arXiv subjects
Publications and source records attributed to S. Denisov.
In the case when the weight and its inverse belong to BMO(T), we prove the asymptotics of the monic orthogonal polynomials in L^p, 2<p<p_0. Immediate applications include the estimates on the uniform norm and asymptotics for the polynomial entropy.
We study the recursion (aka Schur) parameters for monic polynomials orthogonal on the unit circle with respect to a weight which provides negative answer to the conjecture of Steklov.
On the twentieth anniversary of the observation of the top quark, we trace our understanding of this heaviest of all known particles from the prediction of its existence, through the searches and discovery, to the current knowledge of its production mechanisms and properties. We also discuss the central role of the top quark in the Standard Model and the windows that it opens for seeking new physics beyond the Standard Model.
We present a numerical approach to calculate non-equilibrium eigenstates of a periodically time-modulated quantum system. The approach is based on the use of a chain of single-step time-independent propagating operators. Each operator is time-specific and constructed by combining the Magnus expansion of the time-dependent system Hamiltonian with the Chebyshev expansion of an operator exponent. A construction of a unitary matrix of the Floquet operator, which evolves a system state over the full modulation period, is performed by propagating the identity matrix over the period. The independence of the evolutions of basis vectors makes the propagation stage suitable for implementation on a parallel cluster. Once the propagation stage is completed, a routine diagonalization of the Floquet matrix is performed. Finally, an additional propagation round, now with the eigenvectors as the initial states, allows to resolve the time-dependence of the Floquet states and calculate their characteristics. We demonstrate the accuracy and scalability of the algorithm by applying it to calculate the Floquet states of two quantum models, namely (i) a synthesized random-matrix Hamiltonian and (ii) a many-body Bose-Hubbard dimer, both of the size up to $10^4$ states.
We obtain the sharp estimates on the growth of the uniform norm of orthonormal polynomials for measures satisfying the Steklov condition. This improves the earlier results by Rakhmanov and completely settles a problem by Steklov. The sharp estimates for the polynomial entropy in the Steklov class are obtained as well.
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The Lévy walk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, bio-physics, and behavioral science demonstrate that this particular type of random walks provides significant insight into complex transport phenomena. This review provides a self-consistent introduction to Lévy walks, surveys their existing applications, including latest advances, and outlines further perspectives.
Strong anomalous diffusion, where $\langle |x(t)|^q \rangle \sim t^{q ν(q)}$ with a nonlinear spectrum $ν(q) \neq \mbox{const}$, is wide spread and has been found in various nonlinear dynamical systems and experiments on active transport in living cells. Using a stochastic approach we show how this phenomena is related to infinite covariant densities, i.e., the asymptotic states of these systems are described by non-normalizable distribution functions. Our work shows that the concept of infinite covariant densities plays an important role in the statistical description of open systems exhibiting multi-fractal anomalous diffusion, as it is complementary to the central limit theorem.
We obtain the sharp lower bound for the uniform norm of the orthogonal polynomials in the Steklov class. We also prove the sharp estimates for the polynomial entropy in this class.
The primary motivation of the GlueX experiment is to search for and ultimately study the pattern of gluonic excitations in the meson spectrum produced in $γp$ collisions. Recent lattice QCD calculations predict a rich spectrum of hybrid mesons that have both exotic and non-exotic $J^{PC}$, corresponding to $q\bar{q}$ states ($q=u,$ $d,$ or $s$) coupled with a gluonic field. A thorough study of the hybrid spectrum, including the identification of the isovector triplet, with charges 0 and $\pm1$, and both isoscalar members, $|s\bar{s}\ >$ and $|u\bar{u}\ > + |d\bar{d}\ >$, for each predicted hybrid combination of $J^{PC}$, may only be achieved by conducting a systematic amplitude analysis of many different hadronic final states. Detailed studies of the performance of the \gx detector have indicated that identification of particular final states with kaons is possible using the baseline detector configuration. The efficiency of kaon detection coupled with the relatively lower production cross section for particles containing hidden strangeness will require a high intensity run in order for analyses of such states to be feasible. We propose to collect a total of 200 days of physics analysis data at an average intensity of $5\times 10^7$ tagged photons on target per second. This data sample will provide an order of magnitude statistical improvement over the initial GlueX running, which will allow us to begin a program of studying mesons and baryons containing strange quarks. In addition, the increased intensity will permit us to study reactions that may have been statistically limited in the initial phases of GlueX. Overall, this will lead to a significant increase in the potential for \gx to make key experimental advances in our knowledge of hybrid mesons and excited $Ξ$ baryons.
Space-time correlation functions constitute a useful instrument from the research toolkit of continuous-media and many-body physics. We adopt here this concept for single-particle random walks and demonstrate that the corresponding space-time velocity auto-correlation functions reveal correlations which extend in time much longer than estimated with the commonly employed temporal correlation functions. A generic feature of considered random-walk processes is an effect of velocity echo identified by the existence of time-dependent regions where most of the walkers are moving in the direction opposite to their initial motion. We discuss the relevance of the space-time velocity correlation functions for the experimental studies of cold atom dynamics in an optical potential and charge transport on micro- and nano-scales.
