# Theory of Complex Systems Department

##
Marian Smoluchowski Institute of Physics

Jagiellonian University

## Quantum Gravity and Cosmology

Unifying quantum theory with general relativity to form a complete and predictive theory of quantum gravity is one the great outstanding challenges of modern physics. Here, at the Marian Smoluchowski Institute of Physics our ambitious aim is to achieve this unification via an approach known as Causal Dynamical Triangulations (CDT). A key strength of CDT is the simplicity of construction: we assume only the central principles of Quantum Theory and General Relativity, including few additional ingredients. CDT models continuous spacetime via the connectivity of an ensemble of locally flat d-dimensional triangular building blocks. In close analogy to the sum over all possible paths in Feynman's path integral approach to Quantum Mechanics, CDT sums over all allowed spacetime geometries. A central feature of CDT is the foliation of spacetime into space-like hypersurfaces of fixed topology.

Analytical methods in 4-dimensional Causal Dynamical Triangulations have thus far proved intractable due to the complex nonperturbative sum over geometries. However, with the advent of powerful computational tools, numerical approaches to dynamical triangulations can now be successfully employed via Monte Carlo simulations. Due to this fact the implementation of our research is predominately numerical and utilizes a computational cluster and network of computer nodes within the department.

Despite the simplicity of construction, or perhaps because of it, CDT has produced a number of important results and conceptual insights, and is now widely regarded as a serious contender for a nonperturbative and background independent theory of Quantum Gravity. Some of the successes of the CDT approach include evidence for a classical limit that closely resembles general relativity on large distance scales, while on short distance scales it has yielded some exciting clues as to the nature of space-time at the Planck scale. In particular, there is evidence that 4-dimensional space-time dynamically emerges on large distance scales from a lower dimensional geometry at the Planck scale. This intriguing phenomenon, known as dimensional reduction, has since been observed in a number of other approaches to Quantum Gravity and is an active field of research.

Although CDT has enjoyed a number of successes, of course many questions still remain. Does CDT have a well defined continuum limit? Can CDT help us to understand whether dimension and metric signature are fixed or dynamical quantities? Is the introduction of a causality condition via the foliation of space-time an essential ingredient in the formulation of quantum gravity, or can this condition be relaxed? Can CDT help us to understand other approaches to quantum gravity such as Horava-Lifshitz gravity, Loop Quantum Cosmology or asymptotically safe gravity? And ultimately, how can we successfully unite quantum theory with General Relativity? Our research group is actively pursuing answers to these important questions.

## Random Matrix Theory

One can look at random matrix theory (hereafter RMT) as an alternative to classical probability calculus, where instead of single random variable we have to deal with a huge set of random numbers arranged in a matrix-like structure. Such construction is not only possible, but it shares amazing similarities to classical probability calculus. Moreover, this correspondence can be formalized at the mathematical level in the case where the size of the random matrix tends to infinity. By no means this is a severe restriction, since in contemporary applications the sizes of random matrices can easily reach the order of 10^4 (financial engineering), 10^7 (wireless networks) or even 10^10 (genetics). So, almost paradoxically, the bigger the size of the random matrix, the more definite prediction we can make on its statistical properties.

The cornerstone of this new calculus of large matrices is the study of the spectra (eigenvalues) of the matrices. Alike in a classical probability calculus, powerful central limit theorems exist in random matrix theory. This is the reason, why so many similar, macroscopic spectral properties are shared by diverse and unrelated complex random systems (in analogy to the ubiquitous Gaussian distribution in single-valued random structures). We call this phenomenon macroscopic universality of RMT. Macroscopic - as a distinction from the so-called microscopic universality of RMT, a second powerful phenomenon responsible for the wide scope of applications of RMT. Microscopic universality of RMT is the consequence of interactions between the eigenvalues. Since this interaction is long-ranged, certain critical spectral phenomena can emerge locally at the vicinity of some points of the spectra of the matrices. The spectral behavior in the vicinity of these points (fluctuations) depends usually only on the symmetries of the system, therefore can be categorized into universality classes, shared by very different complex systems respecting the underlying symmetry of the matrix model.

