Buchowiecki, Marcin
2010-01-01
A general method for the direct evaluation of the temperature dependence of the quantum-mechanical reaction rate constant in many-dimensional systems is described. The method is based on the quantum instanton approximation for the rate constant, thermodynamic integration with respect to the inverse temperature, and the path integral Monte Carlo evaluation. It can describe deviations from the Arrhenius law due to the coupling of rotations and vibrations, zero-point energy, tunneling, corner-cutting, and other nuclear quantum effects. The method is tested on the Eckart barrier and the full-dimensional H + H_2 -> H_2 + H reaction. In the temperature range from 300K to 1500K, the error of the present method remains within 13% despite the very large deviations from the Arrhenius law. The direct approach makes the calculations much more efficient, and the efficiency is increased even further (by up to two orders of magnitude in the studied reactions) by using optimal estimators for reactant and transition state the...
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Nonperturbative contributions in quantum-mechanical models the instantonic approach
Casahorrán, J
2000-01-01
We review the euclidean path-integral formalism in connection with the one-dimensional non-relativistic particle. The configurations which allow to construct a semiclassical approximation classify themselves into either topological (instantons) and non-topological (bounces) solutions. While the instantons dominate the tunneling phenomena between classical vacua, the bounces describe the decay from a false vacuum to the true one. The quantum amplitudes consist on an exponential associated with the classical contribution multiplied by the fluctuation factor which is given by a functional determinant. The eigenfunctions as well as the energy eigenvalues of the quadratic operators at issue can be written in closed form due to the shape-invariance property. Accordingly we resort to the zeta-function method to compute the functional determinants in a systematic way. The effect of the multi-instantons configurations is also carefully considered. To illustrate the instanton calculus in a relevant model we go to the d...
Quantum Tunneling Rates of Gas-Phase Reactions from On-the-Fly Instanton Calculations.
Beyer, Adrian N; Richardson, Jeremy O; Knowles, Peter J; Rommel, Judith; Althorpe, Stuart C
2016-11-03
The instanton method obtains approximate tunneling rates from the minimum-action path (known as the instanton) linking reactants to the products at a given temperature. An efficient way to find the instanton is to search for saddle-points on the ring-polymer potential surface, which is obtained by expressing the quantum Boltzmann operator as a discrete path-integral. Here we report a practical implementation of this ring-polymer form of instanton theory into the Molpro electronic-structure package, which allows the rates to be computed on-the-fly, without the need for a fitted analytic potential-energy surface. As a test case, we compute tunneling rates for the benchmark H + CH4 reaction, showing how the efficiency of the instanton method allows the user systematically to converge the tunneling rate with respect to the level of electronic-structure theory.
Effects of quantum instantons on the thermodynamics of the CPN-1 model
Andersen, Jens O.; Boer, Daniel; Warringa, Harmen J.
2006-01-01
Using the 1/N expansion, we study the influence of quantum instantons on the thermodynamics of the CPN-1 model in 1+1 dimensions. We do this by calculating the pressure to next-to-leading order in 1/N, without quantum instanton contributions. The fact that the CP1 model is equivalent to the O(3) non
Geodesic family of spherical instantons and cosmic quantum creation
Lapiedra, Ramon
2015-01-01
The Einstein field equations for any spherically symmetric metric and a geodesic perfect fluid source are cast in a canonical simple form, both for Lorentzian metrics and for instantons. Both kinds of metrics are explicitly written for the Lema{\\^{\\i}}tre-Tolman-Bondi family and for a general $\\Lambda$-Friedmann-Lema{\\^{\\i}}tre-Robertson-Walker universe. In the latter case (including of course the instanton version) we study whether the probability of quantum creation of our Universe vanishes or not. It is found, in accordance with previous results, that only the closed model can have a nonzero probability for quantum creation. To obtain this result, we resort to general assumptions, which are satisfied in the particular creation case considered by Vilenkin. On the other hand, Fomin and Tryon suggested that the energy of a quantically creatable universe should vanish. This is in accordance with the above result in which only the closed $\\Lambda$FLRW model is quantically creatable while the open and flat model...
Instantons in Quantum Annealing: Thermally Assisted Tunneling Vs Quantum Monte Carlo Simulations
Jiang, Zhang; Smelyanskiy, Vadim N.; Boixo, Sergio; Isakov, Sergei V.; Neven, Hartmut; Mazzola, Guglielmo; Troyer, Matthias
2015-01-01
Recent numerical result (arXiv:1512.02206) from Google suggested that the D-Wave quantum annealer may have an asymptotic speed-up than simulated annealing, however, the asymptotic advantage disappears when it is compared to quantum Monte Carlo (a classical algorithm despite its name). We show analytically that the asymptotic scaling of quantum tunneling is exactly the same as the escape rate in quantum Monte Carlo for a class of problems. Thus, the Google result might be explained in our framework. We also found that the transition state in quantum Monte Carlo corresponds to the instanton solution in quantum tunneling problems, which is observed in numerical simulations.
Quantum-instanton evaluation of the isotopic effects on the rate constants
Vanicek, Jiri; Miller, William H.
2004-03-01
We present a general quantum-mechanical method suitable for numerical evaluation of the isotopic effects on the rate constants of chemical reactions. Our method is based on the quantum instanton approximation [1-3] and on the path-integral Metropolis Monte-Carlo evaluation of the Boltzmann operator matrix elements. The method is more accurate than existing transition-state theory or semiclassical instanton method since we do not assume a single reaction path and do not use a semiclassical approximation of the Boltzmann operator. In order to calculate the isotopic effect we use a "charging algoritm," whereby the mass of the isotope is continuously changed from the initial to the final value. Direct calculation of the isotopic ratio turns out to be much more efficient than finding the absolute rate constants first and then calculating their ratio. While the Monte-Carlo implementation should make the method accessible to systems with a larger number of atoms, we present numerical results for the Eckart barrier and for the reactions H + H2 arrow H2 + H and H + DH arrow HD + H. [1] W.H. Miller, Y. Zhao, M. Ceotto, and Sandy Yang, J. Chem. Phys. 119, 1329 (2003). [2] T. Yamamoto and W.H. Miller, J. Chem. Phys. (in press). [3] Y. Zhao, T. Yamamoto, and W.H. Miller, J. Chem. Phys. (in press).
Musso, Daniele
2012-01-01
The non-perturbative dynamics of quantum field theories is studied using theoretical tools inspired by string formalism. Two main lines are developed: the analysis of stringy instantons in a class of four-dimensional N=2 gauge theories and the holographic study of the minimal model for a strongly coupled unbalanced superconductor. The field theory instanton calculus admits a natural and efficient description in terms of D-brane models. In addition, the string viewpoint offers the possibility of generalizing the ordinary instanton configurations. Even though such generalized, or stringy, instantons would be absent in a purely field-theoretical, low-energy treatment, we demonstrate that they do alter the IR effective description of the brane dynamics by introducing contributions related to the string scale. In the first part of this thesis we compute explicitly the stringy instanton corrections to the effective prepotential in a class of quiver gauge theories. In the second part of the thesis, we present a deta...
Zhang, Yanchuan; Stecher, Thomas; Cvitaš, Marko T; Althorpe, Stuart C
2014-11-20
Quantum transition-state theory (QTST) and free-energy instanton theory (FEIT) are two closely related methods for estimating the quantum rate coefficient from the free-energy at the reaction barrier. In calculations on one-dimensional models, FEIT typically gives closer agreement than QTST with the exact quantum results at all temperatures below the crossover to deep tunneling, suggesting that FEIT is a better approximation than QTST in this regime. Here we show that this simple trend does not hold for systems of greater dimensionality. We report tests on several collinear and three-dimensional reactions, in which QTST outperforms FEIT over a range of temperatures below crossover, which can extend down to half the crossover temperature (below which FEIT outperforms QTST). This suggests that QTST-based methods such as ring-polymer molecular dynamics (RPMD) may often give closer agreement with the exact quantum results than FEIT.
Klabucar, D; Mekterovic, D; Podobnik, B
2003-01-01
If instantons are introduced into the MIT bag model in such a way that bag radii are allowed to vary, the MIT bag interior can accommodate instanton density which is by an order of magnitude larger than in the case when the radii are fixed (although it is still significantly smaller than in the nonperturbative QCD vacuum). The instanton contribution to baryon mass shifts is also correspondingly larger. The instanton-induced part of the scalar strangeness of the nucleon MIT bag is an order of magnitude larger than found previously, within the linearized approximation. The decrease of the model radii (which is associated with the increase of the instanton density) is very favorable from the standpoint of nuclear physics.
Instantons and large N an introduction to non-perturbative methods in quantum field theory
Marino, Marcos
2015-01-01
This highly pedagogical textbook for graduate students in particle, theoretical and mathematical physics, explores advanced topics of quantum field theory. Clearly divided into two parts; the first focuses on instantons with a detailed exposition of instantons in quantum mechanics, supersymmetric quantum mechanics, the large order behavior of perturbation theory, and Yang-Mills theories, before moving on to examine the large N expansion in quantum field theory. The organised presentation style, in addition to detailed mathematical derivations, worked examples and applications throughout, enables students to gain practical experience with the tools necessary to start research. The author includes recent developments on the large order behaviour of perturbation theory and on large N instantons, and updates existing treatments of classic topics, to ensure that this is a practical and contemporary guide for students developing their understanding of the intricacies of quantum field theory.
The Kodama state for topological quantum field theory beyond instantons
Cartas-Fuentevilla, R
2005-01-01
Constructing a symplectic structure that preserves the ordinary symmetries and the topological invariance for topological Yang-Mills theory, it is shown that the Kodama (Chern-Simons) state traditionally associated with a topological phase of unbroken diffeomorphism invariance for instantons, exists actually for the complete topological sector of the theory. The case of gravity is briefly discussed.
Marochnik, Leonid; Vereshkov, Grigory
2008-01-01
We show that cosmological acceleration, Dark Energy (DE) effect is a consequence of the zero rest mass, conformal non-invariance of gravitons, and 1-loop finiteness of quantum gravity (QG). The effect is due to graviton-ghost condensates arising from the interference of quantum coherent states. The theory is constructed as follows: De Witt-Faddeev-Popov gauged path integral -> factorization of classical and quantum variables -> transition to the 1-loop approximation -> choice of ghost sector, satisfying 1-loop finiteness of the theory off the mass shell. The Bogolyubov-Born-Green-Kirckwood-Yvon (BBGKY) chain for the spectral function of gravitons renormalized by ghosts is used to build a theory of gravitons in the isotropic Universe. We found three exact solutions of the equations that describe virtual graviton and ghost condensates as well as condensates of instanton fluctuations. Exact solutions correspond to various condensates with different graviton-ghost compositions. The formalism of the BBGKY chain ta...
Vanícek, Jirí; Miller, William H
2007-09-21
The quantum instanton approximation is used to compute kinetic isotope effects for intramolecular hydrogen transfer in cis-1,3-pentadiene. Due to the importance of skeleton motions, this system with 13 atoms is a simple prototype for hydrogen transfer in enzymatic reactions. The calculation is carried out using thermodynamic integration with respect to the mass of the isotopes and a path integral Monte Carlo evaluation of relevant thermodynamic quantities. Efficient "virial" estimators are derived for the logarithmic derivatives of the partition function and the delta-delta correlation functions. These estimators require significantly fewer Monte Carlo samples since their statistical error does not increase with the number of discrete time slices in the path integral. The calculation treats all 39 degrees of freedom quantum mechanically and uses an empirical valence bond potential based on a molecular mechanics force field.
Instanton geometry and quantum A{sub {infinity}} structure on the elliptic curve
Energy Technology Data Exchange (ETDEWEB)
Herbst, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Lerche, W. [European Lab. for Particle Physics (CERN), Geneva (Switzerland); Nemeschansky, D. [University of Southern California, Los Angeles, CA (United States). Dept. of Physics
2006-03-15
We first determine and then study the complete set of non-vanishing A-model correlation functions associated with the 'long-diagonal branes' on the elliptic curve. We verify that they satisfy the relevant A{sub {infinity}} consistency relations at both classical and quantum levels. In particular we find that the A{sub {infinity}} relation for the annulus provides a reconstruction of annulus instantons out of disk instantons. We note in passing that the naive application of the Cardy-constraint does not hold for our correlators, confirming expectations. Moreover, we analyze various analytical properties of the correlators, including instanton flops and the mixing of correlators with different numbers of legs under monodromy. The classical and quantum A{sub {infinity}} relations turn out to be compatible with such homotopy transformations. They lead to a non-invariance of the effective action under modular transformations, unless compensated by suitable contact terms which amount to redefinitions of the tachyon fields. (orig.)
Uniform approximation by (quantum) polynomials
Drucker, A.; de Wolf, R.
2011-01-01
We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous functions by polynomials. We provide two proofs, based respectivel
On quantum and approximate privacy
Klauck, H
2001-01-01
This paper studies privacy in communication complexity. The focus is on quantum versions of the model and on protocols with only approximate privacy against honest players. We show that the privacy loss (the minimum divulged information) in computing a function can be decreased exponentially by using quantum protocols, while the class of privately computable functions (i.e., those with privacy loss 0) is not increased by quantum protocols. Quantum communication combined with small information leakage on the other hand makes certain functions computable (almost) privately which are not computable using quantum communication without leakage or using classical communication with leakage. We also give an example of an exponential reduction of the communication complexity of a function by allowing a privacy loss of o(1) instead of privacy loss 0.
Vandoren, Stefan
2008-01-01
This is a self-contained set of lecture notes on instantons in (super) Yang-Mills theory in four dimensions and in quantum mechanics. First the basics are derived from scratch: the regular and singular one-instanton solutions for Yang-Mills theories with gauge groups SU(2) and SU(N), their bosonic and fermionic zero modes, the path integral instanton measure, and supersymmetric Yang-Mills theories in Euclidean space. Then we discuss applications: the \\theta-angle of QCD, the solution of the U(1) problem, the way Higgs fields solve the large-instanton problem, and tunneling and phase transitions in quantum mechanics and in nonabelian gauge theories. These lecture notes are an extension of a review on Yang-Mills and D-instantons written in 2000 by both authors and A.Belitsky
Classical solutions in quantum field theory solitons and instantons in high energy physics
Weinberg, Erick J
2012-01-01
Classical solutions play an important role in quantum field theory, high energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on ...
Energy Technology Data Exchange (ETDEWEB)
Vanicek, Jiri; Miller, William H.
2007-06-13
The quantum instanton approximation is used to compute kinetic isotope effects for intramolecular hydrogen transfer in cis-1,3-pentadiene. Due to the importance of skeleton motions, this system with 13 atoms is a simple prototype for hydrogen transfer in enzymatic reactions. The calculation is carried out using thermodynamic integration with respect to the mass of the isotopes and a path integral Monte Carlo evaluation of relevant thermodynamic quantities. Efficient 'virial' estimators are derived for the logarithmic derivatives of the partition function and the delta-delta correlation functions. These estimators require significantly fewer Monte Carlo samples since their statistical error does not increase with the number of discrete time slices in the path integral. The calculation treats all 39 degrees of freedom quantum-mechanically and uses an empirical valence bond potential based on a modified general AMBER force field.
Approximate Quantum Adders with Genetic Algorithms: An IBM Quantum Experience
Directory of Open Access Journals (Sweden)
Li Rui
2017-07-01
Full Text Available It has been proven that quantum adders are forbidden by the laws of quantum mechanics. We analyze theoretical proposals for the implementation of approximate quantum adders and optimize them by means of genetic algorithms, improving previous protocols in terms of efficiency and fidelity. Furthermore, we experimentally realize a suitable approximate quantum adder with the cloud quantum computing facilities provided by IBM Quantum Experience. The development of approximate quantum adders enhances the toolbox of quantum information protocols, paving the way for novel applications in quantum technologies.
Approximate Quantum Adders with Genetic Algorithms: An IBM Quantum Experience
Li, Rui; Alvarez-Rodriguez, Unai; Lamata, Lucas; Solano, Enrique
2017-07-01
It has been proven that quantum adders are forbidden by the laws of quantum mechanics. We analyze theoretical proposals for the implementation of approximate quantum adders and optimize them by means of genetic algorithms, improving previous protocols in terms of efficiency and fidelity. Furthermore, we experimentally realize a suitable approximate quantum adder with the cloud quantum computing facilities provided by IBM Quantum Experience. The development of approximate quantum adders enhances the toolbox of quantum information protocols, paving the way for novel applications in quantum technologies.
Menzeleev, Artur R; Ananth, Nandini; Miller, Thomas F
2011-08-21
The use of ring polymer molecular dynamics (RPMD) for the direct simulation of electron transfer (ET) reaction dynamics is analyzed in the context of Marcus theory, semiclassical instanton theory, and exact quantum dynamics approaches. For both fully atomistic and system-bath representations of condensed-phase ET, we demonstrate that RPMD accurately predicts both ET reaction rates and mechanisms throughout the normal and activationless regimes of the thermodynamic driving force. Analysis of the ensemble of reactive RPMD trajectories reveals the solvent reorganization mechanism for ET that is anticipated in the Marcus rate theory, and the accuracy of the RPMD rate calculation is understood in terms of its exact description of statistical fluctuations and its formal connection to semiclassical instanton theory for deep-tunneling processes. In the inverted regime of the thermodynamic driving force, neither RPMD nor a related formulation of semiclassical instanton theory capture the characteristic turnover in the reaction rate; comparison with exact quantum dynamics simulations reveals that these methods provide inadequate quantization of the real-time electronic-state dynamics in the inverted regime.
Twisted $\\mathbb{C}P^{N-1}$ instanton projectors and the $N$-level quantum density matrix
Shermer, Scott
2014-01-01
Twisted classical solutions to the $\\mathbb{C}P^{N-1}$ model play a key role in the analysis of such models on the spatially compactified cylinder $\\mathbb{S}_L^1 \\times {\\mathbb{R}^1}$ and have recently been shown to be important for the resurgent structure of this quantum field theory. Instantons and non-self-dual solutions both fractionalize, and domain walls formed by such topological solutions can be associated with $N$-vacua having maximally repulsive energy eigenvalues. The purpose of this paper is to reinforce this view through the investigation of a number of parallels between the $\\mathbb{C}P^{N-1}$ model and $N$-level quantum mechanical density matrices. Specifically, we demonstrate the existence of a time-evolution equation for the $\\mathbb{C}P^{N-1}$ instanton projector analogous to the Liouville-von Neumann equation in the quantum mechanical formalism. The group theoretical analysis of density matrices and the $\\mathbb{C}P^{N-1}$ model are also closely related. Finally, we explore the emergence ...
QCD-instantons and conformal inversion symmetry
Energy Technology Data Exchange (ETDEWEB)
Klammer, D.
2006-07-15
Instantons are an essential and non-perturbative part of Quantum Chromodynamics, the theory of strong interactions. One of the most relevant quantities in the instanton calculus is the instanton-size distribution, which can be described on the one hand within the framework of instanton perturbation theory and on the other hand investigated numerically by means of lattice computations. A rapid onset of a drastic discrepancy between these respective results indicates that the underlying physics is not yet well understood. In this work we investigate the appealing possibility of a symmetry under conformal inversion of space-time leading to this deviation. The motivation being that the lattice data seem to be invariant under an inversion of the instanton size. Since the instanton solution of a given size turns into an anti-instanton solution having an inverted size under conformal inversion of space-time, we ask in a first investigation, whether this property is transferred to the quantum level. In order to introduce a new scale, which is indicated by the lattice data and corresponds to the average instanton size as inversion radius, we project the instanton calculus onto the four-dimensional surface of a five-dimensional sphere via stereographic projection. The radius of this sphere is associated with the average instanton size. The result for the instanton size-distribution projected onto the sphere agrees surprisingly well with the lattice data at qualitative level. The resulting symmetry under an inversion of the instanton size is almost perfect. (orig.)
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
The generalized Fubini instanton
Energy Technology Data Exchange (ETDEWEB)
Yurova, A.A. [Department of Higher Mathematics, Kaliningrad State Technical University, 236000, Soviet Avenue 1, Kaliningrad (Russian Federation)], E-mail: yurov@freemail.ru; Yurov, A.V. [Department of Theoretical Physics, Russian State University of I. Kant, 236041, Aleksandra Nevskogo street 14, Kaliningrad (Russian Federation)], E-mail: artyom_yurov@mail.ru
2008-06-02
We show that (1+2) nonlinear Klein-Gordon equation with negative coupling admits an exact solution which appears to be the linear superposition of the plane wave and the nonsingular rational soliton. We show that the same approach allows to construct the solution of similar properties for the Euclidean {phi}{sup 4} model with broken symmetry. Interestingly, this regular solution will be of instanton type only in the D{<=}5 Euclidean space. Thus one can use the generalized Fubini instantons (in quantum cosmology for example) only for the case of the single infinite extra dimension.
Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations
Energy Technology Data Exchange (ETDEWEB)
Weinstein, Marvin; /SLAC
2009-02-12
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for the behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will
Chaotic instantons in scalar field theory
Addazi, Andrea
2016-01-01
We consider a new class of instantons in context of quantum field theory of a scalar field coupled with a chaotic background source field. We show how the instanton associated to the quantum tunneling from a metastable false to the true vacuum will be corrected by an exponential enhancement factor. Possible implications are discussed.
Gravitational Instantons and Cosmological Constant
Cyriac, Josily
2015-01-01
The cosmological dynamics of an otherwise empty universe in the presence of vacuum fields is considered. Quantum fluctuations at the Planck scale leads to a dynamical topology of space-time at very small length scales, which is dominated by compact gravitational instantons. The Planck scale vacuum energy acts as a source for the curvature of the these compact gravitational instantons and decouples from the large scale energy momentum tensor of the universe, thus making the observable cosmological constant vanish. However, a Euclidean functional integral over all possible topologies of the gravitational instantons generates a small non-zero value for the large scale cosmological constant, which agrees with the present observations.
Constrained instanton and black hole creation
Institute of Scientific and Technical Information of China (English)
WU Zhongchao; XU Donghui
2004-01-01
A gravitational instanton is considered as the seed for the creation of a universe. However, there exist too few instantons. To include many interesting phenomena in the framework of quantum cosmology, the concept of constrained gravitational instanton is inevitable. In this paper we show how a primordial black hole is created from a constrained instanton. The quantum creation of a generic black hole in the closed or open background is completely resolved. The relation of the creation scenario with gravitational thermodynamics and topology is discussed.
Korshunov instantons out of equilibrium
Titov, M.; Gutman, D. B.
2016-04-01
Zero-dimensional dissipative action possesses nontrivial minima known as Korshunov instantons. They have been known so far only for imaginary time representation that is limited to equilibrium systems. In this work we reconstruct and generalise Korshunov instantons using real-time Keldysh approach. This allows us to formulate the dissipative action theory for generic nonequilibrium conditions. Possible applications of the theory to transport in strongly biased quantum dots are discussed.
Rational approximations and quantum algorithms with postselection
Mahadev, U.; de Wolf, R.
2015-01-01
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using post-selection. We show that the minimal degree of the former equals (up to a factor of 2) the minimal query complexity of the latter. We gi
Uncertainty relations and approximate quantum error correction
Renes, Joseph M.
2016-09-01
The uncertainty principle can be understood as constraining the probability of winning a game in which Alice measures one of two conjugate observables, such as position or momentum, on a system provided by Bob, and he is to guess the outcome. Two variants are possible: either Alice tells Bob which observable she measured, or he has to furnish guesses for both cases. Here I derive uncertainty relations for both, formulated directly in terms of Bob's guessing probabilities. For the former these relate to the entanglement that can be recovered by action on Bob's system alone. This gives an explicit quantum circuit for approximate quantum error correction using the guessing measurements for "amplitude" and "phase" information, implicitly used in the recent construction of efficient quantum polar codes. I also find a relation on the guessing probabilities for the latter game, which has application to wave-particle duality relations.
Ring-polymer instanton theory of electron transfer in the nonadiabatic limit
Energy Technology Data Exchange (ETDEWEB)
Richardson, Jeremy O., E-mail: jeremy.richardson@fau.de [Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7/B2, 91058 Erlangen (Germany)
2015-10-07
We take the golden-rule instanton method derived in the previous paper [J. O. Richardson, R. Bauer, and M. Thoss, J. Chem. Phys. 143, 134115 (2015)] and reformulate it using a ring-polymer instanton approach. This gives equations which can be used to compute the rates of electron-transfer reactions in the nonadiabatic (golden-rule) limit numerically within a semiclassical approximation. The multidimensional ring-polymer instanton trajectories are obtained efficiently by minimization of the action. In this form, comparison with Wolynes’ quantum instanton method [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] is possible and we show that our semiclassical approach is the steepest-descent limit of this method. We discuss advantages and disadvantages of both methods and give examples of where the new approach is more accurate.
Zeroth WKB Approximation in Quantum Mechanics
Sergeenko, M N
2002-01-01
Solution of the Schr\\"odinger's equation in the zero order WKB approximation is analyzed. We observe and investigate several remarkable features of the WKB$_0$ method. Solution in the whole region is built with the help of simple connection formulas we derive from basic requirements of continuity and finiteness for the wave function in quantum mechanics. We show that, for conservative quantum systems, not only total energy, but also momentum is the constant of motion. We derive the quantization conditions for two and more turning point problems. Exact energy eigenvalues for solvable and some ``insoluble'' potentials are obtained. The eigenfunctions have the form of a standing wave, $A_n\\cos(k_nx+\\delta_n)$, and are the asymptote of the exact solution.
Semiclassical approximations to quantum time correlation functions
Egorov, S. A.; Skinner, J. L.
1998-09-01
Over the last 40 years several ad hoc semiclassical approaches have been developed in order to obtain approximate quantum time correlation functions, using as input only the corresponding classical time correlation functions. The accuracy of these approaches has been tested for several exactly solvable gas-phase models. In this paper we test the accuracy of these approaches by comparing to an exactly solvable many-body condensed-phase model. We show that in the frequency domain the Egelstaff approach is the most accurate, especially at high frequencies, while in the time domain one of the other approaches is more accurate.
Dissipative tunneling in structures with quantum dots and quantum molecules
Dahnovsky, Yu. I.; Krevchik, V. D.; Semenov, M. B.; Yamamoto, K.; Zhukovsky, V. Ch.; Aringazin, A. K.; Kudryashov, E. I.; Mayorov, V. G.
2005-01-01
The problem of tunneling control in systems "quantum dot - quantum well" (as well as "quantum dot - quantum dot" or quantum molecule) and "quantum dot - bulk contact" is studied as a quantum tunneling with dissipation process in the semiclassical (instanton) approximation. For these systems temperature and correlation between a quantum dot radius and a quantum well width (or another quantum dot radius) are considered to be control parameters. The condition for a single electron blockade is fo...
Energy Technology Data Exchange (ETDEWEB)
Li, Yimin; Miller, Wlliam H.
2006-02-22
One of the outstanding issues in the quantum instanton (QI) theory (or any transition state-type theory) for thermal rate constants of chemical reactions is the choice of an appropriate ''dividing surface'' (DS) that separates reactants and products. (In the general version of the QI theory, there are actually two dividing surfaces involved.) This paper shows one simple and general way for choosing DS's for use in QI Theory, namely using the family of (hyper) planes normal to the minimum energy path (MEP) on the potential energy surface at various distances s along it. Here the reaction coordinate is not one of the dynamical coordinates of the system (which will in general be the Cartesian coordinates of the atoms), but rather simply a parameter which specifies the DS. It is also shown how this idea can be implemented for an N-atom system in 3d space in a way that preserves overall translational and rotational invariance. Numerical application to a simple system (the colliner H + H{sub 2} reaction) is presented to illustrate the procedure.
Bergshoeff, E. A.; Hartong, J.; Ploegh, A.; Sorokin, D.
2008-01-01
We construct the half-supersymmetric instanton solutions that are electric-magnetically dual to the recently discussed half-supersymmetric Q7-branes. We call these instantons "Q-instantons". Whereas the D-instanton is most conveniently described using the RR axion chi and the dilaton phi, the Q-inst
Marochnik, Leonid; Vereshkov, Grigory
2013-01-01
We discuss a special class of quantum gravity phenomena that occur on the scale of the Universe as a whole at any stage of its evolution. These phenomena are a direct consequence of the zero rest mass of gravitons, conformal non-invariance of the graviton field, and one-loop finiteness of quantum gravity. The effects are due to graviton-ghost condensates arising from the interference of quantum coherent states. Each of coherent states is a state of gravitons and ghosts of a wavelength of the order of the horizon scale and of different occupation numbers. The state vector of the Universe is a coherent superposition of vectors of different occupation numbers. To substantiate the reliability of macroscopic quantum effects, the formalism of one-loop quantum gravity is discussed in detail. The theory is constructed as follows: Faddeev-Popov path integral in Hamilton gauge -> factorization of classical and quantum variables, allowing the existence of a self-consistent system of equations for gravitons, ghosts and m...
Baulieu, L.; Toppan, Francesco
2016-11-01
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang-Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Directory of Open Access Journals (Sweden)
L. Baulieu
2016-11-01
Full Text Available We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang–Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al. and condensed matter properties (Kane et al., where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Energy Technology Data Exchange (ETDEWEB)
Baulieu, L., E-mail: baulieu@lpthe.jussieu.fr [LPTHE – Sorbonne Universités, UPMC, 4 Place Jussieu, 75 005 Paris (France); Toppan, Francesco [CBPF, Rio de Janeiro, Rua Dr. Xavier Sigaud 150, Urca, cep 22290-180 (RJ) (Brazil)
2016-11-15
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang–Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Baulieu, Laurent
2016-01-01
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang-Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories of effective models are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Monte Carlo calculation of quantum tunneling in the dilute instanton limit
Cross, M. C.
1986-01-01
A new approach for estimating small quantum tunneling rates by Monte Carlo calculation is proposed and demonstrated on a simple one-dimensional model. The application to many-body situations such as atomic exchange in solid 3He is discussed.
Bonelli, Giulio; Tanzini, Alessandro; Vasko, Petr
2014-01-01
We show that the exact partition function of U(N) six-dimensional gauge theory with eight supercharges on C^2 x S^2 provides the quantization of the integrable system of hydrodynamic type known as gl(N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S^2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl(N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl(N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W_N algebrae, thus providing a gauge theoretical proof of AGT correspondence.
Instantons in four-Fermi term broken supersymmetric quantum mechanics with general potential
Energy Technology Data Exchange (ETDEWEB)
Hatzinikitas, Agapitos; Smyrnakis, Ioannis [University of Crete, Department of Applied Mathematics, L. Knosou-Ambelokipi, 71409 Iraklio, Crete (Greece)
2004-01-09
We have shown here how to find an integral representation for the solution of the Euclidean equations of motion of a quantum mechanical point particle in a general potential and in the presence of a four-Fermi term. The classical action in this theory depends explicitly on a set of four fermionic collective coordinates. The corrections to the classical action due to the presence of fermions are of topological nature in the sense that they depend only on the values of the fields at the boundary points {tau} {yields} {+-} {infinity}. As an application, the quantum mechanical sine-Gordon model with a four-Fermi term is solved explicitly and the corrections to the classical action are computed.
Richardson, Jeremy O
2016-01-01
The ring-polymer instanton approach is applied to compute the ground-state tunnelling splitting of four isotopomers of the formic acid dimer using the accurate PES of Qu and Bowman [Phys. Chem. Chem. Phys., 2016, 18, 24835]. As well as performing the calculations in full dimensionality, we apply a reduced-dimensionality approach to study how the results converge as successively more degrees of freedom are included. The instanton approximation compares well to exact quantum results where they are available but shows that nearly all the modes are required to quantitatively obtain the tunnelling splitting. The full-dimensional instanton calculation reproduces the experimental results, with an error of only about 20 percent.
Designing quantum information processing via structural physical approximation
Bae, Joonwoo
2017-10-01
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantum mechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.
Skyrmions from Instantons inside Domain Walls
Eto, M; Ohashi, K; Tong, D; Eto, Minoru; Nitta, Muneto; Ohashi, Keisuke; Tong, David
2005-01-01
Some years ago, Atiyah and Manton described a method to construct approximate Skyrmion solutions from Yang-Mills instantons. Here we present a dynamical realization of this construction using domain walls in a five-dimensional gauge theory. The non-abelian gauge symmetry is broken in each vacuum but restored in the core of the domain wall, allowing instantons to nestle inside the wall. We show that the worldvolume dynamics of the wall is given by the Skyrme model, including the four-derivative term, and the instantons appear as Skyrmions.
Phases of dense matter with holographic instantons
Preis, Florian
2016-01-01
We discuss nuclear matter and the transition to quark matter in the decompactified limit of the Sakai-Sugimoto model. Nuclear matter is included through instantons on the flavor branes of the model. Our approximation is based on the flat-space solution, but we allow for a dynamical instanton width and deformation and compute the energetically preferred number of instanton layers in the bulk as a function of the baryon chemical potential. We determine the regions in parameter space where the binding energy of nuclear matter is like in QCD, and compute the phase diagram in the plane of temperature and chemical potential.
Malpetti, Daniele; Roscilde, Tommaso
2017-02-01
The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical
Instantons in a Lagrangian model of turbulence
Grigorio, Leonardo S; Pereira, Rodrigo M; Chevillard, Laurent
2016-01-01
The role of instantons is investigated in the Lagrangian model for the velocity gradient evolution known as the Recent Fluid Deformation approximation. After recasting the model into the path-integral formalism, the probability distribution function is computed along with the most probable path in the weak noise limit through the saddle-point approximation. Evaluation of the instanton solution is implemented numerically by means of the iteratively Chernykh-Stepanov method. In the case of the longitudinal velocity gradient statistics, due to symmetry reasons, the number of degrees of freedom can be reduced to one, allowing the pdf to be evaluated analytically as well, thereby enabling a prediction of the scaling of the moments as a function of Reynolds number. It is also shown that the instanton solution lies on the Vieillefosse line concerning the RQ-plane. We illustrate how instantons can be unveiled in the stochastic dynamics performing a conditional statistics.
Lattice quantum chromodynamics with approximately chiral fermions
Energy Technology Data Exchange (ETDEWEB)
Hierl, Dieter
2008-05-15
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
WKB-type Approximation to Noncommutative Quantum Cosmology
Mena, E; Sabido, M
2007-01-01
In this work, we develop and apply the WKB approximation to several examples of noncommutative quantum cosmology, obtaining the time evolution of the noncommutative universe, this is done starting from a noncommutative quantum formulation of cosmology where the noncommutativity is introduced by a deformation on the minisuperspace variables. This procedure gives a straightforward algorithm to incorporate noncommutativity to cosmology and inflation.
The Instanton-Dyon Liquid Model III: Finite Chemical Potential
Liu, Yizhuang; Zahed, Ismail
2016-01-01
We discuss an extension of the instanton-dyon liquid model that includes light quarks at finite chemical potential in the center symmetric phase. We develop the model in details for the case of SU_c(2)\\times SU_f(2) by mapping the theory on a 3-dimensional quantum effective theory. We analyze the different phases in the mean-field approximation. We extend this analysis to the general case of SU_c(N_c)\\times SU_f(N_f) and note that the chiral and diquark pairings are always comparable.
Path Integrals and the WKB approximation in Loop Quantum Cosmology
Ashtekar, Abhay; Henderson, Adam
2010-01-01
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.
Path integrals and the WKB approximation in loop quantum cosmology
Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam
2010-12-01
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.
Optimal query error of quantum approximation on some Sobolev classes
Institute of Scientific and Technical Information of China (English)
2008-01-01
We study the approximation of the imbedding of functions from anisotropic and general-ized Sobolev classes into Lq([0,1]d) space in the quantum model of computation. Based on the quantum algorithms for approximation of finite imbedding from LpN to LNq , we develop quantum algorithms for approximating the imbedding from anisotropic Sobolev classes B(Wpr ([0,1]d)) to Lq([0,1]d) space for all 1 q,p ∞ and prove their optimality. Our results show that for p < q the quantum model of computation can bring a speedup roughly up to a squaring of the rate in the classical deterministic and randomized settings.
Explorations into quantum state diffusion beyond the Markov approximation
Broadbent, Curtis J.; Jing, Jun; Yu, Ting; Eberly, Joseph H.
2011-05-01
The non-Markovian quantum state diffusion equation is rapidly becoming a powerful tool for both theoretical and numerical investigations into non-trivial problems in quantum optical QED. It has been used to rederive the exact master equation for quantum Brownian motion, as well as an optical cavity or a two-level atom which is either damped or dephased under the rotating wave approximation. The exact quantum state diffusion equations for the spin-1 system have also been found, and general theorems have now been derived for solving the N-cavity, N-qubit, and N-level systems. Here, we build upon the results of Ref. to explore other problems from quantum optical QED using the non-Markovian quantum state diffusion equation.
Instantons and the Hartle-Hawking-Maldacena Proposal for dS/CFT
de Haro, Sebastian
2014-01-01
We test the Maldacena proposal for the Hartle-Hawking late time quantum state in an asymptotically de Sitter universe. In particular, we calculate the on-shell action for scalar instantons on the southern hemisphere of the four-sphere and compare the result with the renormalized on-shell action for scalar instantons in EAdS$_4$. The two results agree provided the corresponding instanton moduli as well as the curvature radii are analytically continued. The instanton solutions in de Sitter are novel and satisfy mixed boundary conditions. We also point out that instantons on $S^4$ calculate the regularized volume of EAdS$_4$, while instantons on EAdS$_4$ calculate the volume of $S^4$, where the boundary condition of the instanton in one space is identified with the radius of curvature of the other. We briefly discuss the implications of the above geometric property of instantons for higher-spin holography.
Instantons and the Hartle-Hawking-Maldacena proposal for dS/CFT
de Haro, Sebastian; Petkou, Anastasios C.
2014-11-01
We test the Maldacena proposal for the Hartle-Hawking late time quantum state in an asymptotically de Sitter universe. In particular, we calculate the on-shell action for scalar instantons on the southern hemisphere of the four-sphere and compare the result with the renormalized on-shell action for scalar instantons in EAdS4. The two results agree provided the corresponding instanton moduli as well as the curvature radii are analytically continued. The instanton solutions in de Sitter are novel and satisfy mixed boundary conditions. We also point out that instantons on S 4 calculate the regularized volume of EAdS4, while instantons on EAdS4 calculate the volume of S 4, where the boundary condition of the instanton in one space is identified with the radius of curvature of the other. We briefly discuss the implications of the above geometric property of instantons for higher-spin holography.
Approximations for strongly-coupled supersymmetric quantum mechanics
Kabat, D; Kabat, Daniel; Lifschytz, Gilad
2000-01-01
We advocate a set of approximations for studying the finite temperature behavior of strongly-coupled theories in 0+1 dimensions. The approximation consists of expanding about a Gaussian action, with the width of the Gaussian determined by a set of gap equations. The approximation can be applied to supersymmetric systems, provided that the gap equations are formulated in superspace. It can be applied to large-N theories, by keeping just the planar contribution to the gap equations. We analyze several models of scalar supersymmetric quantum mechanics, and show that the Gaussian approximation correctly distinguishes between a moduli space, mass gap, and supersymmetry breaking at strong coupling. Then we apply the approximation to a bosonic large-N gauge theory, and argue that a Gross-Witten transition separates the weak-coupling and strong-coupling regimes. A similar transition should occur in a generic large-N gauge theory, in particular in 0-brane quantum mechanics.
Experimental approximation of the Jones polynomial with one quantum bit.
Passante, G; Moussa, O; Ryan, C A; Laflamme, R
2009-12-18
We present experimental results approximating the Jones polynomial using 4 qubits in a liquid state nuclear magnetic resonance quantum information processor. This is the first experimental implementation of a complete problem for the deterministic quantum computation with one quantum bit model of quantum computation, which uses a single qubit accompanied by a register of completely random states. The Jones polynomial is a knot invariant that is important not only to knot theory, but also to statistical mechanics and quantum field theory. The implemented algorithm is a modification of the algorithm developed by Shor and Jordan suitable for implementation in NMR. These experimental results show that for the restricted case of knots whose braid representations have four strands and exactly three crossings, identifying distinct knots is possible 91% of the time.
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
Open string pair creation from worldsheet instantons
Energy Technology Data Exchange (ETDEWEB)
Schubert, Christian [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Muehlenberg 1, D-14476 Potsdam (Germany); Torrielli, Alessandro [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)
2010-10-08
Worldline instantons provide a particularly elegant way to derive Schwinger's well-known formula for the pair creation rate due to a constant electric field in quantum electrodynamics. In this communication, we show how to extend this method to the corresponding problem of open string pair creation. (fast track communication)
Lorentz invariance and the semiclassical approximation of loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Kozameh, Carlos N; Parisi, Florencia [Facultad de Matematica, AstronomIa y FIsica, Universidad Nacional de Cordoba, Ciudad Universitaria (5000) Cordoba (Argentina)
2004-06-07
It is shown that the field equations derived from an effective interaction Hamiltonian for Maxwell and gravitational fields in the semiclassical approximation of loop quantum gravity using rotational invariant states (such as weave states) are Lorentz invariant. To derive this result, which is in agreement with the observational evidence, we use the geometrical properties of the electromagnetic field.
Electroweak instantons/sphalerons at VLHC?
Ringwald, Andreas
2003-01-01
There is a close analogy between electroweak instanton-induced baryon plus lepton number (B+L) violating processes in Quantum Flavor Dynamics (QFD) and hard QCD instanton-induced chirality violating processes in deep-inelastic scattering. In view of the recent information about the latter both from lattice simulations and from the H1 experiment at HERA, it seems worthwhile to reconsider electroweak B+L violation at high energies. We present a state of the art evaluation of QFD instanton-induced parton-parton cross-sections, as relevant at future high energy colliders in the hundreds of TeV regime, such as the projected Very Large Hadron Collider (VLHC). We find that the cross-sections are unobservably small in a conservative fiducial kinematical region inferred from the above mentioned QFD--QCD analogy. An extrapolation -- still compatible with lattice results and HERA -- beyond this conservative limit indicates possible observability at VLHC.
Instantons, Fluxons and Open Gauge String Theory
Griguolo, L; Szabó, R J; Griguolo, Luca; Seminara, Domenico; Szabo, Richard J.
2004-01-01
We use the exact instanton expansion to illustrate various string characteristics of noncommutative gauge theory in two dimensions. We analyse the spectrum of the model and present some evidence in favour of Hagedorn and fractal behaviours. The decompactification limit of noncommutative torus instantons is shown to map in a very precise way, at both the classical and quantum level, onto fluxon solutions on the noncommutative plane. The weak-coupling singularities of the usual Gross-Taylor string partition function for QCD on the torus are studied in the instanton representation and its double scaling limit, appropriate for the mapping onto noncommutative gauge theory, is shown to be a generating function for the volumes of the principal moduli spaces of holomorphic differentials. The noncommutative deformation of this moduli space geometry is described and appropriate open string interpretations are proposed in terms of the fluxon expansion.
Local Random Quantum Circuits are Approximate Polynomial-Designs
Brandão, Fernando G. S. L.; Harrow, Aram W.; Horodecki, Michał
2016-09-01
We prove that local random quantum circuits acting on n qubits composed of O( t 10 n 2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether random quantum circuits were a t-design for any t > 3. The proof is based on an interplay of techniques from quantum many-body theory, representation theory, and the theory of Markov chains. In particular we employ a result of Nachtergaele for lower bounding the spectral gap of frustration-free quantum local Hamiltonians; a quasi-orthogonality property of permutation matrices; a result of Oliveira which extends to the unitary group the path-coupling method for bounding the mixing time of random walks; and a result of Bourgain and Gamburd showing that dense subgroups of the special unitary group, composed of elements with algebraic entries, are ∞-copy tensor-product expanders. We also consider pseudo-randomness properties of local random quantum circuits of small depth and prove that circuits of depth O( t 10 n) constitute a quantum t-copy tensor-product expander. The proof also rests on techniques from quantum many-body theory, in particular on the detectability lemma of Aharonov, Arad, Landau, and Vazirani. We give applications of the results to cryptography, equilibration of closed quantum dynamics, and the generation of topological order. In particular we show the following pseudo-randomness property of generic quantum circuits: Almost every circuit U of size O( n k ) on n qubits cannot be distinguished from a Haar uniform unitary by circuits of size O( n ( k-9)/11) that are given oracle access to U.
High-energy limit of quantum electrodynamics beyond Sudakov approximation
Directory of Open Access Journals (Sweden)
Alexander A. Penin
2015-05-01
Full Text Available We study the high-energy behavior of the scattering amplitudes in quantum electrodynamics beyond the leading order of the small electron mass expansion in the leading logarithmic approximation. In contrast to the Sudakov logarithms, the mass-suppressed double-logarithmic radiative corrections are induced by a soft electron pair exchange and result in enhancement of the power-suppressed contribution, which dominates the amplitudes at extremely high energies. Possible applications of our result to the analysis of the high-energy processes in quantum chromodynamics is also discussed.
High-energy limit of quantum electrodynamics beyond Sudakov approximation
Energy Technology Data Exchange (ETDEWEB)
Penin, Alexander A., E-mail: penin@ualberta.ca [Department of Physics, University of Alberta, Edmonton, Alberta T6G 2J1 (Canada); Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology, 76128 Karlsruhe (Germany)
2015-05-18
We study the high-energy behavior of the scattering amplitudes in quantum electrodynamics beyond the leading order of the small electron mass expansion in the leading logarithmic approximation. In contrast to the Sudakov logarithms, the mass-suppressed double-logarithmic radiative corrections are induced by a soft electron pair exchange and result in enhancement of the power-suppressed contribution, which dominates the amplitudes at extremely high energies. Possible applications of our result to the analysis of the high-energy processes in quantum chromodynamics is also discussed.
Slow-roll approximation in loop quantum cosmology
Luc, Joanna
2016-01-01
The slow-roll approximation is an analytical approach to study dynamical properties of the inflationary universe. In this article, systematic construction of the slow-roll expansion for effective loop quantum cosmology is presented. The analysis is performed up to the fourth order in both slow-roll parameters and the parameter controlling the strength of deviation from the classical case. The expansion is performed for three types of the slow-roll parameters: Hubble slow-roll parameters, Hubble flow parameters and potential slow-roll parameters. An accuracy of the approximation is verified by comparison with the numerical phase space trajectories for the case with a massive potential term. The results obtained in this article may be helpful in the search for the subtle quantum gravitational effects with use of the cosmological data.
Slow-roll approximation in loop quantum cosmology
Luc, Joanna; Mielczarek, Jakub
2017-01-01
The slow-roll approximation is an analytical approach to study dynamical properties of the inflationary universe. In this article, systematic construction of the slow-roll expansion for effective loop quantum cosmology is presented. The analysis is performed up to the fourth order in both slow-roll parameters and the parameter controlling the strength of deviation from the classical case. The expansion is performed for three types of the slow-roll parameters: Hubble slow-roll parameters, Hubble flow parameters and potential slow-roll parameters. An accuracy of the approximation is verified by comparison with the numerical phase space trajectories for the case with a massive potential term. The results obtained in this article may be helpful in the search for the subtle quantum gravitational effects with use of the cosmological data.
