Continuum approach to real time dynamics of 1+1D gauge field theory: out of horizon correlations of the Schwinger model

We develop a truncated Hamiltonian method to study nonequilibrium real time dynamics in the Schwinger model - the quantum electrodynamics in D=1+1. This is a purely continuum method that captures reliably the invariance under local and global gauge transformations and does not require a discretisation of space-time. We use it to study a phenomenon that is expected not to be tractable using lattice methods: we show that the 1+1D quantum electrodynamics admits the dynamical horizon violation effect which was recently discovered in the case of the sine-Gordon model. Following a quench of the model, oscillatory long-range correlations develop, manifestly violating the horizon bound. We find that the oscillation frequencies of the out-of-horizon correlations correspond to twice the masses of the mesons of the model suggesting that the effect is mediated through correlated meson pairs. We also report on the cluster violation in the massive version of the model, previously known in the massless Schwinger model. The results presented here reveal a novel nonequilibrium phenomenon in 1+1D quantum electrodynamics and make a first step towards establishing that the horizon violation effect is present in gauge field theory.Comment: 9+7 pages, 7 figures. V2: Additional results adde

Dinamika CO2 in procesi raztapljanja v kraški vadozni coni

The dynamics and distribution of carbon dioxide (CO2) in karst systems are crucial for understanding fundamental karst processes, namely precipitation and dissolution, which drive karst development both at the surface and underground. The study of CO2 transport provides valuable insights into the role of karst systems in the global carbon cycle and the impact on present climate, but also into the growth of speleothems, which are one of the most reliable terrestrial archives for palaeoclimate reconstruction. Due to the complexity of karst systems, long-term monitoring and high-resolution analyses of cave air and water geochemistry are essential to better understand the controlling factors that affect these processes and their outcomes. In the framework of this dissertation, cave climate and water hydrochemistry monitoring was established in a side-passages of the renowned Postojna Cave in Slovenia during 2017–2021. In the Pisani Passage, high CO2 concentrations, large temporal variations and a heterogeneous distribution of CO2, as well as extreme dissolution features, have already been detected in previous studies. The aim of the present study was to investigate these observations in depth and to find the reasons for their occurrence. This led to creating of a conceptual model for CO2 transport in karst systems that would be valid not only in this case but in karst areas worldwide. The first focus of the study is dedicated to understanding the spatio-temporal dynamics of the partial pressure of CO2 (pCO2) in the Pisani Passage, which is mainly transported by advection (i.e., cave ventilation). Continuous measurements of airflow velocity, air temperature and pCO2 showed (1) that airflow through the karst massif is driven by both the action of the chimney effect and external winds, and (2) that the relationship between the direction of airflow, the configuration of airflow pathways and the connection to the outside explains the observed variations in pCO2. Due to the particular configuration of the airflow pathways, the terminal chamber of Pisani Passage accumulates high levels of CO2 (>10,000 ppm) and forms high vertical gradients of up to 1000 ppm/m. The pCO2 is low and uniform during updraft when outside air flows into the cave chamber through open, unobstructed passages (i.e., high-flow, low-pCO2 pathways). When the airflow reverses direction to downdraft, the chamber is fed by low-flow, high-pCO2 pathways that enter the cave passage through a CO2-rich fracture network embedded in a vadose zone. The spatial distribution of inlets and outlets results in minimal mixing between the low and high pCO2 pathways, leading to high and persistent pCO2 gradients. In addition to the chimney effect driving the seasonal ventilation of the cave, the specific signs of a secondary wind-driven effect were also foundwhich is the second focus of this study. Wind flow over irregular topography leads to near-surface air pressure variations, and thus, pressure differences between cave entrances at different locations. Pressure differences depend on wind speed and direction and their relationship to surface topography and the location of cave entrances. Winds can act in the same or opposite direction as the chimney effect, either