Simulational Methods in Physics

# Werkstatt-Seminar: Simulational Methods in Physics

The seminar takes place on

Wednesdays, 15.15 hrs

At some dates, the seminar will be shifted to a different day.

Venue: Seminar Room of the ITP, Philosophenweg 16.

It covers topics in elementary particle physics, biophysics, atomic, molecular, and quantum physics.

## SS 2010

• 19 May 2010 - Alexej Weber (Heidelberg)
Casimir Effect in the Worldline Formalism
In my talk I will discuss the interplay between geometry and temperature in the Casimir effect for the inclined-plates, sphere-plate and cylinder-plate configurations. The worldline approach used allows the precise computation of Casimir energies in arbitrary geometries. I show the dependence of the Casimir force on the separation parameter and temperature T, and present Casimir phenomena which are dominated by long-range fluctuations. I demonstrate that for open geometries, thermal energy densities are typically distributed on scales of thermal wavelengths. Whereas the high temperature behavior is always found to be linear in T, richer power-law behaviors at small temperatures emerge. In particular, thermal forces can develop a non-monotonic behavior.

## WS 2009/2010

• 13 January 2010 - Julien Serreau (Paris)
Decoherence and thermalization of a pure quantum state in quantum field theory
We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N-expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. Restricting one's attention (or ability to measure) to a subset of the infinite hierarchy of correlation functions, the system is described by an effective (reduced) density matrix which, unlike the full density matrix, has a nontrivial time evolution. In particular, starting from a pure quantum state, we observe the loss of putity/coherence and, on longer time scales, thermalization of the reduced density matrix. We point out that the physics of decoherence is well described by classical statistical field theory.

• 16 December 2009 - Jürgen Schaffner-Bielich (Heidelberg)
An inflationary QCD phase transition in the early universe?
We explore a scenario that allows for a strong first order phase-transition of QCD at non-negligible baryon number in the early universe and its possible cosmological observable consequences. The main assumption is a quasi-stable QCD-vacuum state that leads to a short period of inflation, consequently diluting the net baryon to photon ratio to it's today observed value. A strong mechanism for baryogenesis is needed to start out with a baryon asymmetry of order unity, e.g. as provided by Affleck-Dine baryogenesis. The cosmological implications are direct effects on primordial density fluctuations up to dark matter mass scales of 1 - 10 solar masses, change in the spectral slope up to mass scales of 10**6 - 10**7 solar masses, production of primordial magnetic fields with initial strength up to 1012 Gauss and a gravitational wave spectrum with present day peak strain amplitude of at most h_c = 4.7 * 10-15 around a frequency of 4*10-8 Hz. The little QCD inflation scenario could be probed with the upcoming heavy ion research facility FAIR at GSI, Darmstadt.

## SS 2009

• 8 July 2009 - Neda Sadooghi (Tehran)
The Speed of Sound in a magnetized Quark-Gluon-Plasma

• 1 July 2009 - Svend Domdey (Heidelberg)
Testing the Scale Dependence of the Scale Factor in Double Dijet Production at the LHC
The scale factor is the effective cross section used to characterize the measured rate of inclusive double dijet production in high energy hadron collisions. It is sensitive to the two-parton distributions in the hadronic projectile. In principle, the scale factor depends on the center of mass energy and on the minimal transverse energy of the jets contributing to the double dijet cross section. Here, we point out that proton-proton collisions at the LHC will provide for the first time experimental access to these scale dependences in a logarithmically wide, nominally perturbative kinematic range of minimal transverse energy between 10 GeV and 100 GeV. This constrains the dependence of two-parton distribution functions on parton momentum fractions and parton localization in impact parameter space. Novel information is to be expected about the transverse growth of hadronic distribution functions in the range of semi-hard Bjorken x (0.001 < x < 0.1) and high resolution Q^2. We discuss to what extent one can disentangle different pictures of the $x$-evolution of two-parton distributions in the transverse plane by measuring double-hard scattering events at the LHC.

• 30 June 2009 - Erhard Seiler (Munich)
The complex Langevin method: Successes and Difficulties
The complex Langevin method provides in principle a solution to the problem of simulating quantum field theories with complex action. It has also been shown to work remarkably well in various examples. On the other hand it runs into unexpected difficulties in other cases. I will discuss the mathematical basis of the method, as far as it exists, and point out open mathematical and as practical problems.