Li, Jun; Lu, Dawei; Luo, Zhihuang; Laflamme, Raymond; Peng, Xinhua; Du, Jiangfeng
2016-07-01
Precisely characterizing and controlling realistic quantum systems under noises is a challenging frontier in quantum sciences and technologies. In developing reliable controls for open quantum systems, one is often confronted with the problem of the lack of knowledge on the system controllability. The purpose of this paper is to give a numerical approach to this problem, that is, to approximately compute the reachable set of states for coherently controlled quantum Markovian systems. The approximation consists of setting both upper and lower bounds for system's reachable region of states. Furthermore, we apply our reachability analysis to the control of the relaxation dynamics of a two-qubit nuclear magnetic resonance spin system. We implement some experimental tasks of quantum state engineering in this open system at a near optimal performance in view of purity: e.g., increasing polarization and preparing pseudopure states. These results demonstrate the usefulness of our theory and show interesting and promising applications of environment-assisted quantum dynamics.
Energy Technology Data Exchange (ETDEWEB)
Park, J.S. [Amsterdam Univ. (Netherlands). Inst. voor Theoretische Fysica
1997-05-26
Motivated by twisted N=4 supersymmetric Yang-Mills theory in four dimensions, a natural extension of the monad (ADHM) construction relevant to D-instantons is considered. We show that a family of Yang-Mills instantons can be constructed from D-instantons. We discuss some possible roles of reciprocity in D-brane physics. We conjecture the existence of universal instantons together with a generalized Fourier-Nahm transformation as a unifying framework of D-brane physics. (orig.).
Variational principles in instanton problems
Energy Technology Data Exchange (ETDEWEB)
D' yakonov, D.I.; Petrov, V.Yu. (AN SSSR, Leningrad. Inst. Yadernoj Fiziki)
1984-01-01
The authors suggest a simple approximate method of evaluating path integrals for problems in which subbarrier transitions (instantons) play an important role. This method, based on Feyman's variational principle, is a generalization of the semi-classical approximation. When there is a quasiclassical parameter in a problem, the method is reduced to approximate calculations of Gauss' functional integrals (i.e. functional determinants). The authors derive general formulas for such integrals, which prove to be valid for a broad class of potentials, and verify the accuracy of the approximation using the examples of double-well and periodic potentials. In both cases the accuracy in determining the level splitting proves to be within several percent.
Renormalization of the frozen Gaussian approximation to the quantum propagator.
Tatchen, Jörg; Pollak, Eli; Tao, Guohua; Miller, William H
2011-04-07
The frozen Gaussian approximation to the quantum propagator may be a viable method for obtaining "on the fly" quantum dynamical information on systems with many degrees of freedom. However, it has two severe limitations, it rapidly loses normalization and one needs to know the Gaussian averaged potential, hence it is not a purely local theory in the force field. These limitations are in principle remedied by using the Herman-Kluk (HK) form for the semiclassical propagator. The HK propagator approximately conserves unitarity for relatively long times and depends only locally on the bare potential and its second derivatives. However, the HK propagator involves a much more expensive computation due to the need for evaluating the monodromy matrix elements. In this paper, we (a) derive a new formula for the normalization integral based on a prefactor free HK propagator which is amenable to "on the fly" computations; (b) show that a frozen Gaussian version of the normalization integral is not readily computable "on the fly"; (c) provide a new insight into how the HK prefactor leads to approximate unitarity; and (d) how one may construct a prefactor free approximation which combines the advantages of the frozen Gaussian and the HK propagators. The theoretical developments are backed by numerical examples on a Morse oscillator and a quartic double well potential.
Instantons and nonleptonic hyperon decays
Energy Technology Data Exchange (ETDEWEB)
Horvat, D.; Narancic, Z. [Department of Physics, Faculty of Electrical Engineering, University of Zagreb, 41000 Zagreb (Croatia); Tadic, D. [Department of Physics, Faculty of Natural Sciences, University of Zagreb, 41000 Zagreb (Croatia)
1995-06-01
The instanton-induced term is included in an analysis of nonleptonic strangeness-changing hyperon decays. The same type of analysis has led previously to a reasonable qualitative, and to some extent quantitative, description of the decay amplitudes. The instanton contributions do not improve old results. Data favor a very small instanton influence.
Approximating macroscopic observables in quantum spin systems with commuting matrices
Ogata, Yoshiko
2011-01-01
Macroscopic observables in a quantum spin system are given by sequences of spatial means of local elements $\\frac{1}{2n+1}\\sum_{j=-n}^n\\gamma_j(A_{i}), \\; n\\in{\\mathbb N},\\; i=1,...,m$ in a UHF algebra. One of their properties is that they commute asymptotically, as $n$ goes to infinity. It is not true that any given set of asymptotically commuting matrices can be approximated by commuting ones in the norm topology. In this paper, we show that for macroscopic observables, this is true.
Periodic instantons and domain structure in a ferromagnetic film
Zheng, G.-P.; Liang, J.-Q.; Nie, Y.-H.; Yin, W.
2003-11-01
We in this paper study periodic instantons and domain structures in a theoretical film consisting of biaxial-anisotropic ferromagnets. In a proper approximation the equation of motion of the magnetization vector as a space-time function in the film is reduced to the 1 + 2-dimensional sine-Gordon field equation in strong anisotropy limit. Static periodic instantons, which are solutions of Euclidean field equantion, and various new domain structures are obtained analytically. We also investigate the energy density and stability of the periodic instantons.
Moduli Space Dynamics of Noncommutative U(2) Instantons
Iskauskas, Andrew
2015-01-01
We consider the low energy dynamics of charge two instantons on noncommutative $\\mathbb{R}^{2}_{NC}\\times\\mathbb{R}^{2}_{NC}$ in U(2) 5-dimensional super-Yang-Mills, using the Manton approximation for slow-moving instantons to calculate the moduli space metric. By employing the ADHM construction, we are able to understand some aspects of the geometry and topology of the system. We also consider the effect of adding a potential to the moduli space, giving scattering results for noncommutative dyonic instantons.
On Exceptional Instanton Strings
Del Zotto, Michele
2016-01-01
According to a recent classification of 6d (1,0) theories within F-theory there are only 5 "pure" 6d gauge theories which have a UV superconformal fixed point. The corresponding gauge groups are $SU(3),SO(8),F_4,E_6,E_7$, and $E_8$. These exceptional models have BPS strings which are also instantons for the corresponding gauge groups. For $G$ simply-laced, we determine the 2d $\\mathcal{N}=(0,4)$ worldsheet theories of such BPS instanton strings by a simple geometric engineering argument. These are given by a twisted $S^2$ compactification of the 4d $\\mathcal{N}=2$ theories of type $H_2, D_4, E_6, E_7$ and $E_8$ (and their higher rank generalizations), where the 6d instanton number is mapped to the rank of the corresponding 4d SCFT. This determines their anomaly polynomials and, via topological strings, establishes an interesting relation among the corresponding $T^2 \\times S^2$ partition functions and the Hilbert series for moduli spaces of $G$ instantons. Such relations allow to bootstrap the corresponding e...
The Instanton-Dyon Liquid Model V: Twisted Light Quarks
Liu, Yizhuang; Zahed, Ismail
2016-01-01
We discuss an extension of the instanton-dyon liquid model that includes twisted light quarks in the fundamental representation with explicit $Z_{N_c}$ symmetry for the case with equal number of colors $N_c$ and flavors $N_f$. We map the model on a 3-dimensional quantum effective theory, and analyze it in the mean-field approximation. The effective potential and the vacuum chiral condensates are made explicit for $N_f=N_c=2, 3$. The low temperature phase is center symmetric but breaks spontaneously flavor symmetry with $N_f-1$ massless pions. The high temperature phase breaks center symmetry but supports finite and unequal quark condensates.
Instanton Counting Through Non-abelian Localization
Martens, J
2005-01-01
In this dissertation we study the problem of calculating equivariant volumes of moduli-spaces of framed instantons. The motivation for this is given by instanton counting, a recent development in theoretical physics that gives a direct approach to the non-perturbative study of certain super-symmetric quantum field theories. We develop a strategy for calculating the integrals using a combination of several techniques in symplectic geometry and equivariant cohomology. Most importantly we use an equivariant version of non-abelian localization, applied to the ADHM-construction of the moduli-spaces. Furthermore, we reduce the problem to a compact setting by means of varying compactifications using symplectic cuts, recovering the original integral over a non-compact space as the limit of integrals over compact spaces. In contrast with previous applications, in our case the contribution at infinity introduced by these compactifications turns out to be of primordial importance. We illustrate this method by explicitly...
Nitta, Muneto
2014-01-01
Yang-Mills instantons in a pure Yang-Mills theory in four Euclidean space can be promoted to particle-like topological solitons in d=4+1 dimensional space-time. When coupled to Higgs fields, they transform themselves in the Higgs phase into Skyrmions, lumps and sine-Gordon kinks, with trapped inside a non-Abelian domain wall, non-Abelian vortex and monopole string, respectively. Here, we point out that a closed monopole string, non-Abelian vortex sheet and non-Abelian domain wall in S^1, S^2 and S^3 shapes, respectively, are all Yang-Mills instantons if their S^1, S^2 and S^3 moduli, respectively, are twisted along their world-volumes.
BOOK REVIEW: Solitons, Instantons, and Twistors Solitons, Instantons, and Twistors
Witt, Donald M.
2011-04-01
Solitons and instantons play important roles both in pure and applied mathematics as well as in theoretical physics where they are related to the topological structure of the vacuum. Twistors are a useful tool for solving nonlinear differential equations and are useful for the study of the antiself-dual Yang-Mills equations and the Einstein equations. Many books and more advanced monographs have been written on these topics. However, this new book by Maciej Dunajski is a complete first introduction to all of the topics in the title. Moreover, it covers them in a very unique way, through integrable systems. The approach taken in this book is that of mathematical physics à la field theory. The book starts by giving an introduction to integrable systems of ordinary and partial differential equations and proceeds from there. Gauge theories are not covered until chapter 6 which means the reader learning the material for the first time can build up confidence with simpler models of solitons and instantons before encountering them in gauge theories. The book also has an extremely clear introduction to twistor theory useful to both mathematicians and physicists. In particular, the twistor theory presentation may be of interest to string theorists wanting understand twistors. There are many useful connections to research into general relativity. Chapter 9 on gravitational instantons is great treatment useful to anyone doing research in classical or quantum gravity. There is also a nice discussion of Kaluza-Klein monopoles. The three appendices A-C cover the necessary background material of basic differential geometry, complex manifolds, and partial differential equations needed to fully understand the subject. The reader who has some level of expertise in any of the topics covered can jump right into that material without necessarily reading all of the earlier chapters because of the extremely clear writing style of the author. This makes the book an excellent reference on
ADHM Construction of (Anti-)Self-dual Instantons in Eight Dimensions
Nakamula, Atsushi; Takesue, Koki
2016-01-01
We study the ADHM construction of (anti-)self-dual instantons in eight dimensions. We propose the general scheme to construct the (anti-)self-dual gauge field configurations $F \\wedge F = \\pm *_8 F \\wedge F$ whose finite topological charges are given by the fourth Chern number. We show that our construction reproduces the known $\\text{SO}(8)$ one-instanton solution. We also construct multi-instanton solutions of 't Hooft and Jackiw-Nohl-Rebbi (JNR) types in the dilute instanton gas approximation. The well-separated configurations of multi-instantons reproduce the correct topological charges with high accuracy. We also show that our construction is generalized to (anti-)self-dual instantons in $4n \\ (n=3,4, \\ldots)$ dimensions.
Instantons in Lifshitz field theories
Energy Technology Data Exchange (ETDEWEB)
Fujimori, Toshiaki; Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)
2015-10-05
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for “the superpotential” defining “the detailed balance condition”. The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4+1 dimensions, for which we take the Chern-Simons term as the superpotential.
Converting Neutron Stars into Strange Stars: Instanton Model
Gurovich, Victor Ts
2014-01-01
We estimate the quasiclassical probability of the homogeneous nuclear matter transition to a strange matter when a detonation wave propagates radially inside a sphere of nuclear matter. For this purpose we make use of instanton method which is known in the quantum field theory.
Derivation of instanton rate theory from first principles
Richardson, Jeremy O
2015-01-01
Instanton rate theory is used to study tunneling events in a wide range of systems including low-temperature chemical reactions. Despite many successful applications, the method has never been obtained from first principles, relying instead on the "ImF" premise. In this paper, the same expression for the rate of barrier penetration at finite temperature is rederived from quantum scattering theory [W. H. Miller, S. D. Schwartz, and J. W. Tromp, J. Chem. Phys. 79, 4889 (1983)] using a semiclassical Green's function formalism. This justifies the instanton approach and provides a route to deriving the rate of other processes.
Derivation of instanton rate theory from first principles
Richardson, Jeremy O.
2016-03-01
Instanton rate theory is used to study tunneling events in a wide range of systems including low-temperature chemical reactions. Despite many successful applications, the method has never been obtained from first principles, relying instead on the "Im F" premise. In this paper, the same expression for the rate of barrier penetration at finite temperature is rederived from quantum scattering theory [W. H. Miller, S. D. Schwartz, and J. W. Tromp, J. Chem. Phys. 79, 4889 (1983)] using a semiclassical Green's function formalism. This justifies the instanton approach and provides a route to deriving the rate of other processes.
The curious incident of multi-instantons and the necessity of Lefschetz thimbles
Behtash, Alireza; Sulejmanpasic, Tin; Ünsal, Mithat
2015-01-01
We show that compatibility of supersymmetry with exact semi-classics demands that in calculating multi-instanton amplitudes, the "separation" quasi-zeromode must be complexified and the integration cycles must be found by using complex gradient flow (or Picard-Lefschetz equations.) As a non-trivial application, we study $\\mathcal N=2$ extended supersymmetric quantum mechanics. Even though in this case supersymmetry is unbroken, the instanton--anti-instanton amplitude (naively calculated) seems to lift the ground state energy. We show, however, that the instanton--anti-instanton event consists of two parts: a fermion-correlated and a scalar-correlated event. Although both of these contributions are naively positive-definite and the latter is superficially higher order in the perturbative coupling, we show that the two contributions exactly cancel when they are evaluated on Lefschetz thimbles. This gives strong evidence that the semi-classical expansion using Lefschetz thimbles is not only a meaningful prescrip...
Instantons in lepton pair production
Energy Technology Data Exchange (ETDEWEB)
Brandenburg, A.; Ringwald, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Utermann, A. [Vrije Univ., Amsterdam (Netherlands). Dept. of Physics and Astronomy
2006-05-15
We consider QCD instanton-induced contributions to lepton pair production in hadron-hadron collisions. We relate these contributions to those known from deep inelastic scattering and demonstrate that they can be calculated reliably for sufficiently large momentum transfer. We observe that the instanton contribution to the angular distribution of the lepton pairs at finite momentum transfer strongly violates the Lam-Tung relation - a relation between coefficient functions of the angular distribution which is valid within the framework of ordinary perturbation theory. The drastic violation of this relation, as seen in experimental data, might be related to such instanton-induced effects. (Orig.)
Institute of Scientific and Technical Information of China (English)
Liu Yu-Min; Yu Zhong-Yuan
2009-01-01
Calculations of electronic structures about the semiconductor quantum dot and the semiconductor quantum ring are presented in this paper. To reduce the calculation costs, for the quantum dot and the quantum ring, their simplified axially symmetric shapes are utilized in our analysis. The energy dependent effective mass is taken into account in solving the Schrodinger equations in the single band effective mass approximation. The calculated results show that the energy dependent effective mass should be considered only for relatively small volume quantum dots or small quantum rings. For large size quantum materials, both the energy dependent effective mass and the parabolic effective mass can give the same results. The energy states and the effective masses of the quantum dot and the quantum ring as a function of geometric parameters are also discussed in detail.
Heats of Segregation of BCC Binaries from ab Initio and Quantum Approximate Calculations
Good, Brian S.
2004-01-01
We compare dilute-limit heats of segregation for selected BCC transition metal binaries computed using ab initio and quantum approximate energy methods. Ab initio calculations are carried out using the CASTEP plane-wave pseudopotential computer code, while quantum approximate results are computed using the Bozzolo-Ferrante-Smith (BFS) method with the most recent LMTO-based parameters. Quantum approximate segregation energies are computed with and without atomistic relaxation, while the ab initio calculations are performed without relaxation. Results are discussed within the context of a segregation model driven by strain and bond-breaking effects. We compare our results with full-potential quantum calculations and with available experimental results.
An approximate approach to quantum mechanical study of biomacromolecules
Chen, Xihua
method/basis-set levels of the quantum chemical calculation on the MFCC-downhill simplex optimization are also discussed. Finally, the MFCC-downhill simplex method is tested, as a general multiatomic case study, on a molecular system of cyclo-AAGAGG·H 2O to optimize the binding structure of water molecule to the fixed cyclohexapeptide. The MFCC-downhill simplex optimization results in good agreement with the crystal structure. The MFCC-downhill simplex method should be applicable to optimize the structures of ligands that bind to biomacromolecules such as proteins and DNAs. In Chapter 4, we propose a new approximate method for efficient calculation of biomacromolecular electronic properties, using a Density Matrix (DM) scheme which is integrated with the MFCC approach. In this MFCC-DM method, a biomacro-molecule such as a protein is partitioned by an MFCC scheme into properly capped fragments and concaps whose density matrices are calculated by conventional ab initio methods. These sub-system density matrices are then assembled to construct the full system density matrix which is finally employed to calculate the electronic energy, dipole moment, electronic density, electrostatic potential, etc., of the protein using Hartree-Fock or Density Functional Theory methods. By this MFCC-DM method, the self-consistent field (SCF) procedure for solving the full Hamiltonian problem is circumvented. Two implementations of this approach, MFCC-SDM and MFCC-GDM, are discussed. Systematic numerical studies are carried out on a series of extended polyglycines CH3CO-(GLY) n-NHCH3 (n=3-25) and excellent results are obtained. In Chapter 5, we present an improvement of MFCC-DM method and introduce a pairwise interaction correction (PIC) with which the MFCC-DM method is applicable to study a real-world protein with short-range structural complexity such as hydrogen bonding and close contact. In this MFCC-DM-PIC method, a protein molecule is partitioned into properly capped fragments and
Instanton effects and the landscape of string theory
Halverson, James Heaton
In this dissertation we study non-perturbative effects in four-dimensional N = 1 compactifications of superstring theory and F-theory, primarily focusing on the importance of instanton corrections to the superpotential. We utilize dualities and limits of F-theory to elucidate the physics of M5-instantons. We study the Pfaffian prefactor via heterotic duality and demonstrate its dependence on seven-brane structure and points of enhanced symmetry. Utilizing anomaly inflow and string junctions, we shed light on the localization and representation theoretic structure of instanton zero modes upon movement in moduli space. We perform a geometric uplift of an instanton in a type IIb GUT to an instanton in F-theory and identify a class of geometries which allow for the determinantion of all uncharged instanton corrections. Utilizing Seiberg-Witten theory, we explain the quantum splitting of certain seven-brane stacks. Motivated by the systematic study of instantons, we study the computability structure of the string theory landscape. We cast the study of fairly generic physical properties into the language of computability theory and show that this amounts to solving systems of diophantine equations. Utilizing the negative solution to Hilbert's 10th problem, we argue that in such systematic studies there may be no algorithm by which one can determine all physical effects. This argument holds for any suitably large class of physical theories, including the landscape. We study a large class of semi-realistic N = 1 quiver gauge theories which can arise in string compactifications. We present many MSSM quivers where the presence of anomalous U (1) symmetries and instanton corrections can account for observed phenomenological hierarchies, including the Yukawa couplings of the MSSM. We propose a new mechanism for obtaining small neutrino masses via an instanton-induced Weinberg operator and systematically study singlet-extended standard models. We discuss constraints on chiral
Constituents of Doubly Periodic Instantons
Ford, C; Ford, Chris; Pawlowski, Jan M.
2002-01-01
Using the Nahm transform we investigate doubly periodic charge one SU(2) instantons with radial symmetry. Two special points where the Nahm zero modes have softer singularities are identified as constituent locations. To support this picture, the action density is computed analytically and numerically within a two dimensional slice containing the two constituents. For particular values of the parameters the torus can be cut in half yielding two copies of a twisted charge 1/2 instanton. Such objects comprise a single constituent.
Decomposition of fractional quantum Hall states: New symmetries and approximations
Thomale, R.; Estienne, B.; Regnault, N.; Bernevig, B.A.
2010-01-01
Abstract: We provide a detailed description of a new symmetry structure of the monomial (Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall states first obtained in Ref. 1, which we now extend to spin-singlet states. We show that the Haldane-Rezayi spin-singlet state can
Smirnov, Andrey
2013-01-01
A torus action on a symplectic variety allows one to construct solutions to the quantum Yang-Baxter equations (R-matrices). For a torus action on cotangent bundles over flag varieties the resulting R-matrices are the standard rational solutions of the Yang-Baxter equation, which are well known in the theory of quantum integrable systems. The torus action on the instanton moduli space leads to more complicated R-matrices, depending additionally on two equivariant parameters t_1 and t_2. In this paper we derive an explicit expression for the R-matrix associated with the instanton moduli space. We study its matrix elements and its Taylor expansion in the powers of the spectral parameter. Certain matrix elements of this R-matrix give a generating function for the characteristic classes of tautological bundles over the Hilbert schemes in terms of the bosonic cut-and-join operators. In particular we rederive from the R-matrix the well known Lehn's formula for the first Chern class. We explicitly compute the first s...
Can Gravitational Instantons Really Constrain Axion Inflation?
Hebecker, Arthur; Theisen, Stefan; Witkowski, Lukas T
2016-01-01
Axions play a central role in inflationary model building and other cosmological applications. This is mainly due to their flat potential, which is protected by a global shift symmetry. However, quantum gravity is known to break global symmetries, the crucial effect in the present context being gravitational instantons or Giddings-Strominger wormholes. We attempt to quantify, as model-independently as possible, how large a scalar potential is induced by this general quantum gravity effect. We pay particular attention to the crucial issue which solutions can or cannot be trusted in the presence of a moduli-stabilisation and a Kaluza-Klein scale. An important conclusion is that, due to specific numerical prefactors, the effect is surprisingly small even in UV-completions with the highest possible scale offered by string theory. As we go along, we discuss in detail Euclidean wormholes, cored and extremal instantons, and how the latter arise from 5d Reissner-Nordstrom black holes. We attempt to dispel possible do...
Vladimirov, Igor G
2012-01-01
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with non-quadratic Hamiltonians. The linearization proceeds by approximating the actual Hamiltonian of the quantum system by a quadratic function of its observables which corresponds to the Hamiltonian of a quantum harmonic oscillator. This approximation is carried out in a mean square optimal sense with respect to a Gaussian reference quantum state and leads to a self-consistent linearization procedure where the mean vector and quantum covariance matrix of the system observables evolve in time according to the effective linear dynamics. We demonstrate the proposed Hamiltonian-based Gaussian linearization for the quantum Duffing oscillator whose Hamiltonian is a quadro-quartic polynomial of the momentum and position operators. The results of the paper are applicable t...
Uniform WKB, Multi-instantons, and Resurgent Trans-Series
Dunne, Gerald V
2014-01-01
We illustrate the physical significance and mathematical origin of resurgent trans-series expansions for energy eigenvalues in quantum mechanical problems with degenerate harmonic minima, by using the uniform WKB approach. We provide evidence that the perturbative expansion, combined with a global eigenvalue condition, contains all information needed to generate all orders of the non-perturbative multi-instanton expansion. This provides a dramatic realization of the concept of resurgence, whose structure is naturally encoded in the resurgence triangle. We explain the relation between the uniform WKB approach, multi-instantons, and resurgence theory. The essential idea applies to any perturbative expansion, and so is also relevant for quantum field theories with degenerate minima which can be continuously connected to quantum mechanical systems.
On Duru-Kleinert Path Integral In Quantum Cosmology
Jafarizadeh, M A; Rastegar, A R
1998-01-01
We show that the Duru-Kleinert fixed energy amplitude leads to the path integral for the propagation amplitude in the closed FRW quantum cosmology with scale factor as one degree of freedom. Then, using the Duru-Kleinert equivalence of corresponding actions, we calculate the tunneling rate, with exact prefactor, through the dilute-instanton approximation to first order in
Can gravitational instantons really constrain axion inflation?
Hebecker, Arthur; Mangat, Patrick; Theisen, Stefan; Witkowski, Lukas T.
2017-02-01
Axions play a central role in inflationary model building and other cosmological applications. This is mainly due to their flat potential, which is protected by a global shift symmetry. However, quantum gravity is known to break global symmetries, the crucial effect in the present context being gravitational instantons or Giddings-Strominger wormholes. We attempt to quantify, as model-independently as possible, how large a scalar potential is induced by this general quantum gravity effect. We pay particular attention to the crucial issue which solutions can or cannot be trusted in the presence of a moduli-stabilisation and a Kaluza-Klein scale. An important conclusion is that, due to specific numerical prefactors, the effect is surprisingly small even in UV-completions with the highest possible scale offered by string theory.
Horwitz, L P; Horwitz, Lawrence P.; Oron, Ori
2004-01-01
We discuss in this Chapter a series of theoretical developments which motivate the introduction of a quantum evolution equation for which the eikonal approximation results in the geodesics of a four dimensional manifold. This geodesic motion can be put into correspondence with general relativity. One obtains in this way a quantum theory on a flat spacetime, obeying the rules of the standard quantum theory in Lorentz covariant form, with a spacetime dependent Lorentz tensor $g_{\\mu\
Instantons in 2D U(1) Higgs model and 2D CP(N-1) sigma models
Lian, Yaogang
2007-12-01
In this thesis I present the results of a study of the topological structures of 2D U(1) Higgs model and 2D CP N-1 sigma models. Both models have been studied using the overlap Dirac operator construction of topological charge density. The overlap operator provides a more incisive probe into the local topological structure of gauge field configurations than the traditional plaquette-based operator. In the 2D U(1) Higgs model, we show that classical instantons with finite sizes violate the negativity of topological charge correlator by giving a positive contribution to the correlator at non-zero separation. We argue that instantons in 2D U(1) Higgs model must be accompanied by large quantum fluctuations in order to solve this contradiction. In 2D CPN-1 sigma models, we observe the anomalous scaling behavior of the topological susceptibility chi t for N ≤ 3. The divergence of chi t in these models is traced to the presence of small instantons with a radius of order a (= lattice spacing), which are directly observed on the lattice. The observation of these small instantons provides detailed confirmation of Luscher's argument that such short-distance excitations, with quantized topological charge, should be the dominant topological fluctuations in CP1 and CP 2, leading to a divergent topological susceptibility in the continuum limit. For the CPN-1 models with N > 3 the topological susceptibility is observed to scale properly with the mass gap. Another topic presented in this thesis is an implementation of the Zolotarev optimal rational approximation for the overlap Dirac operator. This new implementation has reduced the time complexity of the overlap routine from O(N3 ) to O(N), where N is the total number of sites on the lattice. This opens up a door to more accurate lattice measurements in the future.
Maeda, Takashi; Nakatsu, Toshio
We study a statistical model of random plane partitions. The statistical model has interpretations as five-dimensional { N}=1 supersymmetric SU(N) Yang-Mills on ℝ4 × S1 and as Kähler gravity on local SU(N) geometry. At the thermodynamic limit a typical plane partition called the limit shape dominates in the statistical model. The limit shape is linked with a hyperelliptic curve, which is a five-dimensional version of the SU(N) Seiberg-Witten curve. Amoebas and the Ronkin functions play intermediary roles between the limit shape and the hyperelliptic curve. In particular, the Ronkin function realizes an integration of thermodynamical density of the main diagonal partitions, along one-dimensional slice of it and thereby is interpreted as the counting function of gauge instantons. The radius of S1 can be identified with the inverse temperature of the statistical model. The large radius limit of the five-dimensional Yang-Mills is the low temperature limit of the statistical model, where the statistical model is frozen to a ground state that is associated with the local SU(N) geometry. We also show that the low temperature limit corresponds to a certain degeneration of amoebas and the Ronkin functions known as tropical geometry.
Maeda, T; Maeda, Takashi; Nakatsu, Toshio
2006-01-01
We study a statistical model of random plane partitions. The statistical model has interpretations as five-dimensional $\\mathcal{N}=1$ supersymmetric SU(N) Yang-Mills on $\\mathbb{R}^4\\times S^1$ and as K\\"ahler gravity on local SU(N) geometry. At the thermodynamic limit a typical plane partition called the limit shape dominates in the statistical model. The limit shape is linked with a hyperelliptic curve, which is a five-dimensional version of the SU(N) Seiberg-Witten curve. Amoebas and the Ronkin functions play intermediary roles between the limit shape and the hyperelliptic curve. In particular, the Ronkin function realizes an integration of thermodynamical density of the main diagonal partitions, along one-dimensional slice of it and thereby is interpreted as the counting function of gauge instantons. The radius of $S^1$ can be identified with the inverse temperature of the statistical model. The large radius limit of the five-dimensional Yang-Mills is the low temperature limit of the statistical model, w...
Approximation of quantum observables by molecular dynamics simulations
Sandberg, Mattias
2016-01-06
In this talk I will discuss how to estimate the uncertainty in molecular dynamics simulations. Molecular dynamics is a computational method to study molecular systems in materials science, chemistry, and molecular biology. The wide popularity of molecular dynamics simulations relies on the fact that in many cases it agrees very well with experiments. If we however want the simulation to predict something that has no comparing experiment, we need a mathematical estimate of the accuracy of the computation. In the case of molecular systems with few particles, such studies are made by directly solving the Schrodinger equation. In this talk I will discuss theoretical results on the accuracy between quantum mechanics and molecular dynamics, to be used for systems that are too large to be handled computationally by the Schrodinger equation.
Improved WKB approximation for quantum tunneling: Application to heavy-ion fusion
Energy Technology Data Exchange (ETDEWEB)
Toubiana, A.J. [Universidade Federal do Rio de Janeiro, Departamento de Engenharia Nuclear, Escola Politecnica, C.P. 68529, Rio de Janeiro, RJ (Brazil); Ecole CentraleSupelec, Gif-sur-Yvette (France); Paris Saclay, Saint-Aubin (France); Canto, L.F. [Universidade Federal do Rio de Janeiro, Instituto de Fisica, C.P. 68528, Rio de Janeiro (Brazil); Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil); Hussein, M.S. [Universidade de Sao Paulo, Instituto de Estudos Avancados, C.P. 72012, Sao Paulo, SP (Brazil); Universidade de Sao Paulo, Instituto de Fisica, C.P. 66318, Sao Paulo, SP (Brazil); Instituto Tecnologico de Aeronautica, CTA, Departamento de Fisica, Sao Jose dos Campos, Sao Paulo, SP (Brazil)
2017-02-15
In this paper we revisit the one-dimensional tunnelling problem. We consider Kemble's approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical continuation of the radial coordinate to the complex plane. We investigate the validity of this approximation by comparing their predictions for the cross section and for the barrier distribution with the corresponding quantum-mechanical results. We find that the extended Kemble's approximation reproduces the results of quantum mechanics with great accuracy. (orig.)
Breakdown of the dipole approximation for large quantum dot emitters coupled to an interface
DEFF Research Database (Denmark)
Stobbe, Søren; Johansen, Jeppe; Löffler, A.
2008-01-01
We measured time-resolved photoluminescence from large quantum dots near a semiconductor-air interface. Far from the interface our data are consistent with dipole theory, but near the interface they question the validity of the dipole approximation.......We measured time-resolved photoluminescence from large quantum dots near a semiconductor-air interface. Far from the interface our data are consistent with dipole theory, but near the interface they question the validity of the dipole approximation....
A note on the semi-classical approximation in quantum gravity
Lifschytz, G; Ortiz, M; Lifschytz, Gilad; Mathur, Samir D; Ortiz, Miguel
1996-01-01
We re-examine the semiclassical approximation in the canonical formulation of quantum gravity. It is shown that the usual interpretation of a WKB state does not give an adequate semiclassical description of both matter and gravity degrees of freedom. A state for the gravitational field is proposed which has the necessary properties to describe quantum field theory on a background spacetime with small quantum fluctuations. Its connection with WKB states is clarified using a reduced phase space formalism. This state is used to give a qualitative analysis of the effects of geometry fluctuations, which can be related to the breakdown of the semiclassical approximation near a black hole horizon.
Rossi, Mariana; Paesani, Francesco; Bowman, Joel; Ceriotti, Michele
2014-01-01
Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer (LMon) model and a mixed quantum-classical (MQC) model as representatives of the first family of methods, and centroid molecular dynamics (CMD) and thermostatted ring polymer molecular dynamics (TRPMD) as examples of the latter. We use as benchmarks D$_2$O doped with HOD and pure H$_2$O at three distinc...
ADHM Revisited: Instantons and Wilson Lines
Tong, David
2014-01-01
We revisit the well-studied D0-D4 system of D-branes and its relationship to the ADHM construction. It is well known that the D0-branes appear as instantons in the D4-brane worldvolume. We add a Wilson line to the D4-brane in the guise of an extended fundamental string and determine how this affects the D0-brane dynamics. As the D0-brane moves in the presence of the Wilson line, it experiences a Lorentz force, proportional to its Yang-Mills gauge connection. From the perspective of the D0-brane quantum mechanics, this force emerges through the ADHM construction of the self-dual gauge connection.
Spin Physics through QCD Instantons
Qian, Yachao
2015-01-01
We review some aspects of spin physics where QCD instantons play an important role. In particular, their large contributions in semi-inclusive deep-inelastic scattering and polarized proton on proton scattering. We also review their possible contribution in the $\\mathcal{P}$-odd pion azimuthal charge correlations in peripheral $AA$ scattering at collider energies.
Multi - instantons and Maldacena's conjecture
Dorey, N.; Hollowood, T.J.; Khoze, V.V.; Mattis, M.P.; Vandoren, S.
2007-01-01
We examine certain n-point functions Gn in N = 4 supersymmetric SU(N) gauge theory at the conformal point. In the large-N limit, we are able to sum all leading-order multiinstanton contributions exactly. We find compelling evidence for Maldacena’s conjecture: (1) The large-N k-instanton collective c
Kawabata, Shiro; Golubov, Alexander A.
2007-01-01
We theoretically investigate macroscopic quantum tunneling (MQT) in a current-biased π junction with a superconductor (S) and an insulating ferromagnet (IF). By using the functional integral method and the instanton approximation, the influence of the quasiparticle dissipation on MQT is found to be
Baryon- and lepton-number violation by electroweak instantons
Noble, Robert J.
1982-02-01
We make a quantitative study of instanton-induced baryon- and lepton-number-violating processes in an SU(2)×U(1) electroweak gauge theory at zero and finite temperatures (in the "dilute-instanton-gas" approximation). As an example we consider a simplified model involving only the proton, neutron, electron, and electron neutrino. At zero temperature the total cross sections for p+n-->e¯+ν¯ and eleven other similar reactions are of order s×10-195 cm2, where s is the total center-of-momentum energy squared in GeV2. The neutron decays via n-->p¯+e¯+ν¯ with a lifetime of the order 10146 years. The cross sections and neutron decay width decrease with temperature because color-electric-charge screening reduces the self-dual-instanton density at finite temperature. At high temperature the cross sections (for a given s) and neutron decay width fall off as T-473 in this simplified model. It is suggested that correctly treating the instanton gas as very dense (as discussed by Berg, Luscher, and Stehr) and including finite-energy tunneling solutions could increase the predicted reaction rates.
Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space
Bracken, A. J.
2002-01-01
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Classical mechanics can now be viewed as a deformation of quantum mechanics. The forms of semiquantum approximations to classical mechanics are indicated.
How Low Can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?
Ambainis, Andris
2012-01-01
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of approximate degree and bounded-error quantum query complexity. We show that for these measures the correct lower bound is Omega(log n / log log n), and we exhibit quantum algorithms for two functions where this bound is achieved.
Dynamical R-parity violations from exotic instantons
Addazi, Andrea
2015-01-01
We show how R-parity can be dynamically broken by non-perturbative quantum gravity effects. In particular, in D-brane models, Exotic instantons provide a simple and calculable mechanism for the generation of R-parity violating bilinear, trilinear and higher order superpotential terms. We show examples of MSSM-like D-brane models, in which one Exotic Instanton induces only one term among the possible R-parity violating superpotentials. Naturally, the idea can be generalized for other gauge groups. As a consequence, a dynamical violation of R-parity does not necessarily destabilize the proton, {\\it i.e} a strong fine tuning is naturally avoided, in our case. For example, a Lepton violating superpotential term can be generated without generating Baryon violating ones, and {\\it viceversa}. This has strong implications in phenomenology: neutrino, neutron-antineutron, electric dipole moments, dark matter and LHC physics.
Instantons and Extreme Value Statistics of Random Matrices
Atkin, Max R
2014-01-01
We discuss the distribution of the largest eigenvalue of a random N x N Hermitian matrix. Utilising results from the quantum gravity and string theory literature it is seen that the orthogonal polynomials approach, first introduced by Majumdar and Nadal, can be extended to calculate both the left and right tail large deviations of the maximum eigenvalue. This framework does not only provide computational advantages when considering the left and right tail large deviations for general potentials, as is done explicitly for the first multi-critical potential, but it also offers an interesting interpretation of the results. In particular, it is seen that the left tail large deviations follow from a standard perturbative large N expansion of the free energy, while the right tail large deviations are related to the non-perturbative expansion and thus to instanton corrections. Considering the standard interpretation of instantons as tunnelling of eigenvalues, we see that the right tail rate function can be identifie...
Energy Technology Data Exchange (ETDEWEB)
Zhang, Hou-Dao [Department of Chemistry, Hong Kong University of Science and Technology, Hong Kong (China); Yan, YiJing, E-mail: yyan@ust.hk [Department of Chemistry, Hong Kong University of Science and Technology, Hong Kong (China); iChEM and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026 (China)
2015-12-07
The issue of efficient hierarchy truncation is related to many approximate theories. In this paper, we revisit this issue from both the numerical efficiency and quantum mechanics prescription invariance aspects. The latter requires that the truncation approximation made in Schrödinger picture, such as the quantum master equations and their self–consistent–Born–approximation improvements, should be transferable to their Heisenberg–picture correspondences, without further approximations. We address this issue with the dissipaton equation of motion (DEOM), which is a unique theory for the dynamics of not only reduced systems but also hybrid bath environments. We also highlight the DEOM theory is not only about how its dynamical variables evolve in time, but also the underlying dissipaton algebra. We demonstrate this unique feature of DEOM with model systems and report some intriguing nonlinear Fano interferences characteristics that are experimentally measurable.
Zhang, Hou-Dao; Yan, YiJing
2015-12-07
The issue of efficient hierarchy truncation is related to many approximate theories. In this paper, we revisit this issue from both the numerical efficiency and quantum mechanics prescription invariance aspects. The latter requires that the truncation approximation made in Schrödinger picture, such as the quantum master equations and their self-consistent-Born-approximation improvements, should be transferable to their Heisenberg-picture correspondences, without further approximations. We address this issue with the dissipaton equation of motion (DEOM), which is a unique theory for the dynamics of not only reduced systems but also hybrid bath environments. We also highlight the DEOM theory is not only about how its dynamical variables evolve in time, but also the underlying dissipaton algebra. We demonstrate this unique feature of DEOM with model systems and report some intriguing nonlinear Fano interferences characteristics that are experimentally measurable.
2008-01-01
We discuss approximations of vertex couplings of quantum graphs using families of thin branched manifolds. We show that if a Neumann type Laplacian on such manifolds is amended by suitable potentials, the resulting Schr\\"odinger operators can approximate non-trivial vertex couplings. The latter include not only the delta-couplings but also those with wavefunctions discontinuous at the vertex. We work out the example of the symmetric delta'-couplings and conjecture that the same method can be ...
Adiabatic Dynamics of Instantons on S 4
Franchetti, Guido; Schroers, Bernd J.
2016-10-01
We define and compute the L 2 metric on the framed moduli space of circle invariant 1-instantons on the 4-sphere. This moduli space is four dimensional and our metric is {SO(3) × U(1)} symmetric. We study the behaviour of generic geodesics and show that the metric is geodesically incomplete. Circle-invariant instantons on the 4-sphere can also be viewed as hyperbolic monopoles, and we interpret our results from this viewpoint. We relate our results to work by Habermann on unframed instantons on the 4-sphere and, in the limit where the radius of the 4-sphere tends to infinity, to results on instantons on Euclidean 4-space.
Membrane Instantons and de Sitter Vacua
Energy Technology Data Exchange (ETDEWEB)
Davidse, Marijn [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands); Saueressig, Frank [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht(Netherlands); Theis, Ulrich [Institute for Theoretical Physics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, D-07743 Jena (Germany); Vandoren, Stefan [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)
2005-09-01
We investigate membrane instanton effects in type-IIA strings compactified on rigid Calabi-Yau manifolds. These effects contribute to the low-energy effective action of the universal hypermultiplet. In the absence of additional fivebrane instantons, the quaternionic geometry of this hypermultiplet is determined by solutions of the three-dimensional Toda equation. We construct solutions describing membrane instantons, and find perfect agreement with the string theory prediction. In the context of flux compactifications we discuss how membrane instantons contribute to the scalar potential and the stabilization of moduli. Finally, we demonstrate the existence of meta-stable de Sitter vacua.
A new approximation method for time-dependent problems in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico)]. E-mail: paolo@ucol.mx; Aranda, Alfredo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico)]. E-mail: fefo@ucol.mx; Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Diag. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)]. E-mail: fernande@quimica.unlp.edu.ar; Jones, Hugh [Department of Physics, Imperial College, London SW7 2AZ (United Kingdom)]. E-mail: h.f.jones@imperial.ac.uk
2005-06-06
We propose an approximate solution of the time-dependent Schroedinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of the method by applying it to the time development of the wave-function in the quantum-mechanical version of the inflationary slow-roll transition.
Validity of the local self-energy approximation: Application to coupled quantum impurities
Mitchell, A.
2015-01-01
We examine the quality of the local self-energy approximation, applied here to models of multiple quantum impurities coupled to an electronic bath. The local self-energy is obtained by solving a single-impurity Anderson model in an effective medium that is determined self-consistently, similar to
Approximating relational observables by absolute quantities: a quantum accuracy-size trade-off
Miyadera, Takayuki; Loveridge, Leon; Busch, Paul
2016-05-01
The notion that any physical quantity is defined and measured relative to a reference frame is traditionally not explicitly reflected in the theoretical description of physical experiments where, instead, the relevant observables are typically represented as ‘absolute’ quantities. However, the emergence of the resource theory of quantum reference frames as a new branch of quantum information science in recent years has highlighted the need to identify the physical conditions under which a quantum system can serve as a good reference. Here we investigate the conditions under which, in quantum theory, an account in terms of absolute quantities can provide a good approximation of relative quantities. We find that this requires the reference system to be large in a suitable sense.
Zimmermann, Tomas
2011-01-01
We propose to measure nonadiabaticity of molecular quantum dynamics rigorously with the quantum fidelity between the Born-Oppenheimer and fully nonadiabatic dynamics. It is shown that this measure of nonadiabaticity applies in situations where other criteria, such as the energy gap criterion or the extent of population transfer, fail. We further propose to estimate this quantum fidelity efficiently with a generalization of the dephasing representation to multiple surfaces. Two variants of the multiple-surface dephasing representation (MSDR) are introduced, in which the nuclei are propagated either with the fewest-switches surface hopping (FSSH) or with the locally mean field dynamics (LMFD). The LMFD can be interpreted as the Ehrenfest dynamics of an ensemble of nuclear trajectories, and has been used previously in the nonadiabatic semiclassical initial value representation. In addition to propagating an ensemble of classical trajectories, the MSDR requires evaluating nonadiabatic couplings and solving the Sc...
Energy Technology Data Exchange (ETDEWEB)
Jin, Jinshuang, E-mail: jsjin@hznu.edu.cn [Department of Physics, Hangzhou Normal University, Hangzhou 310036 (China); Li, Jun [Department of Physics, Hangzhou Normal University, Hangzhou 310036 (China); College of Physics and Electronic Engineering, Dezhou University, Dezhou 253023 (China); Liu, Yu [State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 (China); Li, Xin-Qi, E-mail: lixinqi@bnu.edu.cn [State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 (China); Department of Physics, Beijing Normal University, Beijing 100875 (China); Department of Chemistry, Hong Kong University of Science and Technology, Kowloon (Hong Kong); Yan, YiJing, E-mail: yyan@ust.hk [Department of Chemistry, Hong Kong University of Science and Technology, Kowloon (Hong Kong); Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China)
2014-06-28
Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.
Jin, Jinshuang; Li, Jun; Liu, Yu; Li, Xin-Qi; Yan, YiJing
2014-06-28
Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.
Institute of Scientific and Technical Information of China (English)
聂一行; 李志坚; 梁九卿; 严启伟
2003-01-01
Crossover from classical to quantum regimes of the barrier transition rate in a biaxial ferromagnetic magnet with a magnetic field applied along hard anisotropy axis is investigated. We show that the type of action-temperature diagrams can be determined by counting the number of bifurcation points. The model possesses not only the known type Ⅰ and Ⅱ, but also the interesting type Ⅲ and Ⅳ of transition which do not occur in general.
The DSUBm approximation scheme for the coupled cluster method and applications to quantum magnets
Directory of Open Access Journals (Sweden)
R.F. Bishop
2009-01-01
Full Text Available A new approximate scheme, DSUBm, is described for the coupled cluster method. We apply it to two well-studied (spin-1/2 Heisenberg antiferromagnet spin-lattice models, namely: the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the sublattice magnetization and the quantum critical point. They are in good agreement with those from such alternative methods as spin-wave theory, series expansions, exact diagonalization techniques, quantum Monte Carlo methods and those from the CCM using the LSUBm scheme.
Instanton Calculus, Topological Field Theories and N = 2 Super Yang-Mills Theories
Bellisai, D; Tanzini, A; Travaglini, G; Bellisai, Diego; Fucito, Francesco; Tanzini, Alessandro; Travaglini, Gabriele
2000-01-01
The results obtained by Seiberg and Witten for the low-energy Wilsonian effective actions of N=2 supersymmetric theories with gauge group SU(2) are in agreement with instanton computations carried out for winding numbers one and two. This suggests that the instanton saddle point saturates the non-perturbative contribution to the functional integral. A natural framework in which corrections to this approximation are absent is given by the topological field theory built out of the N=2 Super Yang-Mills theory. After extending the standard construction of the Topological Yang-Mills theory to encompass the case of a non-vanishing vacuum expectation value for the scalar field, a BRST transformation is defined (as a supersymmetry plus a gauge variation), which on the instanton moduli space is the exterior derivative. The topological field theory approach makes the so-called "constrained instanton" configurations and the instanton measure arise in a natural way. As a consequence, instanton-dominated Green's functions...