enhancing, diminishing or even reversing the direction of density-driven airflows. In the case of Postojna Cave, north and northeast winds enhance the downdraft and limit updraft, while the opposite is true for south winds, which enhance the updraft and limit downdraft. To investigate the importance of wind-driven flow, a computational fluid dynamics model was used to calculate the wind pressure field over Postojna Cave and the pressure differences between selected points for different configurations of wind speed and direction. These values were compared with those obtained from airflow measurements in the cave and from simple theoretical considerations. Despite the simplicity of the approach and the complexity of the caPoznavanje časovne in prostorske porazdelitve ogljikovega dioksida (CO2) v kraških sistemih je ključno za razumevanje raztapljanja in izločanja karbonatov v krasu. Ti procesi poganjajo razvoj krasa na površini in v podzemlju. Prav tako raziskave prenosa CO2 v kraških sistemih nudijo oceno pomena kraških procesov v globalnem kroženju ogljika in posledično njihovega globalnega klimatskega pomena. CO2 ima ključno vlogo pri rasti kapnikov, ki so eden najzanesljivejših kopenskih arhivov za paleoklimatske raziskave. Dolgoročna opazovanja in analize parametrov jamskega zraka in kemičnih parametrov vode v kraških jamah nam omogočajo določitev ključnih dejavnikov in mehanizmov, ki vplivajo na kraške procese. V okviru te disertacije smo v obdobju 2017–2021 vzpostavili monitoring jamskega zraka in geokemije vode v stranskih rovih Postojnske jame v Sloveniji. V Pisanem rovu so bile v prejšnjih študijah že odkrite visoke koncentracije CO2, velika časovna in prostorska spremenljivost CO2 ter sledi intenzivnega raztapljanja matične kamnine in sige. Namen te študije je raziskati in pojasniti ta opažanja z vidika temeljnih procesov v krasu in sestaviti širše veljaven konceptualni model prenosa CO2 v kraških sistemih. V prvem delu se osredotočamo na razumevanje prostorske in časovne spremenljivosti parcialnega tlaka CO2 (pCO2) v Pisanem rovu. Pri tem predpostavimo, da je glavni dejavnik prenosa CO2 naravno prezračevanje kraškega masiva. Analiza samodejnih meritev hitrosti zračnega toka, temperature zraka in pCO2 v visoki časovni ločljivosti je pokazala da: (1) pretok zraka skozi kraški masiv poganjata učinek dimnika (vzgon) in tlačne razlike, ki jih povzročajo zunanji vetrovi, (2) opaženo prostorsko in časovno porazdelitev CO2 lahko pojasnimo z razmerjem med smerjo podzemnega zračnega toka in konfiguracijo zračnih poti, ki povezujejo jamo z zunanjo atmosfero. Zaradi teh dejavnikov v končni dvorani Pisanega rova opazujemo izjemno časovno in prostorsko spremenljivost koncentracije CO2 v zraku. V zimskem režimu, ko zunanji zrak priteka v dvorano skozi glavni jamski vhod in velike dobro prezračene rove z nizkim pCO2, je pCO2 v dvorani stalno nizek. Ko zračni tok obrne smer, v dvorano s površja zrak doteka skozi mrežo razpok, z različnim pretokom in koncentracijo CO2. Prostorska porazdelitev dotokov in iztokov povzroča minimalno mešanje med potmi z nizkim in visokim pCO2, kar vodi do močnih in obstojnih gradientov pCO2. V drugem delu naloge obravnavamo dejavnike, ki vsiljujejo tok zraka v kraškem masivu. Meritve so pokazale, da v primeru Postojnske jame poleg učinka dimnika, pretok zraka vsiljuje tudi zunanji veter. Tok vetra po nepravilnem reliefu povzroča spremembe zračnega tlaka blizu površine in posledično tlačne razlike med vhodi v jamo na različnih mestih. Te razlike so odvisne od zveze med hitrostjo in smerjo vetra ter oblikovanostjo površja in položaj jamskih vhodov. Vetrovi lahko vsiljujejo tok zraka v isti ali nasprotni smeri kot učinek dimnika, tako da povečajo, zmanjšajo, ali celo obrnejo smer zračnega toka, ki bi ga povzročal samo vzgon. V primeru Postojnske jame severni in severovzhodni veter spodbujata poletni režim in omejujeta zimski režim, južni veter pa krepi zimski režim in omejuje poletni režim naravnega prezračevanja zaradi učinka dimnika. V raziskavi smo z uporabo računske dinamike tekočin (CFD) izračunali tlačno polje vetra nad Postojnsko jamo in tlačne razlike med izbranimi točkami za različne konfiguracije hitrosti in smeri vetra. Te vrednosti smo primerjali z ocenami tlačnih razlik, ki smo jih dobili iz meritev pretoka zraka v jami in preprostih teoretičnih izhodišč. Kljub enostavnemu pristopu in kompleksnosti jamskega sistema, smo dobili zadovoljivo ujemanje. Raziskava prinaša prvo kvantitativno oceno relativnega prispevka površinskih vetrov k prezračevanju kraškega podzemlja. V tretjem delu obravnavamo tvorbo korozijskih kotlic, ki jih najdemo pod številnimi curki v končnem delu Pisanega rova. Raziskave temeljijo na st

