prof. Vesselin Tonchev
(Institute of Physical Chemistry, Bulgarian Academy of Sciences, Sofia, Bulgaria)

Diffusion-limited vs. kinetics-limited regime of step bunching: How to distinguish in between?

In this talk are presented numerical results from models of unstable vicinal crystal growth. In particular, they resolve the long-standing controversy between numerical results on the minimal step-step distance lmin in bunches and predictions of continuum theory - while the size-scaling exponent of lmin is found the same in diffusion-limited (DL) and kinetics-limited (KL) regime, and the time-scaling exponent of the bunch size N is predicted also to be the same and equal to 1/2, the scaling exponents of the bunch width W and lmin are predicted to distinguish in between. Using results from the model of unstable vicinal growth of Sato and Uwaha (SU) we propose a solution to that puzzle. Results from other models are discussed as well, and especially from vicinal Cellular Automata (vicCA). In particular, for the vicCA it is the time-scaling exponent of the macrostep size Nm that makes the difference, instead of that of W in the SU-model. In the prelude an account is given of the numerical results for the size-scaling of lmin in the two regimes for evaporation affected sublimation and the experimental evidence for DL regime. These are confronted with the predictions of the Pimpinelli et al. theory of universality classes in bunching and the correction of Krug et al. (KTSP) [1] to account for the differences in two regimes. Especially in the ρ = -1 universality class to which are expected to belong both vicinal evaporation and growth, only the time-scaling of W can distinguish between the two regimes. KTSP predict additionally that the time-scaling exponent of W in the KL regime is shifted with respect to the DL regime. Systematic numerical results for intermediate asymptotics from the SU-model [2] are obtained in the two regimes. These results show that the time-scaling exponents of W for the DL and for the KL are both shifted (differently) but the size-scaling exponent of lmin remains the same. Since SU model does not permit! studying the infinite Ehrlich-Schwoebel barrier we study his using vicCA[3]. In this model the time-scaling exponent of N is also invariant for DL and KL regimes (=1/3). Since there is no step-step repulsion incorporated in the model, besides bunching of mono-steps a macrostep formation is observed, thus lmin=0. The time-scaling exponent of Nm is 1/4 in the DL and 1/5 in the KL (see Fig. 1).

[1] Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002); Krug et al., Phys. Rev. B 71, 206103 (2005).
[2] M. Sato and M. Uwaha, Surface science 493, 494 (2001).
[3] F. Krzyżewski, M. Załuska-Kotur, A. Krasteva, H. Popova, V. Tonchev, arXiv:1601.07371.

PDF file with full abstract and figures:    ( )

dr hab. Maciej Janowicz
(Szkoła Główna Gospodarstwa Wiejskiego)

Lower bounds for ground-state energy, overlap integrals and expectation values for driven Bose-Hubbard model

The problem of coupled resonators with nonlinear self-interaction of light in each resonator is essentially dynamical and such that the dissipation has to be taken into account. However, if the rotating wave approximation is justified, one obtains a well-defined time-independent Hamiltonian, the spectral properties of which are worth of attention. Using an old Lieb-Yamazaki technique and Weinhold's criteria, lower bounds for the energy of the ground and lowest excited states have been obtained for nearest-neighbors coupling between resonators. Those bounds have then been used to obtain lower bounds for the overlap integrals between the exact and a specially constructed trial wave function. The overlap integrals, in turn, have been employed to compute expectation values of some positive operators, including density-density correlation functions.

dr Krzysztof Wohlfeld
(Uniwersytet Warszawski)

Spin-orbital separation in the 1D cuprates

In contrast to collective magnetic excitations (such as e.g. magnons), the collective excitations which carry orbital degree of freedom (often called orbitons) are very hard to detect. Nevertheless, recent advancements in resonant inelastic x-ray scattering have allowed for a rather unambiguous detection of orbitons in various transition metal oxides -- in particular the quasi-1D copper oxides [1, 2]. Strikingly, a closer investigation of the observed 1D orbiton dispersion suggested that this dispersion could not be understood using a simple orbital wave picture [1, 3]. Instead it occurred that the orbitons are in general very strongly coupled to spin excitations. It is then only in 1D that they can decouple leading to a particularly strong dispersion which is due to a phenonemonen called spin-orbital separation: the initial orbital excitation fractionalizes into an independent orbiton and spinon excitation.