Exact Coleman-de Luccia Instantons
Kanno, Sugumi
2011-01-01
We present exact Coleman-de Luccia (CdL) instantons, which describe vacuum decay from Anti de Sitter (AdS) space, de Sitter (dS) space and Minkowski space to AdS space. We systematically obtain these exact solutions by considering deformation of Hawking-Moss (HM) instantons. We analytically calculate decay rates and discuss a subtlety in the interpretation.
Conformal Symmetry on the Instanton Moduli Space
Tian, Y
2004-01-01
The conformal symmetry on the instanton moduli space is discussed using the ADHM construction, where a viewpoint of "homogeneous coordinates" for both the spacetime and the moduli space turns out to be useful. An interesting 5-dimensional interpretation of the SU(2) single-instanton is also mentioned.
Instantons, quivers and noncommutative Donaldson-Thomas theory
Energy Technology Data Exchange (ETDEWEB)
Cirafici, Michele, E-mail: cirafici@math.ist.utl.pt [Centro de Analise Matematica, Geometria e Sistemas Dinamicos, Departamento de Matematica, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Sinkovics, Annamaria, E-mail: A.Sinkovics@damtp.cam.ac.uk [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Szabo, Richard J., E-mail: R.J.Szabo@ma.hw.ac.uk [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom); Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom)
2011-12-11
We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.
Instanton bound states in ABJM theory
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Yasuyuki [DESY Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst. and Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2013-06-15
The partition function of the ABJM theory receives non-perturbative corrections due to instanton effects. We study these non-perturbative corrections, including bound states of worldsheet instantons and membrane instantons, in the Fermi-gas approach. We require that the total non-perturbative correction should be always finite for arbitrary Chern-Simons level. This finiteness is realized quite non-trivially because each bound state contribution naively diverges at some levels. The poles of each contribution should be canceled out in total. We use this pole cancellation mechanism to find unknown bound state corrections from known ones. We conjecture a general expression of the bound state contribution. Summing up all the bound state contributions, we find that the effect of bound states is simply incorporated into the worldsheet instanton correction by a redefinition of the chemical potential in the Fermi-gas system. Analytic expressions of the 3- and 4-membrane instanton corrections are also proposed.
Singular Instantons and Painlevé VI
Muñiz Manasliski, Richard
2016-06-01
We consider a two parameter family of instantons, which is studied in [Sadun L., Comm. Math. Phys. 163 (1994), 257-291], invariant under the irreducible action of SU_2 on S^4, but which are not globally defined. We will see that these instantons produce solutions to a one parameter family of Painlevé VI equations (P_VI}) and we will give an explicit expression of the map between instantons and solutions to P_{VI}. The solutions are algebraic only for that values of the parameters which correspond to the instantons that can be extended to all of S^4. This work is a generalization of [Muñiz Manasliski R., Contemp. Math., Vol. 434, Amer. Math. Soc., Providence, RI, 2007, 215-222] and [Muñiz Manasliski R., J. Geom. Phys. 59 (2009), 1036-1047, arXiv:1602.07221], where instantons without singularities are studied.
Efficient Approximation of the Dynamics of One-Dimensional Quantum Spin Systems
Osborne, Tobias J.
2006-10-01
In this Letter we show that an arbitrarily good approximation to the propagator eitH for a 1D lattice of n quantum spins with Hamiltonian H may be obtained with polynomial computational resources in n and the error γ and exponential resources in |t|. Our proof makes use of the finitely correlated state or matrix product state formalism exploited by numerical renormalization group algorithms like the density matrix renormalization group. There are two immediate consequences of this result. The first is that Vidal’s time-dependent density matrix renormalization group will require only polynomial resources to simulate 1D quantum spin systems for logarithmic |t|. The second consequence is that continuous-time 1D quantum circuits with logarithmic |t| can be simulated efficiently on a classical computer, despite the fact that, after discretization, such circuits are of polynomial depth.
Average-Case Complexity Versus Approximate Simulation of Commuting Quantum Computations
Bremner, Michael J.; Montanaro, Ashley; Shepherd, Dan J.
2016-08-01
We use the class of commuting quantum computations known as IQP (instantaneous quantum polynomial time) to strengthen the conjecture that quantum computers are hard to simulate classically. We show that, if either of two plausible average-case hardness conjectures holds, then IQP computations are hard to simulate classically up to constant additive error. One conjecture relates to the hardness of estimating the complex-temperature partition function for random instances of the Ising model; the other concerns approximating the number of zeroes of random low-degree polynomials. We observe that both conjectures can be shown to be valid in the setting of worst-case complexity. We arrive at these conjectures by deriving spin-based generalizations of the boson sampling problem that avoid the so-called permanent anticoncentration conjecture.
Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach.
Ramakrishnan, Raghunathan; Dral, Pavlo O; Rupp, Matthias; von Lilienfeld, O Anatole
2015-05-12
Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approximate legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger molecular sets than used for training. For thermochemical properties of up to 16k isomers of C7H10O2 we present numerical evidence that chemical accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qualitative relationship between molecular entropy and electron correlation. The transferability of our approach is demonstrated, using semiempirical quantum chemistry and machine learning models trained on 1 and 10% of 134k organic molecules, to reproduce enthalpies of all remaining molecules at density functional theory level of accuracy.
Big Data meets Quantum Chemistry Approximations: The $\\Delta$-Machine Learning Approach
Ramakrishnan, Raghunathan; Rupp, Matthias; von Lilienfeld, O Anatole
2015-01-01
Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approximate legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger molecular sets than used for training. For thermochemical properties of up to 16k constitutional isomers of C$_7$H$_{10}$O$_2$ we present numerical evidence that chemical accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qualitative relationship between molecular entropy and electron correlation. The transferability of our approach is demonstrated, using semi-empirical quantum chemistry and machine learning models trained on 1 and 10\\% of 134k organ...
Murthy, Ganpathy
2001-11-01
A microscopic Hamiltonian theory of the fractional quantum Hall effect developed by Shankar and the present author based on the fermionic Chern-Simons approach has recently been quite successful in calculating gaps and finite-tempertature properties in fractional quantum Hall states. Initially proposed as a small-q theory, it was subsequently extended by Shankar to form an algebraically consistent theory for all q in the lowest Landau level. Such a theory is amenable to a conserving approximation in which the constraints have vanishing correlators and decouple from physical response functions. Properties of the incompressible fractions are explored in this conserving approximation, including the magnetoexciton dispersions and the evolution of the small-q structure factor as ν-->12. Finally, a formalism capable of dealing with a nonuniform ground-state charge density is developed and used to show how the correct fractional value of the quasiparticle charge emerges from the theory.
Approximate solutions to the quantum problem of two opposite charges in a constant magnetic field
Energy Technology Data Exchange (ETDEWEB)
Ardenghi, J.S., E-mail: jsardenghi@gmail.com [IFISUR, Departamento de Física (UNS-CONICET), Avenida Alem 1253, Bahía Blanca, Buenos Aires (Argentina); Gadella, M., E-mail: manuelgadella1@gmail.com [Department of Theoretical, Atomic Physics and Optics and IMUVA, University of Valladolid, 47011 Valladolid (Spain); Grinnell College, Department of Physics, Grinnell, 50112 IA (United States); Negro, J., E-mail: jnegro@fta.uva.es [Department of Theoretical, Atomic Physics and Optics and IMUVA, University of Valladolid, 47011 Valladolid (Spain)
2016-05-06
We consider two particles of equal mass and opposite charge in a plane subject to a perpendicular constant magnetic field. This system is integrable but not superintegrable. From the quantum point of view, the solution is given by two fourth degree Hill differential equations which involve the energy as well as a second constant of motion. There are two solvable approximations in relation to the value of a parameter. Starting from each of these approximations, a consistent perturbation theory can be applied to get approximate values of the energy levels and of the second constant of motion. - Highlights: • We have studied the quantum model of two charged particles on a plane with opposite charges and a perpendicular constant magnetic field. • This model is integrable, although not superintegrable. • The model under study is described by two fourth degree Hill equations, one trigonometric and the other hyperbolic. • We have considered two distinct approximations that have exact solution. • We have applied a perturbative method to improve the approximation.
D3-instantons, Mock Theta Series and Twistors
Alexandrov, Sergei; Pioline, Boris
2013-01-01
The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2,Z). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2,Z) on the linearized twistor space. Using the modular invariance of the D4-D2-D0 black hole partition function, we show that the standard Darboux coordinates in twistor space have modular anomalies controlled by period integrals of a Siegel-Narain theta series, which can be canceled by a contact transformation generated by a holomorphic mock theta series.
D3-instantons, mock theta series and twistors
Alexandrov, Sergei; Manschot, Jan; Pioline, Boris
2013-04-01
The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2, {Z} ). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2, {Z} ) on the linearized twistor space. Using the modular invariance of the D4-D2-D0 black hole partition function, we show that the standard Darboux coordinates in twistor space have modular anomalies controlled by period integrals of a Siegel-Narain theta series, which can be canceled by a contact transformation generated by a holomorphic mock theta series.
Single-centered black hole microstate degeneracies from instantons in supergravity
Murthy, Sameer
2015-01-01
We obtain holographic constraints on the microscopic degeneracies of black holes by computing the exact macroscopic quantum entropy using localization, including the effects of string worldsheet instantons in the supergravity effective action. For $\\frac14$-BPS black holes in type II string theory on $K3 \\times T^{2}$, the constraints can be explicitly checked against expressions for the microscopic BPS counting functions that are known in terms of certain mock modular forms. We find that the effect of including the infinite sum over instantons in the holomorphic prepotential of the supergravity leads to a sum over Bessel functions with successively sub-leading arguments as in the Rademacher expansion of Jacobi forms -- but begins to disagree with such a structure near an order where the mock modular nature becomes relevant. This leads to a systematic method to recover the polar terms of the microscopic degeneracies from the degeneracy of instantons (the Gromov-Witten invariants). We check explicitly that our...
From QCD-instantons at HERA to electroweak (B+L)-violation at VLHC
Ringwald, A
2002-01-01
This review emphasizes the close analogy between hard QCD instanton-induced chirality violating processes in deep-inelastic scattering and electroweak instanton-induced baryon plus lepton number (B+L) violating processes in Quantum Flavor Dynamics (QFD). Recent information about QCD instantons, both from lattice simulations and from the H1 experiment at HERA, can be used to learn about the fate of electroweak B+L violation at future high energy colliders in the hundreds of TeV regime, such as the projected Very Large Hadron Collider (VLHC). The cross-sections turn out to be unobservably small in a conservative fiducial kinematical region inferred from the above mentioned QCD-QFD analogy. An extrapolation - still compatible with lattice results and HERA - beyond this conservative limit indicates possible observability at VLHC.
Condensates and instanton – torus knot duality. Hidden Physics at UV scale
Directory of Open Access Journals (Sweden)
A. Gorsky
2015-11-01
Full Text Available We establish the duality between the torus knot superpolynomials or the Poincaré polynomials of the Khovanov homology and particular condensates in Ω-deformed 5D supersymmetric QED compactified on a circle with 5d Chern–Simons (CS term. It is explicitly shown that n-instanton contribution to the condensate of the massless flavor in the background of four-observable exactly coincides with the superpolynomial of the T(n,nk+1 torus knot where k is the level of CS term. In contrast to the previously known results, the particular torus knot corresponds not to the partition function of the gauge theory but to the particular instanton contribution and summation over the knots has to be performed in order to obtain the complete answer. The instantons are sitting almost at the top of each other and the physics of the “fat point” where the UV degrees of freedom are slaved with point-like instantons turns out to be quite rich. Also we see knot polynomials in the quantum mechanics on the instanton moduli space. We consider the different limits of this correspondence focusing at their physical interpretation and compare the algebraic structures at the both sides of the correspondence. Using the AGT correspondence, we establish a connection between superpolynomials for unknots and q-deformed DOZZ factors.
Instanton Corrected Non-Supersymmetric Attractors
Dominic, Pramod
2010-01-01
We discuss non-supersymmetric attractors with an instanton correction in Type IIA string theory compactified on a Calabi-Yau three-fold at large volume. For a stable non-supersymmetric black hole, the attractor point must minimize the effective black hole potential. We study the supersymmetric as well as non-supersymmetric attractors for the D0-D4 system with instanton corrections. We show that in simple models, like the STU model, the flat directions of the mass matrix can be lifted by a suitable choice of the instanton parameters.
Doubly Periodic Instantons and their Constituents
Ford, C; Ford, Chris; Pawlowski, Jan M.
2002-01-01
Using the Nahm transform we investigate doubly periodic charge one SU(2) instantons with radial symmetry. Two special points where the Nahm zero modes have softer singularities are identified as the locations of instanton core constituents. For a square torus this constituent picture is closely reflected in the action density. In rectangular tori with large aspect ratios the cores merge to form monopole-like objects. For particular values of the parameters the torus can be cut in half yielding two copies of a twisted charge 1/2 instanton. These findings are illustrated with plots of the action density within a two-dimensional slice containing the constituents.
Purkayastha, Archak; Dhar, Abhishek; Kulkarni, Manas
2016-06-01
We present the Born-Markov approximated Redfield quantum master equation (RQME) description for an open system of noninteracting particles (bosons or fermions) on an arbitrary lattice of N sites in any dimension and weakly connected to multiple reservoirs at different temperatures and chemical potentials. The RQME can be reduced to the Lindblad equation, of various forms, by making further approximations. By studying the N =2 case, we show that RQME gives results which agree with exact analytical results for steady-state properties and with exact numerics for time-dependent properties over a wide range of parameters. In comparison, the Lindblad equations have a limited domain of validity in nonequilibrium. We conclude that it is indeed justified to use microscopically derived full RQME to go beyond the limitations of Lindblad equations in out-of-equilibrium systems. We also derive closed-form analytical results for out-of-equilibrium time dynamics of two-point correlation functions. These results explicitly show the approach to steady state and thermalization. These results are experimentally relevant for cold atoms, cavity QED, and far-from-equilibrium quantum dot experiments.
Adiabatic dynamics of instantons on $S ^4 $
Franchetti, Guido
2015-01-01
We explicitly parameterise the framed moduli space of circle-invariant 1-instantons on the 4-sphere, and compute its $L^2$ metric. With our definition of framing, this moduli space is four dimensional and its metric is $SO(3) \\times U(1)$ symmetric. We study the behaviour of generic geodesics and show that the metric is geodesically incomplete. Circle-invariant instantons on the 4-sphere can also be viewed as hyperbolic monopoles, and we interpret our results from this viewpoint. We relate our results to work by Habermann on unframed instantons on the 4-sphere and, in the limit where the radius of the 4-sphere tends to infinity, to results on instantons on Euclidean 4-space.
Generalized Kaehler geometry of instanton moduli spaces
Bursztyn, Henrique; Gualtieri, Marco
2012-01-01
We prove that Hitchin's generalized Kaehler structure on the moduli space of instantons over a compact, even generalized Kaehler four-manifold may be obtained by generalized Kaehler reduction, in analogy with the usual Kaehler case.
Disc instantons in linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Govindarajan, Suresh E-mail: suresh@chaos.iitm.ernet.in; Jayaraman, T. E-mail: jayaram@imsc.ernet.in; Sarkar, Tapobrata E-mail: tapo@theory.tifr.res.in
2002-12-16
We construct a linear sigma model for open-strings ending on special Lagrangian cycles of a Calabi-Yau manifold. We illustrate the construction for the cases considered by Aganagic and Vafa (AV). This leads naturally to concrete models for the moduli space of open-string instantons. These instanton moduli spaces can be seen to be intimately related to certain auxiliary boundary toric varieties. By considering the relevant Gelfand-Kapranov-Zelevinsky (GKZ) differential equations of the boundary toric variety, we obtain the contributions to the world volume superpotential on the A-branes from open-string instantons. By using an ansatz due to Aganagic, Klemm and Vafa (AKV), we obtain the relevant change of variables from the linear sigma model to the non-linear sigma model variables--the open-string mirror map. Using this mirror map, we obtain results in agreement with those of AV and AKV for the counting of holomorphic disc instantons.
An approximate framework for quantum transport calculation with model order reduction
Energy Technology Data Exchange (ETDEWEB)
Chen, Quan, E-mail: quanchen@eee.hku.hk [Department of Electrical and Electronic Engineering, The University of Hong Kong (Hong Kong); Li, Jun [Department of Chemistry, The University of Hong Kong (Hong Kong); Yam, Chiyung [Beijing Computational Science Research Center (China); Zhang, Yu [Department of Chemistry, The University of Hong Kong (Hong Kong); Wong, Ngai [Department of Electrical and Electronic Engineering, The University of Hong Kong (Hong Kong); Chen, Guanhua [Department of Chemistry, The University of Hong Kong (Hong Kong)
2015-04-01
A new approximate computational framework is proposed for computing the non-equilibrium charge density in the context of the non-equilibrium Green's function (NEGF) method for quantum mechanical transport problems. The framework consists of a new formulation, called the X-formulation, for single-energy density calculation based on the solution of sparse linear systems, and a projection-based nonlinear model order reduction (MOR) approach to address the large number of energy points required for large applied biases. The advantages of the new methods are confirmed by numerical experiments.
Chou, Chia-Chun
2017-02-01
The Schrödinger-Langevin equation is approximately solved by propagating individual quantum trajectories for barrier transmission problems. Equations of motion are derived through use of the derivative propagation method, which leads to a hierarchy of coupled differential equations for the amplitude of the wave function and the spatial derivatives of the complex action along each trajectory. Computational results are presented for a one-dimensional Eckart barrier and a two-dimensional system involving either a thick or thin Eckart barrier along the reaction coordinate coupled to a harmonic oscillator. Frictional effects on the trajectory, the transmitted wave packet, and the transmission probability are analyzed.
An Approximate Framework for Quantum Transport Calculation with Model Order Reduction
Chen, Quan; Yam, Chiyung; Zhang, Yu; Wong, Ngai; Chen, Guanhua
2014-01-01
A new approximate computational framework is proposed for computing the non-equilibrium charge density in the context of the non-equilibrium Green's function (NEGF) method for quantum mechanical transport problems. The framework consists of a new formulation, called the X-formulation, for single-energy density calculation based on the solution of sparse linear systems, and a projection-based nonlinear model order reduction (MOR) approach to address the large number of energy points required for large applied biases. The advantages of the new methods are confirmed by numerical experiments.
Quantum mechanics with applications to quarkonium. [Review, WKB approximation, scale invariance
Energy Technology Data Exchange (ETDEWEB)
Quigg, C.; Rosner, J.L.
1979-02-01
Some methods of nonrelativistic quantum mechanics which are particularly useful for studying the variation of bound-state parameters with constituent mass and excitation energy are reviewed. These techniques rely upon elementary scaling arguments and on the semiclassical (WKB) approximation. They are of general interest, but are applied here to the study of bound systems of a heavy quark and antiquark. Properties of the interquark interaction are extracted from information about masses and leptonic widths of the Psi and T families. It is shown how general methods can be applied to the determination of the electric charge of quarks and to the prediction of properties of new families. 113 references.
Gluing an infinite number of instantons
Tsukamoto, Masaki
2007-01-01
This paper is one step toward infinite energy gauge theory and the geometry of infinite dimensional moduli spaces. We generalize a gluing construction in the usual Yang-Mills gauge theory to an ``infinite energy'' situation. We show that we can glue an infinite number of instantons, and that the resulting instantons have infinite energy in general. Moreover we show that they have an infinite dimensional parameter space. Our construction is a generalization of Donaldson's ``alternating method''.
Information loss problem and roles of instantons
Yeom, Dong-han
2016-01-01
In order to understand the information loss problem, non-perturbative effects will do significant roles. Instantons are in general helpful for this purpose. There are various and rich thin-shell instantons and tunneling channels that eventually result a trivial geometry without a singularity nor an event horizon. We further discuss that there are some subtle examples in asymptotic de Sitter cases that need further investigations.
An approximate quantum Cram\\'{e}r--Rao bound based on skew information
Luati, Alessandra
2011-01-01
A closed-form expression for Wigner-Yanase skew information in mixed-state quantum systems is derived. It is shown that limit values of the mixing coefficients exist such that Wigner-Yanase information is equal to Helstrom information. The latter constitutes an upper bound for the classical expected Fisher information, hence the inverse Wigner-Yanase information provides an approximate lower bound to the variance of an unbiased estimator of the parameter of interest. The advantage of approximating Helstrom's sharp bound lies in the fact that Wigner-Yanase information is straightforward to compute, while it is often very difficult to obtain a feasible expression for Helstrom information. In fact, the latter requires the solution of an implicit second order matrix differential equation, while the former requires just scalar differentiation.
Validity of the local self-energy approximation: Application to coupled quantum impurities
Mitchell, Andrew K.; Bulla, Ralf
2015-10-01
We examine the quality of the local self-energy approximation, applied here to models of multiple quantum impurities coupled to an electronic bath. The local self-energy is obtained by solving a single-impurity Anderson model in an effective medium that is determined self-consistently, similar to the dynamical mean-field theory (DMFT) for correlated lattice systems. By comparing to exact results obtained by using the numerical renormalization group, we determine situations where "impurity-DMFT" is able to capture the physics of highly inhomogeneous systems and those cases where it fails. For two magnetic impurities separated in real space, the onset of the dilute limit is captured, but RKKY-dominated interimpurity singlet formation cannot be described. For parallel quantum dot devices, impurity-DMFT succeeds in capturing the underscreened Kondo physics by self-consistent generation of a critical pseudogapped effective medium. However, the quantum phase transition between high- and low-spin states upon tuning interdot coupling cannot be described.
Phantom of the Hartle-Hawking instanton: connecting inflation with dark energy
Energy Technology Data Exchange (ETDEWEB)
Chen, Pisin [National Taiwan University, Leung Center for Cosmology and Particle Astrophysics, Taipei (China); Stanford University, SLAC National Accelerator Laboratory, Kavli Institute for Particle Astrophysics and Cosmology, Stanford, CA (United States); Qiu, Taotao [Central China Normal University, Institute of Astrophysics, Wuhan (China); Yeom, Dong-han [National Taiwan University, Leung Center for Cosmology and Particle Astrophysics, Taipei (China)
2016-02-15
If the Hartle-Hawking wave function is the correct boundary condition of our universe, the history of our universe will be well approximated by an instanton. Although this instanton should be classicalized at infinity, as long as we are observing a process of each history, we may detect a non-classicalized part of field combinations. When we apply it to a dark energy model, this non-classicalized part of fields can be well embedded to a quintessence and a phantom model, i.e., a quintom model. Because of the property of complexified instantons, the phantomness will be naturally free from a big rip singularity. This phantomness does not cause perturbative instabilities, as it is an effect emergent from the entire wave function. Our work may thus provide a theoretical basis for the quintom models, whose equation of state can cross the cosmological constant boundary phenomenologically. (orig.)
Kwato-Njock, K
2002-01-01
A search is conducted for the determination of expectation values of r sup q between Dirac and quasirelativistic radial wave functions in the quantum-defect approximation. The phenomenological and supersymmetry-inspired quantum-defect models which have proven so far to yield accurate results are used. The recursive structure of formulae derived on the basis of the hypervirial theorem enables us to develop explicit relations for arbitrary values of q. Detailed numerical calculations concerning alkali-metal-like ions of the Li-, Na- and Cu-iso electronic sequences confirm the superiority of supersymmetry-based quantum-defect theory over quantum-defect orbital and exact orbital quantum number approximations. It is also shown that relativistic rather than quasirelativistic treatment may be used for consistent inclusion of relativistic effects.
The rainbow instanton method: A new approach to tunneling splitting in polyatomics
Smedarchina, Zorka; Siebrand, Willem; Fernández-Ramos, Antonio
2012-12-01
A new instanton approach is reported to tunneling at zero-temperature in multidimensional (MD) systems in which a "light particle" is transferred between two equivalent "heavy" sites. The method is based on two concepts. The first is that an adequate MD potential energy surface can be generated from input of the stationary configurations only, by choosing as a basis the normal modes of the transition state. It takes the form of a double-minimum potential along the mode with imaginary frequency and coupling terms to the remaining (harmonic) oscillators. Standard integrating out of the oscillators gives rise to an effective 1D instanton problem for the adiabatic potential, but requires evaluation of a nonlocal term in the Euclidean action, governed by exponential (memory) kernels. The second concept is that this nonlocal action can be treated as a "perturbation," for which a new approximate instanton solution is derived, termed the "rainbow" solution. Key to the approach is avoidance of approximations to the exponential kernels, which is made possible by a remarkable conversion property of the rainbow solution. This leads to a new approximation scheme for direct evaluation of the Euclidean action, which avoids the time-consuming search of the exact instanton trajectory. This "rainbow approximation" can handle coupling to modes that cover a wide range of frequencies and bridge the gap between the adiabatic and sudden approximations. It suffers far fewer restrictions than these conventional approximations and is proving particularly effective for systems with strong coupling, such as proton transfer in hydrogen bonds. Comparison with the known exact instanton action in two-dimensional models and application to zero-level tunneling splittings in two isotopomers of malonaldehyde are presented to show the accuracy and efficiency of the approach.
Applications of instantons to hadronic processes
Zetocha, Valeriu Ioan
Instantons constitute an important part of QCD as they provide a way to reach beyond the perturbative region. In the introductory chapters we present the ideas that constitute the backbone of instanton computation on a simple standard integral. We then turn our attention to QCD instantons and briefly show the steps to compute the effective lagrangian. The effective lagrangian is then used as a main tool for studying instanton contributions to hadronic decays of the scalar glueball, the pseudoscalar charmonium state etac, and the scalar charmonium state chic. Hadronic decays of the eta c are of particular interest. The three main decay channels are KK¯pi, etapipi and eta'pipi, each with an unusually large branching ratio of ˜5%. We show that the total decay rate into three pseudoscalar mesons can be reproduced using an instanton size distribution consistent with phenomenology and lattice results. Instantons correctly reproduce the ratio B(etapipi)/ B(eta'pipi) but over-predict the ratio B(KK¯pi)/B(etapipi). In the next part we study the contribution of instantons to OZI violation in the axial-vector channel. We consider, in particular, the f1-a 1 meson splitting, the flavor singlet and triplet axial coupling of a constituent quark, and the axial coupling constant of the nucleon. Instantons provide a short distance contribution to OZI violating correlation functions which is repulsive in the f1 meson channel and adds to the flavor singlet three-point function of a constituent quark. We compute long distance contributions using numerical simulations of the instanton liquid. We find that the iso-vector axial coupling constant of a constituent quark is (g A3)Q = 0.9 and that of a nucleon is g A3 = 1.28, in good agreement with experiment. The flavor singlet coupling of quark is close to one, while that of a nucleon is suppressed gA0 = 0.8. This number is still significantly larger than the experimental value gA0 = (0.28--0.41). In the last part we present an algorithm
Dimension Changing Phase Transitions in Instanton Crystals
Kaplunovsky, Vadim
2013-01-01
We investigate lattices of instantons and the dimension-changing transitions between them. Our ultimate goal is the 3d->4D transition, which is holographically dual to the phase transition between the baryonic and the quarkyonic phases of cold nuclear matter. However, in this paper (just as in [1]) we focus on lower dimensions -- the 1D lattice of instantons in a harmonic potential V M_2^2x_2^2+M_3^2x_2^2+M_4^2x_4^2 and the zigzag-shaped lattice as a first stage of the 1D->2D transition. We prove that in the low- and moderate-density regimes, interactions between the instantons are dominated by two-body forces. This drastically simplifies finding the ground state of the instantons' orientations, so we made a numeric scan of the whole orientation space instead of assuming any particular ansatz. We find that depending on the M_2/M_3/M_4 ratios, the ground state of instanton orientations can follow a wide variety of patterns. For the straight 1D lattices, we found orientations periodically running over elements ...
Montoya-Castillo, Andrés
2016-01-01
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. $\\bf{144}$, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function $\\mathcal{C}_{zz}...
Energy Technology Data Exchange (ETDEWEB)
Fann, G I [Computational Mathematics Group, Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Harrison, R J [Computational Chemical Sciences Group, Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830 (United States); Beylkin, G [Department of Chemistry, University of Tennessee at Knoxville (United States)
2005-01-01
We describe some recent mathematical results in constructing computational methods that lead to the development of fast and accurate multiresolution numerical methods for solving problems in computational chemistry (the so-called multiresolution quantum chemistry). Using low separation rank representations of functions and operators and representations in multiwavelet bases, we developed a multiscale solution method for integral and differential equations and integral transforms. The Poisson equation and the Schrodinger equation, the projector on the divergence free functions, provide important examples with a wide range of applications in computational chemistry, computational electromagnetic and fluid dynamics. We have implemented these ideas that include adaptive representations of operators and functions in the multiwavelet basis and low separation rank approximation of operators and functions. These methods have been implemented into a software package called Multiresolution Adaptive Numerical Evaluation for Scientific Simulation (MADNESS)
Large D-instanton effects in string theory
Pioline, B.; Vandoren, S.J.G.
2009-01-01
By reduction along the time direction, black holes in 4 dimensions yield instantons in 3 dimensions. Each of these instantons contributes individually at order exp(−|Q|/gs) to certain protected couplings in the three-dimensional effective action, but the number of distinct instantons is expected to
Instantons, Twistors, and Emergent Gravity
Heckman, Jonathan J
2011-01-01
Motivated by potential applications to holography on space-times of positive curvature, and by the successful twistor description of scattering amplitudes, we propose a new dual matrix formulation of N = 4 gauge theory on S(4) coupled to 4D gravity. The matrix model is defined by taking the low energy limit of a holomorphic Chern-Simons theory on CP(3|4), in the presence of a large instanton flux. The theory comes with a choice of S(4) radius L and a parameter N controlling the overall size of the matrices. The flat space variant of the 4D effective theory arises by taking the large N scaling limit of the matrix model, with l_pl^2 ~ L^2 / N held fixed. Its massless spectrum contains both spin one and spin two excitations, which we identify with gluons and gravitons. As shown in the companion paper, the matrix model correlation functions of both these excitations correctly reproduce the corresponding MHV scattering amplitudes. We present evidence that the scaling limit defines a gravitational theory with a fin...
The shape of emergent quantum geometry from an N=4 SYM minisuperspace approximation
Berenstein, David
2010-01-01
We study numerically various wave functions in a gauged matrix quantum mechanics of six commuting hermitian $N\\times N$ matrices. Our simulations span ranges of $N$ up to 10000. This system is a truncated and quenched version of N=4 SYM that serves as a minisuperspace approximation to the full ${\\cal N}=4$ SYM system. This setup encodes aspects of the geometry of the AdS dual in terms of joint eigenvalue distributions for the matrices in the large $N$ limit. We analyze the problem of determining geometric measurements from these fluctuating distributions at finite $N$ and how fast they approach to the large N limit. We treat this eigenvalue geometry information as a proxy for geometric calculations in quantum gravity in a description where gravity is an emergent phenomenon. Our results show that care is needed in choosing the observables that measure the geometry: different choices of observables give different answers, have different size fluctuations at finite $N$ and they converge at different rates to the...
Quantum Theory of (H,H{Sub 2}) Scattering: Approximate Treatments of Reactive Scattering
Tang, K. T.; Karplus, M.
1970-10-01
A quantum mechanical study is made of reactive scattering in the (H, H{sub 2}) system. The problem is formulated in terms of a form of the distorted-wave Born approximation (DWBA) suitable for collisions in which all particles have finite mass. For certain incident energies, differential and total cross sections, as well as other attributes of the reactive collisions, (e.g. reaction configuration), are determined. Two limiting models in the DWBA formulation are compared; in one, the molecule is unperturbed by the incoming atom and in the other, the molecule adiabatically follows the incoming atom. For thermal incident energies and semi-empirical interaction potential employed, the adiabatic model seems to be more appropriate. Since the DWBA method is too complicated for a general study of the (H, H{sub 2}) reaction, a much simpler approximation method, the “linear model” is developed. This model is very different in concept from treatments in which the three atoms are constrained to move on a line throughout the collision. The present model includes the full three-dimensional aspect of the collision and it is only the evaluation of the transition matrix element itself that is simplified. It is found that the linear model, when appropriately normalized, gives results in good agreement with that of the DWBA method. By application of this model, the energy dependence, rotational state of dependence and other properties of the total and differential reactions cross sections are determined. These results of the quantum mechanical treatment are compared with the classical calculation for the same potential surface. The most important result is that, in agreement with the classical treatment, the differential cross sections are strongly backward peaked at low energies and shifts in the forward direction as the energy increases. Finally, the implications of the present calculations for a theory of chemical kinetics are discussed.
Instantons and vortices on noncommutative toric varieties
Cirio, Lucio S.; Landi, Giovanni; Szabo, Richard J.
2014-09-01
We elaborate on the quantization of toric varieties by combining techniques from toric geometry, isospectral deformations and noncommutative geometry in braided monoidal categories, and the construction of instantons thereon by combining methods from noncommutative algebraic geometry and a quantized twistor theory. We classify the real structures on a toric noncommutative deformation of the Klein quadric and use this to derive a new noncommutative four-sphere which is the unique deformation compatible with the noncommutative twistor correspondence. We extend the computation of equivariant instanton partition functions to noncommutative gauge theories with both adjoint and fundamental matter fields, finding agreement with the classical results in all instances. We construct moduli spaces of noncommutative vortices from the moduli of invariant instantons, and derive corresponding equivariant partition functions which also agree with those of the classical limit.
Comparison of polynomial approximations to speed up planewave-based quantum Monte Carlo calculations
Parker, William D; Alfè, Dario; Hennig, Richard G; Wilkins, John W
2013-01-01
The computational cost of quantum Monte Carlo (QMC) calculations of realistic periodic systems depends strongly on the method of storing and evaluating the many-particle wave function. Previous work [A. J. Williamson et al., Phys. Rev. Lett. 87, 246406 (2001); D. Alf\\`e and M. J. Gillan, Phys. Rev. B 70, 161101 (2004)] has demonstrated the reduction of the O(N^3) cost of evaluating the Slater determinant with planewaves to O(N^2) using localized basis functions. We compare four polynomial approximations as basis functions -- interpolating Lagrange polynomials, interpolating piecewise-polynomial-form (pp-) splines, and basis-form (B-) splines (interpolating and smoothing). All these basis functions provide a similar speedup relative to the planewave basis. The pp-splines have eight times the memory requirement of the other methods. To test the accuracy of the basis functions, we apply them to the ground state structures of Si, Al, and MgO. The polynomial approximations differ in accuracy most strongly for MgO ...
Direct Approach to Quantum Tunneling
Andreassen, Anders; Farhi, David; Frost, William; Schwartz, Matthew D.
2016-12-01
The decay rates of quasistable states in quantum field theories are usually calculated using instanton methods. Standard derivations of these methods rely in a crucial way upon deformations and analytic continuations of the physical potential and on the saddle-point approximation. While the resulting procedure can be checked against other semiclassical approaches in some one-dimensional cases, it is challenging to trace the role of the relevant physical scales, and any intuitive handle on the precision of the approximations involved is at best obscure. In this Letter, we use a physical definition of the tunneling probability to derive a formula for the decay rate in both quantum mechanics and quantum field theory directly from the Minkowski path integral, without reference to unphysical deformations of the potential. There are numerous benefits to this approach, from nonperturbative applications to precision calculations and aesthetic simplicity.
On the 5d instanton index as a Hilbert series
Energy Technology Data Exchange (ETDEWEB)
Rodríguez-Gómez, Diego, E-mail: d.rodriguez.gomez@uniovi.es [Department of Physics, Universidad de Oviedo, Avda. Calvo Sotelo 18, 33007 Oviedo (Spain); Zafrir, Gabi, E-mail: gabizaf@techunix.technion.ac.il [Department of Physics, Technion, Israel Institute of Technology, Haifa 32000 (Israel)
2014-01-15
The superconformal index for N=2 5d theories contains a non-perturbative part arising from 5d instantonic operators which coincides with the Nekrasov instanton partition function. In this article, for pure gauge theories, we elaborate on the relation between such instanton index and the Hilbert series of the instanton moduli space. We propose a non-trivial identification of fugacities allowing the computation of the instanton index through the Hilbert series. We show the agreement of our proposal with existing results in the literature, as well as use it to compute the exact index for a pure U(1) gauge theory.
Yang-Mills Instanton Sheaves with Arbitrary Topological Charges
Lai, Sheng-Hong; Lai, I-Hsun
2016-01-01
We use a set of ADHM 3-instanton data to systematically construct a class of SU(2) Yang-Mills instanton solutions with arbitrary topological charges. Moreover, by using the biquaternion calculation with biconjugation operation developed recently, these new ADHM data are used to construct a class of SL(2,C) Yang-Mills instanton sheaves on CP^3 with arbitrary topological charges k greater than 3. This result extends the previous construction of Yang-Mills 2-instanton sheaves to arbitrary higher k-instanton sheaves.
Do instantons like a colorful background?
Energy Technology Data Exchange (ETDEWEB)
Gies, H.; Pawlowski, J.M.; Wetterich, C. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; Jaeckel, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2006-08-15
We investigate chiral symmetry breaking and color symmetry breaking in QCD. The effective potential of the corresponding scalar condensates is discussed in the presence of non-perturbative contributions from the semiclassical one-instanton sector. We concentrate on a color singlet scalar background which can describe chiral condensation, as well as a color cotet scalar background which can generate mass for the gluons. Whereas a non-vanishing singlet chiral field is favored by the instantons, we have found no indication for a preference of color octet backgrounds. (orig.)
Instanton corrections to twist-two operators
Alday, Luis F
2016-01-01
We present the calculation of the leading instanton contribution to the scaling dimensions of twist-two operators with arbitrary spin and to their structure constants in the OPE of two half-BPS operators in $\\mathcal N=4$ SYM. For spin-two operators we verify that, in agreement with $\\mathcal N=4$ superconformal Ward identities, the obtained expressions coincide with those for the Konishi operator. For operators with high spin we find that the leading instanton correction vanishes. This arises as the result of a rather involved calculation and requires a better understanding.
Holism, ambiguity and approximation in the logics of quantum computation: a survey
Dalla Chiara, Maria Luisa; Giuntini, Roberto; Leporini, Roberto
2011-01-01
Quantum computation has suggested some new forms of quantum logic (called quantum computational logics), where meanings of sentences are identified with quantum information quantities. This provides a mathematical formalism for an abstract theory of meanings that can be applied to investigate different kinds of semantic phenomena (in social sciences, in medicine, in natural languages and in the languages of art), where both ambiguity and holism play an essential role.
Instantons, Integrability and Discrete Light-Cone Quantisation
Dorey, Nick
2014-01-01
We study supersymmetric quantum mechanics on the moduli space of Yang-Mills instantons on R^2 x T^2 and its application to the discrete light-cone quantisation (DLCQ) of N=4 SUSY Yang-Mills. In the presence of a target space magnetic field, the model has a discrete spectrum with the wavefunctions of generic energy eigenstates supported away from the singular points of the moduli space. The corresponding Hamiltonian is part of an osp(1,1|4) superalgebra which enlarges to su(1,1|4) superconformal invariance in the sector corresponding to the N=4 theory. The Hamiltonian is isospectral to the light-cone dilatation operator of the N=4 theory in this sector. The model also has an interesting scaling limit where it becomes integrable. We determine the semiclassical spectrum in this limit. We discuss a possible approach to constructing the dilatation operator of N=4 supersymmetric Yang-Mills theory in DLCQ.
Instantons and cosmologies in string theory
Collinucci, Giulio
2005-01-01
This thesis deals with problems in two subdomains of string theory that are a priori unrelated, and in the last chapter, links are established between those two. The first topic of research is that of D-instantons. These are mathematical objects that allow one to compute physical effects that are mi
Cosmological D-instantons and cyclic universes
Bergshoeff, EA; Collinucci, A; Roest, D; Russo, JG; Townsend, PK
2005-01-01
For models of gravity coupled to hyperbolic sigma models, such as the metric-scalar sector of IIB supergravity, we show how smooth trajectories in the 'augmented target space' connect FLRW cosmologies to non-extremal D-instantons through a cosmological singularity. In particular, we find closed cycl
Infinite Charge Algebra of Gravitational Instantons
Hoppe, J; Hoppe, Jens
1994-01-01
Using a formalism of minitwistors, we derive infinitely many conserved charges for the $sl(\\infty )$-Toda equation which accounts for gravitational instantons with a rotational Killing symmetry. These charges are shown to form an infinite dimensional algebra through the Poisson bracket which is isomorphic to two dimensional area preserving diffeomorphism with central extentions.
Group-Theoretical Aspects of Instantons
Meyers, C.; Roo, M. de; Sorba, P.
1979-01-01
We discuss the problem of embeddings in non-Abelian gauge theories. The (ir)redueibility of a gauge field configuration is characterized. For the specific case of instanton solutions we derive a practical criterion for SUn. In the general construction of self-dual solutions the reducibility of the
Membrane and fivebrane instantons from quaternionic
Alexandrov, S.; Saueressig, Frank; Vandoren, S.
2007-01-01
We determine the one-instanton corrections to the universal hypermultiplet moduli space coming both from Euclidean membranes and NS-fivebranes wrapping the cycles of a (rigid) Calabi-Yau threefold. These corrections are completely encoded by a single function characterizing a generic four-dimensiona
D-instantons and asymptotic geometries
Bergshoeff, E.; Behrndt, K.
1998-01-01
The large-N limit of D-3-branes is expected to correspond to a superconformal field theory living on the boundary of the anti-de Sitter space appearing in the near-horizon geometry. Dualizing the D-3-brane to a D-instanton, we show that this limit is equivalent to a type IIB S-duality. In both cases
Group-Theoretical Aspects of Instantons
Meyers, C.; Roo, M. de; Sorba, P.
1979-01-01
We discuss the problem of embeddings in non-Abelian gauge theories. The (ir)redueibility of a gauge field configuration is characterized. For the specific case of instanton solutions we derive a practical criterion for SUn. In the general construction of self-dual solutions the reducibility of the g
Instantons and cosmologies in string theory
Collinucci, Giulio
2005-01-01
This thesis deals with problems in two subdomains of string theory that are a priori unrelated, and in the last chapter, links are established between those two. The first topic of research is that of D-instantons. These are mathematical objects that allow one to compute physical effects that are
Magnetic Monopole Content of Hot Instantons
Brower, R C; Negele, John W; Orginos, K; Tan, C I
1999-01-01
We study the Abelian projection of an instanton in $R^3 \\times S^1$ as a function of temperature (T) and non-trivial holonomic twist ($\\omega$) of the Polyakov loop at infinity. These parameters interpolate between the circular monopole loop solution at T=0 and the static 't Hooft-Polyakov monopole/anti-monopole pair at high temperature.
Montoya-Castillo, Andrés; Reichman, David R.
2017-02-01
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Cz z(t ) =Re ⟨σz(0 ) σz(t ) ⟩ , we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.
Directed energy transfer in films of CdSe quantum dots: beyond the point dipole approximation.
Zheng, Kaibo; Žídek, Karel; Abdellah, Mohamed; Zhu, Nan; Chábera, Pavel; Lenngren, Nils; Chi, Qijin; Pullerits, Tõnu
2014-04-30
Understanding of Förster resonance energy transfer (FRET) in thin films composed of quantum dots (QDs) is of fundamental and technological significance in optimal design of QD based optoelectronic devices. The separation between QDs in the densely packed films is usually smaller than the size of QDs, so that the simple point-dipole approximation, widely used in the conventional approach, can no longer offer quantitative description of the FRET dynamics in such systems. Here, we report the investigations of the FRET dynamics in densely packed films composed of multisized CdSe QDs using ultrafast transient absorption spectroscopy and theoretical modeling. Pairwise interdot transfer time was determined in the range of 1.5 to 2 ns by spectral analyses which enable separation of the FRET contribution from intrinsic exciton decay. A rational model is suggested by taking into account the distribution of the electronic transition densities in the dots and using the film morphology revealed by AFM images. The FRET dynamics predicted by the model are in good quantitative agreement with experimental observations without adjustable parameters. Finally, we use our theoretical model to calculate dynamics of directed energy transfer in ordered multilayer QD films, which we also observe experimentally. The Monte Carlo simulations reveal that three ideal QD monolayers can provide exciton funneling efficiency above 80% from the most distant layer. Thereby, utilization of directed energy transfer can significantly improve light harvesting efficiency of QD devices.
Heats of Segregation of BCC Metals Using Ab Initio and Quantum Approximate Methods
Good, Brian; Chaka, Anne; Bozzolo, Guillermo
2003-01-01
Many multicomponent alloys exhibit surface segregation, in which the composition at or near a surface may be substantially different from that of the bulk. A number of phenomenological explanations for this tendency have been suggested, involving, among other things, differences among the components' surface energies, molar volumes, and heats of solution. From a theoretical standpoint, the complexity of the problem has precluded a simple, unified explanation, thus preventing the development of computational tools that would enable the identification of the driving mechanisms for segregation. In that context, we investigate the problem of surface segregation in a variety of bcc metal alloys by computing dilute-limit heats of segregation using both the quantum-approximate energy method of Bozzolo, Ferrante and Smith (BFS), and all-electron density functional theory. In addition, the composition dependence of the heats of segregation is investigated using a BFS-based Monte Carlo procedure, and, for selected cases of interest, density functional calculations. Results are discussed in the context of a simple picture that describes segregation behavior as the result of a competition between size mismatch and alloying effects
Montoya-Castillo, Andrés; Reichman, David R
2017-02-28
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩, we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.
Typicality in Ensembles of Quantum States: Monte Carlo Sampling vs Analytical Approximations
Fresch, Barbara
2009-01-01
Random Quantum States are presently of interest in the fields of quantum information theory and quantum chaos. Moreover, a detailed study of their properties can shed light on some foundational issues of the quantum statistical mechanics such as the emergence of well defined thermal properties from the pure quantum mechanical description of large many body systems. When dealing with an ensemble of pure quantum states, two questions naturally arise: what is the probability density function on the parameters which specify the state of the system in a given ensemble? And, does there exist a most typical value of a function of interest in the considered ensemble? Here two different ensembles are considered: the Random Pure State Ensemble (RPSE) and the Fixed Expectation Energy Ensemble (FEEE). By means of a suitable parameterization of the wave function in terms of populations and phases, we focus on the probability distribution of the populations in such ensembles. A comparison is made between the distribution i...
Energy Technology Data Exchange (ETDEWEB)
Alemgadmi, Khaled I. K., E-mail: azozkied@yahoo.com; Suparmi; Cari [Department of Physics, the State University of Surabaya (Unesa), Jl. Ketintang, Surabaya 60231 (Indonesia); Deta, U. A., E-mail: utamaalan@yahoo.co.id [Departmet of Physics, Sebelas Maret University, Jl. Ir. Sutami 36A Kentingan, Surakarta 57126 (Indonesia)
2015-09-30
The approximate analytical solution of Schrodinger equation for Q-Deformed Rosen-Morse potential was investigated using Supersymmetry Quantum Mechanics (SUSY QM) method. The approximate bound state energy is given in the closed form and the corresponding approximate wave function for arbitrary l-state given for ground state wave function. The first excited state obtained using upper operator and ground state wave function. The special case is given for the ground state in various number of q. The existence of Rosen-Morse potential reduce energy spectra of system. The larger value of q, the smaller energy spectra of system.
