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Ruin under stochastic dependence between premium and claim arrivalsFeb 15 2016Jun 26 2017We investigate, focusing on the ruin probability, an adaptation of the Cramer-Lundberg model for the surplus process of an insurance company, in which, conditionally on their intensities, the two mixed Poisson processes governing the arrival times of ... More

First passage upwards for state dependent-killed spectrally negative Lévy processesMar 13 2018Apr 14 2018For a spectrally negative L\'evy process (snLp) $X$, killed according to a rate that is a function $\omega$ of its position, we analyse the exit probability of the one-sided upwards-passage problem. When $\omega$ is strictly positive, this problem is ... More

Proper two-sided exits of a Lévy processNov 24 2015It is proved that the two-sided exits of a Levy process are proper, i.e. not a.s. equal to their one-sided counterparts, if and only if said process is not a subordinator or the negative of a subordinator. Furthermore, Levy processes are characterized, ... More

Another characterization of homogeneous Poisson processesOct 23 2016Aug 13 2017For a general renewal process $N$ (allowing delay, defect and multiple simultaneous arrivals) the independence of the first renewal epochs of the marked processes got from $N$ by Bernoulli $0$/$1$ thinning is characterized. This independence is well-known ... More

On laws exhibiting universal ordering under stochastic restartApr 23 2019For each of (i) arbitrary stochastic reset, (ii) deterministic reset with arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense of either (a) first-order stochastic dominance or (b) expectation (i.e. for each of the six possible ... More

A temporal factorization at the maximum for spectrally negative positive self-similar Markov processesMay 10 2018May 15 2018For a spectrally negative positive self-similar Markov process with an a.s. finite overall supremum we provide, in tractable detail, a kind of conditional Wiener-Hopf factorization at the maximum of the absorption time at zero, the conditioning being ... More

Fluctuation theory for upwards skip-free Lévy chainsSep 20 2013May 18 2015A fluctuation theory and, in particular, a theory of scale functions is developed for upwards skip-free L\'evy chains, i.e. for right-continuous random walks embedded into continuous time as compound Poisson processes. This is done by analogy to the spectrally ... More

Excursions of a spectrally negative Lévy process from a two-point setSep 03 2018Let $a\in (0,\infty)$. For a spectrally negative L\'evy process $X$ with infinite variation paths the resolvent of the process killed on hitting the two-point set $V=\{-a,a\}$ is identified. When further $X$ has no diffusion component the Laplace transforms ... More

A note on the times of first passage for `nearly right-continuous' random walksOct 24 2013Aug 12 2014A natural extension of a right-continuous integer-valued random walk is one which can jump to the right by one or two units. First passage times above a given fixed level then admit a tractable Laplace transform (probability generating function). Explicit ... More

Non-random overshoots of Lévy processesJan 18 2013Sep 23 2013The class of Levy processes for which overshoots are almost surely constant quantities is precisely characterized.

Markov chain approximations to scale functions of Lévy processesOct 07 2013Apr 20 2015We introduce a general algorithm for the computation of the scale functions of a spectrally negative L\'evy process $X$, based on a natural weak approximation of $X$ via upwards skip-free continuous-time Markov chains with stationary independent increments. ... More

Markov chain approximations for transition densities of Lévy processesNov 02 2012Jun 26 2013We consider the convergence of a continuous-time Markov chain approximation X^h, h>0, to an R^d-valued Levy process X. The state space of X^h is an equidistant lattice and its Q-matrix is chosen to approximate the generator of X. In dimension one (d=1), ... More

The structure of non-linear martingale optimal transport problemsMar 15 2019We explore the structure of solutions to a family of non-linear martingale optimal transport (MOT) problems that involve conditional expectations in the objective functional. En route general results concerning optimization over (martingale) measures ... More

Ruin under stochastic dependence between premium and claim arrivalsFeb 15 2016We investigate, focusing on the ruin probability, an adaptation of the Cramer-Lundberg model for the surplus process of an insurance company, in which, conditionally on their intensities, the two mixed Poisson processes governing the arrival times of ... More

Exit problems for positive self-similar Markov processes with one-sided jumpsJul 02 2018Mar 06 2019A systematic exposition of scale functions is given for positive self-similar Markov processes (pssMp) with one-sided jumps. The scale functions express as convolution series of the usual scale functions associated with spectrally one-sided L\'evy processes ... More

Observing a Lévy process up to a stopping timeDec 12 2018It is proved that the law of a possibly killed L\'evy process $X$, seen up to and including (resp. up to strictly before) a stopping time, determines already the law of $X$ (resp. up to a compound Poisson component and killing).

