The partition function zeroes of quantum critical points
Energy Technology Data Exchange (ETDEWEB)
Crompton, P.R. [Department of Applied Maths, School of Mathematics, University of Leeds, Leeds, LS2 9JT (United Kingdom)], E-mail: p.crompton@lancaster.ac.uk
2009-04-01
The Lee-Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity e{sup h{delta}}{sup {tau}}, and the Euclidean-time lattice spacing {delta}{tau} can be divergent in the infrared (IR). We recently presented analytic arguments describing how a new space-Euclidean time zeroes expansion can be defined, which reproduces Lee and Yang's scaling but avoids the unresolved branch points associated with the breaking of nonlocal symmetries such as Parity. We now present a first numerical analysis for this new zeroes approach for a quantum spin chain system. We use our scheme to quantify the renormalization group flow of the physical lattice couplings to the IR fixed point of this system. We argue that the generic Finite-Size Scaling (FSS) function of our scheme is identically the entanglement entropy of the lattice partition function and, therefore, that we are able to directly extract the central charge, c, of the quantum spin chain system using conformal predictions for the scaling of the entanglement entropy.
Partition functions for quantum gravity, black holes, elliptic genera and Lie algebra homologies
Energy Technology Data Exchange (ETDEWEB)
Bonora, L., E-mail: bonora@sissa.it [International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A., E-mail: abyts@uel.br [Departamento de Fisica, Universidade Estadual de Londrina, Caixa Postal 6001, Londrina (Brazil)
2011-11-11
There is a remarkable connection between quantum generating functions of field theory and formal power series associated with dimensions of chains and homologies of suitable Lie algebras. We discuss the homological aspects of this connection with its applications to partition functions of the minimal three-dimensional gravities in the space-time asymptotic to AdS{sub 3}, which also describe the three-dimensional Euclidean black holes, the pure N=1 supergravity, and a sigma model on N-fold generalized symmetric products. We also consider in the same context elliptic genera of some supersymmetric sigma models. These examples can be considered as a straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to partition functions represented by means of formal power series that encode Lie algebra properties.
On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers
Geraci, Joseph; Lidar, Daniel A.
2008-05-01
We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and exploit the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in order to obtain the weight enumerator for a certain class of linear codes. In this way we demonstrate that for a certain class of sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCCɛ) graphs, quantum computers provide a polynomial speed up in the difference between the number of edges and vertices of the graph, and an exponential speed up in q, over the best classical algorithms known to date.
On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers
Geraci, J; Geraci, Joseph; Lidar, Daniel A.
2007-01-01
We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and exploit the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in order to obtain the weight enumerator for a certain class of linear codes. In this way we demonstrate that for a certain class of sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_\\epsilon) graphs, quantum computers provide a polynomial speed up in the difference between the number of edges and vertices of the graph, and an exponential speed up in q, over the best classical algorithms known to date.
Partition Function of Spacetime
Makela, Jarmo
2008-01-01
We consider a microscopic model of spacetime, where spacetime is assumed to be a specific graph with Planck size quantum black holes on its vertices. As a thermodynamical system under consideration we take a certain uniformly accelerating, spacelike two-surface of spacetime which we call, for the sake of brevity and simplicity, as {\\it acceleration surface}. Using our model we manage to obtain an explicit and surprisingly simple expression for the partition function of an acceleration surface. Our partition function implies, among other things, the Unruh and the Hawking effects. It turns out that the Unruh and the Hawking effects are consequences of a specific phase transition, which takes place in spacetime, when the temperature of spacetime equals, from the point of view of an observer at rest with respect to an acceleration surface, to the Unruh temperature measured by that observer. When constructing the partition function of an acceleration surface we are forced to introduce a quantity which plays the ro...