Quantum Creation of Topological Black Hole
Wu Zhong Chao
2000-01-01
The constrained instanton method is used to study quantum creation of a vacuum or charged topological black hole. At the WKB level, the relative creation probability is the exponential of a quarter sum of the horizon areas associated with the seed instanton.
Instanton effects on the heavy-quark static potential
Yakhshiev, U. T.; Kim, Hyun-Chul; Turimov, B.; Musakhanov, M. M.; Hiyama, Emiko
2017-08-01
We investigate instanton effects on the heavy-quark potential, including its spin-dependent part, based on the instanton liquid model. Starting with the central potential derived from the instanton vacuum, we obtain the spin-dependent part of the heavy-quark potential. We discuss the results of the heavy-quark potential from the instanton vacuum. Finally, we solve the nonrelativistic two-body problem, associated with the heavy-quark potential from the instanton vacuum. The instanton effects on the quarkonia spectra are marginal but are required for quantitative description of the spectra. Supported by Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Korean government (Ministry of Education, Science and Technology, MEST), Grant Numbers 2016R1D1A1B03935053 (UY) and 2015R1D1A1A01060707 (HChK) and The work was also partly Supported by RIKEN iTHES Project
D-brane Instantons in Type II String Theory
Blumenhagen, Ralph; Kachru, Shamit; Weigand, Timo
2009-01-01
We review recent progress in determining the effects of D-brane instantons in N=1 supersymmetric compactifications of Type II string theory to four dimensions. We describe the abstract D-brane instanton calculus for holomorphic couplings such as the superpotential, the gauge kinetic function and higher fermionic F-terms. This includes a discussion of multi-instanton effects and the implications of background fluxes for the instanton sector. Our presentation also highlights, but is not restricted to the computation of D-brane instanton effects in quiver gauge theories on D-branes at singularities. We then summarize the concrete consequences of stringy D-brane instantons for the construction of semi-realistic models of particle physics or SUSY-breaking in compact and non-compact geometries.
The topology of asymptotically locally flat gravitational instantons
Energy Technology Data Exchange (ETDEWEB)
Etesi, Gabor [Department of Geometry, Mathematical Institute, Faculty of Science, Budapest University of Technology and Economics, Egry J. u. 1 H ep., H-1111 Budapest (Hungary)]. E-mail: etesi@math.bme.hu
2006-10-26
In this Letter we demonstrate that the intersection form of the Hausel-Hunsicker-Mazzeo compactification of a four-dimensional ALF gravitational instanton is definite and diagonalizable over the integers if one of the Kahler forms of the hyper-Kahler gravitational instanton metric is exact. This leads to their topological classification. The proof exploits the relationship between L{sup 2} cohomology and U(1) anti-instantons over gravitational instantons recognized by Hitchin. We then interprete these as reducible points in a singular SU(2) anti-instanton moduli space over the compactification leading to the identification of its intersection form. This observation on the intersection form might be a useful tool in the full geometric classification of various asymptotically locally flat gravitational instantons.
D-brane Instantons in Type II String Theory
Energy Technology Data Exchange (ETDEWEB)
Blumenhagen, Ralph; /Munich, Max Planck Inst.; Cvetic, Mirjam; /Pennsylvania U.; Kachru, Shamit; /Stanford U., Phys. Dept. /SLAC; Weigand, Timo; /SLAC
2009-06-19
We review recent progress in determining the effects of D-brane instantons in N=1 supersymmetric compactifications of Type II string theory to four dimensions. We describe the abstract D-brane instanton calculus for holomorphic couplings such as the superpotential, the gauge kinetic function and higher fermionic F-terms. This includes a discussion of multi-instanton effects and the implications of background fluxes for the instanton sector. Our presentation also highlights, but is not restricted to the computation of D-brane instanton effects in quiver gauge theories on D-branes at singularities. We then summarize the concrete consequences of stringy D-brane instantons for the construction of semi-realistic models of particle physics or SUSY-breaking in compact and non-compact geometries.
D-brane Instantons in Type II String Theory
Energy Technology Data Exchange (ETDEWEB)
Blumenhagen, Ralph; /Munich, Max Planck Inst.; Cvetic, Mirjam; /Pennsylvania U.; Kachru, Shamit; /Stanford U., Phys. Dept. /SLAC; Weigand, Timo; /SLAC
2009-06-19
We review recent progress in determining the effects of D-brane instantons in N=1 supersymmetric compactifications of Type II string theory to four dimensions. We describe the abstract D-brane instanton calculus for holomorphic couplings such as the superpotential, the gauge kinetic function and higher fermionic F-terms. This includes a discussion of multi-instanton effects and the implications of background fluxes for the instanton sector. Our presentation also highlights, but is not restricted to the computation of D-brane instanton effects in quiver gauge theories on D-branes at singularities. We then summarize the concrete consequences of stringy D-brane instantons for the construction of semi-realistic models of particle physics or SUSY-breaking in compact and non-compact geometries.
Instanton contributions to the low-lying hadron mass spectrum
Thomas, Samuel D; Leinweber, Derek B
2014-01-01
The role of instanton-like objects in the QCD vacuum on the mass spectrum of low-lying light hadrons is explored in lattice QCD. Using over-improved stout-link smearing, tuned to preserve instanton-like objects in the QCD vacuum, the evolution of the mass spectrum under smearing is examined. The calculation is performed using a $20^3\\times40$ dynamical fat-link-irrelevant-clover (FLIC) fermion action ensemble with lattice spacing 0.126 fm. Through the consideration of a range of pion masses, the effect of the vacuum instanton content is compared at a common pion mass. While the qualitative features of ground-state hadrons are preserved on instanton-dominated configurations, the excitation spectrum experiences significant changes. The underlying physics revealed shows little similarity to the direct-instanton interaction predictions of the instanton liquid model.
Alexandrov, S.; Pioline, B.; Saueressig, F.; Vandoren, S.J.G.
2009-01-01
Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is an outstanding open problem. We address this issue by relating the quaternionic-Kähler metric on the hypermultiplet moduli space to the complex contact geome
Instanton induced Yukawa couplings from distant E3 and E(-1) instantons
Energy Technology Data Exchange (ETDEWEB)
Goodsell, Mark D. [Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE,F-75005, Paris (France); CNRS, UMR 7589, LPTHE,F-75005, Paris (France); Witkowski, Lukas T. [Institute for Theoretical Physics, University of Heidelberg,Philosophenweg 19, 69120 Heidelberg (Germany)
2016-01-07
We calculate non-perturbative contributions to Yukawa couplings on D3-branes at orbifold singularities due to E3 and fractional E(-1) instantons which do not intersect the visible sector branes. While distant E3 instantons on bulk cycles typically contribute to Yukawa couplings, we find that distant fractional E(-1) can also give rise to new Yukawa couplings. However, fractional E(-1) instantons only induce Yukawa couplings if they are located at a singularity which shares a collapsed homologous two-cycle with the singularity supporting the visible sector. The non-perturbative contributions to Yukawa couplings exhibit a different flavour structure than the tree-level Yukawa couplings and, as a result, they can be sources of flavour violation. This is particularly relevant for schemes of moduli stabilisation which rely on superpotential contributions from E3 instantons, such as KKLT or the Large Volume Scenario. As a byproduct of our analysis, we shed some new light on the properties of annulus diagrams with matter field insertions in stringy instanton calculus.
On the 3-form formulation of axion potentials from D-brane instantons
García-Valdecasas, Eduardo
2016-01-01
The study of axion models and quantum corrections to their potential has experienced great progress by phrasing the axion potential in terms of a 3-form field eating up the 2-form field dual to the axion. Such reformulation of the axion potential has been described for axion monodromy models, and for axion potentials from non-perturbative gauge dynamics. In this paper we propose a 3-form description of the axion potentials from non-gauge D-brane instantons. Interestingly, the required 3-form field does not arise in the underlying geometry, but rather shows up in the KK compactification in the generalized geometry obtained when the backreaction of the D-brane instanton is taken into account.
Dual Quantum Electrodynamics Dyon-Dyon and Charge-Monopole Scattering in a High-Energy Approximation
Gamberg, L P; Gamberg, Leonard; Milton, Kimball A.
2000-01-01
We develop the quantum field theory of electron-point magnetic monopole interactions and more generally, dyon-dyon interactions, based on the original string-dependent ``nonlocal'' action of Dirac and Schwinger. We demonstrate that a viable nonperturbative quantum field theoretic formulation can be constructed that results in a string {\\em independent} cross section for monopole-electron and dyon-dyon scattering. Such calculations can be done only by using nonperturbative approximations such as the eikonal and not by some mutilation of lowest-order perturbation theory.
Instantons and Spin-Flavor effects in Hadron Physics
Kochelev, N I
2008-01-01
We discuss the role of instantons in the spectroscopy of ordinary and exotic hadrons as well as in high energy reactions. We argue that the instanton induced flavor- and spin-dependent quark-quark and quark-gluon interactions can explain many features of the hadron spectrum. The observed anomalous spin and flavor effects in various reactions with hadrons can also be understood within the instanton model for QCD vacuum.
Spin(7)-Instantons, Cayley Submanifolds and Fueter Sections
Walpuski, Thomas
2016-07-01
We prove an existence theorem for Spin(7)-instantons, which are highly concentrated near a Cayley submanifold; thus giving a partial converse to Tian's foundational compactness theorem (Ann Math (2) 151(1):193-268, 2000). As an application, we show how to construct Spin(7)-instantons on Spin(7)-manifolds with suitable local K3 Cayley fibrations. This recovers an example constructed by Lewis (Spin(7) instantons, Ph.D. Thesis, 1998).
d-Brane Instantons in Type II Orientifolds
Blumenhagen, Ralph; Cvetič, Mirjam; Kachru, Shamit; Weigand, Timo
2009-11-01
We review recent progress in determining the effects of d-brane instantons in [Formula: see text] supersymmetric compactifications of Type II string theory to four dimensions. We describe the abstract d-brane instanton calculus for holomorphic couplings such as the superpotential, the gauge kinetic function, and higher fermionic F-terms, and we briefly discuss the implications of background fluxes for the instanton sector. We then summarize the concrete consequences of stringy d-brane instantons for the construction of semirealistic models of particle physics or supersymmetry breaking in compact and noncompact geometries.
Instanton strings and hyper-Kaehler geometry
Dijkgraaf, R
1999-01-01
We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N = (4, 4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS sup 3. We derive a precise map relating the moduli of the K3 type 1113 string compactification to the moduli of these conformal field theories and the corresponding classical hyper-Kahler geometry. We conclude that in the absence of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyper-Kaehler manifolds.
Instanton strings and hyper-Kaehler geometry
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert E-mail: rhd@wins.uva.nl
1999-03-29
We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N = (4, 4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS{sup 3}. We derive a precise map relating the moduli of the K3 type 1113 string compactification to the moduli of these conformal field theories and the corresponding classical hyper-Kahler geometry. We conclude that in the absence of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyper-Kaehler manifolds.
Freezing E3-brane instantons with fluxes
Energy Technology Data Exchange (ETDEWEB)
Bianchi, M.; Martucci, L. [Dipartimento di Fisica, Universita di Roma Tor Vergata (Italy); I.N.F.N., Sezione di Roma Tor Vergata (Italy); Collinucci, A. [Theory Group, Physics Department, CERN, Geneva (Switzerland); Physique Theorique et Mathematique Universite Libre de Bruxelles (Belgium)
2012-07-15
E3-instantons that generate non-perturbative superpotentials in IIB N = 1 compactifications have a much more frequent occurrence than currently believed. Worldvolume fluxes will typically lift the E3-brane geometric moduli and their fermionic superpartners, leaving only the two required universal fermionic zero-modes. We consistently incorporate SL(2,Z) monodromies and world-volume fluxes in the effective theory of the E3-brane fermions and study the resulting zero modes spectrum, highlighting the relation between F-theory and perturbative IIB results. This leads us to a IIB derivation of the index for generation of superpotential terms, which reproduces and generalizes available results. Furthermore, we show how E3 worldvolume fluxes can be explicitly constructed in a one-modulus compactification, such that the instanton has exactly two fermonic zero-modes. This construction is readily applicable to numerous scenarios. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Instanton corrections for m and Ω
Moskovic, Micha; Zein Assi, Ahmad
2017-07-01
In this paper, we study instanton corrections in the N =2⋆ gauge theory by using its description in string theory as a freely-acting orbifold. The latter is used to compute, using the worldsheet, the deformation of the Yang-Mills action. In addition, we calculate the deformed instanton partition function, thus extending the results to the non-perturbative sector of the gauge theory. As we point out, the structure of the deformation is extremely similar to the Ω-deformation, therefore confirming the universality of the construction. Finally, we comment on the realisation of the mass deformation using physical vertex operators by exploiting the equivalence between Scherk-Schwarz deformations and freely-acting orbifolds.
Oscillating Fubini instantons in curved space
Lee, Bum-Hoon; Ro, Daeho; Yeom, Dong-han
2014-01-01
Fubini instanton is a bounce solution which describes the decay of a vacuum state located at the top of the tachyonic potential {\\it via} the tunneling without barrier. We investigate various types of Fubini instantons of a self-gravitating scalar field in a tachyonic quartic potential. With gravity taken into account, we show there exist various types of unexpected solutions including oscillating bounce solutions. In this work, we present numerically oscillating Fubini bounce solutions in de Sitter (dS) and anti-de Sitter (AdS) spaces. We also construct the parametric phase diagrams of the solutions. Of particular significance is that there always exist solutions in all parameter spaces in AdS space. The regions are divided depending on the number of oscillations. On the other hand, dS space allows solutions with codimension-one in parameter spaces. We numerically evaluate semiclassical exponents which give the finite tunneling probabilities.
Two interpretations on thin-shell instantons
Chen, Pisin; Yeom, Dong-han
2015-01-01
For O(4)-symmetric instantons, there are two complementary interpretations for their analytic continuations. One is the nothing-to-something interpretation, where the initial and the final hypersurfaces are disconnected by Euclidean manifolds. The other is the something-to-something interpretation, introduced by Brown and Weinberg, where the initial and the final hypersurfaces are connected by the Euclidean manifold. These interpretations have their own pros and cons and hence these are complementary. In this paper, we consider analytic continuations of thin-shell instantons that have less symmetry, i.e., the spherical symmetry. When we consider the Farhi-Guth-Guven/Fischler-Morgan-Polchinski tunneling, the something-to-something interpretation has been used in the usual literature. On the other hand, we can apply the nothing-to-something interpretation with some limited conditions. We argue that even for both interpretations, we can give the consistent decay rate. As we apply and interpret following the noth...
Instanton Effects in Orbifold ABJM Theory
Honda, Masazumi
2014-01-01
We study the partition function of the orbifold ABJM theory, which is the N=4 necklace quiver Chern-Simons-matter theory with alternating levels, in the Fermi gas formalism. We find that the grand potential of the orbifold ABJM theory is expressed explicitly in terms of that of the ABJM theory. As shown previously, the ABJM grand potential consists of the naive but primary non-oscillatory term and the subsidiary infinitely-replicated oscillatory terms. We find that the subsidiary oscillatory terms of the ABJM theory actually give a non-oscillatory primary term of the orbifold ABJM theory. Also, interestingly, the perturbative part in the ABJM theory results in a novel instanton contribution in the orbifold theory. We also present a physical interpretation for the non-perturbative instanton effects.
Axion cosmology, lattice QCD and the dilute instanton gas
Energy Technology Data Exchange (ETDEWEB)
Borsanyi, S. [Wuppertal Univ. (Germany). Dept. of Physics; Dierigl, M.; Ringwald, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Fodor, Z. [Wuppertal Univ. (Germany). Dept. of Physics; Forschungszentrum Juelich (Germany). Inst. for Advanced Simulation (IAS), Juelich Supercomputing Centre (JSC); Lorand Eoetvoes Univ., Budapest (Hungary). Inst. for Theoretical Physics; Katz, S.D. [Lorand Eoetvoes Univ., Budapest (Hungary). Inst. for Theoretical Physics; MTA-ELTE Lenduelet Lattice Gauge Theory Research Group, Budapest (Hungary); Mages, S.W. [Rgensburg Univ. (Germany); Forschungszentrum Juelich (Germany). Inst. for Advanced Simulation (IAS), Juelich Supercomputing Centre (JSC); Nogradi, D. [Lorand Eoetvoes Univ., Budapest (Hungary). Inst. for Theoretical Physics; MTA-ELTE Lenduelet Lattice Gauge Theory Research Group, Budapest (Hungary); Califonia Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Redondo, J. [Zaragoza Univ. (Spain). Dept. de Fisica Teorica; Max-Planck-Institut fuer Physik, Muenchen (Germany); Szabo, K.K. [Wuppertal Univ. (Germany). Dept. of Physics; Forschungszentrum Juelich (Germany). Inst. for Advanced Simulation (IAS), Juelich Supercomputing Centre (JSC)
2015-08-15
Axions are one of the most attractive dark matter candidates. The evolution of their number density in the early universe can be determined by calculating the topological susceptibility χ(T) of QCD as a function of the temperature. Lattice QCD provides an ab initio technique to carry out such a calculation. A full result needs two ingredients: physical quark masses and a controlled continuum extrapolation from non-vanishing to zero lattice spacings. We determine χ(T) in the quenched framework (infinitely large quark masses) and extrapolate its values to the continuum limit. The results are compared with the prediction of the dilute instanton gas approximation (DIGA). A nice agreement is found for the temperature dependence, whereas the overall normalization of the DIGA result still differs from the non-perturbative continuum extrapolated lattice results by a factor of order ten. We discuss the consequences of our findings for the prediction of the amount of axion dark matter.
Axion cosmology, lattice QCD and the dilute instanton gas
Directory of Open Access Journals (Sweden)
Sz. Borsanyi
2016-01-01
Full Text Available Axions are one of the most attractive dark matter candidates. The evolution of their number density in the early universe can be determined by calculating the topological susceptibility χ(T of QCD as a function of the temperature. Lattice QCD provides an ab initio technique to carry out such a calculation. A full result needs two ingredients: physical quark masses and a controlled continuum extrapolation from non-vanishing to zero lattice spacings. We determine χ(T in the quenched framework (infinitely large quark masses and extrapolate its values to the continuum limit. The results are compared with the prediction of the dilute instanton gas approximation (DIGA. A nice agreement is found for the temperature dependence, whereas the overall normalization of the DIGA result still differs from the non-perturbative continuum extrapolated lattice results by a factor of order ten. We discuss the consequences of our findings for the prediction of the amount of axion dark matter.
Axion cosmology, lattice QCD and the dilute instanton gas
Borsanyi, S; Fodor, Z; Katz, S D; Mages, S W; Nogradi, D; Redondo, J; Ringwald, A; Szabo, K K
2015-01-01
Axions are one of the most attractive dark matter candidates. The evolution of their number density in the early universe can be determined by calculating the topological susceptibility $\\chi(T)$ of QCD as a function of the temperature. Lattice QCD provides an ab initio technique to carry out such a calculation. A full result needs two ingredients: physical quark masses and a controlled continuum extrapolation from non-vanishing to zero lattice spacings. We determine $\\chi(T)$ in the quenched framework (infinitely large quark masses) and extrapolate its values to the continuum limit. The results are compared with the prediction of the dilute instanton gas approximation (DIGA). A nice agreement is found for the temperature dependence, whereas the overall normalization of the DIGA result still differs from the non-perturbative continuum extrapolated lattice results by a factor of order ten. We discuss the consequences of our findings for the prediction of the amount of axion dark matter.
Spiked Instantons from Intersecting D-branes
Nekrasov, Nikita
2016-01-01
The moduli space of spiked instantons that arises in the context of the BPS/CFT correspondence is realised as the moduli space of classical vacua, i.e. low-energy open string field configurations, of a certain stack of intersecting D1-branes and D5-branes in Type IIB string theory. The presence of a constant B-field induces an interesting dynamics involving the tachyon condensation.
Spiked instantons from intersecting D-branes
Directory of Open Access Journals (Sweden)
Nikita Nekrasov
2017-01-01
Full Text Available The moduli space of spiked instantons that arises in the context of the BPS/CFT correspondence [22] is realised as the moduli space of classical vacua, i.e. low-energy open string field configurations, of a certain stack of intersecting D1-branes and D5-branes in Type IIB string theory. The presence of a constant B-field induces an interesting dynamics involving the tachyon condensation.
Instantons on Calabi–Yau cones
Energy Technology Data Exchange (ETDEWEB)
Sperling, Marcus, E-mail: marcus.sperling@itp.uni-hannover.de
2015-12-15
The Hermitian Yang–Mills equations on certain vector bundles over Calabi–Yau cones can be reduced to a set of matrix equations; in fact, these are Nahm-type equations. The latter can be analysed further by generalising arguments of Donaldson and Kronheimer used in the study of the original Nahm equations. Starting from certain equivariant connections, we show that the full set of instanton equations reduce, with a unique gauge transformation, to the holomorphicity condition alone.
Instantons on Calabi–Yau cones
Directory of Open Access Journals (Sweden)
Marcus Sperling
2015-12-01
Full Text Available The Hermitian Yang–Mills equations on certain vector bundles over Calabi–Yau cones can be reduced to a set of matrix equations; in fact, these are Nahm-type equations. The latter can be analysed further by generalising arguments of Donaldson and Kronheimer used in the study of the original Nahm equations. Starting from certain equivariant connections, we show that the full set of instanton equations reduce, with a unique gauge transformation, to the holomorphicity condition alone.
Stringy Instantons and Quiver Gauge Theories
Energy Technology Data Exchange (ETDEWEB)
Florea, Bogdan; Kachru, Shamit; McGreevy, John; Saulina, Natalia
2006-10-24
We explore contributions to the 4D effective superpotential which arise from Euclidean D3 branes (''instantons'') that intersect space-filling D-branes. These effects can perturb the effective field theory on the space-filling branes by nontrivial operators composed of charged matter fields, changing the vacuum structure in a qualitative way in some examples. Our considerations are exemplified throughout by a careful study of a fractional brane configuration on a del Pezzo surface.
Spiked instantons from intersecting D-branes
Nekrasov, Nikita; Prabhakar, Naveen S.
2017-01-01
The moduli space of spiked instantons that arises in the context of the BPS/CFT correspondence [22] is realised as the moduli space of classical vacua, i.e. low-energy open string field configurations, of a certain stack of intersecting D1-branes and D5-branes in Type IIB string theory. The presence of a constant B-field induces an interesting dynamics involving the tachyon condensation.
Quantum trajectories, real, surreal or an approximation to a deeper process?
Hiley, B J; Maroney, O
2000-01-01
The proposal that the one-parameter solutions of the real part of the Schrodinger equation (quantum Hamilton-Jacobi equation) can be regarded as `quantum particle trajectories' has received considerable attention recently. Opinions as to their significance differ. Some argue that they do play a fundamental role as actual particle trajectories, others regard them as mere metaphysical appendages without any physical significance. Recent work has claimed that in some cases the Bohm approach gives results that disagree with those obtained from standard quantum mechanics and, in consequence, with experiment. Furthermore it is claimed that these trajectories have such unacceptable properties that they can only be considered as `surreal'. We re-examine these questions and show that the specific objections raised by Englert, Scully, Sussmann and Walther cannot be sustained. We also argue that contrary to their negative view, these trajectories can provide a deeper insight into quantum processes.
Entropy production in quantum Yang–Mills mechanics in the semiclassical approximation
National Research Council Canada - National Science Library
Tsukiji, Hidekazu; Iida, Hideaki; Kunihiro, Teiji; Ohnishi, Akira; Takahashi, Toru T
2015-01-01
.... We show the efficiency and usefulness of this semiclassical treatment in describing the entropy production of a couple of quantum-mechanical systems, whose classical counter-systems are known to be chaotic...
A direct approach to quantum tunneling
Andreassen, Anders; Frost, William; Schwartz, Matthew D
2016-01-01
The decay rates of quasistable states in quantum field theories are usually calculated using instanton methods. Standard derivations of these methods rely in a crucial way upon deformations and analytic continuations of the physical potential, and on the saddle point approximation. While the resulting procedure can be checked against other semi-classical approaches in some one-dimensional cases, it is challenging to trace the role of the relevant physical scales, and any intuitive handle on the precision of the approximations involved are at best obscure. In this paper, we use a physical definition of the tunneling probability to derive a formula for the decay rate in both quantum mechanics and quantum field theory directly from the Minkowski path integral, without reference to unphysical deformations of the potential. There are numerous benefits to this approach, from non-perturbative applications to precision calculations and aesthetic simplicity.
Jusufi, Kimet
2016-01-01
In the present paper we extend the study of Hawking radiation as a quantum tunneling effect of spin-$1$ particles to the case of a five-dimensional, spherically symmetric, Einstein-Yang-Mills-Gauss-Bonnet (EYMGB) black hole. We solve the Proca equation (PE) by applying the WKB approximation and separation of variables via Hamilton-Jacobi (HJ) equation which results with a set of five differential equations, and reproduce in this way, the Hawking temperature. In the second part of this paper, we extend our results beyond the semiclassical approximation. In particular, we derive the logarithmic correction to the entropy of the EYMGB black hole and show that the quantum corrected specific heat indicates the possible existence of a remnant.
Melton, Cody A
2016-01-01
We compare the fixed-phase approximation with the better known, but closely related fixed-node approximation on several testing examples. We found that both approximations behave very similarly with the fixed-phase results being very close to the fixed-node method whenever nodes/phase were of high and comparable accuracy. The fixed-phase exhibited larger biases when the trial wave functions errors in the nodes/phase were intentionally driven to unrealistically large values. We also present a formalism that enables to describe wave functions with the full antisymmetry in spin-spatial degrees of freedom using our recently developed method for systems with spins as fully quantum variables. This opens new possibilities for simulations of fermionic systems in the fixed-phase approximation formalism.
The Born Approximation and Eikonal Approximation of the Quantum Scattering%量子散射的玻恩近似和程函近似
Institute of Scientific and Technical Information of China (English)
徐中辉; 周祥; 廖昱博
2011-01-01
The theory of scattering is a very important part of the quantum mechanics.The Born approximation and Eikonal approximation of the Scattering cross-section are calculated with the Gauss potential and Lenzjensen potential under a particular incident energy.The results show that the bigger the Electronic energy is,the smaller the total scattering crossection is and the weaker the electron scattering of potential field is.There is little influence of potential to the energetic particle about the Lenz-jensen potential.And the majority of scattered particles are concentrated on a narrow range.%散射理论是量子力学的一项重要内容.在规定的入射能量下,分别给定Gauss位势和Lenz-jensen位势,计算了散射总截面的玻恩近似和程函近似.结果表明对于Gauss位势,电子能量越大,总散射截面越小,势场对电子的散射越弱.对于Lenz-jensen位势,势对高能粒子的影响比较小,大部分散射的粒子集中在小角度范围内.
Single-centered black hole microstate degeneracies from instantons in supergravity
Energy Technology Data Exchange (ETDEWEB)
Murthy, Sameer [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Reys, Valentin [Theory group, Nikhef,Science Park 105, 1098 XG Amsterdam (Netherlands)
2016-04-11
We obtain holographic constraints on the microscopic degeneracies of black holes by computing the exact macroscopic quantum entropy using localization, including the effects of string worldsheet instantons in the supergravity effective action. For (1/4)-BPS black holes in type II string theory on K3×T{sup 2}, the constraints can be explicitly checked against expressions for the microscopic BPS counting functions that are known in terms of certain mock modular forms. We find that the effect of including the infinite sum over instantons in the holomorphic prepotential of the supergravity leads to a sum over Bessel functions with successively sub-leading arguments as in the Rademacher expansion of Jacobi forms — but begins to disagree with such a structure near an order where the mock modular nature becomes relevant. This leads to a systematic method to recover the polar terms of the microscopic degeneracies from the degeneracy of instantons (the Gromov-Witten invariants). We check explicitly that our formula agrees with the known microscopic answer for the first seven values of the magnetic charge invariant.
Approximation of Quantum Stochastic Differential Equations for Input-Output Model Reduction
2016-02-25
ABOVE ADDRESS. Stanford University Office of Sponsored Research 3160 Porter Drive, Suite 100 Palo Alto, CA 94304 -8445 26-Mar-2015 ABSTRACT Number of...Mabuchi, physics colloquium at Univ . of Utah, Salt Lake City, NV, 14 Nov 2013 "Physics with photons: from quantum to bio," H. Mabuchi
Decomposition of fractional quantum Hall model states: product rule symmetries and approximations
Thomale, R.; Estienne, B.; Regnault, N.; Bernevig, B.A.
2011-01-01
We provide a detailed description of a product rule structure of the monomial (Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall (FQH) states derived recently, which we now extend to spin-singlet states. We show that the Haldane-Rezayi spin-singlet state can be obtained
Three Instanton Computations In Gauge Theory And String Theory
Beasley, C E
2005-01-01
We employ a variety of ideas from geometry and topology to perform three new instanton computations in gauge theory and string theory. First, we consider supersymmetric QCD with gauge group SU( Nc) and with Nf flavors. In this theory, it is well known that instantons generate a superpotential if Nf = Nc − 1 and deform the moduli space of supersymmetric vacua if Nf = Nc. We extend these results to supersymmetric QCD with Nf > Nc flavors, for which we show that instantons generate a hierarchy of new, multi- fermion F-terms in the effective action. Second, we revisit the question of which Calabi-Yau compactifications of the heterotic string are stable under worldsheet instanton corrections to the effective space-time superpotential. For instance, compactifications described by (0, 2) linear sigma models are believed to be stable, suggesting a remarkable cancellation among the instanton effects in these theories. We show that this cancellation follows directly from a residue theorem, whose proof relie...
Brizuela, David; Kiefer, Claus; Krämer, Manuel
2016-12-01
We continue our study on corrections from canonical quantum gravity to the power spectra of gauge-invariant inflationary scalar and tensor perturbations. A direct canonical quantization of a perturbed inflationary universe model is implemented, which leads to a Wheeler-DeWitt equation. For this equation, a semiclassical approximation is applied in order to obtain a Schrödinger equation with quantum-gravitational correction terms, from which we calculate the corrections to the power spectra. We go beyond the de Sitter case discussed earlier and analyze our model in the first slow-roll approximation, considering terms linear in the slow-roll parameters. We find that the dominant correction term from the de Sitter case, which leads to an enhancement of power on the largest scales, gets modified by terms proportional to the slow-roll parameters. A correction to the tensor-to-scalar ratio is also found at second order in the slow-roll parameters. Making use of the available experimental data, the magnitude of these quantum-gravitational corrections is estimated. Finally, the effects for the temperature anisotropies in the cosmic microwave background are qualitatively obtained.
Spectral Properties of Schwarzschild Instantons
Jante, Rogelio
2016-01-01
We study spectral properties of the Dirac and scalar Laplace operator on the Euclidean Schwarzschild space, both twisted by a family of abelian connections with anti-self-dual curvature. We show that the zero-modes of the gauged Dirac operator, first studied by Pope, take a particularly simple form in terms of the radius of the Euclidean time orbits, and interpret them in the context of geometric models of matter. For the gauged Laplace operator, we study the spectrum of bound states numerically and observe that it can be approximated with remarkable accuracy by that of the exactly solvable gauged Laplace operator on the Euclidean Taub-NUT space.
Aharonov, D; Eban, E; Landau, Z; Aharonov, Dorit; Arad, Itai; Eban, Elad; Landau, Zeph
2007-01-01
In the first 36 pages of this paper, we provide polynomial quantum algorithms for additive approximations of the Tutte polynomial, at any point in the Tutte plane, for any planar graph. This includes as special cases the AJL algorithm for the Jones polynomial, the partition function of the Potts model for any weighted planer graph at any temperature, and many other combinatorial graph properties. In the second part of the paper we prove the quantum universality of many of the problems for which we provide an algorithm, thus providing a large set of new quantum-complete problems. Unfortunately, we do not know that this holds for the Potts model case; this is left as an important open problem. The main progress in this work is in our ability to handle non-unitary representations of the Temperley Lieb algebra, both when applying them in the algorithm, and, more importantly, in the proof of universality, when encoding quantum circuits using non-unitary operators. To this end we develop many new tools, that allow ...
Self-consistent treatment of v-groove quantum wire band structure in no parabolic approximation
Directory of Open Access Journals (Sweden)
Crnjanski Jasna V.
2004-01-01
Full Text Available The self-consistent no parabolic calculation of a V-groove-quantum-wire (VQWR band structure is presented. A comparison with the parabolic flat-band model of VQWR shows that both, the self-consistency and the nonparabolicity shift sub band edges, in some cases even in the opposite directions. These shifts indicate that for an accurate description of inter sub band absorption, both effects have to be taken into the account.
Zlatanov, Kaloyan N.; Vitanov, Nikolay V.
2017-07-01
The common objective of the application of adiabatic techniques in the field of quantum control is to transfer a quantum system from one discrete energy state to another. These techniques feature both high efficiency and insensitivity to variations in the experimental parameters, e.g., variations in the driving field amplitude, duration, frequency, and shape, as well as fluctuations in the environment. Here we explore the potential of adiabatic techniques for creating arbitrary predefined coherent superpositions of two quantum states. We show that an equally weighted coherent superposition can be created by temporal variation of the ratio between the Rabi frequency Ω (t ) and the detuning Δ (t ) from 0 to ∞ (case 1) or vice versa (case 2), as it is readily deduced from the explicit adiabatic solution for the Bloch vector. We infer important differences between cases 1 and 2 in the composition of the created coherent superposition: The latter depends on the dynamical phase of the process in case 2, while it does not depend on this phase in case 1. Furthermore, an arbitrary coherent superposition of unequal weights can be created by using asymptotic ratios of Ω (t )/Δ (t ) different from 0 and ∞ . We supplement the general adiabatic solution with analytic solutions for three exactly soluble models: two trigonometric models and the hyperbolic Demkov-Kunike model. They allow us not only to demonstrate the general predictions in specific cases but also to derive the nonadiabatic corrections to the adiabatic solutions.
Instantons and Donaldson-Thomas invariants
Energy Technology Data Exchange (ETDEWEB)
Cirafici, M. [Institute for Theoretical Physics and Spinoza Institute, Utrecht University (Netherlands); Department of Physics, University of Patras, Patras (Greece); Sinkovics, A. [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge (United Kingdom); Szabo, R.J. [Department of Mathematics, Heriot-Watt University and Maxwell Institute for Mathematical Sciences, Riccarton, Edinburgh (United Kingdom)
2008-08-05
We review some recent progress in understanding the relation between a six dimensional topological Yang-Mills theory and the enumerative geometry of Calabi-Yau threefolds. The gauge theory localizes on generalized instanton solutions and is conjecturally equivalent to Donaldson-Thomas theory. We evaluate the partition function of the U(N) theory in its Coulomb branch on flat space by employing equivariant localization techniques on its noncommutative deformation. Geometrically this corresponds to a higher dimensional generalization of the ADHM formalism. This formalism can be extended to a generic toric Calabi-Yau. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
Instanton Strings and HyperKaehler Geometry
Dijkgraaf, R.
1998-01-01
We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N=(4,4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS_3. We derive a precise map relating the moduli of the K3 type IIB string compactification to the moduli of these conformal field theories and the corresponding classical hyperkaehler geometry. We conclude that, in the absense of background gauge fields, the metric on ...
Instantons and Massless Fermions in Two Dimensions
Callan, C. G. Jr.; Dashen, R.; Gross, D. J.
1977-05-01
The role of instantons in the breakdown of chiral U(N) symmetry is studied in a two dimensional model. Chiral U(1) is always destroyed by the axial vector anomaly. For N = 2 chiral SU(N) is also spontaneously broken yielding massive fermions and three (decoupled) Goldstone bosons. For N greater than or equal to 3 the fermions remain massless. Realistic four dimensional theories are believed to behave in a similar way but the critical N above which the fermions cease to be massive is not known in four dimensions.
On field theory quantization around instantons
Anselmi, D
2009-01-01
With the perspective of looking for experimentally detectable physical applications of the so-called topological embedding, a procedure recently proposed by the author for quantizing a field theory around a non-discrete space of classical minima (instantons, for example), the physical implications are discussed in a ``theoretical'' framework, the ideas are collected in a simple logical scheme and the topological version of the Ginzburg-Landau theory of superconductivity is solved in the intermediate situation between type I and type II superconductors.
String instantons, fluxes and moduli stabilization
Camara, P G; Maillard, T; Pradisi, G
2007-01-01
We analyze a class of dual pairs of heterotic and type I models based on freely-acting $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$ orbifolds in four dimensions. Using the adiabatic argument, it is possible to calculate non-perturbative contributions to the gauge coupling threshold corrections on the type I side by exploiting perturbative calculations on the heterotic side, without the drawbacks due to twisted moduli. The instanton effects can then be combined with closed-string fluxes to stabilize most of the moduli fields of the internal manifold, and also the dilaton, in a racetrack realization of the type I model.
A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics
Gingold, H.
1991-01-01
A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.
Banks, Tom
2008-09-01
1. Introduction; 2. Quantum theory of free scalar fields; 3. Interacting field theory; 4. Particles of spin one, and gauge invariance; 5. Spin 1/2 particles and Fermi statistics; 6. Massive quantum electrodynamics; 7. Symmetries, Ward identities and Nambu Goldstone bosons; 8. Non-abelian gauge theory; 9. Renormalization and effective field theory; 10. Instantons and solitons; 11. Concluding remarks; Appendices; References; Index.
Alam, Mohosin; Mandal, Swapan; Wahiddin, Mohamed Ridza
2017-09-01
The essence of the rotating wave approximation (RWA) is to eliminate the non-conserving energy terms from the interaction Hamiltonian. The cost of using RWA is heavy if the frequency of the input radiation field is low (e.g. below optical region). The well known Bloch-Siegert effect is the out come of the inclusion of the terms which are normally neglected under RWA. We investigate the fluctuations of the quantum phase of the coherent light and the thermal light coupled to a nondegenerate parametric oscillator (NDPO). The Hamiltonian and hence the equations of motion involving the signal and idler modes are framed by using the strong (classical) pump condition. These differential equations are nonlinear in nature and are found coupled to each other. Without using the RWA, we obtain the analytical solutions for the signal and idler fields. These solutions are obtained up to the second orders in dimensionless coupling constants. The analytical expressions for the quantum phase fluctuation parameters due to Carruther's and Nieto are obtained in terms of the coupling constants and the initial photon numbers of the input radiation field. Moreover, we keep ourselves confined to the Pegg-Barnett formalism for measured phase operators. With and without using the RWA, we compare the quantum phase fluctuations for coherent and thermal light coupled to the NDPO. In spite of the significant departures (quantitative), the qualitative features of the phase fluctuation parameters for the input thermal light are identical for NDPO with and without RWA. On the other hand, we report some interesting results of input coherent light coupled to the NDPO which are substantially different from their RWA counterpart. In spite of the various quantum optical phenomena in a NDPO, we claim that it is the first effort where the complete analytical approach towards the solutions and hence the quantum phase fluctuations of input radiation fields coupled to it are obtained beyond rotating wave
Schmidtke, Daniel; Gemmer, Jochen
2016-01-01
Closed quantum systems obey the Schrödinger equation, whereas nonequilibrium behavior of many systems is routinely described in terms of classical, Markovian stochastic processes. Evidently, there are fundamental differences between those two types of behavior. We discuss the conditions under which the unitary dynamics may be mapped onto pertinent classical stochastic processes. This is first principally addressed based on the notions of "consistency" and "Markovianity." Numerical data are presented that show that the above conditions are to good approximation fulfilled for Heisenberg-type spin models comprising 12-20 spins. The accuracy to which these conditions are met increases with system size.
Instanton Counting and Chern-Simons Theory
Energy Technology Data Exchange (ETDEWEB)
Kashani-Poor, Amir-Kian
2003-02-06
The instanton partition function of N = 2, D = 4 SU(2) gauge theory is obtained by taking the field theory limit of the topological open string partition function, given by a Chern-Simons theory, of a CY3-fold. The CY3-fold on the open string side is obtained by geometric transition from local IP{sup 1} x IP{sup 1} which is used in the geometric engineering of the SU(2) theory. The partition function obtained from the Chern-Simons theory agrees with the closed topological string partition function of local IP{sup 1} x IP{sup 1} proposed recently by Nekrasov. We also obtain the partition functions for local F{sub 1} and F{sub 2} CY3-folds and show that the topological string amplitudes of all three local Hirzebruch surfaces give rise to the same field theory limit. It is shown that a generalization of the topological closed string partition function whose field theory limit is the generalization of the instanton partition function, proposed by Nekrasov, can be determined easily from the Chern-Simons theory.
Coherent states, quantum gravity, and the Born- Oppenheimer approximation. II. Compact Lie groups
Stottmeister, Alexander; Thiemann, Thomas
2016-07-01
In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Additionally, we conjecture the existence of a new form of the Segal-Bargmann-Hall "coherent state" transform for compact Lie groups G, which we prove for G = U(1)n and support by numerical evidence for G = SU(2). The reason for conjoining this conjecture with the main topic of this article originates in the observation that the coherent state transform can be used as a basic building block of a coherent state quantisation (Berezin quantisation) for compact Lie groups G. But, as Weyl and Berezin quantisation for ℝ2d are intimately related by heat kernel evolution, it is natural to ask whether a similar connection exists for compact Lie groups as well. Moreover, since the formulation of space adiabatic perturbation theory requires a (deformation) quantisation as minimal input, we analyse the question to what extent the coherent state quantisation, defined by the Segal-Bargmann-Hall transform, can serve as basis of the former.
On the instanton-induced portion of the nucleon strangeness
Klabucar, D; Melic, B; Picek, I
1999-01-01
We calculate the instanton contribution to the proton strangeness in the MIT bag enriched by the presence of a dilute instanton liquid. The evaluation is based on expressing the nucleon matrix elements of bilinear strange quark operators in terms of a model valence nucleon state and interactions producing quark-antiquark fluctuations on top of that valence state. Our method combines the usage of the evolution operator containing a strangeness source, and the Feynman-Hellmann theorem. The method allows a unified approach to the strangeness in different channels. Only the scalar channel is found to be affected by instantons.
On the creation of the universe via ekpyrotic instantons
Directory of Open Access Journals (Sweden)
Lorenzo Battarra
2015-03-01
Full Text Available We present a new class of complex instantons in the context of ekpyrotic cosmological theories. These instantons, which satisfy the “no-boundary” boundary conditions, describe the emergence of a classical, contracting universe out of nothing. The ekpyrotic attractor is essential in guaranteeing an evolution towards a real, Lorentzian history of the universe. In the context of the no-boundary proposal, the relative probability for such ekpyrotic histories compared to inflationary ones is very high – in fact, assuming a bounce can be successfully incorporated, these new instantons currently describe the most likely origin of the universe.
An Instanton Picture O.P.E. Condensate?
Boucaud, P; Donini, Andrea; Leroy, J P; Le Yaouanc, A; Micheli, J; Moutarde, H; Pène, O; Rodríguez-Quintero, J; Boucaud, Ph.
2002-01-01
Gluon two- and three-point Green Functions computed in Landau gauge from the lattice show the existence of power corrections to the purely perturbative expressions, that can be explained through an Operator Product Expansion as the influence of a non gauge invariant mass dimension two condensate. The relationship of this condensate with topological properties of QCD, namely instantons, will be studied, giving a first estimate of the contribution of instantons to this condensate based in the direct lattice measure, after a cooling process, of the instanton liquid properties.
On the Creation of the Universe via Ekpyrotic Instantons
Battarra, Lorenzo
2014-01-01
We present a new class of complex instantons in the context of ekpyrotic cosmological theories. These instantons, which satisfy the "no-boundary" boundary conditions, describe the emergence of a classical, contracting universe out of nothing. The ekpyrotic attractor is essential in guaranteeing an evolution towards a real, Lorentzian history of the universe. In the context of the no-boundary proposal, the relative probability for such ekpyrotic histories compared to inflationary ones is very high -- in fact, assuming a bounce can be incorporated, these new instantons currently describe the most likely origin of the universe.
Homogeneous Field and WKB Approximation In Deformed Quantum Mechanics with Minimal Length
Tao, Jun; Yang, Haitang
2012-01-01
In the framework of the deformed quantum mechanics with minimal length, we consider the motion of a non-relativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up to $\\mathcal{O}(\\beta)$. We also show that, if the slope of the potential at a turning point is too steep, the WKB connection formula fall apart around the turning point.
Directed Energy Transfer in Films of CdSe Quantum Dots: Beyond the Point Dipole Approximation
DEFF Research Database (Denmark)
Zheng, Kaibo; Zídek, Karel; Abdellah, Mohamed
2014-01-01
Understanding of Förster resonance energy transfer (FRET) in thin films composed of quantum dots (QDs) is of fundamental and technological significance in optimal design of QD based optoelectronic devices. The separation between QDs in the densely packed films is usually smaller than the size...... dynamics of directed energy transfer in ordered multilayer QD films, which we also observe experimentally. The Monte Carlo simulations reveal that three ideal QD monolayers can provide exciton funneling efficiency above 80% from the most distant layer. Thereby, utilization of directed energy transfer can...... ultrafast transient absorption spectroscopy and theoretical modeling. Pairwise interdot transfer time was determined in the range of 1.5 to 2 ns by spectral analyses which enable separation of the FRET contribution from intrinsic exciton decay. A rational model is suggested by taking into account...
Ramos, E.; Silva-Valencia, J.; Franco, R.; Siqueira, E. C.; Figueira, M. S.
2015-11-01
We study the spin-current Seebeck effect through an immersed gate defined quantum dot, employing the U-finite atomic method for the single impurity Anderson model. Our description qualitatively confirms some of the results obtained by an earlier Hartree-Fock work, but as our calculation includes the Kondo effect, some new features will appear in the spin-current Seebeck effect S, which as a function of the gate voltage present an oscillatory shape. At intermediate temperatures, our results show a three zero structure and at low temperatures, our results are governed by the emergence of the Kondo peak in the transmittance, which defines the behavior of the shape of the S coefficient as a function of the parameters of the model. The oscillatory behavior obtained by the Hartree-Fock approximation reproduces the shape obtained by us in a non-interacting system (U=0). The S sign is sensitive to different polarization of the quantum dot, and as a consequence the device could be employed to experimentally detect the polarization states of the system. Our results also confirm that the large increase of S upon increasing U, obtained by the mean field approximation, is correct only for low temperatures. We also discuss the role of the Kondo peak in defining the behavior of the spin thermopower at low temperatures.