On the existence of a minimal generating set for $σ$-algebrasJun 03 2014May 16 2018Does there exist for any $\sigma$-algebra a minimal (with respect to inclusion) generating set? We formulate this problem and answer it in the very special instance of partition generated and standard measurable spaces, the general case remaining open. ... More

On the existence of a minimal generating set for $σ$-algebrasJun 03 2014Does there exist for any $\sigma$-algebra a minimal (with respect to inclusion) generating set? We formulate this problem and answer it in the very special instance of partition generated and standard measurable spaces, the general case remaining open. ... More

Exit problems for positive self-similar Markov processes with one-sided jumpsJul 02 2018A systematic exposition of scale functions is given for positive self-similar Markov processes (pssMp) with one-sided jumps. The scale functions express as convolution series of the usual scale functions associated with spectrally one-sided L\'evy processes ... More

Arithmetic of (independent) sigma-fields on probability spacesSep 14 2018This note gathers what is known about, and provides some new results concerning the operations of intersection, of "generated $\sigma$-field", and of "complementation" for (independent) complete $\sigma$-fields on probability spaces.

Independence times for iid sequences, random walks and Lévy processesApr 20 2017Sep 28 2018For a sequence in discrete time having stationary independent values (respectively, random walk) $X$, those random times $R$ of $X$ are characterized set-theoretically, for which the strict post-$R$ sequence (respectively, the process of the increments ... More

Double hypergeometric Lévy processes and self-similarityApr 12 2019Motivated by a recent paper of Budd, where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of L\'evy processes, called the double hypergeometric class, whose Wiener-Hopf factorisation ... More

Another characterization of homogeneous Poisson processesOct 23 2016For a general renewal process $N$ (with delay and defect) the independence of the first renewal epochs of the marked processes got from $N$ by Bernoulli $0$/$1$ thinning is characterized. By way of corollary we obtain a related characterization of homogeneous ... More

A couple of remarks on the convergence of $σ$-fields on probability spacesJun 09 2016The following modes of convergence of sub-$\sigma$-fields on a given probability space have been studied in the literature: weak convergence, strong convergence, convergence with respect to the Hausdorff metric, almost-sure convergence, set-theoretic ... More

A couple of remarks on the convergence of $σ$-fields on probability spacesJun 09 2016Jun 26 2017The following modes of convergence of sub-$\sigma$-fields on a given probability space have been studied in the literature: weak convergence, strong convergence, convergence with respect to the Hausdorff metric, almost-sure convergence, set-theoretic ... More

Copulas for maxmin systemsDec 30 2015Under a mild condition we give closed-form expressions for copulas of systems that consist of maxima and of minima of subvectors of a given random vector $X$ with continuous marginals. Said expressions appear explicit in the copula of $X$ and the mentioned ... More

On the informational structure in optimal dynamic stochastic controlMar 09 2015Sep 20 2016We formulate a very general framework for optimal dynamic stochastic control problems which allows for a control-dependent informational structure. The issue of informational consistency is investigated. Bellman's principle is formulated and proved. In ... More

On the informational structure in optimal dynamic stochastic controlMar 09 2015May 15 2018We formulate a very general framework for optimal dynamic stochastic control problems which allows for a control-dependent informational structure. The issue of informational consistency is investigated. Bellman's principle is formulated and proved. In ... More

First passage problems for upwards skip-free random walks via the $Φ,W,Z$ paradigmAug 21 2017Apr 14 2018We develop the theory of the $W$ and $Z$ scale functions for right-continuous (upwards skip-free) discrete-time discrete-space random walks, along the lines of the analogue theory for spectrally negative L\'evy processes. Notably, we introduce for the ... More