Quantum Mechanical Single Molecule Partition Function from PathIntegral Monte Carlo Simulations
Energy Technology Data Exchange (ETDEWEB)
Chempath, Shaji; Bell, Alexis T.; Predescu, Cristian
2006-10-01
An algorithm for calculating the partition function of a molecule with the path integral Monte Carlo method is presented. Staged thermodynamic perturbation with respect to a reference harmonic potential is utilized to evaluate the ratio of partition functions. Parallel tempering and a new Monte Carlo estimator for the ratio of partition functions are implemented here to achieve well converged simulations that give an accuracy of 0.04 kcal/mol in the reported free energies. The method is applied to various test systems, including a catalytic system composed of 18 atoms. Absolute free energies calculated by this method lead to corrections as large as 2.6 kcal/mol at 300 K for some of the examples presented.
Kellerstein, M; Verbaarschot, J J M
2016-01-01
The behavior of quenched Dirac spectra of two-dimensional lattice QCD is consistent with spontaneous chiral symmetry breaking which is forbidden according to the Coleman-Mermin-Wagner theorem. One possible resolution of this paradox is that, because of the bosonic determinant in the partially quenched partition function, the conditions of this theorem are violated allowing for spontaneous symmetry breaking in two dimensions or less. This goes back to work by Niedermaier and Seiler on nonamenable symmetries of the hyperbolic spin chain and earlier work by two of the auhtors on bosonic partition functions at nonzero chemical potential. In this talk we discuss chiral symmetry breaking for the bosonic partition function of QCD at nonzero isospin chemical potential and a bosonic random matrix theory at imaginary chemical potential and compare the results with the fermionic counterpart. In both cases the chiral symmetry group of the bosonic partition function is noncompact.
Partition density functional theory
Nafziger, Jonathan
Partition density functional theory (PDFT) is a method for dividing a molecular electronic structure calculation into fragment calculations. The molecular density and energy corresponding to Kohn Sham density-functional theory (KS-DFT) may be exactly recovered from these fragments. Each fragment acts as an isolated system except for the influence of a global one-body 'partition' potential which deforms the fragment densities. In this work, the developments of PDFT are put into the context of other fragment-based density functional methods. We developed three numerical implementations of PDFT: One within the NWChem computational chemistry package using basis sets, and the other two developed from scratch using real-space grids. It is shown that all three of these programs can exactly reproduce a KS-DFT calculation via fragment calculations. The first of our in-house codes handles non-interacting electrons in arbitrary one-dimensional potentials with any number of fragments. This code is used to explore how the exact partition potential changes for different partitionings of the same system and also to study features which determine which systems yield non-integer PDFT occupations and which systems are locked into integer PDFT occupations. The second in-house code, CADMium, performs real-space calculations of diatomic molecules. Features of the exact partition potential are studied for a variety of cases and an analytical formula determining singularities in the partition potential is derived. We introduce an approximation for the non-additive kinetic energy and show how this quantity can be computed exactly. Finally a PDFT functional is developed to address the issues of static correlation and delocalization errors in approximations within DFT. The functional is applied to the dissociation of H2 + and H2.
Matrix string partition function
Kostov, Ivan K; Kostov, Ivan K.; Vanhove, Pierre
1998-01-01
We evaluate quasiclassically the Ramond partition function of Euclidean D=10 U(N) super Yang-Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasiclassical expressions reproduce exactly the recently obtained expression for the partition of the completely reduced SYM theory, including the overall numerical factor. This is an evidence that our quasiclassical calculation might be exact.
Bilal, Adel
2014-01-01
We study two-dimensional quantum gravity on arbitrary genus Riemann surfaces in the Kaehler formalism where the basic quantum field is the (Laplacian of the) Kaehler potential. We do a careful first-principles computation of the fixed-area partition function $Z[A]$ up to and including all two-loop contributions. This includes genuine two-loop diagrams as determined by the Liouville action, one-loop diagrams resulting from the non-trivial measure on the space of metrics, as well as one-loop diagrams involving various counterterm vertices. Contrary to what is often believed, several such counterterms, in addition to the usual cosmological constant, do and must occur. We consistently determine the relevant counterterms from a one-loop computation of the full two-point Green's function of the Kaehler field. Throughout this paper we use the general spectral cutoff regularization developed recently and which is well-suited for multi-loop computations on curved manifolds. At two loops, while all "unwanted" contribut...
