After the application of the replica trick, the finite dimensional spin glass state can be represented by a cubic replicated field theory. The replica symmetry of the original model is spontanously broken in the spin glass state which is, therefore, usually called the replica symmetry broken (RSB) phase. The spin glass transition has been studied by a mixture of Wilson's renormalization group and perturbational methods around the upper critical dimension of the model. The effect of an external magnetic field on the existence of the spin glass state has long been debated for some decades: this important theoretical problem can be clarified by the study of the so called Almeida-Thouless instability. The direct study of the RSB phase is extremely difficult even in the case of zero external magnetic field, when the model possesses an extra symmetry beyond the generic replica symmetry. An extensive second order calculation enables one to unfold the perturbative structure of the zero-magnetic-field spin glass phase.Selected papers: G. Parisi and T. Temesvári: Replica symmetry breaking in and around six dimensions. Nuclear Physics B 858, 293-316 (2012). T. Temesvári: The perturbative structure of spin glass field theory. Nuclear Physics B 880, 528-551 (2014).
The study of nonequilibrium dynamics of low-dimensional isolated quantum systems has been living its renaissance in the last decade, which is mainly due to the amazing success of optical lattice experiments with cold atoms. In the theoretical investigations, a central role is played by integrable models which can show remarkable features such as the lack of thermalization or ballistic transport. One of the simplest setting to study transport properties is to consider an initial state of a quantum chain with the two sides prepared at different thermodynamical parameters (temperature or chemical potential). The initial gradient induces currents and a front region emerges with its size growing linearly in time. The study of these quantum fronts can lead to very interesting observations. In particular, for a chain of free fermions evolving from a step-like initial state, one finds a nontrivial fine structure of the front, which can be directly mapped onto the edge spectrum of certain random matrices.Selected papers: V. Eisler and Z. Rácz: Full counting statistics in a propagating quantum front and random matrix spectra Phys. Rev. Lett. 110, 060602 (2013)
Entanglement plays a central role in understanding the behaviour of quantum many-body systems at ultra low temperatures: it carries essential information about the ground state of the system and can also be applied to investigate certain non-equilibrium dynamical problems. In recent years, the investigation of entanglement properties has become a mainstream approach in many-body physics. In particular, it has provided an unprecedented clarity in understanding the universality of one-dimensional quantum chains at quantum critical points. Furthermore, entanglement plays a key role in the extraordinary success of modern numerical methods, such as the density matrix renormalization group.Selected papers: V. Eisler and Z. Zimborás: On the partial transpose of fermionic Gaussian states, New J. Phys. 17, 053048 (2015), doi:10.1088/1367-2630/17/5/053048 V. Eisler, M-C. Chung, and I. Peschel: Entanglement in composite free-fermion systems, J. Stat Mech. P07011 (2015), doi:10.1088/1742-5468/2015/07/P07011
The building of electronic components close to atomic scales is a fundamental task in the development of the next generations of computers. As a novel solution, the so-called “bottom-up” processing has been suggested. In this method, the creation of the micro- and nano-patterns is done by moving the appropriate material components by chemical fronts, and producing the desired pattern by precipitation reactions at the right spatial positions. In principle, this is simple, but the practical realization is a difficult and unsolved problem. Indeed, at submicron scales, one has to direct small groups of atoms or molecules such that the reaction among them would yield the needed structures at the right positions. The difficulties can be overcome at macroscales but, on approaching the microscales, a number of problems arise. Prominent among them is the finite size of the reaction fronts which gives a lower limit for the smallest wavelength of the resulting patterns. An even more complex issue is the effect of thermal noise which causes fluctuations e.g. in the ionic concentrations of the reagents and thus, the controllability of patterns by electric fields is lost. In general, the uniqueness of the pattern is in danger when noise is present. For example, in case of Liesegang phenomena (extensively studied by us), the characteristic structures are parallel bands or helices and, due to the noise effects, they appear with well defined, measurable probabilities even if the initial- and boundary conditions are identical. The formation of helices by precipitation is in itself a beautiful example of non-trivial symmetry breaking. Our efforts to understand them has the additional importance that clarifying the role of noise may bring us closer to the understanding of noise effects in the more pressing problem of how to control the technologically relevant precipitation processes.Selected papers: S. Thomas, G. Varghese, D. Bárdfalvi, I. Lagzi, and Z. Rácz: Helicoidal precipitation patterns in silica and agarose gels , Chem. Phys. Lett. 599, 159-162 (2014) S. Thomas, I. Lagzi, F. Molnár Jr., and Z. Rácz: Probability of the Emergence of Helical Precipitation Patterns in the Wake of Reaction-Diffusion Fronts , Phys. Rev. Lett. 110, 078303 (2013)
Chaotic behaviour is an irregular, noise-like behaviour that originates in the system's internal dynamics and which often accompanies transport phenomena. In this case it usually appears in the form of transient chaos, with finite duration. In a class of the chaotic systems that we investigate the outflow of the material results from the opening of the system. One example for this is the microlaser in which the laser light exits the system below a certain angle of incidence. Those phenomena can be treated analogously in which only energy escapes from the system, e.g. in the case of sound absorption. These processes' elementary building block is often chaotic scattering between the asymptotically free incoming and outgoing states. One of its least uncovered areas is chaotic scattering with more than two degrees of freedom in which one can infere the quantitative characteristics of chaos by investigating the singularities of the doubly differential cross section.Selected papers: E.G. Altmann, J.S.E. Portela, T. Tél: Chaotic Systems with Absorption , (supplemental material), Phys. Rev. Lett. 111, 144101(1-5) (2013) F. Gonzalez, G. Drótos and C. Jung: "The decay of a normally hyperbolic invariant manifold to dust in a three degrees of freedom scattering system". J. Phys. A. 47, 045101 (2014).