Coupled channel analysis of the rho meson decay in lattice QCDMay 27 2011Apr 18 2014We employ a variational basis with a number of $\bar{q}q$ and $\pi\pi$ lattice interpolating fields with quantum numbers of the $\rho$ resonance to extract the discrete energy spectrum in a finite volume. In the elastic region, this spectrum is related ... More

Inferring Algebraic EffectsDec 09 2013Sep 11 2014We present a complete polymorphic effect inference algorithm for an ML-style language with handlers of not only exceptions, but of any other algebraic effect such as input & output, mutable references and many others. Our main aim is to offer the programmer ... More

Two holes in the t-J model form a bound state for any nonzero J/tNov 21 2013Determination of the parameter regime in which two holes in the t-J model form a bound state represents a long standing open problem in the field of strongly correlated systems. By applying and systematically improving the exact diagonalization method ... More

Homology of dendroidal setsSep 02 2015We define for every dendroidal set X a chain complex and show that this assignment determines a left Quillen functor. Then we define the homology groups $H_n(X)$ as the homology groups of this chain complex. This generalizes the homology of simplicial ... More

Student's opinions about System for automatic assessment of programming tasks Projekt TomoFeb 17 2017In a previous paper a web service called Projekt Tomo intended to ease the process of learning programming for teachers and students has been described. Since the service received a very warm welcome from teachers and students alike we decided to collect ... More

Entanglement Entropy of Eigenstates of Quantum Chaotic HamiltoniansAug 28 2017Nov 29 2017In quantum statistical mechanics, it is of fundamental interest to understand how close the bipartite entanglement entropy of eigenstates of quantum chaotic Hamiltonians is to maximal. For random pure states in the Hilbert space, the average entanglement ... More

Gain of the kinetic energy of bipolarons in the t-J-Holstein model based on electron-phonon couplingAug 19 2010With increasing electron-phonon coupling as described within the t-J-Holstein model, bipolaron kinetic energy is lowered in comparison with that of the polaron. This effect is accompanied with "undressing" of bipolaron from lattice degrees of freedom. ... More

Generalized Gibbs ensemble in integrable lattice modelsApr 13 2016Jun 28 2016The generalized Gibbs ensemble (GGE) was introduced ten years ago to describe observables in isolated integrable quantum systems after equilibration. Since then, the GGE has been demonstrated to be a powerful tool to predict the outcome of the relaxation ... More

More on Diophantine sextuplesSep 22 2016A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely ... More

An Effect System for Algebraic Effects and HandlersJun 26 2013Dec 09 2014We present an effect system for core Eff, a simplified variant of Eff, which is an ML-style programming language with first-class algebraic effects and handlers. We define an expressive effect system and prove safety of operational semantics with respect ... More

Programming with Algebraic Effects and HandlersMar 07 2012Eff is a programming language based on the algebraic approach to computational effects, in which effects are viewed as algebraic operations and effect handlers as homomorphisms from free algebras. Eff supports first-class effects and handlers through ... More

On a special case of Watkins' conjectureNov 17 2016Watkins' conjecture asserts that for a rational elliptic curve $E$ the degree of the modular parametrization is divisible by $2^r$, where $r$ is the rank of $E$. In this paper we prove that if the modular degree is odd then $E$ has rank $0$. Moreover, ... More

Dendroidal sets as models for connective spectraMar 30 2012May 19 2014Dendroidal sets have been introduced as a combinatorial model for homotopy coherent operads. We introduce the notion of fully Kan dendroidal sets and show that there is a model structure on the category of dendroidal sets with fibrant objects given by ... More

Diophantine m-tuples in finite fields and modular formsSep 29 2016For a prime p, a Diophantine m-tuple in $\mathbb{F}_p$ is a set of m nonzero elements of $\mathbb{F}_p$ with the property that the product of any two of its distinct elements is one less than a square. In this paper, we present formulas for the number ... More

SW# - GPU enabled exact alignments on genome scaleApr 22 2013Sequence alignment is one of the oldest and the most famous problems in bioinformatics. Even after 45 years, for one reason or another, this problem is still actual; current solutions are trade-offs between execution time, memory consumption and accuracy. ... More