Generalised twisted partition functions
Petkova, V B
2001-01-01
We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D Conformal Field Theory (CFT). A consistency equation, which gives a classification of twists, is written and solved in particular cases. This generalises old results on twisted torus boundary conditions, gives a physical interpretation of Ocneanu's algebraic construction, and might offer a new route to the study of properties of CFT.
Wong, Kin-Yiu; Gao, Jiali
2008-09-09
In this paper, we describe an automated integration-free path-integral (AIF-PI) method, based on Kleinert's variational perturbation (KP) theory, to treat internuclear quantum-statistical effects in molecular systems. We have developed an analytical method to obtain the centroid potential as a function of the variational parameter in the KP theory, which avoids numerical difficulties in path-integral Monte Carlo or molecular dynamics simulations, especially at the limit of zero-temperature. Consequently, the variational calculations using the KP theory can be efficiently carried out beyond the first order, i.e., the Giachetti-Tognetti-Feynman-Kleinert variational approach, for realistic chemical applications. By making use of the approximation of independent instantaneous normal modes (INM), the AIF-PI method can readily be applied to many-body systems. Previously, we have shown that in the INM approximation, the AIF-PI method is accurate for computing the quantum partition function of a water molecule (3 degrees of freedom) and the quantum correction factor for the collinear H(3) reaction rate (2 degrees of freedom). In this work, the accuracy and properties of the KP theory are further investigated by using the first three order perturbations on an asymmetric double-well potential, the bond vibrations of H(2), HF, and HCl represented by the Morse potential, and a proton-transfer barrier modeled by the Eckart potential. The zero-point energy, quantum partition function, and tunneling factor for these systems have been determined and are found to be in excellent agreement with the exact quantum results. Using our new analytical results at the zero-temperature limit, we show that the minimum value of the computed centroid potential in the KP theory is in excellent agreement with the ground state energy (zero-point energy) and the position of the centroid potential minimum is the expectation value of particle position in wave mechanics. The fast convergent property
On higher spin partition functions
Beccaria, M
2015-01-01
We observe that the partition function of the set of all free massless higher spins s=0,1,2,3,... in flat space is equal to one: the ghost determinants cancel against the "physical" ones or, equivalently, the (regularized) total number of degrees of freedom vanishes. This reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory. The Z=1 property extends also to the AdS background, i.e. the 1-loop vacuum partition function of Vasiliev theory is equal to 1 (assuming a particular regularization of the sum over spins); this was noticed earlier as a consistency requirement for the vectorial AdS/CFT duality. We find that Z=1 is also true in the conformal higher spin theory (with higher-derivative d^{2s} kinetic terms) expanded near flat or conformally flat S^4 background. We also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2-derivative kinetic term but only scalar gauge invariance in flat space. This non...
Partitioned quantum cellular automata are intrinsically universal
Arrighi, Pablo
2010-01-01
There have been several non-axiomatic approaches taken to define Quantum Cellular Automata (QCA). Partitioned QCA (PQCA) are the most canonical of these non-axiomatic definitions. In this work we show that any QCA can be put into the form of a PQCA. Our construction reconciles all the non-axiomatic definitions of QCA, showing that they can all simulate one another, and hence that they are all equivalent to the axiomatic definition. This is achieved by defining generalised n-dimensional intrinsic simulation, which brings the computer science based concepts of simulation and universality closer to theoretical physics. The result is not only an important simplification of the QCA model, it also plays a key role in the identification of a minimal n-dimensional intrinsically universal QCA.
Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning
Smelyanskiy, Vadius; vonToussaint, Udo V.; Timucin, Dogan A.; Clancy, Daniel (Technical Monitor)
2002-01-01
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
Classical and quantum partition bound and detector inefficiency
Laplante, S; Roland, J
2012-01-01
In communication complexity, two players each have an input and they wish to compute some function of the joint inputs. This has been the object of much study and a wide variety of lower bound methods have been introduced to address the problem of showing lower bounds on communication. Recently, Jain and Klauck introduced the partition bound, which subsumes many of the known methods, in particular factorization norm, discrepancy, and the rectangle (corruption) bound. Physicists have considered a closely related scenario where two players share a predefined entangled state. Each is given a measurement as input, which they perform on their share of the system. The outcomes of the measurements follow a distribution which is predicted by quantum mechanics. In an experimental setting, Bell inequalities are used to distinguish truly quantum from classical behavior. We present a new lower bound technique based on the notion of detector inefficiency (where some runs are discarded by either of the players) for the ext...
Compactified webs and domain wall partition functions
Energy Technology Data Exchange (ETDEWEB)
Shabbir, Khurram [Government College University, Department of Mathematics, Lahore (Pakistan)
2017-04-15
In this paper we use the topological vertex formalism to calculate a generalization of the ''domain wall'' partition function of M-strings. This generalization allows calculation of partition function of certain compactified webs using a simple gluing algorithm similar to M-strings case. (orig.)
Partition functions for supersymmetric black holes
Manschot, J.
2008-01-01
This thesis presents a number of results on partition functions for four-dimensional supersymmetric black holes. These partition functions are important tools to explain the entropy of black holes from a microscopic point of view. Such a microscopic explanation was desired after the association of a
Partial domain wall partition functions
Foda, O
2012-01-01
We consider six-vertex model configurations on a rectangular lattice with n (N) horizontal (vertical) lines, and "partial domain wall boundary conditions" defined as 1. all 2n arrows on the left and right boundaries point inwards, 2. n_u (n_l) arrows on the upper (lower) boundary, such that n_u + n_l = N - n, also point inwards, 3. all remaining n+N arrows on the upper and lower boundaries point outwards, and 4. all spin configurations on the upper and lower boundaries are summed over. To generate (n-by-N) "partial domain wall configurations", one can start from A. (N-by-N) configurations with domain wall boundary conditions and delete n_u (n_l) upper (lower) horizontal lines, or B. (2n-by-N) configurations that represent the scalar product of an n-magnon Bethe eigenstate and an n-magnon generic state on an N-site spin-1/2 chain, and delete the n lines that represent the Bethe eigenstate. The corresponding "partial domain wall partition function" is computed in construction {A} ({B}) as an N-by-N (n-by-n) det...
One-loop Partition Functions of 3D Gravity
Giombi, Simone; Yin, Xi
2008-01-01
We consider the one-loop partition function of free quantum field theory in locally Anti-de Sitter space-times. In three dimensions, the one loop determinants for scalar, gauge and graviton excitations are computed explicitly using heat kernel techniques. We obtain precisely the result anticipated by Brown and Henneaux: the partition function includes a sum over "boundary excitations" of AdS3, which are the Virasoro descendants of empty Anti-de Sitter space. This result also allows us to compute the one-loop corrections to the Euclidean action of the BTZ black hole as well its higher genus generalizations.
Perturbative partition function for squashed S^5
Imamura, Yosuke
2012-01-01
We compute the index of 6d N=(1,0) theories on S^5xR containing vector and hypermultiplets. We only consider the perturbative sector without instantons. By compactifying R to S^1 with a twisted boundary condition and taking the small radius limit, we derive the perturbative partition function on a squashed S^5. The 1-loop partition function is represented in a simple form with the triple sine function.
Approximation methods for the partition functions of anharmonic systems
Energy Technology Data Exchange (ETDEWEB)
Lew, P.; Ishida, T.
1979-07-01
The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations.