• 24 June 2009 - Tereza Mendes (Sao Paulo)
Infrared Propagators and Confinement: a Perspective from Lattice Simulations
Lattice studies of the infrared behavior of gluon and ghost propagators may offer a crucial test of confinement scenarios in Yang-Mills theories. However, finite-volume effects clearly become an important issue as the infrared limit is approached. We study the Landau-gauge SU(2) case using data from the largest lattice sizes (i.e. smallest momenta) to date. By imposing rigorous constraints to gain control over the infinite-volume limit, we gain a better understanding of the propagators in terms of more general quantities.

• 17 June 2009 - Jorge Noronha (Columbia University)
Can AdS/CFT be used to describe soft and hard phenomena observed at RHIC?
We show that five-fold constraints due to (1) the observed nuclear modification of heavy quark jets measured via non-photonic electrons, $R_{AA}^e(p_T \sim 6\,{\rm GeV})$, (2) the elliptic transverse perfect fluid'' flow of low transverse momenta pions, $v_2(p_T\sim 1\;{\rm GeV})$ in noncentral Au+Au collisions at 200 AGeV, (3) the entropy density deficiency, $S/S_{SB}$, of strongly coupled Quark-Gluon Plasmas (sQGP), (4) the observed entropy inferred from the pion multiplicity $dN_\pi/dy$, and (5) causal response are analytically related in a class of gauge/string dual models of sQGP dynamics and remarkably compatible with the data with t'Hooft and Gauss-Bonnet parameters in the range of $\lambda\approx 10-25$ and $0< \lambda_{GB}< 0.09$. In addition, the observed five-fold correlation is shown to favor color glass condensate over Glauber initial sQGP conditions within current systematic errors.

• 13 May 2009 - Christian Fischer (Darmstadt)
Deconfinement phase transition and the quark condensate
We study the dual quark condensate as a signal for the deconfinement phase transition. This order parameter for center symmetry has been defined recently by Bilgici et al. within lattice QCD. In this work we determine the dual condensate with functional methods using a formulation of the Dyson-Schwinger equations for the Landau gauge quark propagator on a torus. We study the chiral and deconfinement phase transitions of quenched QCD by related suszeptibilities. The gauge fixed functional formalism yields similar results for the deconfinement transition as lattice QCD.

• 29 April 2009 - Bertrand Delamotte (Paris U., VI, LPTL)
Momentum dependence of correlation functions:
calculations and results obtained for systems at or out-of-equilibrium

## WS 2008/09

• 28 Jan 2009 - Tobias Paul (Heidelberg)
Nonlinear transport of Bose-Einstein condensates - from superfluidity to Anderson Localization

• 21 Jan 2009 - Lev Ananikyan (Heidelberg)
Entanglement in the Heisenberg model

• 8 Jan 2009 - Szabolcs Borsanyi (Wuppertal) 16:15 hrs @ SR Phil 16
(in the frame of the Teilchentee seminar)
From cosmic strings to oscillons

• 10 Dec 2008 - Thomas Gasenzer (Heidelberg) 13:30 hrs @ SR Phil 16
(in the frame of the Werkstatt-Seminar Hochenergiereaktionen)
Non-equilibrium coherence dynamics in one-dimensional Bose gases

• 3 Dec 2008 - Denes Sexty (Darmstadt)
Recent Results of Stochastic Quantisation

## SS 2008

• 18 Jul 2008 - Daniel Spielmann (Heidelberg)
Aspects of Infrared QCD from Stochastic Quantization on the Lattice
In order to understand the mechanism of confinement in QCD, the infrared behavior of Green's functions in Landau gauge has been thoroughly investigated in recent years. Confinement scenarios, such as Gribov-Zwanziger and Kugo-Ojima, have implications for the ghost and gluon propagator in the IR. However, results from continuum methods such as the functional renormalization group and Dyson-Schwinger equations, while corroborating these predictions, contradict the infrared asymptotics found in lattice simulations. After reviewing this situation, I will outline the approach of stochastic quantization including Zwanziger's concept of stochastic gauge fixing as a possible remedy. This method has already previously been adapted to lattice gauge theory in order to tackle the Gribov problem. I will present first results obtained thus for the Landau gauge ghost and gluon propagator, also in the lower-dimensional case, and compare with standard gauge fixing. In addition, I will show numerical evidence on how the stochastic method samples configurations, e.g. from the spectrum of the Faddeev-Popov operator. This is of interest as the Gribov-Zwanziger picture predicts a certain part of configuration space to be responsible for confinement.