No value restriction is needed for algebraic effects and handlersMay 23 2016We present a straightforward, sound Hindley-Milner polymorphic type system for algebraic effects and handlers in a call-by-value calculus, which allows type variable generalisation of arbitrary computations, not just values. This result is surprising. ... More

Supersingular zeros of divisor polynomials of elliptic curves of prime conductorNov 17 2016For a prime number $p$ we study the zeros modulo $p$ of divisor polynomials of rational elliptic curves $E$ of conductor $p$. Ono made the observation that these zeros of are often $j$-invariants of supersingular elliptic curves over $\overline{\mathbb{F}_p}$. ... More

Extinction Dynamics of Cardiac FibrillationAug 06 2018During episodes of atrial fibrillation, the heart's electrical activity becomes disorganized and shows fragmenting spiral waves. To systematically address how this pattern terminates using spatially extended simulations exceeds current computational resources. ... More

Handling Algebraic EffectsDec 05 2013Dec 16 2013Algebraic effects are computational effects that can be represented by an equational theory whose operations produce the effects at hand. The free model of this theory induces the expected computational monad for the corresponding effect. Algebraic effects ... More

Constraints on the Orbital Evolution of TritonMay 11 2005We present simulations of Triton's post-capture orbit that confirm the importance of Kozai-type oscillations in its orbital elements. In the context of the tidal orbital evolution model, these variations require average pericenter distances much higher ... More

Modular forms, de Rham cohomology and congruencesJan 24 2013Apr 22 2013In this paper we show that Atkin and Swinnerton-Dyer type of congruences hold for weakly modular forms (modular forms that are permitted to have poles at cusps). Unlike the case of original congruences for cusp forms, these congruences are nontrivial ... More

Dissociation of a Hubbard--Holstein bipolaron driven away from equilibrium by a constant electric fieldNov 29 2011Mar 27 2012Using a variational numerical method we compute the time-evolution of the Holstein-Hubbard bipolaron from its ground state when at t=0 the constant electric field is switched on. The system is evolved taking into account full quantum effects until it ... More

Impenetrable SU(N) fermions in one-dimensional latticesAug 03 2018Oct 26 2018We study SU(N) fermions in the limit of infinite on-site repulsion between all species. We focus on states in which every pair of consecutive fermions carries a different spin flavor. Since the particle order cannot be changed (because of the infinite ... More

On the Secular Behavior of Irregular SatellitesAug 05 2004Although analytical studies on the secular motion of the irregular satellites have been published recently, these theories have not yet been satisfactorily reconciled with the results of direct numerical integrations. These discrepancies occur because ... More

Quantum adiabatic protocols using emergent local HamiltoniansAug 10 2017Oct 28 2017We present two applications of emergent local Hamiltonians to speed up quantum adiabatic protocols for isolated noninteracting and weakly interacting fermionic systems in one-dimensional lattices. We demonstrate how to extract maximal work from initial ... More

Quantum dynamics of impenetrable SU(N) fermions in one-dimensional latticesMar 25 2019We study quantum quench dynamics in the Fermi-Hubbard model, and its SU(N) generalizations, in one-dimensional lattices in the limit of infinite onsite repulsion between all flavors. We consider families of initial states with generalized Neel order, ... More

Disentangling sources of influence in online social networksNov 26 2018Nov 27 2018Information propagation in online social networks is facilitated by two types of influence - endogenous (peer) influence that is dependent on the network structure and current state of each user and exogenous (external) which is independent of these. ... More

There are infinitely many rational Diophantine sextuples with square denominatorsMar 07 2019A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely ... More

Monochromatic paths in random tournamentsMar 30 2017Dec 09 2017We prove that, with high probability, any $2$-edge-colouring of a random tournament on $n$ vertices contains a monochromatic path of length $\Omega(n / \sqrt{\log n})$. This resolves a conjecture of Ben-Eliezer, Krivelevich and Sudakov and implies a nearly ... More

Directed Ramsey number for treesAug 15 2017Dec 10 2018In this paper, we study Ramsey-type problems for directed graphs. We first consider the $k$-colour oriented Ramsey number of $H$, denoted by $\overrightarrow{R}(H,k)$, which is the least $n$ for which every $k$-edge-coloured tournament on $n$ vertices ... More