Reduced density matrix and entanglement in interacting quantum field theory with Hamiltonian truncation.

Entanglement is the fundamental difference between classical and quantum systems and has become one of the guiding principles in the exploration of high- and low-energy physics. The calculation of entanglement entropies in interacting quantum field theories, however, remains challenging. Here, we present the first method for the explicit computation of reduced density matrices of interacting quantum field theories using truncated Hamiltonian methods. The method is based on constructing an isomorphism between the Hilbert space of the full system and the tensor product of Hilbert spaces of sub-intervals. This naturally enables the computation of the von Neumann and arbitrary R\'enyi entanglement entropies as well as mutual information, logarithmic negativity and other measures of entanglement. Our method is applicable to equilibrium states and non-equilibrium evolution in real time. It is model independent and can be applied to any Hamiltonian truncation method that uses a free basis expansion. We benchmark the method on the free Klein-Gordon theory finding excellent agreement with the analytic results. We further demonstrate its potential on the interacting sine-Gordon model, studying the scaling of von Neumann entropy in ground states and real time dynamics following quenches of the model

Effects of a multi-component exercise program and calcium–vitamin-D3-fortified milk on bone mineral density in older men : a randomised controlled trial

Summary We examined the independent and combined effects of a multi-component exercise program and calcium&ndash;vitamin-D3-fortified milk on bone mineral density (BMD) in older men. Exercise resulted in a 1.8% net gain in femoral neck BMD, but additional calcium&ndash;vitamin D3 did not enhance the response in this group of older well-nourished men.Introduction This 12-month randomised controlled trial assessed whether calcium&ndash;vitamin-D3-fortified milk could enhance the effects of a multi-component exercise program on BMD in older men.Methods Men (n&thinsp; =&thinsp;180) aged 50&ndash;79 years were randomised into: (1) exercise + fortified milk; (2) exercise; (3) fortified milk; or (4) controls. Exercise consisted of high intensity progressive resistance training with weight-bearing impact exercise. Men assigned to fortified milk consumed 400 mL/day of low fat milk providing an additional 1,000 mg/day calcium and 800 IU/day vitamin D3. Femoral neck (FN), total hip, lumbar spine and trochanter BMD and body composition (DXA), muscle strength 25-hydroxyvitamin D and parathyroid hormone (PTH) were assessed.Results There were no exercise-by-fortified milk interactions at any skeletal site. Exercise resulted in a 1.8% net gain in FN BMD relative to no-exercise (p&thinsp;&lt;&thinsp;0.001); lean mass (0.6 kg, p&thinsp;&lt;&thinsp;0.05) and muscle strength (20&ndash;52%, p&thinsp;&lt;&thinsp;0.001) also increased in response to exercise. For lumbar spine BMD, there was a net 1.4&ndash;1.5% increase in all treatment groups relative to controls (all p&thinsp;&lt;&thinsp;0.01). There were no main effects of fortified milk at any skeletal site.Conclusion A multi-component community-based exercise program was effective for increasing FN BMD in older men, but additional calcium&ndash;vitamin D3 did not enhance the osteogenic response.<br /

Out-of-horizon correlations following a quench in a relativistic quantum field theory