Pineiro Orioli, Asier; Berges, Juergen; Signoles, Adrien; Schempp, Hanna; Whitlock, Shannon; Weidemueller, Matthias; Safavi-Naini, Arghavan; Wall, Michael; Schachenmayer, Johannes; Rey, Ana Maria
2016-05-01
Accurate description of the dynamics of quantum spin models is a theoretically challenging problem with widespread applications ranging from condensed matter to high-energy physics. Furthermore recent experimental progress in AMO experiments allows for the physical realization of these models in a variety of setups, such as Rydberg systems and trapped ion experiments, with an unprecedented degree of control and flexibility. Therefore, it is vital to develop efficient theoretical methods capable of simulating the many-body dynamics of such systems. In this work, we employ and extend the recently developed discrete Truncated Wigner Approximation (dTWA), an approximation based on the phase space description of quantum mechanics, to compute the dynamics of two types of spin models: the long-range XY model, which can be realized with Rydberg atoms, and a coupled spin-boson model, which is relevant to trapped ion experiments. Comparisons to experimental results and to available exact solutions to benchmark the method show that the dTWA is capable of capturing important features of the spin evolution and can also help uncovering some underlying non-equilibrium processes.
Brizuela, David; Kraemer, Manuel
2016-01-01
We continue our study on corrections from canonical quantum gravity to the power spectra of gauge-invariant inflationary scalar and tensor perturbations. A direct canonical quantization of a perturbed inflationary universe model is implemented, which leads to a Wheeler-DeWitt equation. For this equation, a semiclassical approximation is applied in order to obtain a Schroedinger equation with quantum-gravitational correction terms, from which we calculate the corrections to the power spectra. We go beyond the de Sitter case discussed earlier and analyze our model in the first slow-roll approximation, considering terms linear in the slow-roll parameters. We find that the dominant correction term from the de Sitter case, which leads to an enhancement of power on the largest scales, gets modified by terms proportional to the slow-roll parameters. A correction to the tensor-to-scalar ratio is also found at second order in the slow-roll parameters. Making use of the available experimental data, the magnitude of the...
Induced wormholes due to quantum effects of spherically reduced matter in large N approximation
Nojiri, S; Odintsov, S D; Osetrin, K E
1999-01-01
Using one-loop effective action in large N and s-wave approximation we discuss the possibility to induce primordial wormholes at the early Universe. An analytical solution is found for self-consistent primordial wormhole with constant radius. Numerical study gives the wormhole solution with increasing throat radius and red-shift function which first increases and then decreases. This may indicate the possibility of a topological phase transition.
Milošević, D. B.; Becker, W.
2016-06-01
A theory of above-threshold ionization of atoms by a strong laser field is formulated. Two versions of the strong-field approximation (SFA) are considered, the direct SFA and the improved SFA, which do not and do, respectively, take into account rescattering of the freed electron off the parent ion. The atomic bound state is included in two different ways: as an expansion in terms of Slater-type orbitals or as an asymptotic wave function. Even though we are using the single-active-electron approximation, multielectron effects are taken into account in two ways: by a proper choice of the ground state and by an adequate definition of the ionization rate. For the case of the asymptotic bound-state wave functions, using the saddle-point method, a simple expression for the T -matrix element is derived for both the direct and the improved SFA. The theory is applied to ionization by a bicircular field, which consists of two coplanar counterrotating circularly polarized components with frequencies that are integer multiples of a fundamental frequency ω . Special emphasis is on the ω -2 ω case. In this case, the threefold rotational symmetry of the field carries over to the velocity map of the liberated electrons, for both the direct and the improved SFA. The results obtained are analyzed in detail using the quantum-orbit formalism, which gives good physical insight into the above-threshold ionization process. For this purpose, a specific classification of the saddle-point solutions is introduced for both the backward-scattered and the forward-scattered electrons. The high-energy backward-scattering quantum orbits are similar to those discovered for high-order harmonic generation. The short forward-scattering quantum orbits for a bicircular field are similar to those of a linearly polarized field. The conclusion is that these orbits are universal, i.e., they do not depend much on the shape of the laser field.
Accelerated nuclear quantum effects sampling with open path integrals
Mazzola, Guglielmo
2016-01-01
We numericaly demonstrate that, in double well models, the autocorrelation time of open path integral Monte Carlo simulations can be much smaller compared to standard ones using ring polymers. We also provide an intuitive explanation based on the role of instantons as transition states of the path integral pseudodynamics. Therefore we propose that, in all cases when the ground state approximation to the finite temperature partition function holds, open path integral simulations can be used to accelerate the sampling in realistic simulations aimed to explore nuclear quantum effects.
Semiconductor quantum wells with BenDaniel-Duke boundary conditions: approximate analytical results
Barsan, Victor; Ciornei, Mihaela-Cristina
2017-01-01
The Schrödinger equation for a particle moving in a square well potential with BenDaniel-Duke boundary conditions is solved. Using algebraic approximations for trigonometric functions, the transcendental equations of the bound states energy are transformed into tractable, algebraic equations. For the ground state and the first excited state, they are cubic equations; we obtain simple formulas for their physically interesting roots. The case of higher excited states is also analysed. Our results have direct applications in the physics of type I and type II semiconductor heterostructures.
Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length
Directory of Open Access Journals (Sweden)
Jun Tao
2015-01-01
Full Text Available In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up to Oβ2. We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point. The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method. We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length.
Quantum Dynamics of Dark and Dark-Bright Solitons beyond the Mean-Field Approximation
Krönke, Sven; Schmelcher, Peter
2014-05-01
Dark solitons are well-known excitations in one-dimensional repulsively interacting Bose-Einstein condensates, which feature a characteristical phase-jump across a density dip and form stability in the course of their dynamics. While these objects are stable within the celebrated Gross-Pitaevskii mean-field theory, the situation changes dramatically in the full many-body description: The condensate being initially in a dark soliton state dynamically depletes and the density notch fills up with depleted atoms. We analyze this process in detail with a particular focus on two-body correlations and the fate of grey solitons (dark solitons with finite density in the notch) and thereby complement the existing results in the literature. Moreover, we extend these studies to mixtures of two repulsively interacting bosonic species with a dark-bright soliton (dark soliton in one component filled with localized atoms of the other component) as the initial state. All these many-body quantum dynamics simulations are carried out with the recently developed multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB).
Dodin, Amro; Brumer, Paul
2015-01-01
We present closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter $\\zeta=\\frac{1}{2}(\\gamma_1+\\gamma_2)/\\Delta_p$, where $\\gamma_i$ are the radiative decay rates of the excited levels $i=1,2$, and $\\Delta_p=\\sqrt{\\Delta^2 + (1-p^2)\\gamma_1\\gamma_2}$ depends on the excited-state level splitting $\\Delta>0$ and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit ($\\zeta\\gg1$), approach a long-lived quasi-steady state in the overdamped limit ($\\zeta\\ll 1$), and display an intermediate behavior at critical damping ($\\zeta= 1$). The sudden incoherent turn-on generat...
Brown, Sandra E
2014-01-01
Free energy differences $\\Delta F:=F-F_{\\text{prism}}$ are computed for several isomers of water hexamer relative to the "prism" isomer using the self-consistent phonons method. %$\\Delta F:=F-F({prism})$ We consider the isotope effect defined by the quantity $\\delta F_{D_2O}:=\\Delta F_{\\rm D_2O}-\\Delta F_{\\rm H_2O}$, and the quantum effect, $\\delta F_{\\hbar=0}:=\\Delta F_{\\hbar=0}-\\Delta F_{\\rm H_2O}$, and evaluate them using different flexible water models. While both $\\delta F_{D_2O}$ and $\\delta F_{\\hbar=0}$ are found to be rather small for all of the potentials, they are especially small for two of the empirical models, q-TIP4P/F and TTM3-F, compared to q-SPC/Fw and the two {\\it abinitio}-based models, WHBB and HBB2-pol. This qualitative difference in the properties of different water models cannot be explained by one being "more accurate" than the other. We speculate as to whether the observed anomalies are caused by the special properties of water systems, or are an artifact of either the potential energ...
Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution
Energy Technology Data Exchange (ETDEWEB)
Kovchegov, Yuri V., E-mail: kovchegov.1@osu.edu [Department of Physics, The Ohio State University, Columbus, OH 43210 (United States); Sievert, Matthew D., E-mail: msievert@bnl.gov [Bldg. 510A, Physics Department, Brookhaven National Laboratory, Upton, NY 11973 (United States)
2016-02-15
We set up a formalism for calculating transverse-momentum-dependent parton distribution functions (TMDs) of a large nucleus using the tools of saturation physics. By generalizing the quasi-classical Glauber–Gribov–Mueller/McLerran–Venugopalan approximation to allow for the possibility of spin–orbit coupling, we show how any TMD can be calculated in the saturation framework. This can also be applied to the TMDs of a proton by modeling it as a large “nucleus.” To illustrate our technique, we calculate the quark TMDs of an unpolarized nucleus at large-x: the unpolarized quark distribution and the quark Boer–Mulders distribution. We observe that spin–orbit coupling leads to mixing between different TMDs of the nucleus and of the nucleons. We then consider the evolution of TMDs: at large-x, in the double-logarithmic approximation, we obtain the Sudakov form factor. At small-x the evolution of unpolarized-target quark TMDs is governed by BK/JIMWLK evolution, while the small-x evolution of polarized-target quark TMDs appears to be dominated by the QCD Reggeon.
Calculating TMDs of an Unpolarized Target: Quasi-Classical Approximation and Quantum Evolution
Kovchegov, Yuri V
2016-01-01
We set up a formalism for calculating transverse-momentum-dependent parton distribution functions (TMDs) using the tools of saturation physics. By generalizing the quasi-classical Glauber-Gribov-Mueller/McLerran-Venugopalan approximation to allow for the possibility of spin-orbit coupling, we show how any TMD can be calculated in the saturation framework. This can also be applied to the TMDs of a proton by modeling it as a large "nucleus." To illustrate our technique, we calculate the quark TMDs of an unpolarized nucleus at large-x: the unpolarized quark distribution and the quark Boer-Mulders distribution. We observe that spin-orbit coupling leads to mixing between different TMDs of the nucleus and of the nucleons. We then consider the evolution of TMDs: at large-x, in the double-logarithmic approximation, we obtain the Sudakov form factor. At small-x the evolution of unpolarized-target quark TMDs is governed by BK/JIMWLK evolution, while the small-x evolution of polarized-target quark TMDs appears to be dom...
A new look at instantons and large- N limit
Azeyanagi, Tatsuo; Hanada, Masanori; Honda, Masazumi; Matsuo, Yoshinori; Shiba, Shotaro
2014-05-01
We analyze instantons in the very strongly coupled large- N limit ( N → ∞ with g 2 fixed) of large- N gauge theories, where the effect of the instantons remains finite. By using the exact partition function of four-dimensional = 2* gauge theories as a concrete example, we demonstrate that each instanton sector in the very strongly coupled large- N limit is related to the one in the 't Hooft limit ( N → ∞ with g 2 N fixed) through a simple analytic continuation. Furthermore we show the equivalence between the instanton partition functions of a pair of large- N gauge theories related by an orbifold projection. This can open up a new way to analyze the partition functions of low/non-supersymmetric theories. We also discuss implication of our result to gauge/gravity dualities for M-theory as well as a possible application to large- N QCD.
A new look at instantons and large-N limit
Azeyanagi, Tatsuo; Honda, Masazumi; Matsuo, Yoshinori; Shiba, Shotaro
2013-01-01
We analyze instantons in the very strongly coupled large-$N$ limit ($N\\to\\infty$ with $g^2$ fixed) of large-$N$ gauge theories, where the effect of the instantons remains finite. By using the exact partition function of four-dimensional ${\\cal N}=2^*$ gauge theories as a concrete example, we demonstrate that each instanton sector in the very strongly coupled large-$N$ limit is related to the one in the 't Hooft limit ($N\\to\\infty$ with $g^2N$ fixed) through a simple analytic continuation. Furthermore we show the equivalence between the instanton partition functions of a pair of large-$N$ gauge theories related by an orbifold projection. This can open up a new way to analyze the partition functions of low/non-supersymmetric theories. We also discuss implication of our result to gauge/gravity dualities for M-theory as well as a possible application to large-$N$ QCD.
D-instantons in Klebanov-Witten model
Imaanpur, Ali
2016-01-01
We study D-instanton solutions in type IIB supergravity on $AdS_5\\times T^{1,1}$, which has a dual ${\\cal N}=1$ $SU(N)\\times SU(N)$ super Yang-Mills theory. Apart from ordinary D(-1)-brane instantons, we discuss wrapped D1-branes over minimal 2-cycles and derive explicit solutions preserving half the supersymmetries. These solutions are identified with Yang-Mills instantons which are (anti)self-dual in both gauge group factors with instanton charge $(k,k')$. By examining the boundary behaviour of the solutions we discuss the coupling to the corresponding dual boundary operators, and identify their vacuum expectation values. We also discuss the boundary terms and compute the action for these solutions.
Quark Propagation in the Instantons of Lattice QCD
Trewartha, Daniel; Leinweber, Derek; Roberts, Dale S
2013-01-01
We quantitatively examine the extent to which instanton degress of freedom, contained within standard Monte-carlo generated gauge-field configurations, can maintain the characteristic features of the mass and renormalisation functions of the non-perturbative quark propagator. We use over-improved stout-link smearing to isolate instanton effects on the lattice. Using a variety of measures, we illustrate how gauge fields consisting almost solely of instanton-like objects are produced after only 50 sweeps of smearing. We find a full vacuum, with a packing fraction more than three times larger than phenomenological models predict. We calculate the overlap quark propagator on these smeared configurations, and find that even at high levels of smearing the majority of the characteristic features of the propagator are reproduced. We thus conclude that instantons contained within standard Monte-carlo generated gauge-field configurations are the degrees of freedom responsible for the dynamical generation of mass observ...
Scattering of instantons, monopoles and vortices in higher dimensions
Ivanova, Tatiana A
2016-01-01
We consider Yang-Mills theory on manifolds ${\\mathbb R}\\times X$ with a $d$-dimensional Riemannian manifold $X$ of special holonomy admitting gauge instanton equations. Instantons are considered as particle-like solutions in $d+1$ dimensions whose static configurations are concentrated on $X$. We study how they evolve in time when considered as solutions of the Yang-Millsequations on ${\\mathbb R}\\times X$ with moduli depending on time $t\\in{\\mathbb R}$. It is shown that in the adiabatic limit, when the metric in the $X$ direction is scaled down, the classical dynamics of slowly moving instantons corresponds to a geodesic motion in the moduli space $\\cal M$ of gauge instantons on $X$. Similar results about geodesic motion in the moduli space of monopoles and vortices in higher dimensions are briefly discussed.
Instanton effects in ABJM theory from Fermi gas approach
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie; Tokyo Institute of Technology (Japan). Dept. of Physics; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst.; Nagoya Univ. (Japan). Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2012-11-19
We study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k=1, 2, 3, 4, 6 up to N=44, 20, 18, 16, 14 respectively, and extract non-perturbative corrections from these exact results. Fitting the resulting non-perturbative corrections by their expected forms from the Fermi gas, we determine unknown parameters in them. After separating the oscillating behavior of the grand potential, which originates in the periodicity of the grand partition function, and the worldsheet instanton contribution, which is computed from the topological string theory, we succeed in proposing an analytical expression for the leading D2-instanton correction. Just as the perturbative result, the instanton corrections to the partition function are expressed in terms of the Airy function.
Instantons and quark zero modes in AdS/QCD
DEFF Research Database (Denmark)
Bechi, Jacopo
2009-01-01
In this paper the quark zero modes creation effect is studied in the context of the AdS/QCD approach. This effect is generated, in presence of instantons, by a new that can be added in the bulk.......In this paper the quark zero modes creation effect is studied in the context of the AdS/QCD approach. This effect is generated, in presence of instantons, by a new that can be added in the bulk....
Temperature-based Instanton Analysis: Identifying Vulnerability in Transmission Networks
Energy Technology Data Exchange (ETDEWEB)
Kersulis, Jonas [Univ. of Michigan, Ann Arbor, MI (United States); Hiskens, Ian [Univ. of Michigan, Ann Arbor, MI (United States); Chertkov, Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Backhaus, Scott N. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Bienstock, Daniel [Columbia Univ., New York, NY (United States)
2015-04-08
A time-coupled instanton method for characterizing transmission network vulnerability to wind generation fluctuation is presented. To extend prior instanton work to multiple-time-step analysis, line constraints are specified in terms of temperature rather than current. An optimization formulation is developed to express the minimum wind forecast deviation such that at least one line is driven to its thermal limit. Results are shown for an IEEE RTS-96 system with several wind-farms.
Missing Yang-Mills instantons on ALE spaces
Hartnoll, S A; Hartnoll, Sean A.; Portugues, Ruben
2002-01-01
We derive an expression for the dimension of the moduli space of SU(n) $k$-instantons on an r-centred ALE metric in terms of the triple $(n,k,r)$. It is shown that if $k \\bmod r > n$ then no $k$-instantons exist. This implies that the corresponding Higgs branch of vacua representing marginally bound D$p$-D$(p+4)$ branes on an ALE background is zero dimensional.
Chaotic and regular instantons in helical shell models of turbulence
De Pietro, Massimo; Biferale, Luca
2016-01-01
Shell models of turbulence have a finite-time blowup, i.e. the enstrophy diverges while the single shell velocities stay finite, in the inviscid limit. The signature of this blowup is represented by self-similar instantonic structures traveling coherently through the inertial range. These solutions might influence the energy transfer and the anomalous scaling properties empirically observed for the forced and viscous models. In this paper we present a study of the instantonic solutions for a class of shell-models of turbulence based on the exact decomposition of the Navier-Stokes equations in helical eigenstates. We found that depending on the helical structure of the shell interactions instantons are chaotic or regular. Some instantonic solutions tend to recover mirror symmetry for scales small enough. All models that have anomalous scaling develop regular non-chaotic instantons. Vice-versa, models that have mean field non-anomalous scaling in the stationary regime are those that have chaotic instantons. Fin...
Bartók, Albert P.
Due to their aesthetic value and high compressive strength, dentists are utilizing ceramics as a material of choice for dental restorations. Among ceramics, zirconia provides high toughness and crack resistance. Residual stresses develop in processing due to factors including coefficient of thermal expansion mismatch, geometry, and grain anisotropy. In the present study, advanced methods were adapted including polychromatic X-ray (Laue) micro-diffraction, which provided grain orientation and residual stresses, and monochromatic diffraction in the sin-squared-psi mode. Analysis tools for both methods were developed to provide grain averaged and grain specific material properties on clinically relevant specimens. Large type II residual stress variations ranging from - 1 to + 1 GPa were observed between grains. Most grains in monolithic zirconia have a mean compressive deviatoric stress of 70 MPa, depending on direction. Another important part of the study was the interface residual stresses which occur at the interface of a base/core region of a dental restoration and the veneer. Type I residual stresses as high as 800 MPa were observed at the interface. A detailed analysis of the effects of simulated mouth motion impact fatigue cycling on the residual stress states revealed significant relaxation of the residual stress from 800 MPa to around 150 MPa within 45,000 cycles. Results from the sin-squared-psi; residual stress measurement technique revealed significantly higher tensile stresses in the zirconia core. Equivelant to approximately one year's service, 45,000 fatigue cycles at a load of 150N led to fracture of the porcelain veneer cusp. Residual stress at the site of fracture indicates relaxation of residual stress. At the interface, stress induced phase transformation of zirconia forming monoclinic phase was observed. Residual stresses can promote crack growth and thereby catastrophic failure. These results have implications for all materials particularly
Nucleon-nucleon interaction with one-pion exchange and instanton-induced interactions
Vanamali, C. S.; Kumar, K. B. Vijaya
2016-11-01
Singlet (S10) and triplet (S31) nucleon-nucleon potentials are obtained in the framework of the SU(2) nonrelativistic quark model using the resonating-group method in the Born-Oppenheimer approximation. The full Hamiltonian used in the investigation includes the kinetic energy, two-body confinement potential, one-gluon-exchange potential (OGEP), one-pion exchange potential (OPEP), and instanton induced interaction (III), which includes the effect of quark exchange between the nucleons. The contribution of the OGEP, III, and OPEP to the nucleon-nucleon adiabatic potential is discussed.
COLOR SUPERCONDUCTIVITY, INSTANTONS AND PARITY (NON?)-CONSERVATION AT HIGH BARYON DENSITY-VOLUME 5.
Energy Technology Data Exchange (ETDEWEB)
GYULASSY,M.
1997-11-11
This one day Riken BNL Research Center workshop was organized to follow-up on the rapidly developing theoretical work on color super-conductivity, instanton dynamics, and possible signatures of parity violation in strong interactions that was stimulated by the talk of Frank Wilczek during the Riken BNL September Symposium. The workshop was held on November 11, 1997 at the center with over 30 participants. The program consisted of four talks on theory in the morning followed by two talks in the afternoon by experimentalists and open discussion. Krishna Rajagopal (MIT) first reviewed the status of the chiral condensate calculations at high baryon density within the instanton model and the percolation transition at moderate densities restoring chiral symmetry. Mark Alford (Princeton) then discussed the nature of the novel color super-conducting diquark condensates. The main result was that the largest gap on the order of 100 MeV was found for the 0{sup +} condensate, with only a tiny gap << MeV for the other possible 1{sup +}. Thomas Schaefer (INT) gave a complete overview of the instanton effects on correlators and showed independent calculations in collaboration with Shuryak (SUNY) and Velkovsky (BNL) confirming the updated results of the Wilczek group (Princeton, MIT). Yang Pang (Columbia) addressed the general question of how breaking of discrete symmetries by any condensate with suitable quantum numbers could be searched for experimentally especially at the AGS through longitudinal A polarization measurements. Nicholas Samios (BNL) reviewed the history of measurements on {Lambda} polarization and suggested specific kinematical variables for such analysis. Brian Cole (Columbia) showed recent E910 measurements of {Lambda} production at the AGS in nuclear collisions and focused on the systematic biases that must be considered when looking for small symmetry breaking effects. Lively discussions led by Robert Jaffe (MIT) focused especially on speculations on the still
ALE spaces from noncommutative U(1) instantons via exact Seiberg-Witten map
Salizzoni, M; Yang, H S; Salizzoni, Mario; Torrielli, Alessandro; Yang, Hyun Seok
2006-01-01
The exact Seiberg-Witten (SW) map of a noncommutative (NC) gauge theory gives the commutative equivalent as an ordinary gauge theory coupled to a field dependent effective metric. We study instanton solutions of this commutative equivalent whose self-duality equation turns out to be the exact SW map of NC instantons. We derive general differential equations governing U(1) instantons and we explicitly get an exact solution corresponding to the single NC instanton. Remarkably the effective metric induced by the single U(1) instanton is the Eguchi-Hanson metric - the simplest gravitational instanton. Surprisingly the instanton number is not quantized but depends on an integration constant. Our result confirms the expected non-perturbative breakdown of the SW map. However, the breakdown of the map arises in a consistent way: The instanton number plays the role of a parameter giving rise to a one-parameter family of Eguchi-Hanson metrics.
Backreacting D-brane instantons on branes at singularities
García-Valdecasas Tenreiro, Eduardo; Uranga, Angel
2017-08-01
Non-perturbative D-brane instanton effects in 4d N=1 string compactifications can be geometrized in terms of a backreacted generalized geometry. We extend earlier results to setups in which the D-brane instanton is charged under the 4d gauge symmetries, and show that the backreacted topology yields the correct charged field theory operators in the 4d effective action. In type IIA models with D6-branes, the backreaction of D2-brane instantons forces the recombination of D6-branes, such that the 4d charged field theory operators arise from basic worldsheet instantons in the backreacted geometry. We provide large classes of examples of D2-brane instanton effects on intersecting D6-brane systems in local models mirror to D3-branes at singularities. The backreacted geometry and the field theory operators are easily encoded in terms of simple operations in the graphs arising from the underlying dimer diagrams. This description agrees, in the appropriate cases, with the complex deformations triggered by certain fractional branes at the bottom of duality cascades.
Non-extremal D-instantons and the AdS/CFT correspondence
Bergshoeff, E.; Collinucci, A.; Ploegh, A.; Vandoren, S.; Riet, T. van
2005-01-01
We investigate non-extremal D-instantons in an asymptotically AdS5 × S5 background and the role they play in the AdS5/CFT4 correspondence. We find that the holographic dual operators of non-extremal D-instanton configurations do not correspond to self-dual Yang-Mills instantons, and we compute
The Cascade is a MMS Instanton
Evslin, J
2004-01-01
Wrap m D5-branes around the 2-cycle of a conifold, place n D3-branes at a point and watch the system relax. The D5-branes source m units of RR 3-form flux on the 3-cycle, which cause dielectric NS5-branes to nucleate and repeatedly sweep out the 3-cycle, each time gaining m units of D3-charge while the stack of D5-branes loses m units of D3-charge. A similar description of the Klebanov-Strassler cascade has been proposed by Kachru, et al. when m>>m-n. Using the T-dual MQCD we argue that the above process occurs for any m and n and in particular may continue for more than one step. The nonbaryonic roots of the SQCD vacua lead to new cascades because, for example, the 3-cycle swept does not link all of the D5's. This decay is the S-dual of a MMS instanton, which is the decay into flux of a brane that is trivial in twisted K-theory. This provides the first evidence for the S-dual of the K-theory classification that does not itself rely upon any strong/weak duality.
Status Report on the Instanton Counting
Directory of Open Access Journals (Sweden)
Sergey Shadchin
2006-01-01
Full Text Available The non-perturbative behavior of the N = 2 supersymmetric Yang-Mills theories is both highly non-trivial and tractable. In the last three years the valuable progress was achieved in the instanton counting, the direct evaluation of the low-energy effective Wilsonian action of the theory. The localization technique together with the Lorentz deformation of the action provides an elegant way to reduce functional integrals, representing the effective action, to some finite dimensional contour integrals. These integrals, in their turn, can be converted into some difference equations which define the Seiberg-Witten curves, the main ingredient of another approach to the non-perturbative computations in the N = 2 super Yang-Mills theories. Almost all models with classical gauge groups, allowed by the asymptotic freedom condition can be treated in such a way. In my talk I explain the localization approach to the problem, its relation to the Seiberg-Witten approach and finally I give a review of some interesting results.
Chiral symmetry breaking, instantons, and monopoles
Di Giacomo, Adriano
2015-01-01
The purpose of this study is to show that monopoles induce the chiral symmetry breaking. In order to indicate the evidence, we add one pair of monopoles with magnetic charges to the quenched SU(3) configurations by a monopole creation operator, and investigate the propaties of the chiral symmetry breaking using the Overlap fermion. We show that instantons are created by the monopoles. The pseudoscalar meson mass and decay constant are computed from the correlation functions, and the renormalization constant $Z_{S}$ is determined by the non perturbative method. The renormalization group invariant chiral condensate in $\\overline{\\mbox{MS}}$-scheme at 2 [GeV] is evaluated by the Gell-Mann-Oakes-Renner formula, and the random matrix theory. Finally, we estimate the renormalization group invariant quark masses $\\bar{m} = (m_{u} + m_{d})/2$, and $m_{s}$ in $\\overline{\\mbox{MS}}$-scheme at 2 [GeV]. The preliminary results indicate that the chiral condensate decreases and the quark masses become slightly heavy by inc...
Macroscopic Quantum Coherence in Magnetic Molecular Clusters
Institute of Scientific and Technical Information of China (English)
JIN Yan-Hong; NIE Yi-Hang; LIANG Jiu-Qing; PU Fu-Cho
2001-01-01
The oscillation of tunnel splitting in Fes molecular clusters is obtained as a function of magnetic field applied along the hard axis by means of the instanton method with both semiclassical treatment and the effective potential field description of the quantum spin system. The theoretical splittings of the instanton method are compared with the numerical result by diagonalization of spin Hamiltonian operators and experimental observations. By taking the appropriate parameters, our theoretical formula yields a result the same as the experimental observation.
Van Gorder, Robert A.
2016-05-01
Very recent experimental work has demonstrated the existence of Kelvin waves along quantized vortex filaments in superfluid helium. The possible configurations and motions of such filaments is of great physical interest, and Svistunov previously obtained a Hamiltonian formulation for the dynamics of quantum vortex filaments in the low-temperature limit under the assumption that the vortex filament is essentially aligned along one axis, resulting in a two-dimensional (2D) problem. It is standard to approximate the dynamics of thin filaments by employing the local induction approximation (LIA), and we show that by putting the two-dimensional LIA into correspondence with the first equation in the integrable Wadati-Konno-Ichikawa-Schimizu (WKIS) hierarchy, we immediately obtain solutions to the two-dimensional LIA, such as helix, planar, and self-similar solutions. These solutions are obtained in a rather direct manner from the WKIS equation and then mapped into the 2D-LIA framework. Furthermore, the approach can be coupled to existing inverse scattering transform results from the literature in order to obtain solitary wave solutions including the analog of the Hasimoto one-soliton for the 2D-LIA. One large benefit of the approach is that the correspondence between the 2D-LIA and the WKIS allows us to systematically obtain vortex filament solutions directly in the Cartesian coordinate frame without the need to solve back from curvature and torsion. Implications of the results for the physics of experimentally studied solitary waves, Kelvin waves, and postvortex reconnection events are mentioned.
Light adjoint quarks in the instanton-dyon liquid model. IV.
Liu, Yizhuang; Shuryak, Edward; Zahed, Ismail
2016-11-01
We discuss the instanton-dyon liquid model with Nf Majorana quark flavors in the adjoint representation of color S Uc(2 ) at finite temperature. We briefly recall the index theorem on S1×R3 for twisted adjoint fermions in a Bogomolny-Prasad-Sommerfeld (BPS) dyon background of arbitrary holonomy and use the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction to derive the adjoint antiperiodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with Nf light and antiperiodic adjoint quarks. We develop the model in details by mapping the theory on a three-dimensional quantum effective theory with adjoint quarks with manifest S U (Nf)×Z4 Nf symmetry. Using a mean-field analysis at weak coupling and strong screening, we show that center symmetry requires the spontaneous breaking of chiral symmetry, which is shown to only take place for Nf=1 . For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry through S U (Nf)×Z4 Nf→O (Nf). As the liquid dilutes with increasing temperature, center symmetry and chiral symmetry are restored. We present numerical and analytical estimates for the transition temperatures.
Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV
Liu, Yizhuang; Zahed, Ismail
2016-01-01
We discuss the instanton-dyon liquid model with $N_f$ Majorana quark flavors in the adjoint representation of color $SU_c(2)$ at finite temperature. We briefly recall the index theorem on $S^1\\times R^3$ for twisted adjoint fermions in a BPS dyon background of arbitrary holonomy, and use the ADHM construction to explicit the adjoint anti-periodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with $N_f$ light and anti-periodic adjoint quarks. We develop the model in details by mapping the theory on a 3-dimensional quantum effective theory with adjoint quarks with manifest $SU(N_f)\\times Z_{4N_f}$ symmetry. Using a mean-field analysis at weak coupling and strong screening, we show that center symmetry requires the spontaneous breaking of chiral symmetry, which is shown to only take place for $N_f=1$. For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry through $SU(N_f)\\times Z_{4N...
Raymond and instantons: some recollections and the use of ADHM
Altes, Chris P Korthals
2016-01-01
After the discovery of the BRST identities in 1974 Raymond spent some two years mostly on instantons. In those years we had a small group at the Centre Physique Th\\'eorique in Marseille discussing the physics and mathematics of instantons. The upshot of our discussions can be found in a set of lectures given by Raymond in Erice in 1977 and a year later in a Physics Reports volume. I present some recollections of that period; mostly how we were influenced by the twistor approach. I discuss the Atiyah-Drinfeld-Hitchin-Manin (ADHM) method to obtain instantons ("calorons") in thermal QCD following earlier work. The building blocks are a prepotential and a gauge invariant propagator. Then I will give surprisingly simple results in terms of these building blocks for the one loop vacuum response to a change in caloron parameters and some physical consequences for the effective action, in particular screening properties.
The instanton method and its numerical implementation in fluid mechanics
Grafke, Tobias; Schäfer, Tobias
2015-01-01
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to...
Instanton superpotentials, Calabi-Yau geometry, and fibrations
Anderson, Lara B.; Apruzzi, Fabio; Gao, Xin; Gray, James; Lee, Seung-Joo
2016-04-01
In this paper we explore contributions to nonperturbative superpotentials arising from instantons wrapping effective divisors in smooth Calabi-Yau fourfolds. We concentrate on the case of manifolds constructed as complete intersections in products of projective spaces or generalizations thereof. We systematically investigate the structure of the cone of effective (algebraic) divisors in the fourfold geometries and employ the same tools recently developed by Anderson et al. [arXiv:1507.03235] to construct more general instanton geometries than have previously been considered in the literature. We provide examples of instanton configurations on Calabi-Yau manifolds that are elliptically and K 3 fibered and explore their consequences in the context of string dualities. The examples discussed include manifolds containing infinite families of divisors with arithmetic genus, χ (D ,OD)=1 , and superpotentials exhibiting modular symmetry.
On Instanton Superpotentials, Calabi-Yau Geometry, and Fibrations
Anderson, Lara B; Gao, Xin; Gray, James; Lee, Seung-Joo
2015-01-01
In this paper we explore contributions to non-perturbative superpotentials arising from instantons wrapping effective divisors in Calabi-Yau four-folds. We concentrate on the case of manifolds constructed as complete intersections in products of projective spaces (CICYs) or generalizations thereof (gCICYs). We investigate the structure of the cone of effective (algebraic) divisors in the four-fold geometries and employ the same tools recently developed in arXiv:1507.03235 to construct more general instanton geometries than have previously been considered in the literature. We provide examples of instanton configurations on Calabi-Yau manifolds that are elliptically and $K3$-fibered and explore their consequences in the context of string dualities. The examples discussed include manifolds containing infinite families of divisors with arithmetic genus, $\\chi(D, \\mathcal{O}_D)=1$ and superpotentials exhibiting modular symmetry.
On instanton effects in the operator product expansion
Alday, Luis F
2016-01-01
We revisit the computation of instanton effects to various correlation functions in ${\\cal N}=4$ SYM and clarify a controversy existing in the literature regarding their consistency with the OPE and conformal symmetry. To check these properties, we examine the conformal partial wave decomposition of four-point correlators involving combinations of half-BPS and Konishi operators and isolate the contribution from the conformal primary scalar operators of twist four. We demonstrate that the leading instanton correction to this contribution is indeed consistent with conformal symmetry and compute the corresponding corrections to the OPE coefficients and the scaling dimensions of such twist-four operators. Our analysis justifies the regularization procedure used to compute ultraviolet divergent instanton contribution to correlation functions involving unprotected operators.
Zoology of instanton solutions in flat potential barriers
Battarra, Lorenzo; Lehners, Jean-Luc
2013-01-01
We perform a detailed study of the existence and the properties of O(4)-invariant instanton solutions in Einstein-scalar theory in the presence of flat potential barriers, i.e. barriers where the second derivative of the potential is small at the top of the barrier. We find a whole zoo of solutions: Hawking-Moss, Coleman-De Luccia (CdL), oscillating instantons, asymmetric CdL as well as other non-standard CdL-like solutions with additional negative modes in their spectrum of fluctuations. Our work shows how these different branches of solutions are connected to each other via "critical" instantons possessing an extra zero mode fluctuation. Overall, the space of finite action euclidean solutions to these theories with flat barriers is surprisingly rich and intricate.
Raymond and instantons: Some recollections and the use of ADHM
Korthals Altes, Chris P.
2016-11-01
After the discovery of the BRST identities in 1974 Raymond spent some two years mostly on instantons. In those years we had a small group at the Centre Physique Théorique in Marseille discussing the physics and mathematics of instantons. The upshot of our discussions can be found in a set of lectures given by Raymond in Erice in 1977 and a year later in a Physics Reports volume. I present some recollections of that period; mostly how we were influenced by the twistor approach. I discuss the Atiyah-Drinfeld-Hitchin-Manin (ADHM) method to obtain instantons ("calorons") in thermal QCD following earlier work. The building blocks are a prepotential and a gauge invariant propagator. Then I will give surprisingly simple results in terms of these building blocks for the one loop vacuum response to a change in caloron parameters and some physical consequences for the effective action.
Raymond and instantons: Some recollections and the use of ADHM
Directory of Open Access Journals (Sweden)
Chris P. Korthals Altes
2016-11-01
Full Text Available After the discovery of the BRST identities in 1974 Raymond spent some two years mostly on instantons. In those years we had a small group at the Centre Physique Théorique in Marseille discussing the physics and mathematics of instantons. The upshot of our discussions can be found in a set of lectures given by Raymond in Erice in 1977 and a year later in a Physics Reports volume. I present some recollections of that period; mostly how we were influenced by the twistor approach. I discuss the Atiyah–Drinfeld–Hitchin–Manin (ADHM method to obtain instantons (“calorons” in thermal QCD following earlier work. The building blocks are a prepotential and a gauge invariant propagator. Then I will give surprisingly simple results in terms of these building blocks for the one loop vacuum response to a change in caloron parameters and some physical consequences for the effective action.
Algebraic deformations of toric varieties II. Noncommutative instantons
Cirio, Lucio; Szabo, Richard J
2011-01-01
We continue our study of the noncommutative algebraic and differential geometry of a particular class of deformations of toric varieties, focusing on aspects pertinent to the construction and enumeration of noncommutative instantons on these varieties. We develop a noncommutative version of twistor theory, which introduces a new example of a noncommutative four-sphere. We develop a braided version of the ADHM construction and show that it parametrizes a certain moduli space of framed torsion free sheaves on a noncommutative projective plane. We use these constructions to explicitly build instanton gauge bundles with canonical connections on the noncommutative four-sphere that satisfy appropriate anti-selfduality equations. We construct projective moduli spaces for the torsion free sheaves and demonstrate that they are smooth. We define equivariant partition functions of these moduli spaces, finding that they coincide with the usual instanton partition functions for supersymmetric gauge theories on C^2.
Quaternionic Kahler Manifolds, Constrained Instantons and the Magic Square: I
Dasgupta, Keshav; Wissanji, Alisha
2007-01-01
The classification of homogeneous quaternionic manifolds has been done by Alekseevskii, Wolf et al using transitive solvable group of isometries. These manifolds are not generically symmetric, but there is a subset of quaternionic manifolds that are symmetric and Einstein. A further subset of these manifolds are the magic square manifolds. We show that all the symmetric quaternionic manifolds including the magic square can be succinctly classified by constrained instantons. These instantons are mostly semilocal, and their constructions for the magic square can be done from the corresponding Seiberg-Witten curves for certain N = 2 gauge theories that are in general not asymptotically free. Using these, we give possible constructions, such as the classical moduli space metrics, of constrained instantons with exceptional global symmetries. We also discuss the possibility of realising the Kahler manifolds in the magic square using other solitonic configurations in the theory, and point out an interesting new sequ...
Instanton dynamics in finite temperature QCD via holography
Directory of Open Access Journals (Sweden)
Masanori Hanada
2015-10-01
Full Text Available We investigate instantons in finite temperature QCD via Witten's holographic QCD. To study the deconfinement phase, we use the setup proposed in [1]. We find that the sizes of the instantons are stabilized at certain values both in the confinement and deconfinement phases. This agrees with the numerical result in the lattice gauge theory. Besides we find that the gravity duals of the large and small instantons in the deconfinement phase have different topologies. We also argue that the fluctuation of the topological charges is large in confinement phase while it is exponentially suppressed in deconfinement phase, and a continuous transition occurs at the Gross–Witten–Wadia (GWW point. It would be difficult to observe the counterpart of this transition in lattice QCD, since the GWW point in QCD may stay at an unstable branch.
D3-instantons, Mock Theta Series and Twistors
Alexandrov, Sergei; Manschot, Jan; Pioline, Boris
2012-01-01
The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2,Z). We prove that this is the case in the one-i...
Instantons and surface tension at a first-order transition
Gupta, Sourendu
1994-04-01
We study the dynamics of the first-order phase transition in the two-dimensional 15-state Potts model, both at and off equilibrium. We find that phase changes take place through nucleation in both cases, and finite volume effects are described well through an instanton computation. Thus a dynamical measurement of the surface tension is possible. We find that the order-disorder surface tension is compatible with perfect wetting. An accurate treatment of fluctuations about the instanton solution is seen to be of great importance. Current Address: Theory Group, TIFR, Homi Bhabha Road, Bombay 400005, India.
Resumming instantons in N=2* theories with arbitrary gauge groups
Billò, M; Fucito, F; Lerda, A; Morales, J F
2016-01-01
We discuss the modular anomaly equation satisfied by the the prepotential of 4-dimensional N=2* theories and show that its validity is related to S-duality. The recursion relations that follow from the modular anomaly equation allow one to write the prepotential in terms of (quasi)-modular forms, thus resumming the instanton contributions. These results can be checked against the microscopic multi-instanton calculus in the case of classical algebras, but are valid also for the exceptional E6, E7, E8, F4 and G2 algebras, where direct computations are not available.
Institute of Scientific and Technical Information of China (English)
ZHANG Yejin; CHEN Weiyou; LIU Caixia; LIU Shiyong
2001-01-01
We have used Harrison′s model and anisotropic parabolic approximation to calculate band structure of In1-x-yGayAlxAs compressively strained quantum well. For design of 1.55 μm wavelength lasers, well widths for the possible compositions are presented. A useful empirical formula is given.
Isaacson, D.; Marchesin, D.; Paes-Leme, P. J.
1980-01-01
This paper is an expanded version of a talk given at the 1979 T.I.C.O.M. conference. It is a self-contained introduction, for applied mathematicians and numerical analysts, to quantum mechanics and quantum field theory. It also contains a brief description of the authors' numerical approach to the problems of quantum field theory, which may best be summarized by the question; Can we compute the eigenvalues and eigenfunctions of Schrodinger operators in infinitely many variables.
Energy Technology Data Exchange (ETDEWEB)
Van Gorder, Robert A., E-mail: Robert.VanGorder@maths.ox.ac.uk [Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG (United Kingdom)
2015-09-15
In a recent paper, we give a study of the purely rotational motion of general stationary states in the two-dimensional local induction approximation (2D-LIA) governing superfluid turbulence in the low-temperature limit [B. Svistunov, “Superfluid turbulence in the low-temperature limit,” Phys. Rev. B 52, 3647 (1995)]. Such results demonstrated that variety of stationary configurations are possible from vortex filaments exhibiting purely rotational motion in addition to commonly discussed configurations such as helical or planar states. However, the filaments (or, more properly, waves along these filaments) can also exhibit translational motion along the axis of orientation. In contrast to the study on vortex configurations for purely rotational stationary states, the present paper considers non-stationary states which exhibit a combination of rotation and translational motions. These solutions can essentially be described as waves or disturbances which ride along straight vortex filament lines. As expected from our previous work, there are a number of types of structures that can be obtained under the 2D-LIA. We focus on non-stationary states, as stationary states exhibiting translation will essentially take the form of solutions studied in [R. A. Van Gorder, “General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation,” Phys. Fluids 26, 065105 (2014)], with the difference being translation along the reference axis, so that qualitative appearance of the solution geometry will be the same (even if there are quantitative differences). We discuss a wide variety of general properties of these non-stationary solutions and derive cases in which they reduce to known stationary states. We obtain various routes to Kelvin waves along vortex filaments and demonstrate that if the phase and amplitude of a disturbance both propagate with the same wave speed, then Kelvin waves will result. We also consider the self
Common Behaviors of Spinor-Type Instantons in 2D Thirring and 4D Gursey Fermionic Models
Directory of Open Access Journals (Sweden)
Fatma Aydogmus
2014-01-01
Full Text Available We investigate two examples of conformal invariant pure spinor fermionic models, which admit particle-like solutions of the classical field equations. For different dimensions and quantum spinor numbers, the vector field visualizations of the models are constructed to provide a better understanding of the spinor-type instanton dynamics in phase space. The hierarchical cluster analysis method investigations of the models are also presented. Finally, the autocorrelation and power spectrum graphs of models are constructed and frequencies of motions are defined.
Special Issue on "Instanton Counting: Moduli Spaces, Representation Theory, and Integrable Systems"
Bruzzo, Ugo; Sala, Francesco
2016-11-01
This special issue of the Journal of Geometry and Physics collects some papers that were presented during the workshop "Instanton Counting: Moduli Spaces, Representation Theory, and Integrable Systems" that took place at the Lorentz Center in Leiden, The Netherlands, from 16 to 20 June 2014. The workshop was supported by the Lorentz Center, the "Geometry and Quantum Theory" Cluster, Centre Européen pour les Mathématiques, la Physique et leurs Interactions (Lille, France), Laboratoire Angevin de Recherche en Mathématiques (Angers, France), SISSA (Trieste, Italy), and Foundation Compositio (Amsterdam, the Netherlands). We deeply thank all these institutions for making the workshop possible. We also thank the other organizers of the workshop, Professors Dimitri Markushevich, Vladimir Rubtsov and Sergey Shadrin, for their efforts and great collaboration.
Exact Thresholds and Instanton Effects in String Theory
Obers, N A
2001-01-01
In this lecture we summarize some recent work on the understanding of instanton effects in string theories with 16 supersymmetries. In particular, we consider F^4 couplings using the duality between the heterotic string on T^4 and type IIA on K_3 at an orbifold point, as well as higher and lower dimensional versions of this string-string duality. At the perturbative level a non-trivial test of the duality, requiring several miraculous identities, is presented by matching a purely one-loop heterotic amplitude to a purely tree-level type II result. A wide variety of non-perturbative effects is shown to occur in this setting, including D-brane instantons for type IIA on K_3 x S^1 and NS5-brane instantons for type IIA on K_3 x T^2. Moreover, the analysis of the three-dimensional case, which possesses a non-perturbative SO(8,24,Z) U-duality, reveals the presence of Kaluza-Klein 5-brane instanton effects, both on the heterotic and the type II side.
Construction of the moduli space of Spin (7)-instantons
Muñoz, Vicente
2016-01-01
We construct the moduli space of Spin(7)-instantons on a hermitian complex vector bundle over a closed 8-dimensional manifold endowed with a (possibly non-integrable) Spin(7)-structure. We find suitable perturbations that achieve regularity of the moduli space, so that it is smooth and of the expected dimension over the irreducible locus.
The instanton method and its numerical implementation in fluid mechanics
Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias
2015-08-01
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.
Multiple D3-instantons and mock modular forms I
Alexandrov, Sergei; Manschot, Jan; Pioline, Boris
2016-01-01
We study D3-instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In a previous work, consistency of D3-instantons with S-duality was established at first order in the instanton expansion, using the modular properties of the M5-brane elliptic genus. We extend this analysis to the two-instanton level, where wall-crossing phenomena start playing a role. We focus on the contact potential, an analogue of the Kahler potential which must transform as a modular form under S-duality. We show that it can be expressed in terms of a suitable modification of the partition function of D4-D2-D0 BPS black holes, constructed out of the generating function of MSW invariants (the latter coincide with Donaldson-Thomas invariants in a particular chamber). Modular invariance of the contact potential then requires that, in case where the D3-brane wraps a reducible divisor, the generating function of MSW invariants must transform as a vector-valued mock modular fo...