Emergent eigenstate solution and emergent Gibbs ensemble for expansion dynamics in optical latticesApr 04 2017Jul 06 2017Within the emergent eigenstate solution to quantum dynamics [Phys. Rev. X 7, 021012 (2017)], one can construct a local operator (an emergent Hamiltonian) of which the time-evolving state is an eigenstate. Here we show that such a solution exists for the ... More

Emergence of states in the phonon spectral function of the Holstein polaron below and above the one-phonon continuumAug 19 2010We investigate the low-energy properties of the Holstein polaron through calculation of the q-dependent phonon spectral function using an improved exact-diagonalization technique, defined over a variational Hilbert space. We perform a comprehensive study ... More

Optical conductivity in the t-J-Holstein ModelDec 11 2008Using recently developed numerical method we compute charge stiffness and optical conductivity of the t-J model coupled to optical phonons. Coherent hole motion is most strongly influenced by the electron-phonon coupling within the physically relevant ... More

Nonequilibrium propagation and decay of a bound pair in driven t-J modelsJul 25 2012Oct 10 2012We perform an accurate time-dependent numerical study of out-of-equilibrium response of a bound state within t-J systems on a two-leg ladder and a square lattice. We show that the bound hole pair decays with the onset of finite steady current if both ... More

Emergent eigenstate solution to quantum dynamics far from equilibriumDec 16 2015Mar 09 2016Recent studies on the dynamics of interacting quantum many-body systems have shed light into this largely unexplored domain in physics. A unique possibility revealed by such studies is the dynamical realization of novel quantum states. Prominent examples ... More

Information measures for a local quantum phase transition: Lattice fermions in a one-dimensional harmonic trapDec 05 2017Apr 06 2018We use quantum information measures to study the local quantum phase transition that occurs for trapped spinless fermions in one-dimensional lattices. We focus on the case of a harmonic confinement. The transition occurs upon increasing the characteristic ... More

Dynamical Evidence for a Late Formation of Saturn's MoonsMar 23 2016We explore the past evolution of Saturn's moons using direct numerical integrations. We find that the past Tethys-Dione 3:2 orbital resonance predicted in standard models likely did not occur, implying that the system is less evolved than previously thought. ... More

Max-min measures on ultrametric spacesFeb 26 2013The ultrametrization of the set of all probability measures of compact support on the ultrametric spaces was first defined by Hartog and de Vink. In this paper we consider a similar construction for the so called max-min measures on the ultrametric spaces. ... More

Multiple perturbations of a singular eigenvalue problemFeb 22 2016We study the perturbation by a critical term and a $(p-1)$-superlinear subcritical nonlinearity of a quasilinear elliptic equation containing a singular potential. By means of variational arguments and a version of the concentration-compactness principle ... More

Rational Diophantine sextuples containing two regular quadruples and one regular quintupleMar 31 2019A set of $m$ distinct nonzero rationals $\{a_1,a_2,\ldots,a_m\}$ such that $a_ia_j+1$ is a perfect square for all $1\leq i<j\leq m$, is called a rational Diophantine $m$-tuple. It is proved recently that there are infinitely many rational Diophantine ... More

Rigidity of the Minimal Grope GroupAug 04 2006We give a systematic definition of the fundamental groups of gropes, which we call grope groups. We show that there exists a nontrivial homomorphism from the minimal grope group M to another grope group G only if G is the free product of M with another ... More

Simulating the Phases of the Moon Shortly After Its FormationMar 10 2015The leading theory for the origin of the Moon is the giant impact hypothesis, in which the Moon was formed out of the debris left over from the collision of a Mars-sized body with the Earth. Soon after its formation, the orbit of the Moon may have been ... More

Modular parametrizations of certain elliptic curvesDec 26 2012Kaneko and Sakai recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a particular differential equation involving modular forms and Ramanujan-Serre ... More

Hungaria Asteroid Family as the Source of Aubrite MeteoritesJun 03 2014The Hungaria asteroids are interior to the main asteroid belt, with semimajor axes between 1.8 and 2 AU, low eccentricities and inclinations of 16-35 degrees. Small asteroids in the Hungaria region are dominated by a collisional family associated with ... More

