HUN-REN-ELTE Theoretical Physics Research Group

Contact:

Pázmány P. stny. 1/A,
H-1117 Budapest,
phone: +3613722524

Disordered systems and nonequilibrium phenomena

The simple model proposed by Edwards and Anderson for the spin glass state, has become by now the paradigm of strongly frustrated complex systems. Using the long-standing methods of statistical field theory, namely the renormalization group and perturbational expansion, we want to clarify the range of applicability of Parisi's replica symmetry breaking theory: i.e. is it a peculiarity of mean field theory defined on the complete graph, or there exists a replica symmetry broken phase even in models defined on lattices with a nontrivial geometry. The following Ising spin glass models are represented by an effective replicated field theory: the short-ranged system on a finite-dimensional hypercubic lattice, the one-dimensional long-ranged model, and the Ising spin glass defined on a hierarchically constructed lattice. We will focus on two important limiting cases: the asymptotical behavior around the zero-external-magnetic-field critical point (i.e. around the proper spin glass transition), and furthermore we aim to set up a low-temperature field theory, so far missing, representing the zero and near-zero temperature spin glass.

Selected papers:
T. Temesvári: Physical observables of the Ising spin glass in 6-epsilon dimensions: Asymptotical behavior around the critical fixed point.
Phys.Rev. B 96, 024411 (2017)

One of the greatest promises of physics of the twenty-first century is the direct manipulation of matter's building blocks that is atoms, and their states in order to utilize all the encrypted technological possibilities to advance mankind's development. The development of quantum mechanics in the twentieth century pointed out that the exact quantum mechanical description of physical systems composed of some ten or hundred atoms poses serious challenges for classical computers. The saturation of Moore's law, that is the attainment of the computational capabilities of computer processors deepened further these problems. Moreover, numerous other non-quantum mechanical problems, like the prime factorization of large numbers cry for computers with larger computational performance. Quantum simulation and quantum computation offers a new way to solve these problems. Quantum computers could solve problems which-according the current state of the art-could be processed on classical computers only with a run time comparable to the lifetime of the Universe.

The main obstacle of building and running quantum computers is the exceptional sensitivity of these devices to the thermal noise originating from the environment. Our research analyze the time evolution of noisy systems and we try to offer new methods aiming the protection of these systems, or unravel the limits and pitfalls of currently existing methods. We analyze the numerical stability of quantum simulators and the reliability of the answers to questions raised to them.

Homogeneous Markov processes are one of the most frequently used tools in building simplified models of nature and society. Nonetheless, the full analytical study of the time evolution of these systems is impossible with exception of some simple cases. In our work, we study the validity of general statements based upon the assumption that the number of the states of the Markov process is large. We cannot describe the full time evolution in detail in this framework, but we are able to study numerous properties of these models which determine their qualitative nature. The advance of these method is the absence of the a priori assumptions taken on the Markov processes. Thus, we are able to predict the behavior of models with disordered, even random parameter sets.

Selected papers:
N. Barankai and J. Stéger: The SIS process in populations with exponential decay
J. Stat. Mech. 2018.1 (2018): 013404.

The understanding of systems subjected to a general time-dependent parameter drift is a challanging task. The conceptual background of this problem os provided by snapshot attractors and their natural probability distribution. We are investigating the change in the character of chaos in systems driven by general temporal forcing, including the existence of dramatic chnages, so-called tipping transitions. We are intending to describe the separation of the oceanic and atmospheric time scales in elemantary models. In the case of a considerable separation, it is worth considering initial ensembles in which the slow variables are not perturbed, and one should monitor the time-evolution of such ensembles. A basic question to answer is whether the uniqueness of the fast variables' distribution is influenced by the explicit time-dependence of the forcing.

Selected papers:
György Károlyi and Tamás Tél: New features of doubly transient chaos: complexity of decay
J.Phys.Complex. 2 (2021) 035001 (16pp); doi: 10.1088/2632-072X/abedc3

Dániel Jánosi and Tamás Tél: Chaos in conservative discrete-time systems subjected to parameter drift
Chaos 31, 033142 (2021); doi: 10.1063/5.0031660

Bálint Kaszás, Ulrike Feudel, and Tamás Tél: Leaking in history space: A way to analyze systems subjected to arbitrary driving
Chaos 28, 033612 (2018); doi: 10.1063/1.5013336