Reinforcement learning with partitioning function system
Institute of Scientific and Technical Information of China (English)
李伟; 叶庆泰; 朱昌明
2004-01-01
The size of state-space is the limiting factor in applying reinforcement learning algorithms to practical cases. A reinforcement learning system with partitioning function (RLWPF) is established, in which statespace is partitioned into several regions. Inside the performance principle of RLWPF is based on a Semi-Markov decision process and has general significance. It can be applied to any reinforcement learning with a large statespace. In RLWPF, the partitioning module dispatches agents into different regions in order to decrease the state-space of each agent. This article proves the convergence of the SARSA algorithm for a Semi-Markov decision process, ensuring the convergence of RLWPF by analyzing the equivalence of two value functions in two Semi-Markov decision processes before and after partitioning. This article can show that the optimal policy learned by RLWPF is consistent with prior domain knowledge. An elevator group system is devised to decrease the average waiting time of passengers. Four agents control four elevator cars respectively. Based on RLWPF, a partitioning module is developed through defining a uniform round trip time as the partitioning criteria, making the wait time of most passengers more or less identical then elevator cars should only answer hall calls in their own region. Compared with ordinary elevator systems and reinforcement learning systems without partitioning module, the performance results show the advantage of RLWPF.
Double-partition Quantum Cluster Algebras
DEFF Research Database (Denmark)
Jakobsen, Hans Plesner; Zhang, Hechun
2012-01-01
A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but sub-classes have been studied previously by other authors. The algebras are indexed by double parti- tions or double flag varieties. Equivalently, they are indexed by broken lines L. By grouping...... together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of one broken line to another. Compatible pairs can be written down. The algebras are equal to their upper cluster algebras. The variables of the quantum seeds are given by elements of the dual canonical basis....
Controllability of multi-partite quantum systems and selective excitation of quantum dots
Energy Technology Data Exchange (ETDEWEB)
Schirmer, S G [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Pullen, I C H [Department of Applied Mathematics and Computing, Open University, Walton Hall, Milton Keynes MK7 6AA (United Kingdom); Solomon, A I [Department of Physics and Astronomy, Open University, Walton Hall, Milton Keynes MK7 6AA (United Kingdom)
2005-10-01
We consider the degrees of controllability of multi-partite quantum systems, as well as necessary and sufficient criteria for each case. The results are applied to the problem of simultaneous control of an ensemble of quantum dots with a single laser pulse. Finally, we apply optimal control techniques to demonstrate selective excitation of individual dots for a simultaneously controllable ensemble of quantum dots.
Combinatorics and complexity of partition functions
Barvinok, Alexander
2016-01-01
Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates. .
Partition functions and graphs: A combinatorial approach
Solomon, A I; Duchamp, G; Horzela, A; Penson, K A; Solomon, Allan I.; Blasiak, Pawel; Duchamp, Gerard; Horzela, Andrzej; Penson, Karol A.
2004-01-01
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the partition function, for example, is essentially a combinatorial problem. In this talk we shall show that one approach is via the normal ordering of the second quantized operators appearing in the partition function. This in turn leads to a combinatorial graphical description, giving essentially Feynman-type graphs associated with the theory. We illustrate this methodology by the explicit calculation of two model examples, the free boson gas and a superfluid boson model. We show how the calculation of partition functions can be facilitated by knowledge of the combinatorics of the boson normal ordering problem; this naturally gives rise to the Bell numbers of combinatorics. The associated graphical representation of these numbers gives a perturbation expansion in terms of a sequen...
Domain wall partition functions and KP
Foda, O; Zuparic, M
2009-01-01
We observe that the partition function of the six vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP tau function and express it as an expectation value of charged free fermions (up to an overall normalization).
The Quantum Biology of Reactive Oxygen Species Partitioning Impacts Cellular Bioenergetics.