Titan-Hyperion Resonance and the Tidal Q of SaturnNov 26 2013Lainey et al. (2012), by re-analyzing long-baseline astrometry of Saturn's moons, have found that the moons' tidal evolution is much faster than previously thought, implying an order of magnitude stronger tidal dissipation within Saturn. This result is ... More

Three colour bipartite Ramsey number of cycles and pathsMar 09 2018The $k$-colour bipartite Ramsey number of a bipartite graph $H$ is the least integer $n$ for which every $k$-edge-coloured complete bipartite graph $K_{n,n}$ contains a monochromatic copy of $H$. The study of bipartite Ramsey numbers was initiated, over ... More

On the Dynamics and Origin of Haumea's MoonsAug 08 2013The dwarf planet Haumea has two large satellites, Namaka and Hi'iaka, which orbit at relatively large separations. Both moons have significant eccentricities and inclinations, in a pattern that is consistent with a past orbital resonance (Ragozzine and ... More

The Arf-Kervaire invariant of framed manifolds as an obstruction to embeddabilityApr 19 2008Aug 17 2010We define a quadratic form which gives an obstruction to embedding $N^{4k+2} \subset \R^{6k+4}$ of a smooth highly connected manifold into Euclidean space, with sufficiently many nondegenerate sections of the normal bundle. As the main corollary we prove ... More

The Complemented System Approach: A Novel Method for Calculating the X-ray Scattering from Computer SimulationsNov 09 2010In this paper, we review the main problem concerning the calculation of X-ray scattering of simulated model systems, namely their finite size. A novel method based on the Rayleigh-Debye-Gans approximation was derived, which allows sidestepping this issue ... More

Multicolour bipartite Ramsey number of pathsJan 17 2019The $k$-colour bipartite Ramsey number of a bipartite graph $H$ is the least integer $N$ for which every $k$-edge-coloured complete bipartite graph $K_{N,N}$ contains a monochromatic copy of $H$. The study of bipartite Ramsey numbers was initiated over ... More

Covering random graphs by monochromatic trees and Helly-type results for hypergraphsFeb 13 2019Feb 19 2019How many monochromatic paths, cycles or general trees does one need to cover all vertices of a given $r$-edge-coloured graph $G$? These problems were introduced in the 1960's and were intensively studied by various researchers over the last 50 years. ... More

Covering random graphs by monochromatic trees and Helly-type results for hypergraphsFeb 13 2019How many monochromatic paths, cycles or general trees does one need to cover all vertices of a given $r$-edge-coloured graph $G$? These problems were introduced in the 1960's and were intensively studied by various researchers over the last 50 years. ... More

On structure sets of manifold pairsAug 10 2009In this paper we systematically describe relations between various structure sets which arise naturally for pairs of compact topological manifolds with boundary. Our consideration is based on a deep analogy between the case of a compact manifold with ... More

A short proof of the Twelve points theoremAug 08 2008We present a short elementary proof of the following Twelve Points Theorem: Let M be a convex polygon with vertices at the lattice points, containing a single lattice point in its interior. Denote by m (resp. m*) the number of lattice points in the boundary ... More

Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic modelsDec 20 2018Feb 13 2019We recently showed [Phys. Rev. Lett. 121, 220602 (2018)] that the average bipartite entanglement entropy of all energy eigenstates of the quantum Ising chain exhibits a universal (for translationally invariant quadratic fermionic models) leading term ... More

Bipolaron in the t-J model coupled to longitudinal and transverse quantum lattice vibrationsAug 21 2009Oct 27 2009We explore the influence of two different polarizations of quantum oxygen vibrations on the spacial symmetry of the bound magnetic bipolaron in the context of the t-J model by using exact diagonalization within a limited functional space. Quadratic electron ... More

Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limitMay 21 2014Sep 10 2014Motivated by recent experiments, we study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and ... More

Decay of rho and a1 mesons on the lattice using distillationNov 02 2011We extract the P-wave pi-pi phase shift for five values of pion relative momenta, which gives information on the rho resonance. The Breit-Wigner formula describes the pi-pi phase shift dependence nicely and we extract m(rho)=792(7)(8) MeV and the coupling ... More