Random matrix theory (and in particular its version known as Free Random Variables) can be therefore described as the probability calculus of the XXI century. Nowadays, it is hard to find a branch of science where it does not have any applications.

## String Theory and AdS/CFT correspondence

description

## Other (related) areas of research

- Network Theory
- Quantum Chromodynamics
- Econophysics
- Mathematical methods of theoretical physics applied to interdisciplinary problems
- ...

# Collaborations

- Institute de Physique Theorique, France
- Stony Brook University, USA
- Niels Bohr Institute, Denmark
- Utrecht University, Holland
- Radboud University, Holland
- Karolinska Institutet and Stockholm University, Sweden
- John Innes Centre in Norwich, UK

# Recent publications

## 2016

**Searching for a Continuum Limit in CDT Quantum Gravity**

J. Ambjorn, D. Coumbe, J. Gizbert-Studnicki, J. Jurkiewicz,**Exploring the new phase transition of CDT**

D.N. Coumbe, J. Gizbert-Studnicki, J. Jurkiewicz,*JOURNAL OF HIGH ENERGY PHYSICS*, 1602 (2016) 144, [arXiv:1510.08672].

## 2015

**A simple non-equilibrium, statistical-physics toy model of thin-film growth**

J.K. Ochab, H. Nagel, W. Janke, B. Waclaw,*Journal of Statistical Mechanics: Theory and Experiment*, P09013 [arXiv:1506.03483].**Universal Spectral Shocks in Random Matrix Theory — Lessons for QCD**

J.-P. Blaizot, J. Grela, M.A. Nowak, P. Warchoł,*Acta Physica Polonica B*, 46 (9), 1785 [open access]**Diffusion in the Space of Complex Hermitian Matrices — Microscopic Properties of the Averaged Characteristic Polynomial and the Averaged Inverse Characteristic Polynomial**

J.-P. Blaizot, J. Grela, M.A. Nowak, P. Warchoł,*Acta Physica Polonica B*, 46 (9), 1801 [open access]**Recent results in CDT quantum gravity**

J. Ambjorn, D. Coumbe, J. Gizbert-Studnicki, J. Jurkiewicz,**Wilson loops in CDT quantum gravity**

J. Ambjorn, A. Goerlich, J. Jurkiewicz, R. Loll,*PHYSICAL REVIEW D*, 92, 024013 (2015), [arXiv:1504.01065].**Signature Change of the Metric in CDT Quantum Gravity?**

J. Ambjorn, D.N. Coumbe, J. Gizbert-Studnicki, J. Jurkiewicz,*JOURNAL OF HIGH ENERGY PHYSICS*, 1508 (2015) 033, [arXiv:1503.08580].**The microscopic structure of 2D CDT coupled to matter**

J. Ambjorn, A. Goerlich, J. Jurkiewicz, H. Zhang,*PHYSICS LETTERS B*, 746 (2015) 359-364, [arXiv:1503.01636].**A c=1 phase transition in two-dimensional CDT/Horava-Lifshitz gravity?**

J. Ambjorn, A. Goerlich, J. Jurkiewicz, H. Zhang,*PHYSICS LETTERS B*, 743 (2015) 435-439, [arXiv:1412.3873].**The spectral dimension in 2D CDT gravity coupled to scalar fields**

J. Ambjorn, A. Goerlich, J. Jurkiewicz, H. Zhang,*MODERN PHYSICS LETTERS A*, 30 (2015) 13, 1550077, [arXiv:1412.3434].**Evidence for Asymptotic Safety from Dimensional Reduction in Causal Dynamical Triangulations**

D.N. Coumbe, J. Jurkiewicz,*JOURNAL OF HIGH ENERGY PHYSICS*, 1503 (2015) 151, [arXiv:1411.7712].