One of the manifestations of relativistic invariance in non-equilibrium quantum field theory is the "horizon effect" a.k.a. light-cone spreading of correlations: starting from an initially short-range correlated state, measurements of two observers at distant space-time points are expected to remain independent until their past light-cones overlap. Surprisingly, we find that in the presence of topological excitations correlations can develop outside of horizon and indeed even between infinitely distant points. We demonstrate this effect for a wide class of global quantum quenches to the sine-Gordon model. We point out that besides the maximum velocity bound implied by relativistic invariance, clustering of initial correlations is required to establish the "horizon effect". We show that quenches in the sine-Gordon model have an interesting property: despite the fact that the initial states have exponentially decaying correlations and cluster in terms of the bosonic fields, they violate the clustering condition for the soliton fields, which is argued to be related to the non-trivial field topology. The nonlinear dynamics governed by the solitons makes the clustering violation manifest also in correlations of the local bosonic fields after the quench.Comment: 19+14 pages, 8 figures, pdflatex, v2: presentation substantially improved, new details concerning the effect are added, v3: reformatted version, references added, results and essential conclusions unchanged, with title update

On the absolutely continuous spectrum of generalized indefinite strings II

We continue to investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two more model examples of generalized indefinite strings under rather wide perturbations. In particular, one of these results allows us to prove that the absolutely continuous spectrum of the isospectral problem associated with the two-component Camassa-Holm system in a certain dispersive regime is essentially supported on the set $(-\infty,-1/2]\cup [1/2,\infty)$.Comment: 27 page

Correlation Functions of the Quantum Sine-Gordon Model in and out of Equilibrium

Complete information on the equilibrium behaviour and dynamics of a quantum field theory (QFT) is provided by multipoint correlation functions. However, their theoretical calculation is a challenging problem, even for exactly solvable models. This has recently become an experimentally relevant problem, due to progress in cold-atom experiments simulating QFT models and directly measuring higher order correlations. Here we compute correlation functions of the quantum sine-Gordon model, a prototype integrable model of central interest from both theoretical and experimental points of view. Building upon the so-called Truncated Conformal Space Approach, we numerically construct higher order correlations in a system of finite size in various physical states of experimental relevance, both in and out of equilibrium. We measure deviations from Gaussianity due to the presence of interaction and analyse their dependence on temperature, explaining the experimentally observed crossover between Gaussian and non-Gaussian regimes. We find that correlations of excited states are markedly different from the thermal case, which can be explained by the integrability of the system. We also study dynamics after a quench, observing the effects of the interaction on the time evolution of correlation functions, their spatial dependence, and their non-Gaussianity as measured by the kurtosis.Comment: Animation of quench dynamics in ancillary material: https://arxiv.org/src/1802.08696/anc/animation.mp4 Version 2: Improved presentation; Version 3: Final version after the peer review proces

Calcium mediates dorsoventral patterning of mesoderm in Xenopus

AbstractCalcium signals participate in the differentiation of electrically excitable and nonexcitable cells; one example of this differentiation is the acquisition of mature neuronal phenotypes [1]. For example, transient elevations of the intracellular calcium concentration have been recorded in the ectoderm of early embryos, and this elevation has been proposed to participate in neural induction [2–5]. Here, we present molecular evidence indicating that voltage-sensitive calcium channels (VSCC) are involved in early developmental processes leading to the establishment of the dorsoventral (D-V) patterning of a vertebrate embryo. We report that α1S VSCC are expressed selectively in the dorsal marginal zone at the early gastrula stage. The expression of the VSCC correlates with elevated intracellular calcium levels, as evaluated by the fluorescence of the intracellular calcium indicator Fluo-3. Misexpression of VSCC leads to a strong dorsalization of the ventral marginal zone and induction of the secondary axis but no direct neuralization of the ectoderm. Moreover, specific inhibition of VSCC by the use of calcicludine results in ventralization of the dorsal mesoderm. Together, these results indicate that calcium channels regulate mesodermal patterning by specificating the D-V identity of the mesodermal cells. The D-V patterning of the mesoderm has been shown to depend on a gradient of BMPs activity. We discuss the possibility that VSCC affect or act downstream of BMPs activity