Solvable Markovian dynamics of lattice quantum spin models

We address the real-time dynamics of lattice quantum spin models coupled to single or multiple Markovian dissipative reservoirs using the method of closed hierarchies of correlation functions. This approach allows us to solve a number of quantum spin models exactly in arbitrary dimensions, which is illustrated explicitly with two examples of driven-dissipative systems. We investigate their respective nonequilibrium steady states as well as the full real-time evolution on unprecedented system sizes. Characteristic time scales are derived analytically, which allows us to understand the nontrivial finite-size scaling of the dissipative gap. The corresponding scaling exponents are confirmed by solving numerically for the full real-time evolution of two-point correlation functions.Comment: 6 pages, 2 figures; version accepted for publication in PR

Functional renormalization group approach to the Yang-Lee edge singularity

We determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in $3 \leq d\leq 6$ Euclidean dimensions. We find very good agreement with high-temperature series data in $d = 3$ dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop $\epsilon = 6-d$ expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG $\beta$ functions is discussed and we estimate the error associated with $\mathcal{O}(\partial^4)$ truncations of the scale-dependent effective action.Comment: 10 pages, 4 figures, updated reference to supplementary materia

On spinodal points and Lee-Yang edge singularities

We address a number of outstanding questions associated with the analytic properties of the universal equation of state of the $\phi^4$ theory, which describes the critical behavior of the Ising model and ubiquitous critical points of the liquid-gas type. We focus on the relation between spinodal points that limit the domain of metastability for temperatures below the critical temperature, i.e., $T < T_{\rm c}$, and Lee-Yang edge singularities that restrict the domain of analyticity around the point of zero magnetic field $H$ for $T > T_{\rm c}$. The extended analyticity conjecture (due to Fonseca and Zamolodchikov) posits that, for $T < T_{\rm c}$, the Lee-Yang edge singularities are the closest singularities to the real $H$ axis. This has interesting implications, in particular, that the spinodal singularities must lie off the real $H$ axis for $d < 4$, in contrast to the commonly known result of the mean-field approximation. We find that the parametric representation of the Ising equation of state obtained in the $\varepsilon = 4-d$ expansion, as well as the equation of state of the ${\rm O}(N)$-symmetric $\phi^4$ theory at large $N$, are both nontrivially consistent with the conjecture. We analyze the reason for the difficulty of addressing this issue using the $\varepsilon$ expansion. It is related to the long-standing paradox associated with the fact that the vicinity of the Lee-Yang edge singularity is described by Fisher's $\phi^3$ theory, which remains nonperturbative even for $d\to 4$, where the equation of state of the $\phi^4$ theory is expected to approach the mean-field result. We resolve this paradox by deriving the Ginzburg criterion that determines the size of the region around the Lee-Yang edge singularity where mean-field theory no longer applies.Comment: 26 pages, 8 figures; v2: shortened Sec. 4.1 and streamlined arguments/notation in Sec. 4.2, details moved to appendix, added reference 1

Mikotoxinok a gabonatermesztésben: az élelmiszerbiztonsági kihívás

A gabonatermesztés a maga 15 millió t éves termelésével a legfontosabb élelmiszer- és takarmány alapanyagokat szolgáltatja. A kalászosokat és a kukoricát a Fusarium fajok fenyegetik leginkább, amelyek termés és minőségi problémákon túl a toxinszennyezéssel (deoxynivalenol, zearalenon, T-1 toxin, fuminizinek) okozzák a legnagyobb kárt. Ezért ezek jelentik az első számú biztonsági kockázatot a veszélyeztetett években. Alapvető nemzetgazdasági érdek az élelmiszer- és takarmánybiztonsági követelmények teljesítése. A feladatot rezisztencianemesítéssel, hatékonyabb fungicides védelemmel és a fajtaminősítéssel együttesen lehet megoldani. A rezisztencianemesítés területén már rendelkezésre állnak a nagymértékben ellenálló búzatörzsek, amelyek felhasználásával intenzív fajtaelőállító programba kezdtünk, hogy termőképes és jó minőségű rezisztens fajtákat állítsunk elő. A fungicides védelem tekintetében kidolgoztunk egy sokkal hatékonyabb eljárást, amely minimális ráfordítással (5 Ft/ha) lényegesen növeli a hatékonyságot. Folyamatban van a búza fajtaminősítési módszertanának kidolgozása, amellyel megvédhetjük a hazai termelőket a nagyon érzékeny fajták elterjedésétől. Ezt a munkát kukoricában szintén el kívánjuk indítani, hogy a takarmánybázis biztonsága megfelelő legyen a veszélyeztetett években is. The cereal production in Hungary (15 million t/year) is hazarded by Fusarium spp. that cause not only yield and quality losses, but through the production of a number of mycotoxins they jeopardize the whole remaining yield (deoxynivalenol, zearalenone, T-2 toxin, fumonisins as most important). Therefore they represent the No. 1 safety problem in epidemic years. There is a fundamental national interest to fulfill the EU regulations for toxin contamination. The task can be solved by breeding for resistance, more effective fungicide use and by a more effective process of registration. For wheat the methodology of breeding is ready, highly resistant lines are in the nursery and an intensive breeding program started several years ago to combine high FHB resistance with high yielding and quality. In the fungicide use we developed a more effective fungicide technology that increases the efficacy of the treatment by about 60% with minimum costs (5 Ft/ha, 1 Euro is about 260 Ft). The methodology for the registration is under development in a project for wheat, for corn the work started. These three activities are necessary to protect growers from the susceptible cultivars, provide them more resistant cultivars, more effective fungicides and better technology to secure safety for humans and the animal husbandry

