TQC - Lectures

Abstract

The random phase approximation (RPA) to the correlation energy and the related GW approximation are among the most promising methods to obtain accurate correlation energy differences and QP energies from diagrammatic perturbation theory at reasonable computational cost for real materials. The calculations are, however, usually two to three orders of magnitude more demanding than conventional density functional theory calculations.

Here, we show that a cubic system size scaling can be readily obtained reducing the computation time by typically one order of magnitude for large systems. Furthermore, the scaling with respect to the number of k points used to sample the Brillouin zone can be reduced to linear order. In combination, this allows accurate and very well-converged single-point RPA and GW calculations, with a time complexity that is roughly on par to self-consistent Hartree-Fock and hybrid-functional calculations [1-2].  Furthermore, the talk discusses the relation between the RPA correlation energy and the GW approximation. It is shown that the GW self-energy is the derivative of the RPA correlation energy with respect to the Green's function. The calculated self-energy can be used to compute QP-energies in the GW approximation, any first derivative of the total energy including forces, as well as corrections to the correlation energy from the changes of the charge density when switching from DFT to a many-body body description (GW singles energy contribution) [3]. First applications of RPA forces to systems with mixed covalent and vdW bonding are discussed. These applications include phonons, relaxation of structures, as well as molecular dynamics simulations.

References

[1] Merzuk Kaltak, Jiří Klimeš, and Georg Kresse, J. Chem. Theory Comput., 10, 2498–2507 (2014).

[2] Merzuk Kaltak, Jiří Klimeš, and Georg Kresse, Phys. Rev. B 90, 054115 (2014).

[3] Jiří Klimeš, M. Kaltak, E. Maggio, and G. Kresse, J. Chem. Phys. 140, 084502 (2015).

Where and when

Donderdag 20 december 2016 om 16:30 in lokaal N0.08, Campus Drie Eiken.

Abstract:

It is generally assumed that a condensate of paired fermions at equilibrium is characterized by a macroscopic wavefunction with a well-defined, immutable phase. In reality, all systems have a finite size and are prepared at non-zero temperature; the condensate then has a finite coherence time, even when the system is isolated in its evolution and the particle number $N$ is fixed. The loss of phase memory is due to interactions of the condensate with the excited modes that constitute a dephasing environment. This fundamental effect, crucial for applications using the condensate of pairs macroscopic coherence, was scarcely studied. In my presentation, I will link the coherence time to the condensate phase dynamics, and show with a microscopic theory that the time derivative of the condensate phase operator $hat{ heta}_0$ is proportional to a chemical potential operator $hat{mu}$ that I will construct including both the pair-breaking and pair-motion excitation branches. In a single realization of energy $E$, $hat{ heta}_0$ evolves at long times as $-2mu_{ m mc}(E)t/hbar$ where $mu_{ m mc}(E)$ is the microcanonical chemical potential; energy fluctuations from one realization to the other then lead to a ballistic spreading of the phase and to a Gaussian decay of the temporal coherence function with a characteristic time $propto N^{1/2}$. In the absence of energy fluctuations, the coherence time scales as $N$ due to the diffusive motion of $hat{ heta}_0$. I will also propose a method to measure the coherence time with ultracold atoms, which we predict to be tens of milliseconds for the canonical ensemble unitary Fermi gas.

When and where: Monday, March 14, 2016, at 16:30, in room N1.08, building N, CDE

Seminar organized by TQC (26/10/2015).

Abstract: cf. attachment here.

Where and when: Tuesday February 23rd 2016 at 16.00 h in auditorium N0.08, Campus Drie Eiken.

Abstract:

The insulator-metal transition in hydrogen is one of the most outstanding problems in condensed matter physics. The high-pressure metallic phase is now predicted to be liquid atomic from T=0 K to very high temperatures. We have conducted measurements of optical properties of hot dense hydrogen created in a Diamond Anvil Cell in the pressure region 1.1 to 1.7 Mbar and temperatures up to 2200 K. We present evidence supportive of a first-order phase transition accompanied by changes in transmittance and  reflectance characteristic of a metal. The phase line of this transition has a negative slope in agreement with theories of the so-called plasma phase transition from liquid molecular to atomic liquid hydrogen.

When and where: Wednesday, January 20, 2016 at  16.00 h in room N0.08, Campus Drie Eiken.

Seminar organized by TQC (26/10/2015).

Abstract

In a recent experiment at Durham University with attractively interacting bosons, we observed quantum reflection o an attractive barrier [1]. The talk will start with modelling these results numerically [1]. Attractively interacting Bosons in quasi-one-dimensional waveguides form weakly bound molecules, bright solitons (Ref. [1] and references therein). Bright solitons were discovered more than 160 years ago in a water channel [2]: a water wave did not change its shape for many kilometres. Ultracold atoms with pairwise attractive interactions allow the creation of micro-versions of these bright solitons. These quantum bright solitons provide an ideal system to study quantum effects in the realm between macroscopic world our physical intuition is based on and the microscopic world of single atoms. The talk will show how many-particle quantum superpositions (Schrodinger-cat states) generated from quantum bright solitons [3, 4] can be used for quantumenhanced interferometry [5]. While decoherence would destroy such quantum superpositions, it can also lead to new physics [6].