Entanglement Entropy of Eigenstates of Quadratic Fermionic HamiltoniansMar 08 2017Jul 12 2017In a seminal paper [D. N. Page, Phys. Rev. Lett. 71, 1291 (1993)], Page proved that the average entanglement entropy of subsystems of random pure states is $S_{\rm ave}\simeq\ln{\cal D}_{\rm A} - (1/2) {\cal D}_{\rm A}^2/{\cal D}$ for $1\ll{\cal D}_{\rm ... More

There are infinitely many rational Diophantine sextuplesJul 02 2015Nov 30 2015A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely ... More

Unexpected composition dependence of the first sharp diffraction peak in an alcohol-aldehyde liquid mixture: n-pentanol and pentanalNov 26 2018The total scattering structure factors of pure liquid n-pentanol, pentanal, and 5 of their mixtures, as determined by high energy synchrotron X-ray diffraction experiments, are presented. For the interpretation of measured data, molecular dynamics computer ... More

Halfway to Rota's basis conjectureOct 17 2018In 1989, Rota made the following conjecture. Given $n$ bases $B_{1},\dots,B_{n}$ in an $n$-dimensional vector space $V$, one can always find $n$ disjoint bases of $V$, each containing exactly one element from each $B_{i}$ (we call such bases transversal ... More

Relaxation dynamics of the Holstein polaronSep 12 2012Keeping the full quantum nature of the problem we compute the relaxation time of the Holstein polaron after it was driven far from the equilibrium by a strong oscillatory pulse. Just after the pulse the polaron's kinetic energy increases and subsequently ... More

Nonequilibrium quantum dynamics of a charge carrier doped into a Mott insulatorMar 10 2011May 09 2011We study real-time dynamics of a charge carrier introduced into undoped Mott insulator propagating under a constant electric field F on the t-J ladder and square lattice. We calculate quasistationary current. In both systems adiabatic regime is observed ... More

Eigenstate thermalization and quantum chaos in the Holstein-polaron modelFeb 08 2019The eigenstate thermalization hypothesis (ETH) is a successful theory that provides sufficient criteria for ergodicity in quantum many-body systems. Most studies were carried out for Hamiltonians relevant for ultracold quantum gases and single-component ... More

Quantum Dynamics of a Driven Correlated System Coupled to PhononsJul 06 2011Dec 08 2011Nonequilibrium interplay between charge, spin and lattice degrees of freedom on a square lattice is studied for a single charge carrier doped in the t-J-Holstein model. In the presence of an uniform electric field we calculate the qusistationary state. ... More

Volume Law and Quantum Criticality in the Entanglement Entropy of Excited Eigenstates of the Quantum Ising ModelAug 27 2018Dec 03 2018Much has been learned about universal properties of entanglement entropies in ground states of quantum many-body lattice systems. Here we unveil universal properties of the average bipartite entanglement entropy of eigenstates of the paradigmatic quantum ... More

Few Islands Approximation of Hamiltonian System with divided Phase SpaceFeb 27 2018Apr 10 2019It is well known that typical Hamiltonian systems have divided phase space consisting of regions with regular dynamics on KAM tori and region(s) with chaotic dynamics called chaotic sea(s). This complex structure makes rigorous analysis of such systems ... More

Mechanism of Ultrafast Relaxation of a Photo-Carrier in Antiferromagnetic Spin BackgroundNov 21 2013May 28 2014We study the relaxation mechanism of a highly excited carrier propagating in the antiferromagnetic background modeled by the $t$-$J$ Hamiltonian on a square lattice. We show that the relaxation consists of two distinct stages. The initial ultrafast stage ... More

Unveiling hidden structure of many-body wavefunctions of integrable systems via sudden expansion experimentsSep 02 2015Feb 22 2016In the theory of Bethe-ansatz integrable quantum systems, rapidities play an important role as they are used to specify many-body states, apart from phases. The physical interpretation of rapidities going back to Sutherland is that they are the asymptotic ... More

On the Expressive Power of User-Defined Effects: Effect Handlers, Monadic Reflection, Delimited ControlOct 28 2016We compare the expressive power of three programming abstractions for user-defined computational effects: Bauer and Pretnar's effect handlers, Filinski's monadic reflection, and delimited control. This comparison allows a precise discussion about the ... More