• 25 Jun 2008 - Matthias Ohliger (Berlin)
Diagrammatic Green's Function Approach to the Bose-Hubbard Model
Following an approach first used by W. Metzner in the context of electrons in conductors we use a diagrammatic hopping expansion to calculate both grand potential and finite temperature Green's functions of the Bose-Hubbard Model used to describe Bosons in an optical lattice. This allows us to reconstruct in a qualitative way the time-of-flight absorption pictures, which are taken after the optical lattice is switched off. Furthermore, the technique makes summations of subsets of diagrams possible, leading to non-perturbative results needed to locate the boundary between the superfluid and the Mott phase for finite temperatures. Whereas the first-order calculation reproduces the seminal mean-field result, the second order goes beyond and shifts the phase boundary in the immediate vicinity of the critical parameters determined by Monte-Carlo simulations of the Bose-Hubbard model. In the second part, we examine the superfluid-Mott insulator transition of spin-1 Bosons in an optical lattice where we extend previous mean-field studies to finite temperature. We find an interesting asymmetry between Mott-states with even and odd filling factors which continuously disappears for higher temperature.

• 6 Jun 2008 - Sascha Zöllner (Heidelberg) 14:00 hrs @ SR Phil 16
Fermionizing One-dimensional Bosons: Mechanism and Tunneling Dynamics

• 29 May 2008 - L. Mühlbacher (Freiburg) 14:15 @ SR Phil 19
(In the frame of the Seminar on Theory of Complex Systems)
Real-time Quantum Monte Carlo simulations for non-equilibrium systems: A diagrammatic path-integral approach

## WS 2007/08

• 20 Feb 2008 - Svend Domdey (Heidelberg)
Gluon jet fragmentation in the Quark-Gluon Plasma

• 6 Feb 2008 - Valya Khoze (Durham)
Aspects of Seiberg Duality and its Applications

• 21 Jan 2008 - David Hutchinson (Otago/Paris) 11:00 hrs @ KIP, SR 2.402
(in the framework of the Journal-Club Seminar on Ultracold Gases)
Effects of Disorder in Ultra-cold, dilute gases
The possibility of using ultracold atoms to observe strong localization of matter waves is now a subject of both theoretical and experimental interest. These systems offer unprecedented control over inter-particle interactions, imposed potentials and the level of disorder in the system as compared to their condensed matter analogues. The two-dimensional (2D) case is of particular interest. The prevailing view has been that in the 2D electron gas there is no metallic state, but recent experiments are suggestive of a metal-insulator transition in very dilute systems. We investigate theoretically the possibility of observing strongly localized states, corresponding to the insulating phase, review the experimental position in the field in the dilute 2D gas and discuss potential future experiments.

• 11 Jan 2008 - Lorenz von Smekal (Adelaide) 14:30 hrs @ SR Pw 16
Modified Lattice Landau Gauge
The infrared behaviour of QCD Green's functions in Landau gauge has been focus of intense study. Different non-perturbative approaches all lead to the same overall picture. These include Dyson-Schwinger Equations, Functional Renormalisation Group Equations, Stochastic Quantisation, and Lattice Landau Gauge Simulations. Finite volume effects are being increasingly well understood. I will briefly review the situation. But do covariant gauges have the potential to be truly non-perturbative in the first place? BRST constructions have long been blamed for only being perturbatively well defined. Lattice definitions are plagued by the Neuberger problem. I will describe ways to avoid this problem, and the modifications necessary to implement these, including first results from Monte-Carlo simulations using a modified lattice Landau gauge.

• 17 Dec 2007 - Peter Schlagheck/Tobias Paul (Regensburg/Orsay) 11:00 hrs @ KIP, SR 2.402
(in the framework of the Journal-Club Seminar on Ultracold Gases)
P. Schlagheck: Nonlinear transport of Bose-Einstein condensates through disorder
T. Paul: Bose-Einstein condensates in presence of defects and disorder
Superfluidity and Anderson localization are genuine many-body manifestations of quantum coherence which are nowadays revisited in interacting dilute Bose gases. In the first part of the talk we study the coherent flow of interacting Bose-condensed atoms in presence of a single defect or an extended disordered potential. We show that a variation of the condensate velocity v with respect to the defect or disordered potential induces different regimes of quantum transport. At velocities v small compared to the sound velocity c of the condensate the flow shows superfluid behavior, whereas a domain of time dependent flow is reached when v becomes comparable to c. For velocities v considerably larger then the sound velocity a regime of quasi-dissipationless transport is found where the creation of elementary excitations is strongly oppressed. We point out that in this domain, depending of the extent of the disordered region, the system enters an Anderson localized phase. In the second part we consider the experimentally relevant situation where the condensate oscillates in a shallow harmonic trap to which a small defect- or disorder- potential is superimposed. We obtain a global picture characterizing the dynamical properties of the dipole oscillations (e.g. damping of the oscillations), where we can recover the different regimes of quantum transport presented in the first part of the talk. We discuss our findings in the context of recent experiments [1,2,3] and address the question under which circumstances Anderson localization is of relevance for these systems.