## 2014

**Scale-free fluctuations in behavioral performance: Delineating changes in spontaneous behavior of humans with induced sleep deficiency**

J.K. Ochab, J. Tyburczyk, et. al,*PLoS One*, e107542, [open access]**Inflationary power spectra with quantum holonomy corrections**

J. Mielczarek,*JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS*, 1403, 048 [arXiv:1311.1344].**Observational issues in loop quantum cosmology**

A. Barrau, T. Cailleteau, J. Grain and J. Mielczarek,*CLASSICAL AND QUANTUM GRAVITY*, 31, 053001, [arXiv:1309.6896].**Universal shocks in the Wishart random matrix ensemble. II. Nontrivial initial conditions**

J-P. Blaizot, M. A. Nowak, P. Warchoł,*PHYSICAL REVIEW E*, 89, 042130, [arXiv:1306.4014].**Dysonian dynamics of the Ginibre ensemble**

Z. Burda, J. Grela, M. A. Nowak, W. Tarnowski, P. Warchoł,*PHYSICAL REVIEW LETTERS*, 113, 104102, [arXiv:1403.7738].**Dynamics of popstar record sales on phonographic market-stochastic model**

A. Jarynowski, A. Buda,*ACTA PHYSICA POLONICA B*, (PS), 2, (7), [arXiv:]**Studying possible outcomes in model of sexually transmitted virus (HPV) causing cervical cancer for Poland**

A. Jarynowski, A. Serafimovic,*ADVANCES IN INTELLIGENT SYSTEMS AND COMPUTING*, 229, 129, [arXiv:]**Dynamic network approach to marriage/divorces problem**

A. Jarynowski, P. Nyczka,*IEEE/ACM EUROPEAN NETWORK INTELLIGENCE CONFERENCE. IEEE COMPUTER SOCIETY*, DOI 10.1109/ENIC.2014.24, [arXiv:]**Durability of links between assets in financial markets. Minimal spanning trees and correlations**

A. Buda, A. Jarynowski,*IEEE/ACM European Network Intelligence Conference. IEEE Computer Society*, DOI 10.1109/ENIC.2014.18, [arXiv:]**Obliczeniowe nauki społeczne w praktyce**

A. Jarynowski, A. Buda,*WN: WROCŁAW*, ISBN 978-83-63089-92-4, [arXiv:]**Statistics of thermalization in Bjorken Flow**

J. Jankowski, G. Plewa, M. Spalinski ,*JOURNAL OF HIGH ENERGY PHYSICS*, [arXiv:1411.1969]**Renormalization Group Flow in CDT**

J. Ambjorn, A. Goerlich, J. Jurkiewicz, A. Kreienbuehl, R. Loll,*CLASSICAL AND QUANTUM GRAVITY*, 31 (2014) 165003, [arXiv:1405.4585].**The effective action in 4-dim CDT. The transfer matrix approach**

Jan Ambjorn, Jakub Gizbert-Studnicki, Andrzej Görlich, Jerzy Jurkiewicz,*JOURNAL OF HIGH ENERGY PHYSICS*, 1406 (2014) 034 , [arXiv:1403.5940].

## 2013

**Euclidian 4d quantum gravity with a non-trivial measure term**

J. Ambjorn, L. Glaser, A. Gorlich, J. Jurkiewicz,*JOURNAL OF HIGH ENERGY PHYSICS*, 10, 100, [arXiv:1307.2270].**Causal Dynamical Triangulations and the search for a theory of quantum gravity**

J. Ambjorn, A. Gorlich, J. Jurkiewicz, R. Loll,*INTERNATIONAL JOURNAL OF MODERN PHYSICS D*, 22 (9), 1330019, [arXiv:].**Hydrodynamic gradient expansion in gauge theory plasmas**

M. Heller, R. A. Janik, P. Witaszczyk,*PHYSICAL REVIEW LETTERS*, 110, 211602, [arXiv:1302.0697].**Twist-two operators and the BFKL regime - nonstandard solutions of the Baxter equation**