Usselman, Robert J; Chavarriaga, Cristina; Castello, Pablo R; Procopio, Maria; Ritz, Thorsten; Dratz, Edward A; Singel, David J; Martino, Carlos F
2016-12-20
Quantum biology is the study of quantum effects on biochemical mechanisms and biological function. We show that the biological production of reactive oxygen species (ROS) in live cells can be influenced by coherent electron spin dynamics, providing a new example of quantum biology in cellular regulation. ROS partitioning appears to be mediated during the activation of molecular oxygen (O2) by reduced flavoenzymes, forming spin-correlated radical pairs (RPs). We find that oscillating magnetic fields at Zeeman resonance alter relative yields of cellular superoxide (O2(•-)) and hydrogen peroxide (H2O2) ROS products, indicating coherent singlet-triplet mixing at the point of ROS formation. Furthermore, the orientation-dependence of magnetic stimulation, which leads to specific changes in ROS levels, increases either mitochondrial respiration and glycolysis rates. Our results reveal quantum effects in live cell cultures that bridge atomic and cellular levels by connecting ROS partitioning to cellular bioenergetics.
The Quantum Biology of Reactive Oxygen Species Partitioning Impacts Cellular Bioenergetics
Usselman, Robert J.; Chavarriaga, Cristina; Castello, Pablo R.; Procopio, Maria; Ritz, Thorsten; Dratz, Edward A.; Singel, David J.; Martino, Carlos F.
2016-12-01
Quantum biology is the study of quantum effects on biochemical mechanisms and biological function. We show that the biological production of reactive oxygen species (ROS) in live cells can be influenced by coherent electron spin dynamics, providing a new example of quantum biology in cellular regulation. ROS partitioning appears to be mediated during the activation of molecular oxygen (O2) by reduced flavoenzymes, forming spin-correlated radical pairs (RPs). We find that oscillating magnetic fields at Zeeman resonance alter relative yields of cellular superoxide (O2•-) and hydrogen peroxide (H2O2) ROS products, indicating coherent singlet-triplet mixing at the point of ROS formation. Furthermore, the orientation-dependence of magnetic stimulation, which leads to specific changes in ROS levels, increases either mitochondrial respiration and glycolysis rates. Our results reveal quantum effects in live cell cultures that bridge atomic and cellular levels by connecting ROS partitioning to cellular bioenergetics.
Topological String Partition Function on Generalised Conifolds
Gasparim, Elizabeth; Suzuki, Bruno; Torres-Gomez, Alexander
2016-01-01
We show that the partition function on a generalised conifold $C_{m,n}$ with ${m+n \\choose m}$ crepant resolutions can be equivalently computed on the compound du Val singularity $A_{m+n-1}\\times \\mathbb C$ with a unique crepant resolution.
Polynomial Structure of Topological String Partition Functions
Zhou, Jie
2015-01-01
We review the polynomial structure of the topological string partition functions as solutions to the holomorphic anomaly equations. We also explain the connection between the ring of propagators defined from special K\\"ahler geometry and the ring of almost-holomorphic modular forms defined on modular curves.
Remarks on partition functions of topological string theory on generalized conifolds
Takasaki, Kanehisa
2013-01-01
The notion of topological vertex and the construction of topological string partition functions on local toric Calabi-Yau 3-folds are reviewed. Implications of an explicit formula of partition functions for the generalized conifolds are considered. Generating functions of part of the partition functions are shown to be tau functions of the KP hierarchy. The associated Baker-Akhiezer functions play the role of wave functions, and satisfy $q$-difference equations. These $q$-difference equations represent the quantum mirror curves conjectured by Gukov and Su{\\l}kowski.
Quantum mechanical fragment methods based on partitioning atoms or partitioning coordinates.
Wang, Bo; Yang, Ke R; Xu, Xuefei; Isegawa, Miho; Leverentz, Hannah R; Truhlar, Donald G
2014-09-16
atoms for capping dangling bonds, and we have shown that they can greatly improve the accuracy. Finally we present a new approach that goes beyond QM/MM by combining the convenience of molecular mechanics with the accuracy of fitting a potential function to electronic structure calculations on a specific system. To make the latter practical for systems with a large number of degrees of freedom, we developed a method to interpolate between local internal-coordinate fits to the potential energy. A key issue for the application to large systems is that rather than assigning the atoms or monomers to fragments, we assign the internal coordinates to reaction, secondary, and tertiary sets. Thus, we make a partition in coordinate space rather than atom space. Fits to the local dependence of the potential energy on tertiary coordinates are arrayed along a preselected reaction coordinate at a sequence of geometries called anchor points; the potential energy function is called an anchor points reactive potential. Electrostatically embedded fragment methods and the anchor points reactive potential, because they are based on treating an entire system by quantum mechanical electronic structure methods but are affordable for large and complex systems, have the potential to open new areas for accurate simulations where combined QM/MM methods are inadequate.