Non-extremal instantons and wormholes in string theory
Bergshoeff, E.; Collinucci, A.; Gran, U.; Roest, D.; Vandoren, S.
2007-01-01
We construct the most general non-extremal spherically symmetric instanton solution of a gravity-dilaton-axion system with SL(2,R) symmetry, for arbitrary euclidean spacetime dimension D ≥ 3. A subclass of these solutions describe completely regular wormhole geometries, whose size is determined by a
A new look at instantons and large-N limit
Energy Technology Data Exchange (ETDEWEB)
Azeyanagi, Tatsuo [Center for the Fundamental Laws of Nature, Harvard University,Cambridge, Massachusetts 02138 (United States); Hanada, Masanori [Yukawa Institute for Theoretical Physics, Kyoto University,Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502 (Japan); The Hakubi Center for Advanced Research, Kyoto University, Yoshida-Ushinomiya-cho, Sakyo-ku, Kyoto 606-8501 (Japan); KEK Theory Center, High Energy Accelerator Research Organization (KEK), Oho, Tsukuba, Ibaraki 305-0801 (Japan); Honda, Masazumi [Yukawa Institute for Theoretical Physics, Kyoto University,Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502 (Japan); KEK Theory Center, High Energy Accelerator Research Organization (KEK), Oho, Tsukuba, Ibaraki 305-0801 (Japan); Matsuo, Yoshinori; Shiba, Shotaro [KEK Theory Center, High Energy Accelerator Research Organization (KEK), Oho, Tsukuba, Ibaraki 305-0801 (Japan)
2014-05-05
We analyze instantons in the very strongly coupled large-N limit (N→∞ with g{sup 2} fixed) of large-N gauge theories, where the effect of the instantons remains finite. By using the exact partition function of four-dimensional N=2{sup ∗} gauge theories as a concrete example, we demonstrate that each instanton sector in the very strongly coupled large-N limit is related to the one in the ’t Hooft limit (N→∞ with g{sup 2}N fixed) through a simple analytic continuation. Furthermore we show the equivalence between the instanton partition functions of a pair of large-N gauge theories related by an orbifold projection. This can open up a new way to analyze the partition functions of low/non-supersymmetric theories. We also discuss implication of our result to gauge/gravity dualities for M-theory as well as a possible application to large-N QCD.
Flow of geometries and instantons on the null orbifold
Energy Technology Data Exchange (ETDEWEB)
Berkooz, Micha [Weizmann Institute of Science, Rehovot 76100 (Israel); Komargodski, Zohar [Weizmann Institute of Science, Rehovot 76100 (Israel); Reichmann, Dori [Weizmann Institute of Science, Rehovot 76100 (Israel); Shpitalnik, Vadim [Weizmann Institute of Science, Rehovot 76100 (Israel)
2005-12-15
We study condensation of twisted sector states in the null orbifold geometry. As the singularity is time-dependent, we probe it using D-Instantons. We present evidence that the null-orbifold flows to the Z{sub N} orbifold. We also comment on the subtleties of quantizing the closed superstring in this background.
Generalized Kähler Geometry of Instanton Moduli Spaces
Bursztyn, Henrique; Gualtieri, Marco; Cavalcanti, Gil R.
2015-01-01
We prove that Hitchin’s generalized Kähler structure on the moduli space of instantons over a compact, even generalized Kähler four-manifold may be obtained by generalized Kähler reduction, in analogy with the usual Kähler case. The underlying reduction of Courant algebroids is a realization of Dona
Parabolic vortex equations and instantons of infinite energy
Biquard, Olivier; García-Prada, Oscar
1997-02-01
We study the vortex equations on parabolic bundles over a Riemann surface and prove a Hitchin-Kobayashi-type correspondence relating the existence of solutions to a certain stability condition. This is achieved by translating our problem into a four-dimensional one, via dimensional reduction arguments. In return we obtain examples of instantons of infinite energy.
New explicit instantons and the geometry of the parameter space
Meyers, C.; Roo, M. de
1979-01-01
We obtain a geometrical description of the parameter space of instantons of topological charge k in an SU(n) gauge theory. We show how this space is related to a compact convex set of positive matrices. We give a characterization of points in the parameter space which correspond to embeddings. We de
Non-extremal instantons and wormholes in string theory
Bergshoeff, E.; Collinucci, A.; Gran, U.; Roest, D.; Vandoren, S.
2004-01-01
We construct the most general non-extremal spherically symmetric instanton solution of a gravity-dilaton-axion system with SL(2,R) symmetry, for arbitrary euclidean spacetime dimension D ≥ 3. A subclass of these solutions describe completely regular wormhole geometries, whose size is determined
Non-extremal instantons and wormholes in string theory
Bergshoeff, E; Collinucci, A; Gran, U; Roest, D; Vandoren, S
2005-01-01
We construct the most general non-extremal spherically symmetric instanton solution of a gravity-dilatonaxion system with SL(2, R) symmetry, for arbitrary euclidean spacetime dimension D >= 3. A subclass of these solutions describe completely regular wormhole geometries, whose size is determined by
Gravitating Instantons In 3 Dimensional Anti de Sitter Space
Ferstl, A; Weir, V; Ferstl, Andrew; Tekin, Bayram; Weir, Victor
2000-01-01
We study the Einstein-Chern-Simons gravity coupled to Yang-Mills-Higgs theoryin three dimensional Euclidean space with cosmological constant. The classicalequations of motion reduce to Bogomol'nyi type first order equations. There areBPS type instanton (monopole) solutions of finite action which we findnumerically. In addition we point out to some exact solutions which aresingular.
Multiple D3-Instantons and Mock Modular Forms I
Alexandrov, Sergei; Banerjee, Sibasish; Manschot, Jan; Pioline, Boris
2017-07-01
We study D3-instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In a previous work, consistency of D3-instantons with S-duality was established at first order in the instanton expansion, using the modular properties of the M5-brane elliptic genus. We extend this analysis to the two-instanton level, where wall-crossing phenomena start playing a role. We focus on the contact potential, an analogue of the Kähler potential which must transform as a modular form under S-duality. We show that it can be expressed in terms of a suitable modification of the partition function of D4-D2-D0 BPS black holes, constructed out of the generating function of MSW invariants (the latter coincide with Donaldson-Thomas invariants in a particular chamber). Modular invariance of the contact potential then requires that, in the case where the D3-brane wraps a reducible divisor, the generating function of MSW invariants must transform as a vector-valued mock modular form, with a specific modular completion built from the MSW invariants of the constituents. Physically, this gives a powerful constraint on the degeneracies of BPS black holes. Mathematically, our result gives a universal prediction for the modular properties of Donaldson-Thomas invariants of pure two-dimensional sheaves.
Richardson, Jeremy O; Thoss, Michael
2015-01-01
We present semiclassical approximations to Green's functions of multidimensional systems, extending Gutzwiller's work to the classically forbidden region. Based on steepest-descent integrals over these functions, we derive an instanton method for computing the rate of nonadiabatic reactions, such as electron transfer, in the weak-coupling limit, where Fermi's golden-rule can be employed. This generalizes Marcus theory to systems for which the environment free-energy curves are not harmonic and where nuclear tunnelling plays a role. The derivation avoids using the Im F method or short-time approximations to real-time correlation functions. A clear physical interpretation of the nuclear tunnelling processes involved in an electron-transfer reaction is thus provided. In the following paper, we discuss numerical evaluation of the formulae.
Richardson, Jeremy O.; Bauer, Rainer; Thoss, Michael
2015-10-01
We present semiclassical approximations to Green's functions of multidimensional systems, extending Gutzwiller's work to the classically forbidden region. Based on steepest-descent integrals over these functions, we derive an instanton method for computing the rate of nonadiabatic reactions, such as electron transfer, in the weak-coupling limit, where Fermi's golden-rule can be employed. This generalizes Marcus theory to systems for which the environment free-energy curves are not harmonic and where nuclear tunnelling plays a role. The derivation avoids using the Im F method or short-time approximations to real-time correlation functions. A clear physical interpretation of the nuclear tunnelling processes involved in an electron-transfer reaction is thus provided. In Paper II [J. O. Richardson, J. Chem. Phys. 143, 134116 (2015)], we discuss numerical evaluation of the formulae.
Energy Technology Data Exchange (ETDEWEB)
Radozycki, Tomasz [Cardinal Stefan Wyszynski University, Faculty of Mathematics and Natural Sciences, College of Sciences, Warsaw (Poland)
2015-09-15
The Lorentz transformation properties of the equal-time bound-state Bethe-Salpeter amplitude in the two-dimensional massless quantum electrodynamics (the so-called Schwinger model) are considered. It is shown that while boosting a bound state (a 'meson') this amplitude is subject to approximate Lorentz contraction. The effect is exact for large separations of constituent particles ('quarks'), while for small distances the deviation is more significant. For this phenomenon to appear, the full function, i.e. with the inclusion of all instanton contributions, has to be considered. The amplitude in each separate topological sector does not exhibit such properties. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Radożycki, Tomasz, E-mail: t.radozycki@uksw.edu.pl [Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszyński University, Wóycickiego 1/3, 01-938, Warsaw (Poland)
2015-09-24
The Lorentz transformation properties of the equal-time bound-state Bethe–Salpeter amplitude in the two-dimensional massless quantum electrodynamics (the so-called Schwinger model) are considered. It is shown that while boosting a bound state (a ‘meson’) this amplitude is subject to approximate Lorentz contraction. The effect is exact for large separations of constituent particles (‘quarks’), while for small distances the deviation is more significant. For this phenomenon to appear, the full function, i.e. with the inclusion of all instanton contributions, has to be considered. The amplitude in each separate topological sector does not exhibit such properties.
Quantum Creation of BTZ Black Hole
Wu Zhong Chao
1999-01-01
The constrained Instanton method is used to study quantum creation of a BTZ black hole. It is found that the relative creation probability is the exponential of the negative sum of the entropy associated with the outer and inner black hole horizons. The quantum creation of the 4- or higher dimensional versions of the BTZ black hole are also studied.
Jusufi, K.
2016-12-01
In the present paper we study the Hawking radiation as a quantum tunneling effect of spin-1 particles from a five-dimensional, spherically symmetric, Einstein-Yang-Mills-Gauss-Bonnet (5D EYMGB) black hole. We solve the Proca equation (PE) by applying the WKB approximation and separation of variables via Hamilton-Jacobi (HJ) equation which results in a set of five differential equations, and reproduces, in this way, the Hawking temperature. In the second part of this paper, we extend our results beyond the semiclassical approximation. In particular, we derive the logarithmic correction to the entropy of the EYMGB black hole and show that the quantum corrected specific heat indicates the possible existence of a remnant.
On Fluxed Instantons and Moduli Stabilisation in IIB Orientifolds and F-theory
Grimm, Thomas W; Palti, Eran; Weigand, Timo
2011-01-01
We study the superpotential induced by Euclidean D3-brane instantons carrying instanton flux, with special emphasis on its significance for the stabilisation of Kahler moduli and Neveu-Schwarz axions in Type IIB orientifolds. Quite generally, once a chiral observable sector is included in the compactification, arising on intersecting D7-branes with world-volume flux, resulting charged instanton zero modes prevent a class of instantons from participating in moduli stabilisation. We show that instanton flux on Euclidean D3-branes can remove these extra zero modes and helps in reinstating full moduli stabilisation within a geometric regime. We comment also on the F-theoretic description of this effect of alleviating the general tension between moduli stabilisation and chirality. In addition we propose an alternative solution to this problem based on dressing the instantons with charged matter fields which is unique to F-theory and cannot be realised in the weak coupling limit.
Thin-shell instanton tunneling: something-to-something or nothing-to-something?
Chen, Pisin; Yeom, Dong-han
2016-01-01
There exist two interpretations of instantons in the literature. The first interpretation regards instanton as divider between the initial and final hypersurfaces. The Coleman-De Luccia instanton is one such an example. The second interpretation, proposed by Brown and Weinberg, considers instanton as connector between the initial and final hypersurfaces. In this proceedings, we try to suitably and intuitively argue that these two interpretations are complementary to each other under certain conditions. Furthermore, we demonstrate that the decay rate obtained from the Euclidean treatment and the Hamiltonian treatment both are consistent with each other, which may help to dissolve some concerns about the validity of regularization technique employed in the treatment of the cusp singularity of instantons. Based on these, we argue that instantons can be a sensible tool to address the information loss problem.
Heavy quark potential and jet quenching parameter in a D-instanton background
Zhang, Zi-qiang; Chen, Gang
2016-01-01
Applying the AdS/CFT correspondence, two important quantities, heavy quark potential and jet quenching parameter, are calculated in a D-instanton background. This dual gravitational theory is related to a near horizon limit of stack of black D3-branes with homogeneously distributed D-instantons. It is shown that the presence of instantons affects heavy quark potential and jet quenching parameter.
Directory of Open Access Journals (Sweden)
Oscar Bolina
2000-07-01
Full Text Available It is shown that, with an appropriate scaling, the energy of low-lying excitations of the (1, 1,...,1 interface in the d-dimensional quantum Heisenberg model are given by the spectrum of the (d-1-dimensional Laplacian on a suitable domain.
Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory
Okuyama, Kazumi
2016-01-01
We study instanton corrections to the vacuum expectation value (VEV) of 1/6 BPS Wilson loops in ABJM theory from the Fermi gas approach. We mainly consider Wilson loops in the fundamental representation and winding Wilson loops, but we also initiate the study of Wilson loops with two boundaries. We find that the membrane instanton corrections to the Wilson loop VEV are determined by the refined topological string in the Nekrasov-Shatashvili limit, and the pole cancellation mechanism between membrane instantons and worldsheet instantons works also in the Wilson loop VEVs as in the case of the partition functions.
Instanton strings and hyper-Kähler geometry
Dijkgraaf, Robbert
1999-03-01
We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N = (4, 4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS 3. We derive a precise map relating the moduli of the K3 type 1113 string compactification to the moduli of these conformal field theories and the corresponding classical hyper-Kahler geometry. We conclude that in the absence of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyper-Kähler manifolds.
Instanton Strings and HyperKähler Geometry
Dijkgraaf, R
1999-01-01
We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N=(4,4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS_3. We derive a precise map relating the moduli of the K3 type IIB string compactification to the moduli of these conformal field theories and the corresponding classical hyperkaehler geometry. We conclude that, in the absense of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyperkaehler manifolds.
Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
de la Ossa, Xenia; Svanes, Eirik Eik
2016-01-01
We describe the infinitesimal moduli space of pairs $(Y, V)$ where $Y$ is a manifold with $G_2$ holonomy, and $V$ is a vector bundle on $Y$ with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical $G_2$ cohomology $H^*_{{\\check{\\rm d}}_E}(Y,E)$ developed by Reyes-Carri\\'on and Fern\\'andez and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli $H^1_{{\\check{\\rm d}}_A}(Y,{\\rm End}(V))$ plus the moduli of the $G_2$ structure preserving the instanton condition. The latter piece is contained in $H^1_{{\\check{\\rm d}}_\
Direct instantons, topological charge screening and QCD glueball sum rules
Forkel, H
2003-01-01
Nonperturbative Wilson coefficients of the operator product expansion (OPE) for the spin-0 glueball correlators are derived and analyzed. A systematic treatment of the direct instanton contributions is given, based on realistic instanton size distributions and renormalization at the operator scale. In the pseudoscalar channel, topological charge screening is identified as an additional source of (semi-) hard nonperturbative physics. The screening contributions are shown to be vital for consistency with the anomalous axial Ward identity, and previously encountered pathologies (positivity violations and the disappearance of the 0^{-+} glueball signal) are traced to their neglect. On the basis of the extended OPE, a comprehensive quantitative analysis of eight Borel-moment sum rules in both spin-0 glueball channels is then performed. The nonperturbative OPE coefficients turn out to be indispensable for consistent sum rules and for their reconciliation with the underlying low-energy theorems. The topological shor...
SU(5) orientifolds, Yukawa couplings, Stringy Instantons and Proton Decay
Kiritsis, Elias; Schellekens, Bert; 10.1016
2009-01-01
We construct a large class of SU(5) orientifold vacua with tadpole cancellation both for the standard and the flipped case. We give a general analysis of superpotential couplings up to quartic order in orientifold vacua and identify the properties of needed Yukawa couplings as well as the baryon number violating couplings. We point out that successful generation of the perturbatively forbidden Yukawa couplings entails a generically disastrous rate for proton decay from an associated quartic term in the superpotential, generated from the same instanton effects. This problem seems generic and may appear in F-theory vacua as well. We search for the appropriate instanton effects that generate the missing Yukawa couplings in the SU(5) vacua we constructed and find them in a small subset of them.
Worldsheet Instantons and Torsion Curves, Part A: Direct Computation
Braun, V; Ovrut, B A; Scheidegger, E; Braun, Volker; Kreuzer, Maximilian; Ovrut, Burt A.; Scheidegger, Emanuel
2007-01-01
As a first step towards studying vector bundle moduli in realistic heterotic compactifications, we identify all holomorphic rational curves in a Calabi-Yau threefold X with Z_3 x Z_3 Wilson lines. Computing the homology, we find that H_2(X,Z)=Z^3+Z_3+Z_3. The torsion curves complicate our analysis, and we develop techniques to distinguish the torsion part of curve classes and to deal with the non-toric threefold X. In this paper, we use direct A-model computations to find the instanton numbers in each integral homology class, including torsion. One interesting result is that there are homology classes that contain only a single instanton, ensuring that there cannot be any unwanted cancellation in the non-perturbative superpotential.
Instantons on the 5-sphere and M5-branes
Kim, Hee-Cheol; Kim, Seok
2012-01-01
We calculate the partition functions of supersymmetric gauge theories on S^5, which acquire non-perturbative contributions from instanton loops wrapping its Hopf fiber. The instantons on the CP^2 base equivariantly localize to 3 fixed points of SU(3) Cartans. Using our results, we study the index of the 6d (2,0) theory. We first study the partition functions of maximal SYM with AD(E) gauge groups, which agree with the gravity dual indices on AdS_7 in the large N limits. We also show that the most general partition function of the Abelian theory agrees with the index for a free 6d tensor supermultiplet. We explain possible ambiguities in our 5d approach, role of maximal SUSY, and the Wilson loops on S^5 dual to M2-brane Wilson surfaces in AdS_7.
Skyrmions, multi-instantons and $SU(\\infty)$-Toda equation
Plansangkate, Prim
2016-01-01
We construct Skyrmions from holonomy of the spin connection of multi-Taub-NUT instantons with the centres positioned along a line in $\\mathbb{R}^3.$ Our family of Skyrmions includes the Taub-NUT Skyrmion previously constructed by Dunajski. However, we demonstrate that different gauges of the spin connection can result in Skyrmions with different topological degrees. As a by-product, we present a method to compute the degrees of the Taub-NUT and Atiyah-Hitchin Skyrmions analytically; these degrees are well defined as a preferred gauge is fixed by the $SU(2)$ symmetry of the two metrics. Regardless of the gauge, the domain of our Skyrmions is the space of orbits of the axial symmetry of the multi-Taub-NUT instantons. We obtain an expression for the induced metric on the space and its associated solution to the $SU(\\infty)$-Toda equation.
Confinement in a correlated Instanton-Dyon Ensemble
Lopez-Ruiz, Miguel Angel; Jiang, Yin; Liao, Jinfeng
2017-07-01
Confinement is a remarkable nonperturbative phenomena emerging from QCD and QCD-like theories. A theoretical understanding of these transitions and their interrelations is of fundamental importance. While it is widely perceived that their dynamics arises from nontrivial topological configurations in Yang-Mills theories, a concrete and sophisticated realization of such idea is an outstanding challenge. We report significant progress along this direction by the construction of a new framework based on correlated ensemble of instanton-dyons, namely the constituents of the finite-temperature instantons with non-trivial holonomy. We present a comprehensive numerical study of confinement properties in SU(2) Yang-Mills theory at finite temperature, obtaining important observables such as the effective holonomy potential, the static quark potentials from Polyakov loop correlators as well as spatial Wilson loops, among others.
Probing Wilson Loops in the QCD Instanton Vacuum
Liu, Yizhuang
2014-01-01
We discuss the quark and gluon condensates in the presence of a rectangular Wilson loop using the QCD instanton vacuum with three light dynamical quarks. The scalar quark condensate is found to decrease while the gluon condensate to increase. We also derive the static potential between two QCD dipoles and show that it is attractive but short ranged at large distances. Its relevance to static QCD string interactions is discussed.
Black Five-Branes and Fluxbranes on Gravitational Instantons
Vazquez-Poritz, Justin F
2012-01-01
We apply a U-duality based solution-generating technique to construct supergravity solutions which describe nonextremal D5-branes and fluxbranes on various gravitational instantons. This includes an F7-brane wrapped on a sphere, which remains weakly-coupled in the asymptotic region. We construct various superpositions of nonextremal D5-branes and fluxbranes that have angular momentum fixed by the parameters associated with their mass and two magnetic charges.
Twisted Bundle on Noncommutative Space and U(1) Instanton
Ho, P M
2000-01-01
We study the notion of twisted bundles on noncommutative space. Due to theexistence of projective operators in the algebra of functions on thenoncommutative space, there are twisted bundles with non-constant dimension.The U(1) instanton solution of Nekrasov and Schwarz is such an example. As amathematical motivation for not excluding such bundles, we find gaugetransformations by which a bundle with constant dimension can be equivalent toa bundle with non-constant dimension.
Two dimensional RG flows and Yang-Mills instantons
Gava, Edi; Narain, K S
2010-01-01
We study RG flow solutions in (1,0) six dimensional supergravity coupled to an anti-symmetric tensor and Yang-Mills multiplets corresponding to a semisimple group $G$. We turn on $G$ instanton gauge fields, with instanton number $N$, in the conformally flat part of the 6D metric. The solution interpolates between two (4,0) supersymmetric $AdS_3\\times S^3$ backgrounds with two different values of $AdS_3$ and $S^3$ radii and describes an RG flow in the dual 2D SCFT. For the single instanton case and $G=SU(2)$, there exist a consistent reduction ansatz to three dimensions, and the solution in this case can be interpreted as an uplifted 3D solution. Correspondingly, we present the solution in the framework of N=4 $(SU(2)\\ltimes \\mathbf{R}^3)^2$ three dimensional gauged supergravity. The flows studied here are of v.e.v. type, driven by a vacuum expectation value of a (not exactly) marginal operator of dimension two in the UV. We give an interpretation of the supergravity solution in terms of the D1/D5 system in ty...
Hadronic correlation functions in the random instanton-dyon ensemble
Larsen, Rasmus; Shuryak, Edward
2017-08-01
It is known since the 1980s that the instanton-induced 't Hooft effective Lagrangian not only can solve the so-called U (1 )a problem, by making the η' meson heavy etc., but it can also lead to chiral symmetry breaking. In the 1990s it was demonstrated that, taken to higher orders, this Lagrangian correctly reproduces effective forces in a large set of hadronic channels, mesonic and baryonic ones. Recent progress in understanding gauge topology at finite temperatures is related with the so-called instanton-dyons, the constituents of the instantons. Some of them, called L -dyons, possess the antiperiodic fermionic zero modes, and thus form a new version of the 't Hooft effective Lagrangian. This paper is our first study of a wide set of hadronic correlation function. We found that, at the lowest temperatures at which this approach is expected to be applicable, those may be well compatible with what is known about them based on phenomenological and lattice studies, provided L and M type dyons are strongly correlated.
Martín-Benito, Mercedes; Marugán, Guillermo A Mena
2013-01-01
We develop approximation methods in the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field, for the case of three-torus spatial topology. The loop quantization of the homogeneous gravitational sector of the Gowdy model (according to the improved dynamics prescription) and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical results calls for the introduction of well justified approximations. We first show how to approximate the homogeneous part of the Hamiltonian constraint, corresponding to Bianchi I geometries, as if it described a Friedmann-Robertson-Walker (FRW) model corrected with anisotropies. This approximation is valid in the high-energy sector of the FRW geometry (concerning its contribution to the constraint) and for anisotropy profiles that are sufficiently smooth. In addition, for certain families of states associated to regimes of physical interest, with negligible effects of the anisotro...
Mora, P J; Woodard, R P
2013-01-01
We use the Hartree approximation to the Einstein equation on de Sitter background to solve for the one loop correction to the graviton mode function. This should give a reasonable approximation to how the ensemble of inflationary gravitons affects a single external graviton. At late times we find that the one loop correction to the plane wave mode function $u(\\eta,k)$ goes like $G H^2 \\ln(a)/a^2$, where $a$ is the inflationary scale factor. One consequence is that the one loop corrections to the "electric" components of the linearized Weyl tensor grow compared to the tree order result.
THE DYSON-SCHWINGER EQUATION FOR A MODEL WITH INSTANTONS - THE SCHWINGER MODEL
Adam, C.
1995-01-01
Using the exact path integral solution of the Schwinger model -- a model where instantons are present -- the Dyson-Schwinger equation is shown to hold by explicit computation. It turns out that the Dyson-Schwinger equation separately holds for every instanton sector. This is due to Theta-invariance of the Schwinger model.
Instanton-induced Effective Vertex in the Seiberg-Witten Theory with Matter
Lee, B K; Lee, ByungKoo; Nam, Soonkeon
1997-01-01
The instanton-induced effective vertex is derived for N=2 supersymmetric QCD (SQCD) with arbitrary mass matter hypermultiplets for the case of SU(2). The leading term of the low energy effective lagrangian obtained from this vertex agrees with one-instanton effective term of the Seiberg-Witten result.
On the non-existence of orthogonal instanton bundles on P^{2n+1}
Directory of Open Access Journals (Sweden)
Łucja Farnik
2009-11-01
Full Text Available In this paper we prove that there do not exist orthogonal instanton bundles on P^{2n+1} . In order to demonstrate this fact, we propose a new way of representing the invariant, introduced by L. Costa and G. Ottaviani, related to a rank 2n instanton bundle on P^{2n+1}.
Weak gravity conjecture as a razor criterium for exotic D-brane instantons
Addazi, Andrea
2017-01-01
We discuss implications of weak gravity conjecture (WGC) for exotic D-brane instantons. In particular, WGC leads to indirect stringent bounds on non-perturbative superpotentials generated by exotic instantons with many implications for phenomenology: R-parity violating processes, neutrino mass, μ-problem, neutron-antineutron transitions and collider physics.
Reanalyzing Pentaquark Θ+(1540) in Framework of QCD Sum Rules Approach with Direct Instantons
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this article, we study the pentaquark state Θ+(1540) with a (scalar) diquark-(pseudoscalar) diquarkantiquark type interpolating current in the framework of the QCD sum rules approach by including the contributions from the direct instantons. The numerical results indicate that the contributions from the direct instantons are very small and can be safely neglected.
Topological susceptibility and Instanton size distribution from over-improved cooling
de Forcrand, Philippe; Kim, Seyong
1995-01-01
We measure the topological susceptibility by cooling with an over-improved action. In contrast with usual cooling, large instantons survive over-improved cooling {\\em indefinitely}. By varying the parameter of the over-improved cooling action, we measure the instanton size distribution.
The strong coupling constant at small momentum as an instanton detector
Boucaud, P; Le Yaouanc, A; Leroy, J P; Micheli, J; Moutarde, H; Pène, O; Rodríguez-Quintero, J; Boucaud, Ph.
2003-01-01
We present a study of $\\alpha_{MOM}(p)$ at small p computed from the lattice. It shows a dramatic $\\propto p^4$ law which can be understood within an instanton liquid model. In this framework the prefactor gives a direct measure of the instanton density in thermalised configurations. A preliminary result for this density is 5.27(4) fm^{-4}.
Thomas-Fermi approximation in two p-type delta-doped quantum wells in GaAs an Si
Energy Technology Data Exchange (ETDEWEB)
Gaggero-Sager, L. M. [Universidad Autonoma de Zacatecas, Zacatecas (Mexico); M' Peko, J. C.; Perez Alvarez, R. [Universidad de La Habana, Ciudad Habana (Cuba)
2001-04-01
Thomas-Fermi calculations of the hole subband structure in two coupled p-type d-doped GaAs and Si quantum wells are carried out as a function of the impurity concentration and the distance l between them. A simple formula is obtained for the potential as a function of these two magnitudes by both types of systems. The numerical results for a double Be-{delta}-doped GaAs (double B-{delta}-doped Si) quantum well show that the energy levels degenerate for l{>=}300 A(l{>=}200 A) for an impurity concentration of 1 x 10{sup 1}3 cm{sup -2}. [Spanish] Presentamos calculos de la estructura de subbandas de huecos, utilizando la aproximacion de Thomas-Fermi para dos pozos cuanticos d-dopados tipo p en GaAs y Si, como funcion de la concentracion de impurezas y de la distancia l entre ambos para los dos tipos de sistemas. Los resultados numericos muestran que para un pozo doble de B-{delta}-dopado GaAs (pozo doble de B-{delta}-dopado Si) con una concentracion de 1 x 10{sup 1}3 cm{sup -2} los niveles estan degenerados para l{>=}300 A(l{>=}200 A).
Energy Technology Data Exchange (ETDEWEB)
Strobel, Eckhard, E-mail: eckhard.strobel@irap-phd.eu [ICRANet, Piazzale della Repubblica 10, 65122 Pescara (Italy); Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, 00185 Rome (Italy); Université de Nice Sophia Antipolis, 28 Avenue de Valrose, 06103 Nice Cedex 2 (France); Xue, She-Sheng, E-mail: xue@icra.it [ICRANet, Piazzale della Repubblica 10, 65122 Pescara (Italy); Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, 00185 Rome (Italy)
2014-09-15
We present an analytic calculation of the semiclassical electron–positron pair creation rate by time-dependent electrical fields. We use two methods, first the imaginary time method in the WKB-approximation and second the world-line instanton approach. The analytic tools for both methods are generalized to time-dependent electric fields with more than one component. For the WKB method an expansion of the momentum spectrum of produced pairs around the canonical momentum P{sup →}=0 is presented which simplifies the computation of the pair creation rate. We argue that the world-line instanton method of [1] implicitly performs this expansion of the momentum spectrum around P{sup →}=0. Accordingly, the generalization to more than one component is shown to agree with the WKB result obtained via this expansion. However the expansion is only a good approximation for the cases where the momentum spectrum is peaked around P{sup →}=0. Thus the expanded WKB result and the world-line instanton method of [1] as well as the generalized method presented here are only applicable in these cases. We study the two-component case of a rotating electric field and find a new analytic closed form for the momentum spectrum using the generalized WKB method. The momentum spectrum for this field is not peaked around P{sup →}=0.
QCD-instantons at LHC. Theoretical aspects; QCD-Instantonen am LHC. Theoretische Aspekte
Energy Technology Data Exchange (ETDEWEB)
Petermann, M.
2007-06-15
Instantons are nonperturbative, topologically nontrivial field configurations, which occur in every nonabelian gauge theory. They can be understood as tunneling processes between topologically distinct vacua. Although being a basic theoretical aspect of the Standard Model, a direct experimental verification of instanton processes is still lacking. In this thesis the general discovery potential for QCD-instantons at the LHC is studied in detail by means of instanton perturbation theory. In this context the close correspondence between the leading instanton induced processes at HERA and at LHC becomes important. Essential aspects and differences to deep inelastic scattering can already be revealed by studying the simplest process. Based on these results inclusive cross sections are calculated including the emission of final state gluons. Compared to deep inelastic scattering, a large enhancement of the cross section is found. (orig.)
The ADHM-like constructions for instantons on CP2 and three-dimensional gauge theories
Mekareeya, Noppadol; Rodríguez-Gómez, Diego
2015-02-01
We study the moduli spaces of self-dual instantons on CP2 in a simple group G. When G is a classical group, these instanton solutions can be realized using ADHM-like constructions which can be naturally embedded into certain three-dimensional quiver gauge theories with four supercharges. The topological data for such instanton bundles and their relations to the quiver gauge theories are described. Based on such gauge theory constructions, we compute the Hilbert series of the moduli spaces of instantons that correspond to various configurations. The results turn out to be equal to the Hilbert series of their counterparts on C2 upon an appropriate mapping. We check the former against the Hilbert series derived from the blowup formula for the Hirzebruch surface F1 and find an agreement. The connection between the moduli spaces of instantons on such two spaces is explained in detail.
The ADHM-like constructions for instantons on CP2 and three-dimensional gauge theories
Directory of Open Access Journals (Sweden)
Noppadol Mekareeya
2015-02-01
Full Text Available We study the moduli spaces of self-dual instantons on CP2 in a simple group G. When G is a classical group, these instanton solutions can be realized using ADHM-like constructions which can be naturally embedded into certain three-dimensional quiver gauge theories with four supercharges. The topological data for such instanton bundles and their relations to the quiver gauge theories are described. Based on such gauge theory constructions, we compute the Hilbert series of the moduli spaces of instantons that correspond to various configurations. The results turn out to be equal to the Hilbert series of their counterparts on C2 upon an appropriate mapping. We check the former against the Hilbert series derived from the blowup formula for the Hirzebruch surface F1 and find an agreement. The connection between the moduli spaces of instantons on such two spaces is explained in detail.
Einstein Manifolds, Abelian Instantons, Bundle Reduction, and the Cosmological Constant
Soo, C P
2001-01-01
The anti-self-dual projection of the spin connections of certain four-dimensional Einstein manifolds can be Abelian in nature. These configurations signify bundle reductions. By a theorem of Kobayashi and Nomizu such a process is predicated on the existence of a covariantly constant field. It turns out that even without fundamental Higgs fields and other physical matter, gravitational self-interactions can generate this mechanism if the cosmological constant is non-vanishing. This article identifies the order parameter, and clarifies how these Abelian instanton solutions are associated with a Higgs triplet which causes the bundle reduction from SO(3) gauge group to U(1).
Topological duality twist and brane instantons in F-theory
Energy Technology Data Exchange (ETDEWEB)
Martucci, Luca [Dipartimento di Fisica ed Astronomia “Galileo Galilei”, Università di Padova andINFN - Sezione di Padova,Via Marzolo 8, I-35131 Padova (Italy)
2014-06-30
A variant of the topological twist, involving SL(2,ℤ) dualities and hence named topological duality twist, is introduced and explicitly applied to describe a U(1) N=4 super Yang-Mills theory on a Kähler space with holomorphically space-dependent coupling. Three-dimensional duality walls and two-dimensional chiral theories naturally enter the formulation of the duality twisted theory. Appropriately generalized, this theory is relevant for the study of Euclidean D3-brane instantons in F-theory compactifications. Some of its properties and implications are discussed.
Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
Moriyama, Sanefumi
2016-01-01
We study the partition function of the orientifold ABJM theory, which is a superconformal Chern-Simons theory associated with the orthosymplectic supergroup. We find that the partition function associated with any orthosymplectic supergroup can be realized as that of a Fermi gas system whose density matrix is identical to that associated with the corresponding unitary supergroup with a projection to the even or odd chirality. Furthermore we propose an identity and use it to identify all of the Gopakumar-Vafa invariants for the worldsheet instanton effects systematically.
Studies on instantons, twistor strings, and half-BPS geometries
Ricci, Riccardo
2006-12-01
In this Dissertation we discuss three different topics. We begin by studying supersymmetric instantons for Yang-Mills theories on non-anticommutative superspace. Performing an iterative expansion in the non-commutativity parameter C, we solve the equation of motions for U(2) Super Yang-Mills with and without matter. For pure Yang-Mills, we solve the equations exactly. In addition to the usual 't Hooft SU(2) instanton, the deformation turns on a non-trivial U(1) conncetion which depends on the fermionic collective coordinates and the deformation parameter C. In the Higgs phase on the other hand, we solve the equations of motion to leading order in the coupling constant. Even though the instanton effective action receives a contribution of order C 2, the gluino condensate and the non-perturbative Affleck-Dine-Seiberg superpotential remain as in N = 1 super Yang-Mills. The second topic is related to twister strings. Perturbative super Yang-Mills can be reinterpreted as a D-instanton expansion of the topological B-model on the supermanifold CP3|4 . We extend this contruction to N = 1 and N = 2 quiver gauge theories by contructing fermionic orbifolds of CP3|4 . Topological string suggest some efficient rules for computing Yang-Mills perturbative amplitudes. We consider possible extensions of these rules to gravity amplitudes. We conclude by analyzing some mathematical aspects of super Calabi-Yau manifolds. The final topic is devoted to the study of half-BPS type IIB supergravity solutions. The moduli space of these solutions can be associated to a one-dimensional, zero temperature fermion gas in a harmonic potential. We studied a natural generalization of the fermion-supergravity map, considering the fermions at non-zero temperature. We found that the ADM energy of the supergravity solution reproduces the thermal fermion energy. One important effect of the temperature is that the background develops a null singularity. This singularity is naked, that is not "covered" by
Pavšič, Matej
2014-01-01
It is shown how a string living in a higher dimensional space can be approximated as a point particle with squared extrinsic curvature. We consider a generalized Howe-Tucker action for such a "rigid particle" and consider its classical equations of motion and constraints. We find that the algebra of the Dirac brackets between the dynamical variables associated with velocity and acceleration contains the spin tensor. After quantization, the corresponding operators can be represented by the Dirac matrices, projected onto the hypersurface that is orthogonal to the direction of 4-momentum. A condition for the consistency of such a representation is that the states must satisfy the Dirac equation with a suitable effective mass. The Pauli-Lubanski vector composed with such projected Dirac matrices is equal to the Pauli-Lubanski vector composed with the usual, non projected, Dirac matrices, and its eigenvalues thus correspond to spin one half states.
Instanton-dyon Ensembles III: Exotic Quark Flavors
Larsen, Rasmus
2016-01-01
"Exotic quarks" in the title refers to a modification of quark periodicity condition on the thermal circle by introduction of some phases -- known also as "flavor holonomies" -- different quark flavors. These phases provide a valuable tool, to be used for better understanding of deconfinement and chiral restoration phase transitions: by changing them one can dramatically modify both phase transitions. In the language of instanton constituents -- instanton-dyons or monopoles -- it has a very direct explanation: the interplay of flavor and color holonomies can switch topological zero modes between various dyon types. The model we will study in detail, the so called $Z_{N_c}$-symmetric QCD model with equal number of colors and flavors $N_c=N_f=2$ and special arrangement of flavor and color holonomies, ensure "most democratic" setting, in which each quark flavor and each dyon type are in one-to-one correspondence. The usual QCD has the opposite "most exclusive" arrangement: all quarks are antiperiodic and thus al...
Worst configurations (instantons) for compressed sensing over reals: a channel coding approach
Energy Technology Data Exchange (ETDEWEB)
Chertkov, Michael [Los Alamos National Laboratory; Chilappagari, Shashi K [UNIV OF AZ; Vasic, Bane [UNIV OF AZ
2010-01-01
We consider Linear Programming (LP) solution of a Compressed Sensing (CS) problem over reals, also known as the Basis Pursuit (BasP) algorithm. The BasP allows interpretation as a channel-coding problem, and it guarantees the error-free reconstruction over reals for properly chosen measurement matrix and sufficiently sparse error vectors. In this manuscript, we examine how the BasP performs on a given measurement matrix and develop a technique to discover sparse vectors for which the BasP fails. The resulting algorithm is a generalization of our previous results on finding the most probable error-patterns, so called instantons, degrading performance of a finite size Low-Density Parity-Check (LDPC) code in the error-floor regime. The BasP fails when its output is different from the actual error-pattern. We design CS-Instanton Search Algorithm (ISA) generating a sparse vector, called CS-instanton, such that the BasP fails on the instanton, while its action on any modification of the CS-instanton decreasing a properly defined norm is successful. We also prove that, given a sufficiently dense random input for the error-vector, the CS-ISA converges to an instanton in a small finite number of steps. Performance of the CS-ISA is tested on example of a randomly generated 512 * 120 matrix, that outputs the shortest instanton (error vector) pattern of length 11.
Provably Efficient Instanton Search Algorithm for LP decoding of LDPC codes over the BSC
Chilappagari, Shashi Kiran
2008-01-01
We consider Linear Programming (LP) decoding of a Low-Density Parity-Check (LDPC) code performing over the Binary Symmetric Channel (BSC). The LP decoder fails when it outputs a pseudo-codeword which is not a codeword. Following the approach of [1], we design an efficient algorithm termed the Instanton Search Algorithm (ISA) which, given a random input, generates a set of flips, called BSC-instanton, such that the LP decoder decodes the instanton into a pseudo-codeword distinct from the all-zero-codeword while any reduction of the instanton leads to the all-zero-codeword. We prove that (a) the LP decoder fails for any set of flips with support vector including an instanton; (b) for any original input, the algorithm outputs an instanton in the number of steps upper-bounded by twice the number of actual flips in the input. Repeated sufficient number of times, the ISA outcomes the number of unique instantons of different sizes. We illustrate the performance of the algorithm on the [155,64,20] Tanner code and sho...
Nissenbaum, Daniel; Lin, Hsin; Barbiellini, Bernardo; Bansil, Arun
2009-03-01
To study the performance of the Stochastic Gradient Approximation (SGA) for variational Quantum Monte Carlo methods, we have considered lithium nano-clusters [1] described by Hartree-Fock wavefunctions multiplied by two-body Jastrow factors with a single variational parameter b. Even when the system size increases, we have shown the feasibility of obtaining an accurate value of b that minimizes the energy without an explicit calculation of the energy itself. The present SGA algorithm is so efficient because an analytic gradient formula is used and because the statistical noise in the gradient is smaller than in the energy [2]. Interestingly, in this scheme the absolute value of the gradient is less important than the sign of the gradient. Work supported in part by U.S. DOE. [1] D. Nissenbaum et al., Phys. Rev. B 76, 033412 (2007). [2] A. Harju, J. Low. Temp. Phys. 140, 181 (2005).
The information metric on the moduli space of instantons with global symmetries
Directory of Open Access Journals (Sweden)
Emanuel Malek
2016-02-01
Full Text Available In this note we revisit Hitchin's prescription [1] of the Fisher metric as a natural measure on the moduli space of instantons that encodes the space–time symmetries of a classical field theory. Motivated by the idea of the moduli space of supersymmetric instantons as an emergent space in the sense of the gauge/gravity duality, we extend the prescription to encode also global symmetries of the underlying theory. We exemplify our construction with the instanton solution of the CPN sigma model on R2.
Search for QCD-instanton induced events in deep inelastic ep scattering at HERA
Abramowicz, H; Adamus, M; Adler, V; Aghuzumtsyan, G; Antonioli, P; Antonov, A; Arneodo, M; Bailey, D S; Bamberger, A; Barakbaev, A N; Barbagli, G; Barbi, M; Bari, G; Barreiro, F; Bartsch, D; Basile, M; Behrens, U; Bell, M; Bellagamba, L; Benen, A; Bertolin, A; Bhadra, S; Bloch, I; Bodmann, B; Bold, T; Boos, E G; Borras, K; Boscherini, D; Brock, I; Brook, N H; Brugnera, R; Brümmer, N; Bruni, A; Bruni, G; Bussey, P J; Butterworth, J M; Bylsma, B; Caldwell, A; Capua, M; Cara Romeo, G; Carli, T; Carlin, R; Catterall, C D; Chekanov, S; Chiochia, V; Chwastowski, J; Ciborowski, J; Ciesielski, R; Cifarelli, Luisa; Cindolo, F; Cloth, P; Cole, J E; Collins-Tooth, C; Contin, A; Cooper-Sarkar, A M; Coppola, N; Cormack, C; Corradi, M; Corriveau, F; Cottrell, A; D'Agostini, G; Dal Corso, F; Danilov, P; Dannheim, D; De Pasquale, S; Dementiev, R K; Derrick, M; Deshpande, Abhay A; Devenish, R C E; Dhawan, S; Dobur, D; Dolgoshein, B A; Doyle, A T; Drews, G; Durkin, L S; Dusini, S; Eisenberg, Y; Ermolov, P F; Eskreys, Andrzej; Ferrando, J; Ferrero, M I; Figiel, J; Filges, D; Foster, B; Foudas, C; Fourletov, S; Fourletova, J; Fricke, U; Fusayasu, T; Gabareen, A; Galas, A; Gallo, E; Garfagnini, A; Geiser, A; Genta, C; Gialas, I; Giusti, P; Gladilin, L K; Gladkov, D; Glasman, C; Gliga, S; Goers, S; Golubkov, Yu A; Goncalo, R; González, O; Göttlicher, P; Grabowska-Bold, I; Grijpink, S; Grzelak, G; Gutsche, O; Gwenlan, C; Haas, T; Hain, W; Hall-Wilton, R; Hamatsu, R; Hamilton, J; Hanlon, S; Hart, J C; Hartmann, H; Hartner, G; Heaphy, E A; Heath, G P; Helbich, M; Heusch, C A; Hilger, E; Hillert, S; Hirose, T; Hochman, D; Holm, U; Iacobucci, G; Iga, Y; Inuzuka, M; Irrgang, P; Jakob, P; Jones, T W; Kagawa, S; Kahle, B; Kaji, H; Kananov, S; Karstens, F; Kataoka, M; Katkov, I I; Kcira, D; Khein, L A; Kim, J Y; Kim, Y K; Kind, O; Kisielewska, D; Kitamura, S; Klimek, K; Koffeman, E; Kohno, T; Kooijman, P; Koop, T; Korzhav, I A; Kotanski, A; Kötz, U; Kowal, A M; Kowal, M; Kowalski, H; Kowalski, T; Krakauer, D; Kramberger, G; Kreisel, A; Krumnack, N; Kuze, M; Kuzmin, V A; Labarga, L; Labes, H; Lainesse, J; Lammers, S; Lee, J H; Lelas, D; Levchenko, B B; Levman, G M; Levy, A; Li, L; Lightwood, M S; Lim, H; Lim, I T; Limentani, S; Ling, T Y; Liu, X; Löhr, B; Lohrmann, E; Loizides, J H; Long, K R; Longhin, A; Lukina, O Yu; Luzniak, P; Maddox, E; Magill, S; Mankel, R; Margotti, A; Marini, G; Martin, J F; Mastroberardino, A; Matsuzawa, K; Mattingly, M C K; McCubbin, N A; Mellado, B; Melzer-Pellmann, I A; Menary, S R; Metlica, F; Meyer, U; Miglioranzi, S; Milite, M; Mirea, A; Monaco, V; Montanari, A; Mus, B; Nagano, K; Namsoo, T; Nania, R; Nguyen, C N; Nigro, A; Ning, Y; Notz, D; Nowak, R J; Nuncio-Quiroz, A E; Oh, B Y; Olkiewicz, K; Pac, M Y; Padhi, S; Paganis, S; Palmonari, F; Parenti, A; Park, I H; Patel, S; Paul, E; Pavel, N; Pawlak, J M; Pelfer, P G; Pellegrino, A; Pesci, A; Piotrzkowski, K; Plucinsky, P P; Pokrovskiy, N S; Polini, A; Posocco, M; Proskuryakov, A S; Przybycien, M B; Rautenberg, J; Raval, A; Reeder, D D; Ren, Z; Renner, R; Repond, J; Riveline, U; Karshon, M; Robins, S; Rosin, M; Rurua, L; Ruspa, M; Sacchi, R; Salehi, H; Sartorelli, G; Savin, A A; Saxon, D H; Schagen, S; Schioppa, M; Schlenstedt, S; Schleper, P; Schmidke, W B; Schneekloth, U; Sciulli, F; Shcheglova, L M; Skillicorn, I O; Slominski, W; Smith, W H; Soares, M; Solano, A; Son, D; Sosnovtsev, V V; Stairs, D G; Stanco, L; Standage, J; Stifutkin, A; Stoesslein, U; Stonjek, S; Stopa, P; Straub, P B; Suchkov, S; Susinno, G; Suszycki, L; Sutton, M R; Sztuk, J; Szuba, D; Szuba, J; Tandler, J; Tapper, A D; Targett-Adams, C; Tassi, E; Tawara, T; Terron, J; Tiecke, H G; Tokushuku, K; Tsurugai, T; Turcato, M; Tymieniecka, T; Ukleja, A; Ukleja, J; Vázquez, M; Velthuis, J J; Vlasov, N N; Voss, K C; Walczak, R; Walsh, R; Wang, M; Weber, A; Whitmore, J J; Wick, K; Wiggers, L; Wills, H H; Wing, M; Wolf, G; Yamada, S; Yamashita, T; Yamazaki, Y; Yoshida, R; Youngman, C; Zambrana, M; Zawiejski, L; Zeuner, W; Zhautykov, B O; Zichichi, A; Ziegler, A; Zotkin, S A; De Wolf, E; Del Peso, J
2003-01-01
A search for QCD-instanton-induced events in deep inelastic ep scattering has been performed with the ZEUS detector at the HERA collider, using data corresponding to an integrated luminosity of 38 pb^{-1}. A kinematic range defined by cuts on the photon virtuality, Q^2 > 120 GeV^2, and on the Bjorken scaling variable, x > 10^{-3}, has been investigated. The QCD-instanton induced events were modelled by the Monte Carlo generator QCDINS. A background-independent, conservative 95% confidence level upper limit for the instanton cross section of 26 pb is obtained, to be compared with the theoretically expected value of 8.9 pb.