R. A. Janik,*JOURNAL OF HIGH ENERGY PHYSICS*, 11, 153, [arXiv:1309.2844].**Burgers-like equation for spontaneous breakdown of the chiral symmetry in QCD**

J.-P. Blaizot, M. A. Nowak, P. Warchoł,*PHYSICS LETTERS B*, 06, 022, [arXiv:1303.2357].**Universal shocks in the Wishart random-matrix ensemble**

J.-P. Blaizot, M. A. Nowak, P. Warchoł,*PHYSICAL REVIEW E*, 87, 052134, [arXiv:1211.0029].**Collective correlations of Brodmann areas fMRI study with RMT-denoising**

Z. Burda, J. Kornelsen, M. A. Nowak, B. Porebski, U. Sboto-Frankenstein, B. Tomanek, J. Tyburczyk,*ACTA PHYSICA POLONICA B*, 44, 1243, [arXiv:1306.3825].**Maximal entropy random walk in community detection**

J. K. Ochab, Z. Burda,*EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS*, 6, 01730, [arXiv:1208.3688].**Commutative law for products of infinitely large isotropic random matrices**

Z. Burda, G. Livan, A. Święch,*PHYSICAL REVIEW E*, 88, 022107, [arXiv:1303.5360].**Quantum states of the bouncing universe**

J. P. Gazeau, J. Mielczarek, W. Piechocki,*PHYSICAL REVIEW D*, 87, 123508, [arXiv:1303.1687].**Introduction to 4d Causal Dynamical Triangulations**

A. Goerlich,*ACTA PHYSICA POLONICA B*, 44, 2559, [arXiv:].**Introduction to Causal Dynamical Triangulations**

A. Goerlich,*LECTURE NOTES IN PHYSICS*, 8632, 93, [arXiv:].**Euclidean 4D quantum gravity with a non-trivial measure term**

A. Goerlich,*PROCEEDINGS OF SCIENCE*, Lattice 094, [arXiv:1307.2270].**Nod‐factors associated with Medicago truncatula nodule infection differentially induce calcium influx and calcium spiking in root hairs**

G. Morieri, E. Martinez, A. Jarynowski, H. Driguez, R. Morris, G. Oldroyd, J. Downie,*NEW PHYTOLOGIST*, 200 (3), 656, [arXiv:]**Network structure of phonographic market with characteristic similarities between artists**

A. Buda, A. Jarynowski,*ACTA PHYSICA POLONICA A*, 123, 3, [arXiv:1210.0225]**Social networks analysis in discovering the narrative structure of literary fiction**

A. Jarynowski, S. Boland,*BIULLETIN ISI*, 12, 35, [arXiv:]**Reading Stockholm Riots 2013 using Internet media**

A. Jarynowski, A. Rostami,*PROCEEDINGS OF 6TH LANGUAGE AND TECHNOLOGY CONFERENCE, WUAM:POZNAŃ*, [arXiv:]**Modelowanie epidemiologiczne przy wykorzystaniu analizy tymczasowych sieci społecznych**

A. Jarynowski,*POSTĘPY INŻYNIERII BIOMEDYCZNEJ, EDS. L. LENIOWSKA, Z. NAWROT, INPRONA: RZESZÓW*, [arXiv:]**Nowe metody wspomagania komputerowego w epidemiologii zakaźnych chorób szpitalnych, a dowód prima facie w postępowaniach sądowych o zakażenia szpitalne**

A. Jarynowski, J. Pawłowski,*ETYKA WOBEC WSPÓŁCZESNYCH WYZWAŃ, ED. A.BOBKO, UNIWERSYTET RZESZOWSKI: RZESZÓW*, [arXiv:]**Modelowanie epidemiologiczne na sieciach społecznych na przykładzie zakażeń szpitalnych i chorób przenoszonych drogą płciową**

A. Jarynowski,*STUDIA I MATERIAŁY INFORMATYKI STOSOWANEJ*, 5 (10), 13, [arXiv:]