References:
[1] J. Schlappa, K. Wohlfeld et al.; Nature 485, 82 (2012).
[2] V. Bisogni, K. Wohlfeld, et al.; Phys. Rev. Lett. 114, 096402 (2015).
[3] K. Wohlfeld, M. Daghofer, S. Nishimoto, G. Khaliullin, and J. van den Brink; Phys. Rev. Lett. 107, 147201 (2011).

dr Emilia Witkowska
(Instytut Fizyki PAN)

Kibble-Zurek mechanism in antiferromagnetic spinor condensates

I will present our work concerning the dynamics and outcome of a quantum phase transition from an antiferromagnetic to a phase-separated ground state in a spin-1 Bose-Einstein condensate of ultracold atoms. We demonstrate the occurrence of two scaling laws, for the number of spin domain seeds just after the phase transition, and for the number of spin domains in the final, stable configuration. Only the first scaling can be explained by the standard Kibble-Zurek mechanism. We explain the occurrence of two scaling laws by a model including postselection of spin domains for the uniform system and transport of local magnetization for the trapped system.

Piotr Szańkowski
(Instytut Fizyki PAN)

Noise Spectroscopy with Qubit Probe

The discovery of Spin Echo in NMR led to development of Dynamical Decoupling (DD) techniques, where a qubit is undergoing a complex control scheme that effectively decouples it from the influence of the environmental noise. Initially, DD was conceived and applied as a way to extend the lifetime of qubit's quantum properties (its coherence), so that it could remain useful for various quantum-based task (like information processing or metrology) despite the unavoidable interference from the environment. Recently, there has been a paradigm shift in the literature. The environmental noise does not have to be merely a nuisance that stands in the way of "truly" interesting applications of qubits. Noise generated by a complex system bears useful information about its source - similarly how light from a distant star can be used to get a glimpse into it's innerworkings. Indeed, qubit under DD acts as a spectrometer which can analyze the fluctuation of the environmental signal; analogically to spectroscopy of light from celestial bodies. A single qubit driven by DD sequence can serve as a spectrometer of local noise. When two (or more) spatially separated qubits are used instead, one can reconstruct the spectrum of cross-correlations of noises acting at various locations. By adjusting the types of sequences used on each qubit it is possible, for example, to determine some transport properties of the environment, or to check whether its different part parts are causally correlated. These are just a few examples of potential applications stemming from DD-based noise spectroscopy.

dr hab. Janusz Stafiej
(Uniwersytet Kardynała Stefana Wyszyńskiego)

Korozja, pasywacja, nanopory w modelach typu automatów komórkowych

Przedstawione zostaną cztery zagadnienia z prac prelegenta dotyczących zjawisk korozji i pasywacji.

1. Przejście od wolnej do szybkiej korozji w modelu procesu korozyjnego, w którym następuje rozdział przestrzeni anodowych kwaśnych i katodowych zasadowych w wyniku autokatalitycznego charakteru procesu korozyjnego.
2. Model procesu pasywacji opartu na migracji anionów (wakansów, defektów) w warstwie pasywnej. Przejście od reżymu kontrolowanego reakcją do reżymu kontrolowanego dyfuzją.
3. Model procesu pasywacji oparty na asymetrycznym błądzeniu przypadkowym (Walker model). Przejście od reżymu gołej powierzchni do reżymu powierzchni pokrytej warstwą pasywną.
4. Model WOW (walker on walker) tworzenia się porów w warstwie pasywnej.

prof. Alexey Kavokin
(University of Southampton)

New quantum effect in a two-dimensional electron gas

We demonstrate that the temperature derivative of the chemical potential of a two-dimensional electron gas (2DEG) exhibits quantized dips where the chemical potential passes through the electron levels of size quantization. We find analytically the shape of the dips accounting for the elastic and inelastic scattering processes in 2DEG. In the limit of no scattering, at zero magnetic field, the dips depend only on the subband quantization number and are independent on material parameters, shape of the confining potential and temperature. The smearing of the dips is a direct measure of the disorder induced smearing of the electronic denisty of states. This peculiar quantum effect should manifest itself in various optical and electronic transport experiments [1].