[1] C. Fort et al., Phys. Rev. Lett. 95, 170410 (2005)
[2] J. E. Lye et al., Phys. Rev. A 75, 061603 (2007)
[3] P. Engels and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007)

• 5 Dec 2007 - Michael M. Wolf (MPQ München)
Entanglement based tools for Quantum Many-Body Physics
The talk will address recent attempts of applying tools and insights from Quantum Information Theory in Quantum Many-Body Physics. Motivated by entropic area laws we will discuss powerful entanglement based representations of quantum many-body states - so called MPS/PEPS representations. These lead to both, novel analytic results (on solvable models, quantum phase transitions, RG flows, etc) and new numerical simulation methods beyond DMRG and Monte Carlo techniques.

• 27 Nov 2007 - Axel Maas (Bratislava) 16:15 hrs @ SR Pw 16
Gluons at finite temperature
Gluons are not part of the physical spectrum at zero temperature. It is a natural question to ask, whether this is changed after a phase transition which occurs when heating up a system of gluons. Results on this question from lattice gauge theory and functional methods will be presented. These indicate that gluons are never part of the physical spectrum, not even at large or asymptotically high temperatures.

• 21 Nov 2007 - Thomas Gasenzer (Heidelberg)
(together with Kalter-Quanten-Kaffee-Seminar)
Functional renormalisation group approach to far-from-equilibrium quantum field dynamics

• 7 Nov 2007 - Prof. Y. Igarashi (Niigata University)
Quantum Master Equation for Yang-Mills theory in ERG
We discuss a general method to derive the Ward-Takahashi identity for the Wilson action for gauge theories, especially for Yang-Mills theory, in ERG. The identity makes it possible to realize a gauge symmetry even in the presence of a momentum cutoff. In the cutoff dependent realization, the nilpotency of the BRS transformation is lost. We apply the Batalin-Vilkovisky antifield formalism to lift the Ward-Takahashi identity to a quantum master equation. The extended BRS transformation regains nilpotency.

## SS 2007

• 21 Sep 2007 - Alexander Branschädel (Heidelberg) 14:15 hrs @ SR Pw 16
Transport equations for an ultracold Bose gas

• 10 Jul 2007 - Falk Bruckmann (Regensburg) 14:15 hrs @ SR Pw 16
Instanton constituents in sigma models and Yang-Mills theory

• 8 Jun 2007 - Daniel Spielmann (Tuebingen) 14:15 hrs @ SR Pw 16
On confinement in Sp(2) lattice gauge theory

• 1 Jun 2007 - Cedric Bodet (Mons) 14:15 hrs @ SR Pw 16
Heavy tetraquark stability
Jim Kallarckal (Aachen)
Lepton flavor violating processes in quantum field theory

• 10 May 2007 - Markus Oberthaler (Heidelberg) 16:15 hrs @ SR Pw 16
title tba
(Teilchentee)

• 3 May 2007 - Dieter Heermann (Heidelberg) 14:15 hrs @ SR Pw 19
A new class of random matrices
(Seminar zur Theorie komplexer Systeme)

• 26 Apr 2007 - Manfred Bohn (Heidelberg) 14:15 hrs @ SR Pw 19
A model for polymers with loops
(Seminar zur Theorie komplexer Systeme)

• 20 Apr 2007 - Michael Fromm (Tübingen) 15:00 hrs @ SR Pw 19!
SU(2) projection of SU(3)
Assuming that certain classes of gauge field configurations, lying in subalgebras of the Lie gauge group's Lie algebra, are the relevant degrees of freedom (dof) for confinement, the corresponding subgroups of the gauge group are directly accessed with lattice gauge theory: As happened before within the Dual Superconductor model (U(1)^(N-1)) investigations or alternatively within the Center Vortex picture (Z_N) access is achieved via gauge fixing and subsequent gauge projection. Leaving a remnant symmetry, the degrees of freedom of the symmetry left are then investigated as for their confining behaviour. Aim of this work was the application to SU(3), the subgroup being a SU(2) in "spin s = 1" representation.

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