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Schroedinger method as field theoretical model to describe structure formation

Cora Uhlemann Bielefeld University
October 21, 2014

PIRSA:14100076
Astrophysics
14/15 PSI - Statistical Mechanics - Lecture 11

Anton Burkov University of Waterloo

October 21, 2014

PIRSA:14100099
14/15 PSI - Quantum Field Theory I (A) - Lecture 11
- Tibra Ali Perimeter Institute for Theoretical Physics
- Dan Wohns Perimeter Institute for Theoretical Physics
October 21, 2014

PIRSA:14100042
14/15 PSI - Conformal Field Theory - Lecture 10

Freddy Cachazo Perimeter Institute for Theoretical Physics

October 20, 2014

PIRSA:14100022
14/15 PSI - Statistical Mechanics - Lecture 10

Anton Burkov University of Waterloo

October 20, 2014

PIRSA:14100098
14/15 PSI - Quantum Field Theory I (A) - Lecture 10
- Tibra Ali Perimeter Institute for Theoretical Physics
- Dan Wohns Perimeter Institute for Theoretical Physics
October 20, 2014

PIRSA:14100041
14/15 PSI - Conformal Field Theory - Lecture 9

Pedro Vieira Perimeter Institute for Theoretical Physics

October 17, 2014

PIRSA:14100019
14/15 PSI - Quantum Field Theory I (A) - Lecture 9
- Tibra Ali Perimeter Institute for Theoretical Physics
- Dan Wohns Perimeter Institute for Theoretical Physics
October 17, 2014

PIRSA:14100038
14/15 PSI - Statistical Mechanics - Lecture 9

Anton Burkov University of Waterloo

October 17, 2014

PIRSA:14100095
14/15 PSI - Conformal Field Theory - Lecture 8

Pedro Vieira Perimeter Institute for Theoretical Physics

October 16, 2014

PIRSA:14100018
14/15 PSI - Quantum Field Theory I (A) - Lecture 8
- Tibra Ali Perimeter Institute for Theoretical Physics
- Dan Wohns Perimeter Institute for Theoretical Physics
October 16, 2014

PIRSA:14100037
Is B-Mode Polarization of the CMB the Holy Grail of Inflation?

Robert Brandenberger McGill University - Department of Physics
October 16, 2014

PIRSA:14100002
General Relativity & Quantum Cosmology

Schroedinger method as field theoretical model to describe structure formation

Cora Uhlemann Bielefeld University
October 21, 2014

PIRSA:14100076
Astrophysics
We investigate large-scale structure formation of collisionless dark matter in the phase space description based on the Vlasov equation whose nonlinearity is induced solely by gravitational interaction according to the Poisson equation. Determining the time-evolution of density and velocity demands solving the full Vlasov hierarchy for the cumulants of the distribution function. In the presence of long-range interaction no consistent truncation is known apart from the dust model which is incapable of describing the formation of bound structures due to the inability to generate higher cumulants like velocity dispersion. Our goal is to find a simple ansatz for the phase space distribution function that approximates the full Vlasov distribution function and can serve as theoretical N-body double to replace the dust model. We present the Schroedinger method which is based on the coarse-grained Wigner probability distribution obtained from a wave function fulfilling the Schroedinger-Poisson equation as sought-after model. We show that its evolution equation approximates the Vlasov equation in a controlled way, cures the shell-crossing singularities of the dust model and is able to describe multi-streaming which is crucial for halo formation. This feature has already been employed in cosmological simulations of large-scale structure formation by Widrow & Kaiser (1993). We explain how the coarse-grained Wigner ansatz allows to calculate higher cumulants like velocity dispersion analytically from density and velocity in a self-consistent manner. On this basis we show that instead of solving the Vlasov-Poisson system one can use the Schrödinger method and solve the Schrödinger-Poission equation to directly determine density and velocity and all higher cumulants. As a first application we study the coarse-grained dust model, which is a limiting case of the Schrödinger method, within Eulerian and Lagrangian perturbation theory.
14/15 PSI - Statistical Mechanics - Lecture 11

Anton Burkov University of Waterloo

October 21, 2014

PIRSA:14100099
14/15 PSI - Quantum Field Theory I (A) - Lecture 11
- Tibra Ali Perimeter Institute for Theoretical Physics
- Dan Wohns Perimeter Institute for Theoretical Physics
October 21, 2014

PIRSA:14100042
14/15 PSI - Conformal Field Theory - Lecture 10

Freddy Cachazo Perimeter Institute for Theoretical Physics

October 20, 2014

PIRSA:14100022
14/15 PSI - Statistical Mechanics - Lecture 10

Anton Burkov University of Waterloo

October 20, 2014

PIRSA:14100098
14/15 PSI - Quantum Field Theory I (A) - Lecture 10
- Tibra Ali Perimeter Institute for Theoretical Physics
- Dan Wohns Perimeter Institute for Theoretical Physics
October 20, 2014