[1] A.A. Varlamov, A.V. Kavokin and Yu.M. Galperin, Quantisation of entropy in a quasi-two-dimensional electron gas, Phys. Rev. B 93, 155404 (2016).

mgr Maciej Pieczarka
(Politechnika Wrocławska)

Wpływ nieporządku na propagację nierównowagowego kondensatu polarytonów ekscytonowych

Kondensaty polarytonów ekscytonowych są nowym typem kondensatów bozonowych, których nieodłączną właściwością jest brak równowagi termodynamicznej, wynikający z ich krótkiego czasu życia (krótszego niż czas termalizacji gazu). Pomimo tego faktu, zachowują one wiele właściwości charakterystycznych dla kondensatów arcyzimnych atomów, takich jak nadciekłość, czy generacja kwantowych wirów i solitonów. Charakterystyczną cechą optycznych mikrownęk półprzewodnikowych, w których generowane są polarytony, jest wbudowany naturalny nieporządek, wynikający z zastosowanego procesu technologicznego. Nieporządek może wpływać na stopień koherencji w kondensatach polarytonów ekscytonowych, jak również generować nietrywialne rozkłady prądów i wzbudzeń. W tym wystąpieniu przybliżę efekty nieporządku na kondensaty polarytonów propagujących z niezerowym pądem. Omówię zaobserwowane eksperymentalnie efekty rozpraszania polarytonów w silnym potencjale losowym w strukturze, co skutkowało generacją wzbudzeń typu Bogolubowa o liniowej dyspersji oraz obsadzeniem wirtualnej gałęzi wzbudzeń o energii negatywnej względem energii wytworzonego kondensatu. Przedstawione zostaną również efekty polaryzacji spinowej obu gałęzi wzbudzeń oraz ewolucje czasowe badanych zjawisk.

Jacek Dobrzyniecki
(Instytut Fizyki PAN)

Ścisła dynamika dwóch ultrazimnych bozonów umieszczonych
w jednowymiarowej podwójnej studni potencjału

Przeanalizowano ewolucję dwóch ultrazimnych bozonów umieszczonych w podwójnej studni potencjału początkowo umieszczonych w jednej ze studni. Porównano dynamikę przewidywaną przez ścisły dwuciałowy hamiltonian z dynamiką uzyskaną w ramach uproszczonych modeli dwumodowych. Pokazano, że dla niskiej bariery potencjału i odpowiednio silnego oddziaływania wszystkie modele dwumodowe załamują się i są niewystarczające do prawidłowego opisu dynamicznych własności układu. W szczególności źle opisują one korelacje pomiędzy bozonami.

prof. dr hab. Jan Mostowski
(Instytut Fizyki PAN)

Integral equation approach to electromagnetic field in dielectrics

We study static electric field and electromagnetic waves in dielectric media. As opposed to the standard approach we formulate and solve integral equations for the field. We discuss the case of electrostatic field of a point charge placed inside a dielectric. Integral equation approach allows to find and interpret the dielectric constant in terms of molecular polarizability. Next we discuss propagation of electromagnetic waves using the same integral equation approach. We derive dispersion relation and find reflection and transmission coefficients at the boundary between vacuum and the dielectric. The present approach supplements the standard approach based on macroscopic Maxwell's equations and contributes to better understanding of some electromagnetic effects.

dr Barbara Dietz
(Instytut Fizyki PAN)

Microwave Billiards, Graphene and Fullerene C60

We determined experimentally the eigenvalues of quantum billiards with the shapes of a rectangle and of Africa, respectively, that contained circular scatterers forming a triangular grid, so-called Dirac billiards. For this, high-precision measurements have been performed with superconducting microwave billiards. In the first part of my talk I will shortly review the salient properties of classical, quantum and microwave billiards. In the second part of my talk, I will present results concerning the particular features of the density of states (DOS) of Dirac billiards, which resembles that of a graphene flake, and their spectral fluctuation properties. I will demonstrate that the van Hove singularities, that show up as sharp peaks in the DOS, divide the band structure into regions where the system is governed by the non-relativistic Schrödinger equation of the quantum billiard and the Dirac equation of the graphene billiard of corresponding shape, respectively. In the third part of my talk I will present experiments that have been performed using a spherical superconducting microwave resonator with the geometric structure of the C60 fullerene molecule. Firstly, we studied the exceptional spectral properties emerging from the symmetries of the icosahedral structure of the carbon lattice. Secondly, we determined the number of zero modes with eigenvalues at the Dirac point to test the predictions of the Atiyah-Singer index theorem, which relates it to the topology of the curved carbon lattice. For this purpose, we performed numerical calculations in order to extend the experimental results to larger fullerene molecules.