Gluon Green functions free of Quantum fluctuations
Athenodorou, A; De Soto, F; Rodríguez-Quintero, J; Zafeiropoulos, S
2016-01-01
This letter reports on how the Wilson flow technique can efficaciously kill the short-distance quantum fluctuations of 2- and 3-gluon Green functions, removes the $\\Lambda_{\\rm QCD}$ scale and destroys the transition from the confining non-perturbative to the asymptotically-free perturbative sector. After the Wilson flow, the behavior of the Green functions with momenta can be described in terms of the quasi-classical instanton background. The same behavior also occurs, before the Wilson flow, at low-momenta. This last result permits applications as, for instance, the detection of instanton phenomenological properties or a cheap lattice calibration.
Energy Technology Data Exchange (ETDEWEB)
Richardson, Jeremy O., E-mail: jeremy.richardson@fau.de; Bauer, Rainer; Thoss, Michael [Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7/B2, 91058 Erlangen (Germany)
2015-10-07
We present semiclassical approximations to Green’s functions of multidimensional systems, extending Gutzwiller’s work to the classically forbidden region. Based on steepest-descent integrals over these functions, we derive an instanton method for computing the rate of nonadiabatic reactions, such as electron transfer, in the weak-coupling limit, where Fermi’s golden-rule can be employed. This generalizes Marcus theory to systems for which the environment free-energy curves are not harmonic and where nuclear tunnelling plays a role. The derivation avoids using the Im F method or short-time approximations to real-time correlation functions. A clear physical interpretation of the nuclear tunnelling processes involved in an electron-transfer reaction is thus provided. In Paper II [J. O. Richardson, J. Chem. Phys. 143, 134116 (2015)], we discuss numerical evaluation of the formulae.
Zhukovsky, V. Ch.; Krevchik, V. D.; Semenov, M. B.; Krevchik, P. V.; Zaytsev, R. V.; Egorov, I. A.
2016-11-01
The field and temperature dependence of the probability of two-dimensional dissipative tunneling is studied in the framework of one-instanton approximation for a model double-well oscillator potential in an external electric field at finite temperature with account for the influence of two local phonon modes for quantum dots in a system of a combined atomic force and a scanning tunneling microscope. It is demonstrated that in the mode of synchronous parallel transfer of tunneling particles from the cantilever tip to the quantum dot the two local phonon modes result in the occurrence of two stable peaks in the curve of the 2D dissipative tunneling probability as a function of the field. Qualitative comparison of the theoretical curve in the limit of weak dissociation and the experimental current-voltage characteristic for quantum dots that grow from colloidal gold under a cantilever tip at the initial stage of quantum-dot formation when the quantum dot size does not exceed 10 nm is performed. It is established that one of the two stable peaks that correspond to interaction of tunneling particles with two local phonon modes in the temperature dependence of the 2D dissipative tunneling probability can be split in two, which corresponds to the tunneling channel interference mechanism. It is found that the theoretically predicted and experimentally observed mode of quantum beats occurs near the bifurcation point.
Non-extremal D-instantons and the AdS/CFT correspondence
Energy Technology Data Exchange (ETDEWEB)
Bergshoeff, Eric [Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Collinucci, Andres [Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Ploegh, Andre [Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Riet, Thomas van [Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Vandoren, Stefan [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)
2006-01-15
We investigate non-extremal D-instantons in an asymptotically AdS{sub 5} x S{sup 5} background and the role they play in the AdS{sub 5}/CFT{sub 4} correspondence. We find that the holographic dual operators of non-extremal D-instanton configurations do not correspond to self-dual Yang-Mills instantons, and we compute explicitly the deviation from self-duality. Furthermore, a class of non-extremal D-instantons yield Euclidean axionic wormhole solutions with two asymptotic boundaries. After Wick rotating, this provides a playground for investigating holography in the presence of cosmological singularities in a closed universe.
Metric of the SU(N) caloron moduli space and its relation to instantons
Diakonov, D; Diakonov, Dmitri; Gromov, Nikolay
2005-01-01
Calorons of the SU(N) gauge group with non-trivial holonomy, i.e. periodic instantons with arbitrary eigenvalues of the Polyakov line at spatial infinity, can be viewed as composed of N Bogomolnyi--Prasad--Sommerfeld (BPS) monopoles or dyons. We find the metric of the moduli space of the SU(N) calorons in terms of the constituent monopole positions and their U(1) phases. In the small temperature limit calorons reduce locally to the standard instantons with trivial holonomy, whose moduli space is usually written in terms of the instanton center, size and orientation in the color space. We show that these collective coordinates can be explicitly written through dyons positions and phases. We also check that the standard instanton measure coincides exactly with that of N dyons.
Octet Magnetic Moments with Null Instantons and Semibosonized Nambu-Jona-Lasinio Model
Bukina, E N
1999-01-01
It is shown that the difference between the magnetic moment results in the quark model with null instantons and semibosonized Nambu-Jona-Lasinio model lies in the description of the magnetic moment of the $ \\Lambda$-hyperon.
Path Dependence of the Quark Nonlocal Condensate within the Instanton Model
Trevisan, L A; Tomio, Lauro; Tomio, Lauro
2004-01-01
Within the instanton liquid model, we study the dependence of the gauge invariant two--point quark correlator on the path used to perform the color parallel transport between two points in the Euclidean space.
Search for QCD Instanton-Induced Processes at HERA in the High-$Q^2$ Domain
Andreev, Vladimir; Begzsuren, Khurelbaatar; Belousov, Anatoli; Bolz, Arthur; Boudry, Vincent; Brandt, Gerhard; Brisson, Violette; Britzger, Daniel; Buniatyan, Armen; Bylinkin, Alexander; Bystritskaya, Lena; Campbell, Alan; Cantun Avila, Karla~Beatriz; Cerny, Karel; Chekelian, Vladimir; Contreras, Guillermo; Cvach, Jaroslav; Dainton, John; Daum, Karin; Diaconu, Cristinel; Dobre, Monica; Dodonov, Vitaliy; Eckerlin, Guenter; Egli, Stephan; Elsen, Eckhard; Favart, Laurent; Fedotov, Alexandre; Feltesse, Joel; Ferencei, Jozef; Fleischer, Manfred; Fomenko, Alexander; Gabathuler, Erwin; Gayler, Joerg; Ghazaryan, Samvel; Goerlich, Lidia; Gogitidze, Nelly; Gouzevitch, Maxime; Grab, Christoph; Grebenyuk, Anastasia; Greenshaw, Timothy; Grindhammer, Guenter; Haidt, Dieter; Henderson, Rob~CW; Hladky, Jan; Hoffmann, Dirk; Horisberger, Roland; Hreus, Tomas; Huber, Florian; Jacquet, Marie; Janssen, Xavier; Jung, Hannes; Kapichine, Mikhail; Katzy, Judith; Kiesling, Christian; Klein, Max; Kleinwort, Claus; Kogler, Roman; Kostka, Peter; Kretzschmar, Jan; Krücker, Dirk; Krüger, K.; Landon, Murrough; Lange, Wolfgang; Laycock, Paul; Lebedev, Andrei; Levonian, Sergey; Lipka, Katerina; List, Benno; List, Jenny; Lobodzinski, Bogdan; Malinovski, Evgenij; Martyn, Hans-Ulrich; Maxfield, Steve~J; Mehta, Andrew; Meyer, Andreas; Meyer, Hinrich; Meyer, Joachim; Mikocki, Stanislav; Morozov, Anatoly; Müller, Katharina; Naumann, Thomas; Newman, Paul~R; Niebuhr, Carsten; Nowak, Grazyna; Olsson, Jan~Erik; Ozerov, Dmitri; Pascaud, Christian; Patel, Girish; Perez, Emmanuelle; Petrukhin, Alexey; Picuric, Ivana; Pirumov, Hayk; Pitzl, Daniel; Placakyte, Ringaile; Pokorny, Boris; Polifka, Richard; Radescu, Voica; Raicevic, Natasa; Ravdandorj, Togoo; Reimer, Petr; Rizvi, Eram; Robmann, Peter; Roosen, Robert; Rostovtsev, Andrei; Rotaru, Marina; Rusakov, Serguei; Salek, David; Sankey, Dave~PC; Sauter, Michel; Sauvan, Emmanuel; Schmitt, Stefan; Schoeffel, Laurent; Schöning, Andre; Sefkow, Felix; Shushkevich, Stanislav; Soloviev, Yuri; Sopicki, Pawel; South, David; Spaskov, Vladimir; Specka, Arnd; Steder, Michael; Stella, Bruno; Straumann, Ulrich; Sykora, Tomas; Thompson, Paul; Traynor, Daniel; Truöl, Peter; Tsakov, Ivan; Tseepeldorj, Baatar; Turnau, Jacek; Valkarova, Alice; Vallee, Claude; Van Mechelen, Pierre; Vazdik, Iakov; Wegener, Dietrich; Wünsch, Eberhard; Zacek, Jozef; Zhang, Zhiqing; Zlebcik, Radek; Zohrabyan, Hamlet; Zomer, Fabian
2016-07-07
Signals of QCD instanton-induced processes are searched for in neutral current deep-inelastic scattering at the electron-proton collider HERA in the kinematic region defined by the Bjorken-scaling variable $x > 10^{-3}$, the inelasticity $0.2< y < 0.7$ and the photon virtuality $150 < Q^2 < 15000$ GeV$^2$. The search is performed using H1 data corresponding to an integrated luminosity of ~$351$ pb$^{-1}$. No evidence for the production of QCD instanton-induced events is observed. Upper limits on the cross section for instanton-induced processes between $1.5$~pb and $6$~pb, at $95\\%$~ confidence level, are obtained depending on the kinematic domain in which instantons could be produced. Compared to earlier publications, the limits are improved by an order of magnitude and for the first time are challenging theory predictions.
Gravitational instanton in Hilbert space and the mass of high energy elementary particles
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S
2004-06-01
While the theory of relativity was formulated in real spacetime geometry, the exact formulation of quantum mechanics is in a mathematical construction called Hilbert space. For this reason transferring a solution of Einstein's field equation to a quantum gravity Hilbert space is far of being a trivial problem. On the other hand {epsilon}{sup ({infinity}}{sup )} spacetime which is assumed to be real is applicable to both, relativity theory and quantum mechanics. Consequently, one may expect that a solution of Einstein's equation could be interpreted more smoothly at the quantum resolution using the Cantorian {epsilon}{sup ({infinity}}{sup )} theory. In the present paper we will attempt to implement the above strategy to study the Eguchi-Hanson gravitational instanton solution and its interpretation by 't Hooft in the context of quantum gravity Hilbert space as an event and a possible solitonic 'extended' particle. Subsequently we do not only reproduce the result of 't Hooft but also find the mass of a fundamental 'exotic' symplictic-transfinite particle m{approx_equal}1.8 MeV as well as the mass M{sub x} and M (Planck) which are believed to determine the GUT and the total unification of all fundamental interactions respectively. This may be seen as a further confirmation to an argument which we put forward in various previous publications in favour of an alternative mass acquisition mechanism based on unification and duality considerations. Thus even in case that we never find the Higgs particle experimentally, the standard model would remain substantially intact as we can appeal to tunnelling and unification arguments to explain the mass. In fact a minority opinion at present is that finding the Higgs particle is not a final conclusive argument since one could ask further how the Higgs particle came to its mass which necessitates a second Higgs field. By contrast the present argument could be viewed as an ultimate theory
Gravitational instantons, self-duality and geometric flows
Bourliot, F; Petropoulos, P M; Spindel, Ph
2009-01-01
We discuss four-dimensional "spatially homogeneous" gravitational instantons. These are self-dual solutions of Euclidean vacuum Einstein's equations with potentially non-vanishing cosmological constant. They are endowed with a product structure R \\times M_3 leading to a natural foliation into three-dimensional subspaces evolving in Euclidean time. For a large class of three-dimensional subspaces, the dynamics coincides with the geometric flow on the three-dimensional homogeneous slice, driven by the Ricci tensor plus an so(3) gauge connection. The metric on the three-dimensional space is related to the vielbein of the three-dimensional subspace, while the gauge field is inherited from the anti-self-dual component of the four-dimensional Levi--Civita connection.
Instanton transition in thermal and moduli deformed de Sitter cosmology
Kounnas, Costas; Partouche, Hervé
2008-04-01
We consider the de Sitter cosmology deformed by the presence of a thermal bath of radiation and/or time-dependent moduli fields. Depending on the parameters, either a first or second-order phase transition can occur. In the first case, an instanton allows a double analytic continuation. It induces a probability to enter the inflationary evolution by tunnel effect from another cosmological solution. The latter starts with a big bang and, in the case the transition does not occur, ends with a big crunch. A temperature duality exchanges the two cosmological branches. In the limit where the pure de Sitter universe is recovered, the tunnel effect reduces to a “creation from nothing”, due to the vanishing of the big bang branch. However, the latter may be viable in some range of the deformation parameter. In the second case, there is a smooth evolution from a big bang to the inflationary phase.
Instanton transition in thermal and moduli deformed de Sitter cosmology
Kounnas, Costas
2007-01-01
We consider the de Sitter cosmology deformed by the presence of a thermal bath of radiation and/or time-dependent moduli fields. We find that an instanton allowing a double analytic continuation induces a probability to enter this inflationary evolution by tunnel effect from another cosmological solution. The latter starts with a big bang and, in the case the transition does not occur, ends with a big crunch. A temperature duality exchanges the two cosmological branches. In the limit where the pure de Sitter universe is recovered, the tunnel effect reduces to a ''creation from nothing'', due to the vanishing of the big bang branch. However, the latter happens to be viable in some range of the deformation parameters.
Summing up Open String Instantons and N=1 String Amplitudes
Mayr, Peter
2002-01-01
We compute the instanton expansions of the holomorphic couplings in the effective action of certain $\\cx N=1$ supersymmetric four-dimensional open string vacua. These include the superpotential $W(\\phi)$, the gauge kinetic function $f(\\phi)$ and a series of other holomorphic couplings which are known to be related to amplitudes of topological open strings at higher world-sheet topologies. The results are in full agreement with the interpretation of the holomorphic couplings as counting functions of BPS domain walls. Similar techniques are used to compute genus one partition function for the closed topological string on Calabi--Yau 4-fold which gives rise to a theory with the same number of supercharges in two dimensions.
Sasakian quiver gauge theories and instantons on the conifold
Geipel, Jakob C; Popov, Alexander D; Szabo, Richard J
2016-01-01
We consider Spin(4)-equivariant dimensional reduction of Yang-Mills theory on manifolds of the form $M^d \\times T^{1,1}$, where $M^d$ is a smooth manifold and $T^{1,1}$ is a five-dimensional Sasaki-Einstein manifold Spin(4)/U(1). We obtain new quiver gauge theories on $M^d$ extending those induced via reduction over the leaf spaces $\\mathbb{C}P^1 \\times \\mathbb{C}P^1$ in $T^{1,1}$. We describe the Higgs branches of these quiver gauge theories as moduli spaces of Spin(4)-equivariant instantons on the conifold which is realized as the metric cone over $T^{1,1}$. We give an explicit construction of these moduli spaces as K\\"ahler quotients.
Generalized Whittaker states for instanton counting with fundamental hypermultiplets
Kanno, Hiroaki
2012-01-01
M-theoretic construction of N=2 gauge theories implies that the instanton partition function is expressed as the scalar product of coherent states (Whittaker states) in the Verma module of an appropriate two dimensional conformal field theory. We present the characterizing conditions for such states that give the partition function with fundamental hypermultiplets for SU(3) theory and SU(2) theory with a surface operator. We find the states are no longer the coherent states in the strict sense but we can characterize them in terms of a few annihilation operators of lower levels combined with the zero mode (Cartan part) of the Virasoro algebra L_0 or the sl(2) current algebra J_0^0.
Pion radiative weak decay from the instanton vacuum
Shim, Sang-In; Kim, Hyun-Chul
2017-09-01
We investigate the vector and axial-vector form factors for the pion radiative weak decays π+ →e+νe γ and π+ →e+νee+e-, based on the gauged effective chiral action from the instanton vacuum in the large Nc limit. The nonlocal contributions, which arise from the gauging of the action, enhance the vector form factor by about 20%, whereas the axial-vector form factor is reduced by almost 30%. Both the results for the vector and axial-vector form factors at the zero momentum transfer are in good agreement with the experimental data. The dependence of the form factors on the momentum transfer is also studied. The slope parameters are computed and compared with other works.
Instanton transition in thermal and moduli deformed de Sitter cosmology
Energy Technology Data Exchange (ETDEWEB)
Kounnas, Costas [Laboratoire de Physique Theorique, Ecole Normale Superieure, 24 rue Lhomond, F-75231 Paris cedex 05 (France)], E-mail: costas.kounnas@lpt.ens.fr; Partouche, Herve [Centre de Physique Theorique, Ecole Polytechnique, F-91128 Palaiseau cedex (France)], E-mail: herve.partouche@cpht.polytechnique.fr
2008-04-11
We consider the de Sitter cosmology deformed by the presence of a thermal bath of radiation and/or time-dependent moduli fields. Depending on the parameters, either a first or second-order phase transition can occur. In the first case, an instanton allows a double analytic continuation. It induces a probability to enter the inflationary evolution by tunnel effect from another cosmological solution. The latter starts with a big bang and, in the case the transition does not occur, ends with a big crunch. A temperature duality exchanges the two cosmological branches. In the limit where the pure de Sitter universe is recovered, the tunnel effect reduces to a 'creation from nothing', due to the vanishing of the big bang branch. However, the latter may be viable in some range of the deformation parameter. In the second case, there is a smooth evolution from a big bang to the inflationary phase.
Gaussian Sum-Rules, Scalar Gluonium, and Instantons
Steele, T G; Orlandini, G
2002-01-01
Gaussian sum-rules relate a QCD prediction to a two-parameter Gaussian-weighted integral of a hadronic spectral function, providing a clear conceptual connection to quark-hadron duality. In contrast to Laplace sum-rules, the Gaussian sum-rules exhibit enhanced sensitivity to excited states of the hadronic spectral function. The formulation of Gaussian sum-rules and associated analysis techniques for extracting hadronic properties from the sum-rules are reviewed and applied to scalar gluonium. With the inclusion of instanton effects, the Gaussian sum-rule analysis results in a consistent scenario where the gluonic resonance strength is spread over a broad energy range below 1.6 GeV, and indicates the presence of gluonium content in more than one hadronic state.
Self-dual gravitational instantons and geometric flows of all Bianchi types
Petropoulos, P M; Siampos, K
2011-01-01
We investigate four-dimensional, self-dual gravitational instantons endowed with a product structure RxM_3, where M_3 is homogeneous of Bianchi type. We analyze the general conditions under which Euclidean-time evolution in the gravitational instanton can be identified with a geometric flow of a metric on M_3. This includes both unimodular and non-unimodular groups, and the corresponding geometric flow is a general Ricci plus Yang--Mills flow accompanied by a diffeomorphism.
Topological Quantization of Instantons in SU(2) Yang-Mills Theory
Institute of Scientific and Technical Information of China (English)
ZHONG Wo-Jun; DUAN Yi-Shi
2008-01-01
By decomposing SU(2) gauge potential in four-dimensional Euclidean SU(2) Yang-Mills theory in a new way,we find that the instanton number related to the isospin defects of a doublet order parameter can be topologically quantized by the Hopf index and Brouwer degree.It is also shown that the instanton number is just the sum of the topological charges of the isospin defects in the non-trivial sector of Yang-Mills theory.
Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
de la Ossa, Xenia; Larfors, Magdalena; Svanes, Eirik E.
2016-11-01
We describe the infinitesimal moduli space of pairs ( Y, V) where Y is a manifold with G 2 holonomy, and V is a vector bundle on Y with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical G 2 cohomology developed by Reyes-Carrión and Fernández and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli {H}_{{overset{ěe }{d}}_A}^1(Y,End(V)) plus the moduli of the G 2 structure preserving the instanton condition. The latter piece is contained in {H}_{overset{ěe }{d}θ}^1(Y,TY) , and is given by the kernel of a map overset{ěe }{F} which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the map overset{ěe }{F} is given in terms of the curvature of the bundle and maps {H}_{overset{ěe }{d}θ}^1(Y,TY) into {H}_{{overset{ěe }{d}}_A}^2(Y,End(V)) , and moreover can be used to define a cohomology on an extension bundle of TY by End( V). We comment further on the resemblance with the holomorphic Atiyah algebroid and connect the story to physics, in particular to heterotic compactifications on ( Y, V) when α' = 0.
An introduction to quantum gravity
Esposito, Giampiero
2011-01-01
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental interactions, while giving rise to new developments in mathematics. The various competing theories, e.g. string theory and loop quantum gravity, have still to be checked against observations. We review the classical and quantum foundations necessary to study field-theory approaches to quantum gravity, the passage from old to new unification in quantum field theory, canonical quantum gravity, the use of functional integrals, the properties of gravitational instantons, the use of spectral zeta-functions in the quantum theory of the universe, Hawking radiation, some theoretical achievements and some key experimental issues.
Instanton Induced Neutrino Majorana Masses in CFT Orientifolds with MSSM-like spectra
Ibáñez, L E; Uranga, Angel M
2007-01-01
Recently it has been shown that string instanton effects may give rise to neutrino Majorana masses in certain classes of semi-realistic string compactifications. In this paper we make a systematic search for supersymmetric MSSM-like Type II Gepner orientifold constructions admitting boundary states associated with instantons giving rise to neutrino Majorana masses and other L- and/or B-violating operators. We analyze the zero mode structure of D-brane instantons on general type II orientifold compactifications, and show that only instantons with O(1) symmetry can have just the two zero modes required to contribute to the 4d superpotential. We however discuss how the addition of fluxes and/or possible non-perturbative extensions of the orientifold compactifications would allow also instantons with Sp(2) and U(1) symmetries to generate such superpotentials. In the context of Gepner orientifolds with MSSM-like spectra, we find no models with O(1) instantons with just the required zero modes to generate a neutrin...
Hilbert series for moduli spaces of instantons on ℂ{sup 2}/ℤ{sub n}
Energy Technology Data Exchange (ETDEWEB)
Dey, Anindya [Theory Group and Texas Cosmology Center, Department of Physics,University of Texas at Austin, Austin, TX 78712 (United States); Hanany, Amihay [Theoretical Physics Group, The Blackett Laboratory, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom); Mekareeya, Noppadol [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut),Föhringer Ring 6, 80805 München (Germany); Theory Group, Physics Department, CERN,CH-1211, Geneva 23 (Switzerland); Rodríguez-Gómez, Diego [Department of Physics, Universidad de Oviedo,Avda. Calvo Sotelo 18, 33007, Oviedo (Spain); Seong, Rak-Kyeong [Theoretical Physics Group, The Blackett Laboratory, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom); School of Physics, Korea Institute for Advanced Study,85 Hoegi-ro, Seoul 130-722 (Korea, Republic of)
2014-01-31
We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A{sub n−1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiver descriptions do indeed agree, as expected.
Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
Dey, Anindya; Mekareeya, Noppadol; Rodríguez-Gómez, Diego; Seong, Rak-Kyeong
2014-01-01
We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A_{n-1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiv...
Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
Dey, Anindya; Mekareeya, Noppadol; Rodríguez-Gómez, Diego; Seong, Rak-Kyeong
2014-01-01
We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A_{n-1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiv...
Quantum Dynamics of Supergravity on R^3 x S^1
Tong, David
2014-01-01
We study the quantum dynamics of N=1 supergravity in four dimensions with a compact spatial circle. Supersymmetry ensures that the perturbative contributions to the Casimir energy on the circle cancel. However, instanton contributions remain. These render supersymmetric compactification on a circle unstable and the background dynamically decompactifies back to four dimensions. The calculation provides a testing ground for some old ideas in Euclidean quantum gravity. In particular, we show that gravitational instantons are associated to a new, infra-red scale which is naturally exponentially suppressed relative to the Planck scale and arises from the logarithmic running of the Gauss-Bonnet term. There are also some interesting technical details, including the non-cancellation of bosonic and fermionic determinants around the background of a self-dual gravitational instanton, despite the existence of supersymmetry.
Observing Quantum Tunneling in Perturbation Series
Suzuki, H; Suzuki, Hiroshi; Yasuta, Hirofumi
1997-01-01
It is well-known that the quantum tunneling makes conventional perturbation series non-Borel summable. We use this fact reversely and attempt to extract the decay width of the false-vacuum from the actual perturbation series of the vacuum energy density (vacuum bubble diagrams). It is confirmed that, at least in quantum mechanical examples, our proposal provides a complimentary approach to the the conventional instanton calculus in the strong coupling region.
Quantum-mechanical tunneling differential operators, zeta-functions and determinants
Casahorrán, J
2002-01-01
We consider in detail the quantum-mechanical problem associated with the motion of a one-dimensional particle under the action of the double-well potential. Our main tool will be the euclidean (imaginary time) version of the path-integral method. Once we perform the Wick rotation, the euclidean equation of motion is the same as the usual one for the point particle in real time, except that the potential at issue is turned upside down. In doing so, our double-well potential becomes a two-humped potential. As required by the semiclassical approximation we may study the quadratic fluctuations over the instanton which represents in this context the localised finite-action solutions of the euclidean equation of motion. The determinants of the quadratic differential operators are evaluated by means of the zeta-function method. We write in closed form the eigenfunctions as well as the energy eigenvalues corresponding to such operators by using the shape-invariance symmetry. The effect of the multi-instantons configu...
Al-Khalili, Jim
2003-01-01
In this lively look at quantum science, a physicist takes you on an entertaining and enlightening journey through the basics of subatomic physics. Along the way, he examines the paradox of quantum mechanics--beautifully mathematical in theory but confoundingly unpredictable in the real world. Marvel at the Dual Slit experiment as a tiny atom passes through two separate openings at the same time. Ponder the peculiar communication of quantum particles, which can remain in touch no matter how far apart. Join the genius jewel thief as he carries out a quantum measurement on a diamond without ever touching the object in question. Baffle yourself with the bizzareness of quantum tunneling, the equivalent of traveling partway up a hill, only to disappear then reappear traveling down the opposite side. With its clean, colorful layout and conversational tone, this text will hook you into the conundrum that is quantum mechanics.
One-loop and D-instanton corrections to the effective action of open string models
Energy Technology Data Exchange (ETDEWEB)
Schmidt-Sommerfeld, Maximilian
2009-07-02
Methods for the calculation of certain corrections to effective actions, which comprehend the low-energy physics of string compactifications with open strings, are explained. First the shape of such actions is describes and some examples for compactifications are presented, especially a type I string model to which a dual model on the base of the heterotic string is known. Then corrections on the gauge coupling constant and on the gauge-kinetic function are discussed. general procedures for their calculation are sketched and applied to some models. The explicitly determinded corrections depend non-holomorphically on the moduli of the compactification manifold. It is explained that this is not in disagreement on the holomorphy of the gauge-kinetic function and how the latter can be extracted from the calculated results. Next D-instantons and their influence on the low-energy action are detailedly analyzed, whereby the zero modes of the instantons and global Abelian symmetries play a central role. A formula for the caclulation of scattering matrix elements in instanton sectors is given. It is to be expected that the considered instantons contribute to the superpotential of the low-energy action. However from the formula it becomes not immediately clear, how far this is possible. The mentioned formula seems to lead to expressions, which are in disagreement to the holomorphy of the superpotential. It is shown that non-holomorphic terms partly simplify, partly are so composed that the result is in accordance with the holomorphy of the superpotential. The D-instanton calculus is then used in order to derive the ADS superpotential, which is known from field theory. That this is possible is to be considered as successful test of the instanton calculus. D-instanton corrections to the gauge-kinetic functions are considered. S duality between the type I and the heterotic string is used in order to determine how the structure of the zero modes of the relevant instantons looks
Note on a Cohomological Theory of Contact-Instanton and Invariants of Contact Structures
Pan, Yiwen
2014-01-01
In the localization of 5-dimensional N = 1 super-Yang-Mills, contact-instantons arise as non-perturbative contributions. In this note, we revisit such configurations and discuss their generalizations. We propose for contact-instantons a cohomological theory whose BRST observables are invariants of the background contact geometry. To make the formalism more concrete, we study the moduli problem of contact- instanton, and we find that it is closely related to the eqiuivariant index of a canonical Dirac-Kohn operator associated to the geometry. An integral formula is given when the geometry is K-contact. We also discuss the relation to 5d N = 1 super-Yang- Mills, and by studying a contact-instanton solution canonical to the background geometry, we discuss a possible connection between N = 1 theory and contact homology. We also uplift the 5d theory a 6d cohomological theory which localizes to Donaldson-Uhlenbeck-Yau instantons when placed on special geometry.
Instantons near a tachyonic top in anti de Sitter and the no-boundary regulator
Lee, Bum-Hoon; Ro, Daeho; Yeom, Dong-han
2014-01-01
We investigate instantons near the tachyonic top in the anti de Sitter (AdS) background. If the mass around the hill-top is above the Breitenlohner-Freedman (BF) bound, then the top is classically stable. When the BF bound is satisfied, it is already known that there can exist instantons with a non-zero probability, though fine-tunings of the potential are required. On the other hand, we may consider the possibility to obtain instantons with a non-zero probability for more natural shape of potentials. We found that the no-boundary regulator is useful to assign a non-zero probability for general instantons near the tachyonic top within a consistent framework. To use the no-boundary regulator, we need to introduce the complexification of fields. One interesting feature is that, for these AdS instantons, the classicality may not be satisfied after the Wick rotation and hence after the nucleation. This magnifies a novel difference between dS and AdS; a semi-classical boundary observer in AdS may notice the disper...
BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem
Nekrasov, Nikita
2016-01-01
Gieseker-Nakajima moduli spaces $M_{k}(n)$ parametrize the charge $k$ noncommutative $U(n)$ instantons on ${\\bf R}^{4}$ and framed rank $n$ torsion free sheaves $\\mathcal{E}$ on ${\\bf C\\bf P}^{2}$ with ${\\rm ch}_{2}({\\mathcal{E}}) = k$. They also serve as local models of the moduli spaces of instantons on general four-manifolds. We study the generalization of gauge theory in which the four dimensional spacetime is a stratified space $X$ immersed into a Calabi-Yau fourfold $Z$. The local model ${\\bf M}_{k}({\\vec n})$ of the corresponding instanton moduli space is the moduli space of charge $k$ (noncommutative) instantons on origami spacetimes. There, $X$ is modelled on a union of (up to six) coordinate complex planes ${\\bf C}^{2}$ intersecting in $Z$ modelled on ${\\bf C}^{4}$. The instantons are shared by the collection of four dimensional gauge theories sewn along two dimensional defect surfaces and defect points. We also define several quiver versions ${\\bf M}_{\\bf k}^{\\gamma}({\\vec{\\bf n}})$ of ${\\bf M}_{k}...
Instanton-based techniques for analysis and reduction of error floor of LDPC codes
Energy Technology Data Exchange (ETDEWEB)
Chertkov, Michael [Los Alamos National Laboratory; Chilappagari, Shashi K [Los Alamos National Laboratory; Stepanov, Mikhail G [Los Alamos National Laboratory; Vasic, Bane [SENIOR MEMBER, IEEE
2008-01-01
We describe a family of instanton-based optimization methods developed recently for the analysis of the error floors of low-density parity-check (LDPC) codes. Instantons are the most probable configurations of the channel noise which result in decoding failures. We show that the general idea and the respective optimization technique are applicable broadly to a variety of channels, discrete or continuous, and variety of sub-optimal decoders. Specifically, we consider: iterative belief propagation (BP) decoders, Gallager type decoders, and linear programming (LP) decoders performing over the additive white Gaussian noise channel (AWGNC) and the binary symmetric channel (BSC). The instanton analysis suggests that the underlying topological structures of the most probable instanton of the same code but different channels and decoders are related to each other. Armed with this understanding of the graphical structure of the instanton and its relation to the decoding failures, we suggest a method to construct codes whose Tanner graphs are free of these structures, and thus have less significant error floors.
On the instanton contributions to the masses and couplings of E$_{6}$ singlets
Berglund, P; De la Ossa, X C; Derrick, E; Distler, Jacques; Hübsch, T
1995-01-01
We consider the gauge neutral matter in the low--energy effective action for string theory compactification on a \\cym\\ with (2,2) world--sheet supersymmetry. At the classical level these states (the \\sing's of E_6) correspond to the cohomology group H^1(\\M,{\\rm End}\\>T). We examine the first order contribution of instantons to the mass matrix of these particles. In principle, these corrections depend on the \\K\\ parameters t_i through factors of the form e^{2\\p i t_i} and also depend on the complex structure parameters. For simplicity we consider in greatest detail the quintic threefold \\cp4[5]. It follows on general grounds that the total mass is often, and perhaps always, zero. The contribution of individual instantons is however nonzero and the contribution of a given instanton may develop poles associated with instantons coalescing for certain values of the complex structure. This can happen when the underlying \\cym\\ is smooth. Hence these poles must cancel between the coalescing instantons in order that t...
Yang-Mills theory for semidirect products G x g{sup *} and its instantons
Energy Technology Data Exchange (ETDEWEB)
Ruiz Ruiz, F. [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2015-07-15
Yang-Mills theory with a symmetry algebra that is the semidirect product h x h* defined by the coadjoint action of a Lie algebra h on its dual h* is studied. The gauge group is the semidirect product G{sub h} x h*, a noncompact group given by the coadjoint action on h* of the Lie group G{sub h} of h* For h simple, a method to construct the self-antiself dual instantons of the theory and their gauge nonequivalent deformations is presented. Every G{sub h} x h* instanton has an embedded G{sub h} instanton with the same instanton charge, in terms of which the construction is realized. As an example, h = su(2) and instanton charge one is considered. The gauge group is in this case SU(2) x R{sup 3}. Explicit expressions for the selfdual connection, the zero modes and the metric and complex structures of the moduli space are given. (orig.)
Gravitational and Yang-Mills instantons in holographic RG flows
Gava, Edi; Narain, K S
2011-01-01
We study various holographic RG flow solutions involving warped asymptotically locally Euclidean (ALE) spaces of $A_{N-1}$ type. A two-dimensional RG flow from a UV (2,0) CFT to a (4,0) CFT in the IR is found in the context of (1,0) six dimensional supergravity, interpolating between $AdS_3\\times S^3/\\mathbb{Z}_N$ and $AdS_3\\times S^3$ geometries. We also find solutions involving non trivial gauge fields in the form of SU(2) Yang-Mills instantons on ALE spaces. Both flows are of vev type, driven by the vacuum expectation value of a (not exactly) marginal operator. RG flows in four dimensional field theories are studied in the type IIB and type I$'$ context. In type IIB theory, the flow interpolates between $AdS_5\\times S^5/\\mathbb{Z}_N$ and $AdS_5\\times S^5$ geometries. The field theory interpretation is that of an N=2 $SU(n)^N$ quiver gauge theory flowing to N=4 SU(n) gauge theory. In type I$'$ theory the solution describes an RG flow from N=2 quiver gauge theory with a product gauge group to N=2 gauge theor...
Multi-instanton calculus and the AdS / CFT correspondence in N=4 superconformal field theory
Doery, N.; Hollowood, T.J.; Khoze, V.V.; Mattis, M.P.; Vandoren, S.
2007-01-01
We present a self-contained study of ADHM multi-instantons in SU(N) gauge theory, especially the novel interplay with supersymmetry and the large-N limit. We give both field- and string-theoretic derivations of the N = 4 supersymmetric multi-instanton action and collective coordinate integration mea
Confinement, Holonomy and Correlated Instanton-Dyon Ensemble I: SU(2) Yang-Mills Theory
Lopez-Ruiz, Miguel Angel; Liao, Jinfeng
2016-01-01
The mechanism of confinement in Yang-Mills theories remains a challenge to our understanding of nonperturbative gauge dynamics. While it is widely perceived that confinement may arise from chromo-magnetically charged gauge configurations with nontrivial topology, it is not clear what types of configurations could do that and how, in pure Yang-Mills and QCD-like (non-supersymmetric) theories. Recently a promising approach has emerged, based on statistical ensembles of dyons/anti-dyons that are constituents of instanton/anti-instanton solutions with nontrivial holonomy where the holonomy plays a vital role as an effective "Higgsing" mechanism. We report a thorough numerical investigation of the confinement dynamics in SU(2) Yang-Mills theory by constructing such a statistical ensemble of correlated instanton-dyons.
Perturbative and instanton corrections to the OPE of CPOs in N=4 $SYM_{4}$
Arutyunov, G E; Petkou, Anastasios C
2001-01-01
We study perturbative and instanton corrections to the Operator Product Expansion of the lowest weight Chiral Primary Operators of N=4 SYM_4. We confirm the recently observed non-renormalization of various operators (notably of the double-trace operator with dimension 4 in the 20 irrep of SU(4)), that appear to be unprotected by unitarity restrictions. We demonstrate the splitting of the free-field theory stress tensor and R-symmetry current in supermultiplets acquiring different anomalous dimensions in perturbation theory and argue that certain double-trace operators also undergo a perturbative splitting into operators dual to string and two-particle gravity states respectively. The instanton contributions affect only those double-trace operators that acquire finite anomalous dimensions at strong coupling. For the leading operators of this kind, we show that the ratio of their anomalous dimensions at strong coupling to the anomalous dimensions due to instantons is the same number.
Smooth non-extremal D1-D5-P solutions as charged gravitational instantons
Chakrabarty, Bidisha; Virmani, Amitabh
2016-01-01
We present an alternative and more direct construction of the non-supersymmetric D1-D5-P supergravity solutions found by Jejjala, Madden, Ross and Titchener. We show that these solutions --- with all three charges and both rotations turned on --- can be viewed as a charged version of the Myers-Perry instanton. We present an inverse scattering construction of the Myers-Perry instanton metric in Euclidean five-dimensional gravity. The angular momentum bounds in this construction turn out to be precisely the ones necessary for the smooth microstate geometries. We add charges on the Myers-Perry instanton using appropriate SO(4,4) hidden symmetry transformations. The full construction can be viewed as an extension and simplification of a previous work by Katsimpouri, Kleinschmidt and Virmani.
Euler number of Instanton Moduli space and Seiberg-Witten invariants
Sako, A; Sako, Akifumi; Sasaki, Toru
2001-01-01
We show that a partition function of topological twisted N=4 Yang-Mills theory is given by Seiberg-Witten invariants on a Riemannian four manifolds under the condition that the sum of Euler number and signature of the four manifolds vanish. The partition function is the sum of Euler number of instanton moduli space when it is possible to apply the vanishing theorem. And we get a relation of Euler number labeled by the instanton number $k$ with Seiberg-Witten invariants, too. All calculation in this paper is done without assuming duality.
Entropy and equilibrium property of QCD-instanton induced final state in deep-inelastic scattering
Institute of Scientific and Technical Information of China (English)
DENG Wei-Bing; LU Ding; ZHANG Ji-Ying; XU Ming-Mei; Boris Levchenko; LIU Lian-Shou
2008-01-01
The scaling and additivity properties of Rényi entropy in rapidity space of the instanton final state (IFS) and current jet identified by the r-sorting method from the QCDINS Monte Carlo event sample are to saturation with decreasing phase space scale. Furthermore, it is found that the additivity of H2 holds well for the IFS in narrow rapidity windows at different positions. These results indicate that the IFS produced in the instanton-induced process of deep inelastic scattering has reached local equilibrium.
On the Relationship between Large Order Graphs and Instantons for the Double Well Oscillator
Müller, A H
2001-01-01
The double well oscillator is used as a QCD-like model for studying the relationship between large order graphs and the instanton-antiinstanton solution. We derive an equation for the perturbative coefficients of the ground state energy when the number of 3 and/or 4-vertices is fixed and large. These coefficients are determined in terms of an exact``bounce'' solution. When the number of 4-vertices is analytically continued to be near the negative of half the number of 3-vertices the bounce solution approaches the instanton-antiinstanton solution and detremines leading Borel singularity.
Aerts, Patrick Johan Coenraad
1986-01-01
Computational Theoretical Chemnistry is a research area which, as far as electronic structure problems are concerned, encompasses essentially the development of theoretically sound, yet computionally feasable quantum mechanical models for atoms melecules and the solid state. ... Zie: Introduction
Scarani, Valerio; Iblisdir, Sofyan; Gisin, Nicolas; Acin, Antonio
2005-01-01
The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases. These "quantum cloning machines" are important tools for studying a wide variety of tasks, e.g. state estimation and eavesdropping on quantum cryptography. This paper provides a comprehensive review of quantum cloning machines (both for discrete-dimensional an...
Quantum weights of monopoles and calorons with non-trivial holonomy
Diakonov, D
2004-01-01
The functional determinant is computed exactly for quantum oscillations about periodic instantons with non-trivial values of the Polyakov line at spatial infinity (or holonomy). Such instantons can be viewed as composed of the Bogomolnyi--Prasad--Sommerfeld (BPS) monopoles or dyons. We find the weight or the probability with which dyons occur in the pure Yang--Mills partition function. It turns out that dyons experience quantum interactions having the familiar "linear plus Coulomb" form but with the "string tension'' depending on the holonomy. We present an argument that at temperatures below the critical one computed from Lambda_QCD, trivial holonomy becomes unstable, with instantons ``ionizing'' into separate dyons. It may serve as a microscopic mechanism of the confinement-deconfinement phase transition.
Magnetic moments of baryons with null instanton in relation to SU[sub 6] model
Energy Technology Data Exchange (ETDEWEB)
Iwao, Syurei (Kanazawa Univ. (Japan). Faculty of Science)
1993-10-01
A dynamical symmetry breaking effect on the SU[sub 6] model for the magnetic moments of baryons is considered, based on the null instanton picture for them. A certain improvement of the fit to the available data is obtained. (author).
Gravitational instantons of type $D_k$ and a generalization of the Gibbons-Hawking Ansatz
Ionas, Radu A
2016-01-01
We describe a quaternionic-based Ansatz generalizing the Gibbons-Hawking Ansatz to a class of hyperk\\"ahler metrics with hidden symmetries. We then apply it to obtain explicit expressions for gravitational instanton metrics of type $D_k$.
Hidden selection rules, M5-instantons and fluxes in F-theory
Energy Technology Data Exchange (ETDEWEB)
Martucci, Luca [Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Università di Padova, & I.N.F.N. Sezione di Padova, via Marzolo 8, I-35131 Padova (Italy); Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität, Philosophenweg 19, 69120 Heidelberg (Germany)
2015-10-21
We introduce a new approach to investigate the selection rules governing the contributions of fluxed M5-instantons to the F-theory four-dimensional effective action, with emphasis on the generation of charged matter F-terms. The structure of such couplings is unraveled by exploiting the perturbative and non-perturbative homological relations, introduced in our companion paper http://dx.doi.org/10.1007/JHEP09(2015)198, which encode the interplay between the self-dual 3-form flux on the M5-brane, the background 4-form flux and certain fibral curves. The latter are wrapped by time-like M2-branes representing matter insertions in the instanton path integral. In particular, we clarify how fluxed M5-instantons detect the presence of geometrically massive U(1)s which are responsible for ‘hidden’ selection rules. We discuss how for non-generic embeddings the M5-instanton can probe ‘locally massless’ U(1) symmetries if the rank of its Mordell-Weil group is enhanced compared to that of the bulk. As a phenomenological off-spring we propose a new type of non-perturbative corrections to Yukawa couplings which may change the rank of the Yukawa matrix. Along the way, we also gain new insights into the structure of massive U(1) gauge fluxes in the stable degeneration limit.