PIRSA:14100041
14/15 PSI - Conformal Field Theory - Lecture 9

Pedro Vieira Perimeter Institute for Theoretical Physics

October 17, 2014

PIRSA:14100019
14/15 PSI - Quantum Field Theory I (A) - Lecture 9
- Tibra Ali Perimeter Institute for Theoretical Physics
- Dan Wohns Perimeter Institute for Theoretical Physics
October 17, 2014

PIRSA:14100038
14/15 PSI - Statistical Mechanics - Lecture 9

Anton Burkov University of Waterloo

October 17, 2014

PIRSA:14100095
14/15 PSI - Conformal Field Theory - Lecture 8

Pedro Vieira Perimeter Institute for Theoretical Physics

October 16, 2014

PIRSA:14100018
14/15 PSI - Quantum Field Theory I (A) - Lecture 8
- Tibra Ali Perimeter Institute for Theoretical Physics
- Dan Wohns Perimeter Institute for Theoretical Physics
October 16, 2014

PIRSA:14100037
Is B-Mode Polarization of the CMB the Holy Grail of Inflation?

Robert Brandenberger McGill University - Department of Physics
October 16, 2014

PIRSA:14100002
General Relativity & Quantum Cosmology
I will discuss why the search for B-Mode Polarization of the Cosmic Microwave Background (CMB) is very important for early universe cosmology, but that a discovery of such a polarization mode is in no way a confirmation of inflationary cosmology.

Title	Date	Collection	Type	Info
Schroedinger method as field theoretical model to describe structure formation	2014‑10‑21	Cosmology and Gravitation	Scientific Series	View details
14/15 PSI - Statistical Mechanics - Lecture 11	2014‑10‑21	14/15 PSI - Statistical Mechanics	Course	View details
14/15 PSI - Quantum Field Theory I (A) - Lecture 11	2014‑10‑21	14/15 PSI - Quantum Field Theory	Course	View details
14/15 PSI - Conformal Field Theory - Lecture 10	2014‑10‑20	14/15 PSI - Conformal Field Theory	Course	View details
14/15 PSI - Statistical Mechanics - Lecture 10	2014‑10‑20	14/15 PSI - Statistical Mechanics	Course	View details
14/15 PSI - Quantum Field Theory I (A) - Lecture 10	2014‑10‑20	14/15 PSI - Quantum Field Theory	Course	View details
14/15 PSI - Conformal Field Theory - Lecture 9	2014‑10‑17	14/15 PSI - Conformal Field Theory	Course	View details
14/15 PSI - Quantum Field Theory I (A) - Lecture 9	2014‑10‑17	14/15 PSI - Quantum Field Theory	Course	View details
14/15 PSI - Statistical Mechanics - Lecture 9	2014‑10‑17	14/15 PSI - Statistical Mechanics	Course	View details
14/15 PSI - Conformal Field Theory - Lecture 8	2014‑10‑16	14/15 PSI - Conformal Field Theory	Course	View details
14/15 PSI - Quantum Field Theory I (A) - Lecture 8	2014‑10‑16	14/15 PSI - Quantum Field Theory	Course	View details
Is B-Mode Polarization of the CMB the Holy Grail of Inflation?	2014‑10‑16	Quantum Gravity		View details

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Format results

Schroedinger method as field theoretical model to describe structure formation

14/15 PSI - Statistical Mechanics - Lecture 11

14/15 PSI - Quantum Field Theory I (A) - Lecture 11

14/15 PSI - Conformal Field Theory - Lecture 10

14/15 PSI - Statistical Mechanics - Lecture 10

14/15 PSI - Quantum Field Theory I (A) - Lecture 10

14/15 PSI - Conformal Field Theory - Lecture 9

14/15 PSI - Quantum Field Theory I (A) - Lecture 9

14/15 PSI - Statistical Mechanics - Lecture 9

14/15 PSI - Conformal Field Theory - Lecture 8

14/15 PSI - Quantum Field Theory I (A) - Lecture 8

Is B-Mode Polarization of the CMB the Holy Grail of Inflation?

Schroedinger method as field theoretical model to describe structure formation

14/15 PSI - Statistical Mechanics - Lecture 11

14/15 PSI - Quantum Field Theory I (A) - Lecture 11

14/15 PSI - Conformal Field Theory - Lecture 10

14/15 PSI - Statistical Mechanics - Lecture 10

14/15 PSI - Quantum Field Theory I (A) - Lecture 10

14/15 PSI - Conformal Field Theory - Lecture 9

14/15 PSI - Quantum Field Theory I (A) - Lecture 9

14/15 PSI - Statistical Mechanics - Lecture 9

14/15 PSI - Conformal Field Theory - Lecture 8

14/15 PSI - Quantum Field Theory I (A) - Lecture 8

Is B-Mode Polarization of the CMB the Holy Grail of Inflation?