We study the response of ultracold atoms to a weak force in the presence of a temporally strongly modulated optical lattice potential. It is experimentally demonstrated that the strong ac-driving allows for a tailoring of the mobility of a dilute atomic Bose-Einstein condensate with the atoms moving ballistically either along or against the direction of the applied force. Our results are in agreement with a theoretical analysis of the Floquet spectrum of a model system, thus revealing the existence of diabatic Floquet bands in the atom's band spectra and highlighting their role in the non-equilibrium transport of the atoms.
We present an approach to molecular-dynamics simulations of ferrofluids on graphics processing units (GPUs). Our numerical scheme is based on a GPU-oriented modification of the Barnes-Hut (BH) algorithm designed to increase the parallelism of computations. For an ensemble consisting of one million of ferromagnetic particles, the performance of the proposed algorithm on a Tesla M2050 GPU demonstrated a computational-time speed-up of four order of magnitude compared to the performance of the sequential All-Pairs (AP) algorithm on a single-core CPU, and two order of magnitude compared to the performance of the optimized AP algorithm on the GPU. The accuracy of the scheme is corroborated by comparing the results of numerical simulations with theoretical predictions.
The primary motivation of the GlueX experiment is to search for and ultimately study the pattern of gluonic excitations in the meson spectrum produced in gamma p collisions. Recent lattice QCD calculations predict a rich spectrum of hybrid mesons that have both exotic and non-exotic JPC, corresponding to q q-bar (q=u, d, or s) states coupled with a gluonic field. A thorough study of the hybrid spectrum, including the identification of the isovector triplet, with charges 0 and +-1, and both isoscalar members, |s s-bar> and |u u-bar> + |d d-bar>, for each predicted hybrid combination of JPC, may only be achieved by conducting a systematic amplitude analysis of many different hadronic final states. We propose the development of a kaon identification system, supplementing the existing GlueX forward time-of-flight detector, in order to cleanly select meson and baryon decay channels that include kaons. Once this detector has been installed and commissioned, we plan to collect a total of 200 days of physics analysis data at an average intensity of 5 x 10^7 tagged photons on target per second. This data sample will provide an order of magnitude statistical improvement over the initial GlueX data set and, with the developed kaon identification system, a significant increase in the potential for GlueX to make key experimental advances in our knowledge of hybrid mesons and Cascade baryons.
The problem of mutual equilibration between two finite, identical quantum systems, A and B, prepared initially at different temperatures is elucidated. We show that the process of energy exchange between the two systems leads to accurate equipartition within energy shells in the Hilbert space of the total non-interacting, composite system, A \otimes B. This scenario occurs under the general condition of a weak interaction between the systems. We predict that the sole hypothesis of such equipartition is sufficient to obtain a relaxation of the peers, A and B, towards a common thermal-like state. This conjecture is fully corroborated by an exact diagonalization of several quantum models.
The standard Levy walk is performed by a particle that moves ballistically between randomly occurring collisions, when the intercollision time is a random variable governed by a power-law distribution. During instantaneous collision events the particle randomly changes the direction of motion but maintains the same constant speed. We generalize the standard model to incorporate velocity fluctuations into the process. Two types of models are considered, namely, (i) with a walker changing the direction and absolute value of its velocity during collisions only, and (ii) with a walker whose velocity continuously fluctuates. We present full analytic evaluation of both models and emphasize the importance of initial conditions. We show that the type of the underlying Levy walk process can be identified by looking at the ballistic regions of the diffusion profiles. Our analytical results are corroborated by numerical simulations.
For the polynomials orthogonal on the unit circle with respect to the measure from the Szego class we prove that the polynomial entropy integrals can grow. The estimate obtained is sharp.
The Arnold diffusion constitutes a dynamical phenomenon which may occur in the phase space of a non-integrable Hamiltonian system whenever the number of the system degrees of freedom is $M \geq 3$. The diffusion is mediated by a web-like structure of resonance channels, which penetrates the phase space and allows the system to explore the whole energy shell. The Arnold diffusion is a slow process; consequently the mapping of the web presents a very time-consuming task. We demonstrate that the exploration of the Arnold web by use of a graphic processing unit (GPU)-supercomputer can result in distinct speedups of two orders of magnitude as compared to standard CPU-based simulations.
We analyze the performance of quantum ratchets by considering the dynamics of an initially localized wave packet loaded into a flashing periodic potential. The directed center-of-mass motion can be initiated by the uniform modulation of the potential height, provided that the modulation protocol breaks all relevant time- and spatial reflection symmetries. A poor performance of quantum ratchet transport is characterized by a slow net motion and a fast diffusive spreading of the wave packet, while the desirable optimal performance is the contrary. By invoking a quantum analog of the classical Péclet number, namely the quotient of the group velocity and the dispersion of the propagating wave packet, we calibrate the transport properties of flashing quantum ratchets and discuss the mechanisms that yield low-dispersive directed transport.