* Supported by the DFG within the Collaborative Research Center CRC634

dr Krzysztof Jachymski
(Universität Stuttgart, Stuttgart)

Three-body interactions of slow light Rydberg polaritons

Rydberg polaritons have recently emerged as a new promising platform for studying quantum nonlinear optics and few-body physics. In this scheme photons in an atomic medium are tuned near the conditions of electromagnetically induced transparency with a large admixture of the Rydberg state. Strong interactions between Rydberg atoms can be mapped onto effective interactions between the polaritons. We show that in systems consisting of more than two photons, effective many-body interactions appear in addition to two-body ones. We focus on three-body systems in one-dimensional geometry and analyze how the three-body bound state is modified by these interactions and how the correlation functions of outgoing photons can be used to detect them.

dr inż. Paweł Potasz
(Katedra Fizyki Teoretycznej, Politechnika Wrocławska)

Ułamkowe izolatory Cherna przy przejściu pomiędzy siecią Checkerboard a siecią Lieba

Ułamkowe Izolatory Cherna (ang. Fractional Chern Insulators) to nowa klasa skorelowanych nieściśliwych cieczy kwantowych występujących dla ułamkowo zapełnionych płaskich pasm energetycznych o nietrywialnej topologii. W niniejszej pracy analizujemy stabilność fazy FCI ze względu na oddziaływanie z dodatkową podsiecią, której sprzężenie z układem jest kontrolowane za pomocą potencjału na węźle sieci. Odpowiada to przejściu pomiędzy siecią Checkerboard, a siecią Lieba. W układzie analizujemy wielkość wielocząstkowej przerwy energetycznej pomiędzy stanem podstawowym o trzykrotnej degeneracji, a stanami wzbudzonymi. Rozważamy modele z różną fazą odpowiadającą za nietrywialną topologię pasm oraz modelem pasma wypłaszczonego. Głównym wynikiem jest pokazanie silnej korelacji pomiędzy stałością tzw. krzywizny Berry'ego, a wielkością przerwy wielocząstkowej. Jest to związane z analogią pomiędzy fazą FCI, a cieczą Laughlina dla zapełnienia 1/3 najniższego poziomu Landaua.

dr inż. Paweł Potasz
(Katedra Fizyki Teoretycznej, Politechnika Wrocławska)

Ułamkowe izolatory Cherna przy przejściu pomiędzy siecią Checkerboard a siecią Lieba

Seminarium odwołane i przeniesione na późniejszy termin.

Prof. Vesselin Tonchev
("Rostislav Kaischew" Institute of Physical Chemistry, Bulgarian Academy of Sciences, Sofia, Bulgaria)

Phase transitions in 2D Ising-type model with essentially anisotropic interactions: Transfer Matrix study

In the introductory part is presented briefly the Transfer Matrix (TM) method - a powerful and elegant method of the statistical physics. Some technical details of the method, such as block-diagonalization of the resulting matrices, are sketched. The machinery of the TM is applied to a 2D Ising-type model evolving from a real surface science system, Pb/Cu(110), and with essentially anisotropic interactions - attraction Jx between nearest neighbors along x-direction and repulsions Ji between all neighbors up to i-th one along the y-direction, decreasing according to the power law, where a is the lattice constant along y. Thus, the model parameters are: the external magnetic field H, the attraction energy Jx, the power p and the cut-off r of the potential along y. In the ground state analysis are accounted up to 200-th neighbors when the interactions are long-ranged, p = 1, 2. In particular, it is shown that a sequence of distinguishable in the ground state phases (2x1), (3x1), .., (rx1), (1x1) exists when the cut off of the interactions is r-1. When studying the thermal stability of the phases the cut-off r is restricted by the computationally affordable sizes of the TM - up to 9-th neighbors. The thermal behavior of the phases (2x1) and (3x1)+ is studied and the order-disorder transition lines for p = 2 and 3 are found using Nightingale's phenomenological renormalization - comparing the correlation lengths obtained from the two largest eigenvalues of the TM of two systems with similar sizes. Additionally, the TM permits direct estimation of two of the critical indices, that of the correlation length and of the correlation function. A second correlation length is obtained from the largest and the third largest eigenvalue of the TM expecting that the order-disorder transition may happen in two stages due to the interactions anisotropy. The universality of the numerically observed phase transitions is discussed in detail in the concluding part of the talk.