Multicritical behavior in models with two competing order parameters

We employ the nonperturbative functional Renormalization Group to study models with an O(N_1)+O(N_2) symmetry. Here, different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the competition of two order parameters. We discuss the critical behavior of the symmetry-enhanced isotropic, the decoupled and the biconical fixed point, and analyze their stability in the N_1, N_2 plane. We study the fate of non-trivial fixed points during the transition from three to four dimensions, finding evidence for a triviality problem for coupled two-scalar models in high-energy physics. We also point out the possibility of non-canonical critical exponents at semi-Gaussian fixed points and show the emergence of Goldstone modes from discrete symmetries.Comment: 16 pages, 7 figures, 5 tables, minor changes in updated version, identical to published one in Phys. Rev.

Egyéves füzények (Lythrum) Magyarországon: a Hyssopifolia alnemzetség hazai adatainak revíziója

Magyarország területéről eddig az apró termetű, egyéves füzények 4 fajának előfordu­lását közölték. A Lythrum hyssopifolia az ország nagy részén elterjedt. A L. tribracteatum jóval ritkább, előfordulásai főként a Tiszántúl déli részére és a Duna mentére korlátozódnak. A belső-ázsiai elterjedé­sű lenlevelű füzény (L. linifolium) egyetlen európai adata hazánkból származik. Az 1954-ben Tiszaug mellett gyűjtött példány azonban több jellegében is eltér a lenlevelű füzénytől, viszont nagyfo­kú egyezést mutat a Mediterráneumban és a kelet-európai sztyeprégióban élő L. borysthenicum-mal. Ez alapján javasoljuk a L. linfolium törlését a hazai és az európai flórából egyaránt. A negyedik hazai taxon (L. thesioides) egykori magyarországi előfordulását (Nagytétény) herbáriumi példányok bizonyítják, de a faj jelenlegi előfordulása bizonytalan.</jats:p

Discovering and quantifying nontrivial fixed points in multi-field models

We use the functional renormalization group and the $\epsilon$-expansion concertedly to explore multicritical universality classes for coupled $\bigoplus_i O(N_i)$ vector-field models in three Euclidean dimensions. Exploiting the complementary strengths of these two methods we show how to make progress in theories with large numbers of interactions, and a large number of possible symmetry-breaking patterns. For the three- and four-field models we find a new fixed point that arises from the mutual interaction between different field sectors, and we establish the absence of infrared-stable fixed point solutions for the regime of small $N_i$. Moreover, we explore these systems as toy models for theories that are both asymptotically safe and infrared complete. In particular, we show that these models exhibit complete renormalization group trajectories that begin and end at nontrivial fixed points.Comment: 10 pages, 6 figures; minor changes, as published in EPJ

Dissipative Bose-Einstein condensation in contact with a thermal reservoir

We investigate the real-time dynamics of open quantum spin-$1/2$ or hardcore boson systems on a spatial lattice, which are governed by a Markovian quantum master equation. We derive general conditions under which the hierarchy of correlation functions closes such that their time evolution can be computed semi-analytically. Expanding our previous work [Phys. Rev. A 93, 021602 (2016)] we demonstrate the universality of a purely dissipative quantum Markov process that drives the system of spin-$1/2$ particles into a totally symmetric superposition state, corresponding to a Bose-Einstein condensate of hardcore bosons. In particular, we show that the finite-size scaling behavior of the dissipative gap is independent of the chosen boundary conditions and the underlying lattice structure. In addition, we consider the effect of a uniform magnetic field as well as a coupling to a thermal bath to investigate the susceptibility of the engineered dissipative process to unitary and nonunitary perturbations. We establish the nonequilibrium steady-state phase diagram as a function of temperature and dissipative coupling strength. For a small number of particles $N$, we identify a parameter region in which the engineered symmetrizing dissipative process performs robustly, while in the thermodynamic limit $N\rightarrow \infty$, the coupling to the thermal bath destroys any long-range order.Comment: 30 pages, 8 figures; Revised version: Minor changes and references adde

Két új adventív faj előfordulása Magyarországon a buzérfélék (Rubiaceae) családjából

A szerzők két, korábban Magyarországról nem ismert, a Rubiaceae családhoz tartozó faj első adatát közlik. A Délnyugat-Ázsiából származó, dísznövényként Európában szórványosan ülte­tett piros szálkanyak (Phuopsis stylosa) a Vas megyei Csákánydoroszló község közúti árkának degradált mezofil gyepjében telepedett meg. A Mediterráneumban őshonos kőfali galaj (Galium murale) kis állo­mánya a budapesti Keleti pályaudvar egyik használaton kívülimellékvágánya mentén került elő. Előbbi faj feltételezhetően ültetésből vadulhatott ki, míg utóbbi jelenléte a vasúti forgalomnak köszönhető. Mindkét faj egyelőre csak kis egyedszámban van jelen élőhelyén, így inváziós képességük csak több éves megfigyelést követően értékelhető. A fajok beillesztésre kerültek a hazai határozókulcsba.</jats:p