[1] A. L. Marchant, T. P. Billam, M. M. H. Yu, A. Rakonjac, J. L. Helm, J. Polo, C. Weiss, S. A. Gardiner, and S. L. Cornish, "Quantum reflection of bright solitary matter-waves from a narrow attractive potential," (2015), arXiv:1507.04639.
[2] J. S. Russell,  "Report on waves," In Report of the Fourteenth Meeting of the British Association for the Advancement of Science 311{390 (John Murray)(1845).
[3] C. Weiss and Y. Castin, "Creation and detection of a mesoscopic gas in a nonlocal quantum superposition," Phys. Rev. Lett. 102, 010403 (2009).
[4] B. Gertjerenken, T. P. Billam, L. Khaykovich, and C. Weiss, "Scattering bright solitons: Quantum versus mean-field behavior," Phys. Rev. A 86, 033608 (2012).
[5] B. Gertjerenken, T. P. Wiles, and C.Weiss, "Towards quantum-enhanced interferometry with harmonically trapped quantum matter-wave bright solitons," ArXiv e-prints(2015), arXiv:1508.00656.
[6] C. Weiss, S. A. Gardiner, and H.-P. Breuer, "From short-time diffsive to long-time ballistic dynamics: The unusual center-of-mass motion of quantum bright solitons," Phys. Rev. A 91, 063616 (2015).

Where and when

Monday October 26th 2015 at 16.00 h in auditorium N0.08, Campus Drie Eiken.

Course by prof. dr. Nick Proukakis as a visiting professor at the University of Antwerp (06/03 - 15/04/2013).

Abstract

Ultracold atomic gases represent an ideal system for deriving and testing a number of different theoretical models for describing macroscopic quantum systems at nonzero temperatures and far from equilibrium. All these methods are based (subject to some common but well-satisfied approximations) on the same starting hamiltonian, with the noticeable differences between the final models arising from precisely how one obtains effective equations from this hamiltonian. By using a unified treatment (to the extent possible), I will show how such different approaches arise and discuss how they compare to each other, what are their regimes of validity and their limitations and some key applications demonstrating the power of each technique.

The course will start at a basic level, from a review of the T = 0 treatment (Gross--Pitaevskii equation and its derivation from second-quantization), and a reminder of the main features of such 'pure condensates'. A systematic (perturbative) treatment will then show how this can be extended to finite temperatures and non-equilibrium situations wihtin the context of mean-field theory. The meaning of symmetry-breaking and existence of well-defined mean fields in a finite system of fixed atom number will be questioned, and alternative so-called number-conserving approaches will be reviewed. Such methods are more important in one- and two-dimensional settings, due to the absence of Bose-Einstein condensation in the homogeneous limit; in this context I will review stochastic approaches which have been proven to be efficient for modelling such systems. At the end of the course there will be an appropriate guided mini-project of computational nature. Each booked lecture slot should be largely self-contained, although there is a strong continuity from one lecture to the next. This course is largely based on a recent review (Proukakis and Jackson, J. Phys. B 41, 203002 (2008)) and appropriate additional references for further reading will be given at each part. Although aimed specifically at ultracold atoms, the techniques and notions introduced in this course have broader applicability to related systems.

When and where

• Wednesday March 6th, 16:00-18:00: Getting started: review of T=0
• Wednesday, March 20th, 16:00-18:00: Static and dynamic mean-field at nonzero temperatures
• Monday March 25th, 13:45-14:45: Number conserving methods at nonzero temperatures
• Wednesday March 27th, 16:00-18:00: Classical field and stochastic methods
• Monday April 15th, 16:00-18:00: Applications and open problems (location: room U408, Campus Groenenborger)

Location: room N0.08, Campus Drie Eiken (unless otherwise indicated)

Seminar organized by TQC (09/04/2015).

Abstract

Prof. dr. Luca Salasnich will discuss very recent theoretical results [1,2] on the divergent zero-point energy of the D-dimensional superfluid Fermi gas in the BCS-BEC crossover. The divergent zero-point energy of the system is due to both fermionic single-particle excitations and bosonic collective excitations [1,2]. The regularization of the zero-point energy gives remarkable analytical results for composite bosons in two dimensions [1] and in three dimensions [2].

[1] L. Salasnich and F. Toigo, Phys. Rev. A 91, 011604(R) (2015).
[2] L. Salasnich and G. Bighin, Phys. Rev. A 91, 033610 (2015).

Where and when

Monday April 9th 2015 at 16.00 h in auditorium N0.09, Campus Drie Eiken.

Seminar organized by TQC (07/03/2013).

Abstract

Prof. dr. Kleinert, a leading expert in path integration, will describe the link between extreme events, stochastic differential equations, fractional derivatives and quantum field theory.

Where and when

Thursday March 7th 2013 at 16.00 h in room U408, Campus Groenenborger.