Directory of Open Access Journals (Sweden)
E Taghizdehsiskht
2013-09-01
Full Text Available In recent years, semiconductor nanostructures have become the model systems of choice for investigation of electrical conduction on short length scales. Quantum transport is studied in a two dimensional electron gas because of the combination of a large Fermi wavelength and large mean free path. In the present work, a numerical method is implemented in order to contribute to the understanding of quantum transport in narrow channels in different conditions of disorder and magnetic fields. We have used an approach that has proved to be very useful in describing mesoscopic transport. We have assumed zero temperature and phase coherent transport. By using the trick that a conductor connected to infinite leads can be replaced by a finite conductor with the effect of the leads incorporated through a 'self-energy' function, a convenient method was provided for evaluating the Green's function of the whole device numerically. Then, Fisher-Lee relations was used for calculating the transmission coefficients through coherent mesoscopic conductors. Our calculations were done in a model system with Hard-wall boundary conditions in the transverse direction, and the Anderson model of disorder was used in disordered samples. We have presented the results of quantum transport for different strengths of disorder and introduced magnetic fields. Our results confirmed the Landauer formalism for calculation of electronic transport. We observed that weak localization effect can be removed by application of a weak perpendicular magnetic field. Finally, we numerically showed the transition to the integral quantum Hall effect regime through the suppression of backscattering on a disordered model system by calculating the two terminal conductance of a quasi-one-dimensional quantum conductor as a strong magnetic field is applied. Our results showed that this regime is entered when there is a negligible overlap between electron edge states localized at opposite sides of
Search for QCD instanton-induced processes at HERA in the high-Q{sup 2} domain
Energy Technology Data Exchange (ETDEWEB)
Andreev, V. [Lebedev Physical Institute, Moscow (Russian Federation); Baghdasaryan, A. [Yerevan Physics Institute (Armenia); Begzsuren, K. [Mongolian Academy of Sciences, Ulaanbaatar (Mongolia). Inst. of Physics and Technology; Collaboration: H1 Collaboration; and others
2016-03-15
Signals of QCD instanton-induced processes are searched for in neutral current deep-inelastic scattering at the electron-proton collider HERA in the kinematic region defined by the Bjorken-scaling variable x>10{sup -3}, the inelasticity 0.2
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities in terms of the ratio d / d_min where d_min is the dimension of the smallest nontrivial representation of G. As an application, we bound the extent to which a function f : G -> H can be an approximate homomorphism where H is another finite group. We show that if H's representations are significantly smaller than G's, no such f can be much more homomorphic than a random function. We interpret these results as showing that if G is quasirandom, that is, if d_min is large, then G cannot be embedded in a small number of dimensi...
Spin exchange in quantum rings and wires in the Wigner-crystal limit
Fogler, Michael M.; Pivovarov, Eugene
2005-01-01
We present a controlled method for computing the exchange coupling in strongly correlated one-dimensional electron systems. It is based on the asymptotically exact relation between the exchange constant and the pair-correlation function of spinless electrons. Explicit results are obtained for thin quantum rings with realistic Coulomb interactions, by calculating this function via a many-body instanton approach.
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
A case where BO Approximation breaks down
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
@@ The Bom-Oppenheimer (BO)Approximation is ubiquitous in molecular physics,quantum physics and quantum chemistry. However, CAS researchers recently observed a breakdown of the Approximation in the reaction of fluorine with deuterium atoms.The result has been published in the August 24 issue of Science.
Conformally coupled scalars, instantons and vacuum instability in AdS{sub 4}
Energy Technology Data Exchange (ETDEWEB)
De Haro, S. [King' s College London (United Kingdom). Dept. of Mathematics; Papadimitriou, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Petkou, A.C. [Crete Univ., Keraklion (Greece). Dept. of Physics
2006-11-15
We show that a scalar field conformally coupled to AdS gravity in four dimensions with a quartic self-interaction can be embedded into M-theory. The holographic effective action and effective potential are exactly calculated, allowing us to study non-perturbatively the stability of AdS{sub 4} in the presence of the conformally coupled scalar. It is shown that there exists a one-parameter family of conformal scalar boundary conditions for which the boundary theory has an unstable vacuum. In this case, the bulk theory has instanton solutions that mediate the decay of the AdS{sub 4} space. These results match nicely with the vacuum structure and the existence of instantons in an effective three-dimensional boundary model.
Sasakian quiver gauge theories and instantons on cones over lens 5-spaces
Directory of Open Access Journals (Sweden)
Olaf Lechtenfeld
2015-10-01
Full Text Available We consider SU(3-equivariant dimensional reduction of Yang–Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki–Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki–Einstein structure, which are projective planes. We describe the Higgs branches of these quiver gauge theories as moduli spaces of spherically symmetric instantons which are SU(3-equivariant solutions to the Hermitian Yang–Mills equations on the associated Calabi–Yau cones, and further compare them to moduli spaces of translationally-invariant instantons on the cones. We provide an explicit unified construction of these moduli spaces as Kähler quotients and show that they have the same cyclic orbifold singularities as the cones over the lens 5-spaces.
The Resurgence of Instantons: Multi-Cuts Stokes Phases and the Painleve II Equation
Schiappa, Ricardo
2013-01-01
Resurgent transseries have recently been shown to be a very powerful construction in order to completely describe nonperturbative phenomena in both matrix models and topological or minimal strings. These solutions encode the full nonperturbative content of a given gauge or string theory, where resurgence relates every (generalized) multi-instanton sector to each other via large-order analysis. The Stokes phase is the adequate gauge theory phase where an 't Hooft large N expansion exists and where resurgent transseries are most simply constructed. This paper addresses the nonperturbative study of Stokes phases associated to multi-cuts solutions of generic matrix models, constructing nonperturbative solutions for their free energies and exploring the asymptotic large-order behavior around distinct multi-instanton sectors. Explicit formulae are presented for the Z_2 symmetric two-cuts set-up, addressing the cases of the quartic matrix model in its two-cuts Stokes phase; the "triple" Penner potential which yields...
Instantons of M(atrix) Theory in PP-Wave Background
Yee, J T; Yee, Jung-Tay; Yi, Piljin
2003-01-01
M(atrix) theory in PP-wave background possesses a discrete set of classical vacua, all of which preserves 16 supersymmetry and interpretable as collection of giant gravitons. We find Euclidean instanton solutions that interpolate between them, and analyze their properties. Supersymmetry prevents direct mixing between different vacua but still allows effect of instanton to show up in higher order effective interactions, such as analog of v^4 interaction of flat space effective theory. An explicit construction of zero modes is performed, and Goldstone zero modes, bosonic and fermionic, are identified. We further generalize this to massive M(atrix) theory that includes fundamental hypermultiplets, corresponding to insertion of longitudinal fivebranes in the background. After a brief comparison to their counterpart in AdS\\times S, we close with a summary.
Sasakian quiver gauge theories and instantons on cones over lens 5-spaces
Lechtenfeld, Olaf; Sperling, Marcus; Szabo, Richard J
2015-01-01
We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki-Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki-Einstein structure, which are projective planes. We describe the Higgs branches of these quiver gauge theories as moduli spaces of spherically symmetric instantons which are SU(3)-equivariant solutions to the Hermitian Yang-Mills equations on the associated Calabi-Yau cones, and further compare them to moduli spaces of translationally-invariant instantons on the cones. We provide an explicit unified construction of these moduli spaces as K\\"ahler quotients and show that they have the same cyclic orbifold singularities as that of the cones.
N = 2 gauge theories, instanton moduli spaces and geometric representation theory
Szabo, Richard J.
2016-11-01
We survey some of the AGT relations between N = 2 gauge theories in four dimensions and geometric representations of symmetry algebras of two-dimensional conformal field theory on the equivariant cohomology of their instanton moduli spaces. We treat the cases of gauge theories on both flat space and ALE spaces in some detail, and with emphasis on the implications arising from embedding them into supersymmetric theories in six dimensions. Along the way we construct new toric noncommutative ALE spaces using the general theory of complex algebraic deformations of toric varieties, and indicate how to generalize the construction of instanton moduli spaces. We also compute the equivariant partition functions of topologically twisted six-dimensional Yang-Mills theory with maximal supersymmetry in a general Ω-background, and use the construction to obtain novel reductions to theories in four dimensions.
Energy Technology Data Exchange (ETDEWEB)
Perez Ramos, R
2006-09-15
We exactly calculate the double and simple inclusive transverse momentum (kt) distributions and the 2-particle momentum correlations inside high energy hadronic jets at the Modified Leading Logarithmic Approximation (MLLA) of Quantum Chromodynamics. We first obtain the exact solution of the evolution equations at 'small x', which we calculate at the so called 'limiting spectrum'. We then generalize this approximation by performing the steepest descent evaluation. Our predictions are in good agreement with data from Tevatron and improve those which have been obtained in the past. The comparison with forthcoming data (Tevatron, LHC) will further test the hypothesis of Local Hadron Parton Duality, and the eventual need to incorporate next-MLLA corrections. (authors)
A Note on Instanton Effects in ABJM Theory
Wang, Xian-fu; Huang, Min-xin
2014-01-01
We consider the quantum spectral problem appearing the Fermi gas formulation of the ABJM (Aharony-Bergman-Jafferis-Maldacena) matrix model. This is known to related to the refined topological string on local P^1*P^1 Calabi-Yau geometry. In the ABJM setting the problem is formulated by an integral equation, and is somewhat different from the one formulated directly in terms of the Calabi-Yau geometry and studied in our earlier paper. We use the similar method in our earlier paper to determine the non-perturbative contributions to the quantum phase volume in the ABJM case from the Bohr-Sommerfeld quantization condition. As in our earlier paper, the non-perturbative contributions contain higher order smooth corrections beyond those required by singularity cancellations with the perturbative contributions proposed by Kallen and Marino. Our results imply possible new contributions to the grand potential of the ABJM matrix model.
A note on instanton effects in ABJM theory
Wang, Xian-fu; Wang, Xin; Huang, Min-xin
2014-11-01
We consider the quantum spectral problem appearing the Fermi gas formulation of the ABJM (Aharony-Bergman-Jafferis-Maldacena) matrix model. This is known to related to the refined topological string on local ℙ1 × ℙ1 Calabi-Yau geometry. In the ABJM setting the problem is formulated by an integral equation, and is somewhat different from the one formulated directly in terms of the Calabi-Yau geometry and studied in our earlier paper. We use the similar method in our earlier paper to determine the non-perturbative contributions to the quantum phase volume in the ABJM case from the Bohr-Sommerfeld quantization condition. As in our earlier paper, the non-perturbative contributions contain higher order smooth corrections beyond those required by singularity cancellations with the perturbative contributions proposed by Kallen and Marino. Our results imply possible new contributions to the grand potential of the ABJM matrix model.
D-particle bound states and generalized instantons
Energy Technology Data Exchange (ETDEWEB)
Moore, G. [Yale Univ., New Haven, CT (United States). Dept. of Physics; Nekrasov, N. [Institute of Theoretical and Experimental Physics, 117259, Moscow (Russian Federation); Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138 (United States); Shatashvili, S. [Yale Univ., New Haven, CT (United States). Dept. of Physics; Theory Division, CERN, 1211 Geneve 23 (Switzerland)
2000-01-01
We compute the principal contribution to the index in the supersymmetric quantum mechanical systems which are obtained by reduction to 0+1 dimensions of N=1, D=4,6,10 super-Yang-Mills theories with gauge group SU(N). The results are: 1/(N{sup 2}) for D=4,6, sum {sub d} {sub vertical} {sub stroke} {sub N}1/(d{sup 2}) for D=10. We also discuss the D=3 case. (orig.)
The effect of instanton-induced interaction on -wave meson spectra in constituent quark model
Indian Academy of Sciences (India)
Bhavyashri; S Sarangi; Godfrey Saldanha; K B Vijaya Kumar
2008-01-01
The mass spectrum of the -wave mesons is considered in a non-relativistic constituent quark model. The full Hamiltonian used in the investigation includes the kinetic energy, the confinement potential, the one-gluon-exchange potential (OGEP) and the instanton-induced quark-antiquark interaction (III). A good description of the mass spectrum is obtained. The respective role of III and OGEP in the P-wave meson spectrum is discussed.
Instanton-dyon Ensemble with two Dynamical Quarks: the Chiral Symmetry Breaking
Larsen, Rasmus
2015-01-01
This is the second paper of the series aimed at understanding of the ensemble of the instanton-dyons, now with two flavors of light dynamical quarks. The partition function is appended by the fermionic factor, $(det T)^{N_f}$ and Dirac eigenvalue spectra at small values are derived from the numerical simulation of 64 dyons. Those spectra show clear chiral symmetry breaking pattern at high dyon density. Within current accuracy, the confinement and chiral transitions occur at very similar densities.
Dorey, N; Mattis, M P; Slater, M J; Weir, W A
1997-01-01
We discuss the contribution of ADHM multi-instantons to the higher-derivative terms in the gradient expansion along the Coulomb branch of N=2 and N=4 supersymmetric SU(2) gauge theories. In particular, using simple scaling arguments, we confirm the Dine-Seiberg nonperturbative nonrenormalization theorems for the 4-derivative/8-fermion term in the two finite theories (N=4, and N=2 with N_F=4).
Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem
Cherkis, Sergey A; Stern, Mark
2016-01-01
We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series of papers proving the completeness of the bow construction of instantons on multi-Taub-NUT spaces and exploring it in detail.
Gluon Green functions free of quantum fluctuations
Directory of Open Access Journals (Sweden)
A. Athenodorou
2016-09-01
Full Text Available This letter reports on how the Wilson flow technique can efficaciously kill the short-distance quantum fluctuations of 2- and 3-gluon Green functions, remove the ΛQCD scale and destroy the transition from the confining non-perturbative to the asymptotically-free perturbative sector. After the Wilson flow, the behavior of the Green functions with momenta can be described in terms of the quasi-classical instanton background. The same behavior also occurs, before the Wilson flow, at low-momenta. This last result permits applications as, for instance, the detection of instanton phenomenological properties or a determination of the lattice spacing only from the gauge sector of the theory.
Condensates and instanton - torus knot duality. Hidden Physics at UV scale
Gorsky, A
2014-01-01
We establish the duality between the torus knot superpolynomials or the Poincare polynomials of the Khovanov homology and particular condensates in Omega-deformed 5D supersymmetric QED compactified on a circle with 5d Chern-Simons(CS) term. This is the generalization of the Witten's recipe of the evaluation of the knot polynomials via Wilson loops in 3d CS theory for case of the torus knots. It is explicitly shown that $n$-instanton contribution to the condensate of the massless flavor in the background of four-observable, which can be associated with some composite defect, exactly coincides with the superpolynomial of the T(n,nk+1) torus knot where k - is the level of CS term. In contrast to the previously known results, the particular torus knot corresponds not to the partition function of the gauge theory but to the particular instanton contribution and summation over the knots has to be performed in order to obtain the complete answer. The instantons are sitting almost at the top of each other and the phy...
Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction
Nitta, Muneto
2015-01-01
Non-Abelian Josephson junction is a junction of non-Abelian color superconductors sandwiching an insulator, or non-Abelian domain wall if flexible, whose low-energy dynamics is described by a $U(N)$ principal chiral model with the conventional pion mass. A non-Abelian Josephson vortex is a non-Abelian vortex (color magnetic flux tube) residing inside the junction, that is described as a non-Abelian sine-Gordon soliton. In this paper, we propose Josephson instantons and Josephson monopoles, that is, Yang-Mills instantons and monopoles inside a non-Abelian Josephson junction, respectively, and show that they are described as $SU(N)$ Skyrmions and $U(1)^{N-1}$ vortices in the $U(N)$ principal chiral model without and with a twisted mass term, respectively. Instantons with a twisted boundary condition are reduced (or T-dual) to monopoles, implying that ${\\mathbb C}P^{N-1}$ lumps are T-dual to ${\\mathbb C}P^{N-1}$ kinks inside a vortex. Here we find $SU(N)$ Skyrmions are T-dual to $U(1)^{N-1}$ vortices inside a wa...
Instanton effects in ABJM theory with general R-charge assignments
Nosaka, Tomoki
2015-01-01
We study the large N expansion of the partition function of the quiver superconformal Chern-Simons theories deformed by two continuous parameters which correspond to general R-charge assignment to the matter fields. Though the deformation breaks the conformal symmetry, we find that the partition function shares various structures with the superconformal cases, such as the Airy function expression of the perturbative expansion in 1/N with the overall constant A(k) related to the constant map in the ABJM case through a simple rescaling of k. We also identify five kinds of the non-perturbative effects in 1/N which correspond to the membrane instantons. The instanton exponents and the singular structure of the coefficients depend on the continuous deformation parameters, in contrast to the superconformal case where all the parameters are integers associated with the orbifold action on the moduli space. This implies that the singularity of the instanton effects would be observable also in the gravity side.
Indian Academy of Sciences (India)
KAUSHIK MAJI
2016-08-01
We propose a variant of the multiconfiguration time-dependent Hartree (MCTDH) method within the framework of Hermite-distributed approximating functional (HDAF) method. The discretized Hamiltonian is a highly banded Toeplitz matrix which significantly reduces computational cost in terms of both storage and number of operations. The method proposed is employed to carry out the study of tunnelling dynamics of two coupled double well oscillators. We have calculated the orthogonality time \\tau , which is a measure of the time interval for an initial state to evolve into its orthogonal state. It is observed that the coupling has a significant effect on \\tau .
Recursion and growth estimates in renormalizable quantum field theory
Kreimer, D; Kreimer, Dirk; Yeats, Karen
2006-01-01
In this paper we show that there is a Lipatov bound for the radius of convergence for superficially divergent one-particle irreducible Green functions in a renormalizable quantum field theory if there is such a bound for the superficially convergent ones. The radius of convergence turns out to be ${\\rm min}\\{\\rho,1/b_1\\}$, where $\\rho$ is the bound on the convergent ones, the instanton radius, and $b_1$ the first coefficient of the $\\beta$-function.
Pérez, Alejandro; Tuckerman, Mark E.; Müser, Martin H.
2009-05-01
The problems of ergodicity and internal consistency in the centroid and ring-polymer molecular dynamics methods are addressed in the context of a comparative study of the two methods. Enhanced sampling in ring-polymer molecular dynamics (RPMD) is achieved by first performing an equilibrium path integral calculation and then launching RPMD trajectories from selected, stochastically independent equilibrium configurations. It is shown that this approach converges more rapidly than periodic resampling of velocities from a single long RPMD run. Dynamical quantities obtained from RPMD and centroid molecular dynamics (CMD) are compared to exact results for a variety of model systems. Fully converged results for correlations functions are presented for several one dimensional systems and para-hydrogen near its triple point using an improved sampling technique. Our results indicate that CMD shows very similar performance to RPMD. The quality of each method is further assessed via a new χ2 descriptor constructed by transforming approximate real-time correlation functions from CMD and RPMD trajectories to imaginary time and comparing these to numerically exact imaginary time correlation functions. For para-hydrogen near its triple point, it is found that adiabatic CMD and RPMD both have similar χ2 error.
Sastry, R R
1999-01-01
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the cosmological constant problem is addressed. The response of an electron to a weak gravitational field (linear approximation) is studied and the order $\\alpha$ correction to the magnetic gravitational moment is computed.
Explicit Computations of Instantons and Large Deviations in Beta-Plane Turbulence
Laurie, J.; Bouchet, F.; Zaboronski, O.
2012-12-01
We use a path integral formalism and instanton theory in order to make explicit analytical predictions about large deviations and rare events in beta-plane turbulence. The path integral formalism is a concise way to get large deviation results in dynamical systems forced by random noise. In the most simple cases, it leads to the same results as the Freidlin-Wentzell theory, but it has a wider range of applicability. This approach is however usually extremely limited, due to the complexity of the theoretical problems. As a consequence it provides explicit results in a fairly limited number of models, often extremely simple ones with only a few degrees of freedom. Few exception exist outside the realm of equilibrium statistical physics. We will show that the barotropic model of beta-plane turbulence is one of these non-equilibrium exceptions. We describe sets of explicit solutions to the instanton equation, and precise derivations of the action functional (or large deviation rate function). The reason why such exact computations are possible is related to the existence of hidden symmetries and conservation laws for the instanton dynamics. We outline several applications of this apporach. For instance, we compute explicitly the very low probability to observe flows with an energy much larger or smaller than the typical one. Moreover, we consider regimes for which the system has multiple attractors (corresponding to different numbers of alternating jets), and discuss the computation of transition probabilities between two such attractors. These extremely rare events are of the utmost importance as the dynamics undergo qualitative macroscopic changes during such transitions.
Type IIB orientifolds, D-brane instantons and the large volume scenario
Energy Technology Data Exchange (ETDEWEB)
Plauschinn, Erik
2009-07-28
This thesis is concerned with a branch of research in String Theory called String Phenomenology which aims for a better understanding of the connection between String Theory and Particle Physics. In particular, in this work we cover three topics which are important in order to establish this connection. The first topic is about String Theory model building in the context of so-called type IIB orientifolds with orientifold three- and seven-planes. After giving a brief overview, we work out in detail an important consistency condition for String Theory constructions, the so-called tadpole cancellation condition, and we verify explicitly that chiral anomalies are cancelled via the generalised Green-Schwarz mechanism. The second topic is concerned with so-called D-brane instantons which are nonperturbative effects in type II String Theory constructions. We recall the instanton calculus for such configurations, we derive the so-called A eck-Dine-Seiberg superpotential in String Theory and we develop an important constraint, a chiral zero-mode constraint, for instanton contributions in the presence of a realistic Particle Physics sector. The third topic is about moduli stabilisation in type IIB string compactifications. More concretely, we review the so-called KKLT as well as Large Volume Scenario, and we construct and study a model for the latter scenario where the constraint mentioned above has been taken into account explicitly. Although the three topics studied in this thesis are slightly different in nature, there is nevertheless a complex interplay between them with many interrelations. In order to uncover these connections, a detailed study of each individual subject has been performed which has led to new results such as the chiral zero-mode constraint. (orig.)
Applications of the D-instanton calculus in type IIB orientifold compactifications
Energy Technology Data Exchange (ETDEWEB)
Moster, Sebastian
2010-06-22
In this thesis string compactifications are studied in the formalism of the large-volume type IIB string theory. This class of compactifications possesses an in various regards phenomenologically interesting effective low-energy field theory. Theme of this thesis is the further development of these models motivated by recent knowledges in the D-brane instanton calculus of the string theory. After a short, general introduction in the string theory and especially in type IIB orbifolds and their consistency conditions the large-volume models are extensively presented and the hitherto knowledges on their phenomenology - like scale hierarchies, gauge couplings, supersymmetry breaking, and cosmological questions - discussed. An essential part in the construction of the large-volume models is the stabilizing of moduli fields by means of nonperturbative contribution to the superpotential in the effective low-energy field theory, which are caused by D-brane instantons or gaugino condensates. With recent knowledges in the D-brane instanton calculus it is shown that the moduli stabilization with the hitherto applied mechanism is not compatible with the existence of chiral fermions, as they occur in the standard model of elementary particle physics. A modified mechanism is proposed, in which the moduli fields are stabilized by additions of D-terms. Then by so-called ''polyinstanton corrections'' for the gauge-kinetic function a new large-volume scenario is constructed, in which the string scale without fine tuning lies not in an as in these model usual intermediate range of about 10{sup 11} GeV, but at 10{sup 16} GeV. By this this construction becomes interesting also for grand unified theories with SU(5) or SO(10) gauge groups. This is demonstrated on explicit models. Finally supersymmetry breaking is treated in large-volume scenarios. By the new mechanism for the moduli stabilization it is suggested that the supersymmetry breaking is caused by a
Fubini instantons in Dilatonic Einstein-Gauss-Bonnet theory of gravitation
Ro, Daeho; Lee, Bum-Hoon
2016-01-01
We investigate various types of Fubini instantons in Dilatonic Einstein-Gauss-Bonnet theory of gravitation, which describe the decay of the vacuum state at a hilltop potential through the tunneling without a barrier. It is shown that the vacuum states are modified by the non-minimally coupled higher-curvature term. Accordingly, we present the new type of solutions describing the tunneling from new vacuum states in anti-de Sitter and de Sitter backgrounds. The decay probabilities of vacuum states are also influenced. Consequently, we show that the semiclassical exponents can be decreased for specific parameter ranges, which make the tunneling probabilities enhanced.
Closed string tachyons on AdS orbifolds and dual Yang-Mills instantons
Energy Technology Data Exchange (ETDEWEB)
Hikida, Y. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Iizuka, N. [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
2007-06-15
We study the condensation of localized closed string tachyons on AdS orbifolds both from the bulk and boundary theory viewpoints. We first extend the known results for AdS{sub 5}/Z{sub k} to AdS{sub 3}/Z{sub k} case, and we proposed that the AdS{sub 3}/Z{sub k} decays into AdS{sub 3}/Z{sub k'} with k{sup '} < k. From the bulk viewpoint, we obtain a time-dependent gravity solution describing the decay of AdS orbifold numerically. From the dual gauge theory viewpoint, we calculated the Casimir energies of gauge theory vacua and it is found that their values are exactly the same as the masses of dual geometries, even though they are in different parameter regimes of 't Hooft coupling. We also consider AdS{sub 5} orbifold. The decay of AdS{sub 5}/Z{sub k} is dual to the transition between the vacua of dual gauge theory on R{sub t} x S{sup 3}/Z{sub k}. We constructed the instanton solutions describing the transitions by making use of instanton solutions on R{sub t} x S{sup 2}. (orig.)
Shushkov, Philip
2013-06-14
We present a derivation of Marcus theory of electron transfer in solution starting from semiclassical instanton theory. The conventional semiclassical instanton theory provides an inadequate description of the electron transfer process in the inverted Marcus regime. This has been attributed to the lack of backscattering in the product region, which is represented as a semi-infinite continuum of states. For electron transfer processes in condensed phase, the electronic states in the acceptor well are bound, which violates the continuum assumption. We show by detailed analysis of the minimum action path of a model system for electron transfer that the proper tunneling coordinate is a delocalized, "bead-count" mode. The tunneling mode is analytically continued in the complex plane as in the traditional derivation. Unlike the traditional analysis where the method of steepest descent is used, the tunneling coordinate is treated as a quasi-zero mode. This feature allows including the influence of backscattering in the acceptor well and leads to the recovery of the Marcus formula for the rate of electron transfer. The results have implications on the performance of ring polymer molecular dynamics for the study of electron transfer dynamics.
Busch, Paul; Pellonpää, Juha-Pekka; Ylinen, Kari
2016-01-01
This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann’s classic treatise with this title. Fundamental non-classical features of quantum mechanics—indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality—are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4....
Nonequilibrium functional bosonization of quantum wire networks
Energy Technology Data Exchange (ETDEWEB)
Ngo Dinh, Stephane, E-mail: stephane.ngodinh@kit.edu [Institut fuer Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76128 Karlsruhe (Germany); DFG Center for Functional Nanostructures, Karlsruhe Institute of Technology, 76128 Karlsruhe (Germany); Bagrets, Dmitry A. [Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany); Mirlin, Alexander D. [Institut fuer Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76128 Karlsruhe (Germany); Institut fuer Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe (Germany); DFG Center for Functional Nanostructures, Karlsruhe Institute of Technology, 76128 Karlsruhe (Germany); Petersburg Nuclear Physics Institute, 188300 St. Petersburg (Russian Federation)
2012-11-15
We develop a general approach to nonequilibrium nanostructures formed by one-dimensional channels coupled by tunnel junctions and/or by impurity scattering. The formalism is based on nonequilibrium version of functional bosonization. A central role in this approach is played by the Keldysh action that has a form reminiscent of the theory of full counting statistics. To proceed with evaluation of physical observables, we assume the weak-tunneling regime and develop a real-time instanton method. A detailed exposition of the formalism is supplemented by two important applications: (i) tunneling into a biased Luttinger liquid with an impurity, and (ii) quantum Hall Fabry-Perot interferometry. - Highlights: Black-Right-Pointing-Pointer A nonequilibrium functional bosonization framework for quantum wire networks is developed Black-Right-Pointing-Pointer For the study of observables in the weak tunneling regime a real-time instanton method is elaborated. Black-Right-Pointing-Pointer We consider tunneling into a biased Luttinger liquid with an impurity. Black-Right-Pointing-Pointer We analyze electronic Fabry-Perot interferometers in the integer quantum Hall regime.
Arnone, S; Yoshida, K
2001-01-01
Exact renormalization group techniques are applied to mass deformed N=4 supersymmetric Yang-Mills theory, viewed as a regularised N=2 model. The solution of the flow equation, in the local potential approximation, reproduces the one-loop (perturbatively exact) expression for the effective action of N=2 supersymmetric Yang-Mills theory, when the regularising mass, M, reaches the value of the dynamical cutoff. One speculates about the way in which further non-perturbative contributions (instanton effects) may be accounted for.
Instanton calculus and chiral one-point functions in supersymmetric gauge theories
Fujii, S; Moriyama, S; Okada, S; Fujii, Shigeyuki; Kanno, Hiroaki; Moriyama, Sanefumi; Okada, Soichi
2007-01-01
We compute topological one-point functions of the chiral operator Tr (\\phi^k) in the maximally confining phase of N=1 U(N) supersymmetric gauge theory, which is obtained from N=2 theory by turning on a tree level superpotential W(\\Phi). Localization theorem for toric action allows us to express these one-point functions as polynomials in the equivariant parameter \\hbar and the parameter of instanton expansion q=\\Lambda^{2N}. The chiral one-point functions are of particular interest from gauge/string theory correspondence, since they are related to the Gromov-Witten theory of P^1. Based on a combinatorial identity that gives summation formula over Young diagram of relevant functions, we find a relation among chiral one-point functions, which recursively determines the \\hbar expansion of the generating function of one-point functions.
Dynamics of excited instantons in the system of forced Gursey nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Aydogmus, F., E-mail: fatma.aydogmus@gmail.com [Istanbul University, Department of Physics, Faculty of Science (Turkey)
2015-02-15
The Gursey model is a 4D conformally invariant pure fermionic model with a nonlinear spinor self-coupled term. Gursey proposed his model as a possible basis for a unitary description of elementary particles following the “Heisenberg dream.” In this paper, we consider the system of Gursey nonlinear differential equations (GNDEs) formed by using the Heisenberg ansatz. We use it to understand how the behavior of spinor-type Gursey instantons can be affected by excitations. For this, the regular and chaotic numerical solutions of forced GNDEs are investigated by constructing their Poincaré sections in phase space. A hierarchical cluster analysis method for investigating the forced GNDEs is also presented.
On the Octonionic Self Duality equations of 3-brane Instantons arXiv
Floratos, Emmanuel
We study the octonionic selfduality equations for $p=3$-branes in the light cone gauge and we construct explicitly, instanton solutions for spherical and toroidal topologies in various flat spacetime dimensions $(D=5+1,7+1,8+1,9+1)$, extending previous results for $p=2$ membranes. Assuming factorization of time we reduce the self-duality equations to integrable systems and we determine explicitly periodic, in Euclidean time, solutions in terms of the elliptic functions. These solutions describe 4d associative and non-associative calibrations in $D=7,8$ dimensions. It turns out that for spherical topology the calibration is non compact while for the toroidal topology is compact. We discuss possible applications of our results to the problem of 3-brane topology change and its implications for a non-perturbative definition of the 3-brane interactions.
Instanton effects in rank deformed superconformal Chern-Simons theories from topological strings
Moriyama, Sanefumi; Nakayama, Shota; Nosaka, Tomoki
2017-08-01
In the so-called (2, 2) theory, which is the U( N)4 circular quiver superconformal Chern-Simons theory with levels ( k, 0, - k, 0), it was known that the instanton effects are described by the free energy of topological strings whose Gopakumar-Vafa invariants coincide with those of the local D 5 del Pezzo geometry. By considering two types of one-parameter rank deformations U( N)×U( N + M)×U( N + 2 M)×U( N + M) and U( N + M)×U( N)×U( N + M)×U( N), we classify the known diagonal BPS indices by degrees. Together with other two types of one-parameter deformations, we further propose the topological string expression when both of the above two deformations are turned on.
Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index
Benvenuti, Sergio; Ronzani, Massimiliano; Tanzini, Alessandro
2016-01-01
We explore N=(1,0) superconformal six-dimensional theories arising from M5-branes probing a transverse A_k singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5-brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1,0) index, which we compute by letter counting. We finally show that S-duality of the pq-web implies new relations among vertex correlators of qW-algebrae.
N=2 SYM Action as a BRST Exact Term, Topological Yang Mills and Instantons
Ulker, K
2003-01-01
By defining an extended BRST operator that includes the chiral part of N=2 global supersymmetry, it is shown that the full N=2 off-shell Super Yang Mills Action can be represented as an exact BRST term. The action written in this form suggests that the fields of the Topological Yang Mills theory can be defined in terms of composite fields of supersymmetry ghosts and N=2 fields in a natural way. Topological Yang Mills theory is obtained from the ordinary Euclidean N=2 SYM directly as field redefinitions without using twisting procedure. With the help of these results, relation between the recent instanton calculations in N=2 Super Yang Mills and Topological Yang Mills theories is also discussed.
How instanton combinatorics solves Painlev\\'e VI, V and III's
Gamayun, O; Lisovyy, O
2013-01-01
We elaborate on a recently conjectured relation of Painlev\\'e transcendents and 2D CFT. General solutions of Painlev\\'e VI, V and III are expressed in terms of $c=1$ conformal blocks and their irregular limits, AGT-related to instanton partition functions in $\\mathcal{N}=2$ supersymmetric gauge theories with $N_f=0,1,2,3,4$. Resulting combinatorial series representations of Painlev\\'e functions provide an efficient tool for their numerical computation at finite values of the argument. The series involve sums over bipartitions which in the simplest cases coincide with Gessel expansions of certain Toeplitz determinants. Considered applications include Fredholm determinants of classical integrable kernels, scaled gap probability in the bulk of the GUE, and all-order conformal perturbation theory expansions of correlation functions in the sine-Gordon field theory at the free-fermion point.
How instanton combinatorics solves Painlevé VI, V and IIIs
Gamayun, O.; Iorgov, N.; Lisovyy, O.
2013-08-01
We elaborate on a recently conjectured relation of Painlevé transcendents and 2D conformal field theory. General solutions of Painlevé VI, V and III are expressed in terms of c = 1 conformal blocks and their irregular limits, AGT related to instanton partition functions in {N}=2 supersymmetric gauge theories with Nf = 0, 1, 2, 3, 4. The resulting combinatorial series representations of Painlevé functions provide an efficient tool for their numerical computation at finite values of the argument. The series involves sums over bipartitions which, in the simplest cases, coincide with Gessel expansions of certain Toeplitz determinants. Considered applications include Fredholm determinants of classical integrable kernels, scaled gap probability in the bulk of the Gaussian Unitary Ensemble, and all-order conformal perturbation theory expansions of correlation functions in the sine-Gordon field theory at the free-fermion point.
Macroscopic Quantum Coherence in Antiferromagnetic Molecular Magnets
Institute of Scientific and Technical Information of China (English)
HU Hui; LO Rong; ZHU Jia-Lin; XIONG Jia-Jiong
2001-01-01
The macroscopic quantum coherence in a biaxial antiferromagnetic molecular magnet in the presence of magnetic field acting parallel to its hard anisotropy axis is studied within the two-sublattice model. On the basis of instanton technique in the spin-coherent-state path-integral representation, both the rigorous Wentzel-Kramers-Brillouin exponent and pre-exponential factor for the ground-state tunnel splitting are obtained. We find that the quantum fluctuations around the classical paths can not only induce a new quantum phase previously reported by Chiolero and Loss (Phys. Rev. Lett. 80 (1998) 169), but also have great influence on the intensity of the ground-state tunnel splitting. Those features clearly have no analogue in the ferromagnetic molecular magnets. We suggest that they may be the universal behaviors in all antiferromagnetic molecular magnets. The analytical results are complemented by exact diagonalization calculation.
Macroscopic Quantum Coherence in Antiferromagnetic Molecular Magnets
Institute of Scientific and Technical Information of China (English)
HUHui; LURong; 等
2001-01-01
The macroscopic quantum coherence in a biaxial antiferromagnetic molecular magnet in the presence of magnetic field acting parallel to its hard anisotropy axis is studied within the two-sublattice model.On the basis of instanton technique in the spin-coherent-state path-integral representation,both the rigorous Wentzel-Kramers-Brillouin exponent and pre-exponential factor for the ground-state tunnel splitting are obtained.We find that the quantum fluctuations around the classical paths can not only induce a new quantum phase previously reported by Chiolero and Loss (Phys.Rev.Lett.80(1998)169),but also have great influence on the intensity of the ground-state tunnel splitting.Those features clearly have no analogue in the ferromagnetic molecular magnets.We suggest that they may be the universal behaviors in all antiferromagnetic molecular magnets.The analytical results are complemented by exact diagonalization calculation.
Non-minimally coupled pseudoscalars in AdS4 for instantons in CFT3
Naghdi, M.
2016-06-01
For the 11-dimensional supergravity over {{{AdS}}}4× {{{S}}}7/{Z}k, beginning with a general four-form ansatz and the main geometry unchanged, we get a tower of massive and tachyonic pseudoscalars. Indeed, the resultant equations can be assigned to the so-called {φ }4 actions of the non-minimally coupled scalar-tensor theories with a cosmological constant. We focus on a well-known tachyonic and a new massive bulk mode, which are singlet under the internal group and break all supersymmetries, associated with skew-whiffing and Wick-rotating of the background four-form flux, respectively. The first one is the conformally coupled {m}2=-2 pseudoscalar in the bulk of Euclidean AdS4, where an exact instanton solution is found and a marginally triple-trace deformation with a proper dimension-1 operator produces an agreeing boundary solution with finite action. From the action evaluated on the solution, we estimate the decay rate of the vacuum tunneling mediated by the instanton. Another massive {m}2=+4 mode, with the so-called non-minimal coupling parameter ξ =-1/3, also breaks the conformal invariance and so there is no exact solution. Then, based on the AdS4/CFT3 correspondence rules, we propose the dimension-4 ({{{Δ }}}+=+4) boundary operator in the skew-whiffed (anti-M2-branes) theory with which to deform the boundary action—consisting of a singlet fermion, an original scalar and U(1) gauges fields—and find some solutions to be matched with the bulk solutions.
Differential and Twistor Geometry of the Quantum Hopf Fibration
Brain, Simon
2011-01-01
We study a quantum version of the SU(2) Hopf fibration $S^7 \\to S^4$ and its associated twistor geometry. Our quantum sphere $S^7_q$ arises as the unit sphere inside a q-deformed quaternion space $\\mathbb{H}^2_q$. The resulting four-sphere $S^4_q$ is a quantum analogue of the quaternionic projective space $\\mathbb{HP}^1$. The quantum fibration is endowed with compatible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space $\\mathbb{CP}^3_q$ and use it to study a system of anti-self-duality equations on $S^4_q$, for which we find an `instanton' solution coming from the natural projection defining the tautological bundle over $S^4_q$.
On the Nature of Nonperturbative Effects in Stabilized 2D Quantum Gravity
Diego, O; Diego, Oscar; Gonzalez, Jose
1994-01-01
We remark that the weak coupling regime of the stochastic stabilization of 2D quantum gravity has a unique perturbative vacuum, which does not support instanton configurations. By means of Monte Carlo simulations we show that the nonperturbative vacuum is also confined in one potential well. Nonperturbative effects can be assessed in the loop equation. This can be derived from the Ward identities of the stabilized model and is shown to be modified by nonperturbative terms.
Appearance of gauge fields and forces beyond the adiabatic approximation
Energy Technology Data Exchange (ETDEWEB)
Gosselin, Pierre [Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathematiques, Universite Grenoble I, BP74, 38402 Saint Martin d' Heres, Cedex (France); Mohrbach, Herve, E-mail: mohrbach@univ-metz.f [Laboratoire de Physique Moleculaire et des Collisions, ICPMB-FR CNRS 2843, Universite Paul Verlaine-Metz, 57078 Metz Cedex 3 (France)
2010-09-03
We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer approximation to arbitrary quantum systems described by matrix-valued quantum Hamiltonians. The results are illustrated by several physical relevant examples.
Quantum Secure Direct Communication with Quantum Memory
Zhang, Wei; Ding, Dong-Sheng; Sheng, Yu-Bo; Zhou, Lan; Shi, Bao-Sen; Guo, Guang-Can
2017-06-01
Quantum communication provides an absolute security advantage, and it has been widely developed over the past 30 years. As an important branch of quantum communication, quantum secure direct communication (QSDC) promotes high security and instantaneousness in communication through directly transmitting messages over a quantum channel. The full implementation of a quantum protocol always requires the ability to control the transfer of a message effectively in the time domain; thus, it is essential to combine QSDC with quantum memory to accomplish the communication task. In this Letter, we report the experimental demonstration of QSDC with state-of-the-art atomic quantum memory for the first time in principle. We use the polarization degrees of freedom of photons as the information carrier, and the fidelity of entanglement decoding is verified as approximately 90%. Our work completes a fundamental step toward practical QSDC and demonstrates a potential application for long-distance quantum communication in a quantum network.
Quantum Secure Direct Communication with Quantum Memory.
Zhang, Wei; Ding, Dong-Sheng; Sheng, Yu-Bo; Zhou, Lan; Shi, Bao-Sen; Guo, Guang-Can
2017-06-02
Quantum communication provides an absolute security advantage, and it has been widely developed over the past 30 years. As an important branch of quantum communication, quantum secure direct communication (QSDC) promotes high security and instantaneousness in communication through directly transmitting messages over a quantum channel. The full implementation of a quantum protocol always requires the ability to control the transfer of a message effectively in the time domain; thus, it is essential to combine QSDC with quantum memory to accomplish the communication task. In this Letter, we report the experimental demonstration of QSDC with state-of-the-art atomic quantum memory for the first time in principle. We use the polarization degrees of freedom of photons as the information carrier, and the fidelity of entanglement decoding is verified as approximately 90%. Our work completes a fundamental step toward practical QSDC and demonstrates a potential application for long-distance quantum communication in a quantum network.
Misra, A
2002-01-01
Following the work of Lima et al on the exact evaluation of the nonperturbative contribution to the superpotential from open-membrane instanton in Heterotic M-Theory, we evaluate systematically the contribution to the superpotential of a membrane instanton obtained by wrapping of a single M2 brane, once, on an isolated supersymmetric 3-cycle in a G_2-holonomy manifold. We then try to relate the results obtained to those sketched out in Harvey and Moore. We also do a heat-kernel asymptotics analysis to see whether one gets similar UV-divergent terms for (one or both of) the bosonic and fermionic determinants indicative of (partial) cancelation among them. The answer is in the affirmative, as expected by the supersymmetry of the starting membrane action. This work is a first step in understanding the large N Chern-Simons/closed type-A topological string theory duality of Gopakumar and Vafa from M theory point of view.
Bubuianu, Laurençtiu; Vacaru, Sergiu I
2016-01-01
Heterotic supergravity with (1+3)-dimensional domain wall configurations and (warped) internal, six dimensional, almost-K\\"{a}hler manifolds $\\ ^6\\mathbf{X} $ are studied. Considering on ten dimensional spacetime, nonholonomic distributions with conventional double fibrations, 2+2+...=2+2+3+3, and associated $SU(3)$ structures on internal space, we generalize for real, internal, almost symplectic gravitational structures the constructions with gravitational and gauge instantons of tanh-kink type. They include the first $\\alpha ^{\\prime }$ corrections to the heterotic supergravity action, parameterized in a form to imply nonholonomic deformations of the Yang-Mills sector and corresponding Bianchi identities. We show how it is possible to construct a variety of solutions, depending on the type of nonholonomic distributions and deformations of 'prime' instanton configurations characterized by two real supercharges. This corresponds to $\\mathcal{N}=1/2$ supersymmetric, nonholonomic manifolds from the four dimensi...
Squashed entanglement and approximate private states
Wilde, Mark M.
2016-09-01
The squashed entanglement is a fundamental entanglement measure in quantum information theory, finding application as an upper bound on the distillable secret key or distillable entanglement of a quantum state or a quantum channel. This paper simplifies proofs that the squashed entanglement is an upper bound on distillable key for finite-dimensional quantum systems and solidifies such proofs for infinite-dimensional quantum systems. More specifically, this paper establishes that the logarithm of the dimension of the key system (call it log 2K ) in an ɛ -approximate private state is bounded from above by the squashed entanglement of that state plus a term that depends only ɛ and log 2K . Importantly, the extra term does not depend on the dimension of the shield systems of the private state. The result holds for the bipartite squashed entanglement, and an extension of this result is established for two different flavors of the multipartite squashed entanglement.
Green, Michael B; Vanhove, Pierre
2011-01-01
This paper concerns some novel features of maximal parabolic Eisenstein series at certain special values of their analytic parameter s. These series arise as coefficients in the R4 and D4R4 interactions in the low energy expansion of scattering amplitudes in maximally supersymmetric string theory reduced to D=10-d dimensions on a torus T^d, d<8. For each d these amplitudes are automorphic functions on the rank d+1 symmetry group E_d+1. Of particular significance is the orbit content of the Fourier modes of these series when expanded in three different parabolic subgroups, corresponding to certain limits of string theory. This is of interest in the classification of a variety of instantons that correspond to minimal or next-to-minimal BPS orbits. In the limit of decompactification from D to D+1 dimensions many such instantons are related to charged 1/2-BPS or 1/4-BPS black holes with euclidean world-lines wrapped around the large dimension. In a different limit the instantons give nonperturbative correction...
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
Hydrogen Beyond the Classic Approximation
Scivetti, I
2003-01-01
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Quantum Nucleation of Antiferromagnetic Bubbles with Tetragonal and Hexagonal Symmetries
Institute of Scientific and Technical Information of China (English)
PAN Hui; ZHU Jia-Lin; L(U) Rong
2004-01-01
We study the quantum nucleation in a nanometer-scale antiferromagnet placed in a magnetic field at an arbitrary angle. We consider the magnetocrystalline anisotropy with tetragonal symmetry and that with hexagonal symmetry, respectively. Different structures of the tunneling barriers can be generated by the magnitude and the orientation of the magnetic field. We use the instanton method in the spin-coherent-state path-integral representation to calculate the dependence of the rate of quantum nucleation and the crossover temperature on the orientation and strength of the field for bulk solids and two-dimensional films of antiferromagnets, respectively. We find that the rate of quantum nucleation and the crossover temperature from thermal-to-quantum transitions depend on the orientation and strength of the external magnetic field distinctly, which can be tested by use of existing experimental techniques.
Principles of quantum chemistry
George, David V
2013-01-01
Principles of Quantum Chemistry focuses on the application of quantum mechanics in physical models and experiments of chemical systems.This book describes chemical bonding and its two specific problems - bonding in complexes and in conjugated organic molecules. The very basic theory of spectroscopy is also considered. Other topics include the early development of quantum theory; particle-in-a-box; general formulation of the theory of quantum mechanics; and treatment of angular momentum in quantum mechanics. The examples of solutions of Schroedinger equations; approximation methods in quantum c
Curran, Stephen
2009-01-01
In arXiv:0807.0677, K\\"ostler and Speicher observed that de Finetti's theorem on exchangeable sequences has a free analogue if one replaces exchangeability by the stronger condition of invariance under quantum permutations. In this paper we study sequences of noncommutative random variables whose joint distribution is invariant under quantum orthogonal transformations. We prove a free analogue of Freedman's characterization of conditionally independent Gaussian families, namely an infinite sequence of self-adjoint random variables is quantum orthogonally invariant if and only if they form an operator-valued free centered equivariant semicircular family. Similarly, we show that an infinite sequence of noncommutative random variables is quantum unitarily invariant if and only if they form an operator-valued free centered equivariant circular family. We provide an example to show that, as in the classical case, these results fail for finite sequences. We then give an approximation to how far the distribution of ...