCH 7,
Agenda Brief overview of dilute ultra-cold gases
Solid state physics is the study of how atoms arrange themselves into solids and what properties these solids have. Calculate the macroscopic properties.
UT-BATTELLE New method for modeling acoustic waves in plates A powerful boundary element method is developed for plate geometry The new method achieves.
Department of Electronics
Tunable excitons in gated graphene systems
Chapter V Interacting Fields Lecture 3 Books Recommended:
Schrödinger Theory of the Electronic Structure of Matter from a ‘Newtonian’ Perspective Viraht Sahni.
Bose-Einstein Condensation Ultracold Quantum Coherent Gases
Unit-IV Many Electron Atoms.
Quantum Model of the Atom
Quantum Ising Model: finite T correlators
The Stale of a System Is Completely Specified by lts Wave Function
Classical Statistics What is the speed distribution of the molecules of an ideal gas at temperature T? Maxwell speed distribution This is the probabilitity.
Equations for free fermion correlators out of equilibrium
Evaluating expressions and Properties of operations
Let’s consider the consequences of this commutator further
Chapter II Klein Gordan Field Lecture 3 Books Recommended:
Chapter III Dirac Field Lecture 4 Books Recommended:
Reading: Chapters #5 in Shankar; quantum mechanical systems in 1-dim
Solitons.
Presentation transcript:

Quantum Shock Waves Hydrodynamic Singularities in Degenerate 1D quantum systems P. Wiegmann Together with Alexander Abanov

How does a wave packet propagate in degenerate Fermi gas? degenerate Bose gas?

Free fermions in 1D A smooth bump in density or momenta: all gradients << Fermi scale

A single particle: Wave packet consisting of a single particle diffuses

Does quantum coherence (or Fermi sea) make an impact?

Can this question be answered by elementary means? Free Fermions

Hydrodynamics of quantum coherent systems (traditionally called bosonization): String theory Methods: Integrable hierarchies /matrix models

Hydrodynamics: to express particles (fermions or bosons) through hydrodynamics (bosonic) modes: Bose Field

Initial (coherent) state Evolving state Matrix element

Integrability - Free Fermions Tau-function of KP-hierarchy Miwa, Jimbo, Date Virasoro currents ;

Currents of -algebra KP-hierarchy Benjamin-Ono hierarchy

bosonization - linear hydrodynamics: Linearisation of the spectrum: Shape does not change!?

Dispersion - asymmetry between particles and holes

Benjamin-Ono-equation Free Fermions =

Quantum degenerate (or coherent) systems obey dispersive non-dissipative hydrodynamics

dispersive non-dissipative hydrodynamics KdV - equation Non-periodic, non-soliton solution

Hopf equation Wave equation- a linearized version

Shock-wave solution

Burgers Semiclassics: single particle: quantum mechanics

Burgers Hopf -Riemann Benjamin-Ono Fermi-sea: quantum field theory

Witham Modulation

Witham modulation Periodic solution Modulation Shock wave

True, non-linearized hydrodynamics Hamiltonian Jevicki, Sakita, Polchinsky, Free fermions: = Non-linear bosons

Equations: Euler’s Hydrodynamics

Density Current, velocity

Schottky double

Hopf Equation:

Benjamin-Ono equation for matrix element Quantum Hopf equation for operators

Distribution of solitons is sensitive to initial data

Arena for observation: cooled alkali atomic gases

Chain of rolling cloudsMorning glory South AustraliaBelieved to be Benjamin-Ono eq

Morning Glory

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.