Partition functions of web diagrams with an O7$^-$-plane
Hayashi, Hirotaka
2016-01-01
We consider the computation of the topological string partition function for 5-brane web diagrams with an O7$^-$-plane. Since upon quantum resolution of the orientifold plane these diagrams become non-toric web diagrams without the orientifold we are able to apply the topological vertex to obtain the Nekrasov partition function of the corresponding 5d theory. We apply this procedure to the case of 5d $SU(N)$ theories with one hypermultiplet in the antisymmetric representation and to the case of 5d pure $USp(2N)$ theories. For these cases we discuss the dictionary between parameters and moduli of the 5d gauge theory and lengths of 5-branes in the web diagram and moreover we perform comparison of the results obtained via application of the topological vertex and the one obtained via localisation techniques, finding in all instances we consider perfect agreement.
Bounds for the Eventual Positivity of Difference Functions of Partitions
Woodford, Roger
2007-01-01
In this paper we specialize work done by Bateman and Erdos concerning difference functions of partition functions. In particular, we are concerned with partitions into fixed powers of the primes. We show that any difference function of these partition functions is eventually increasing, and derive explicit bounds for when it will attain strictly positive values. From these bounds an asymptotic result is derived.
Supersymmetric partition functions on Riemann surfaces
Benini, Francesco
2016-01-01
We present a compact formula for the supersymmetric partition function of 2d N=(2,2), 3d N=2 and 4d N=1 gauge theories on $\\Sigma_g \\times T^n$ with partial topological twist on $\\Sigma_g$, where $\\Sigma_g$ is a Riemann surface of arbitrary genus and $T^n$ is a torus with n=0,1,2, respectively. In 2d we also include certain local operator insertions, and in 3d we include Wilson line operator insertions along $S^1$. For genus g=1, the formula computes the Witten index. We present a few simple Abelian and non-Abelian examples, including new tests of non-perturbative dualities. We also show that the large N partition function of ABJM theory on $\\Sigma_g \\times S^1$ reproduces the Bekenstein-Hawking entropy of BPS black holes in AdS4 whose horizon has $\\Sigma_g$ topology.
Recursive formulae for the multiplicative partition function
Directory of Open Access Journals (Sweden)
Jun Kyo Kim
1999-01-01
Full Text Available For a positive integer n, let f(n be the number of essentially different ways of writing n as a product of factors greater than 1, where two factorizations of a positive integer are said to be essentially the same if they differ only in the order of the factors. This paper gives a recursive formula for the multiplicative partition function f(n.
Semiclassical partition function for the double-well potential
Kroff, D.; Bessa, A.; de Carvalho, C. A. A.; Fraga, E. S.; Jorás, S. E.
2014-07-01
We compute the partition function and specific heat for a quantum-mechanical particle under the influence of a quartic double-well potential nonperturbatively, using the semiclassical method. Near the region of bounded motion in the inverted potential, the usual quadratic approximation fails due to the existence of multiple classical solutions and caustics. Using the tools of catastrophe theory, we identify the relevant classical solutions, showing that at most two have to be considered. This corresponds to the first step towards the study of spontaneous symmetry breaking and thermal phase transitions in the nonperturbative framework of the boundary effective theory.
Semiclassical partition function for the double-well potential
Kroff, D; de Carvalho, C A A; Fraga, E S; Jorás, S E
2013-01-01
We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the inverted potential, the usual quadratic approximation fails due to the existence of multiple classical solutions and caustics. Using the tools of catastrophe theory, we identify the relevant classical solutions, showing that at most two have to be considered. This corresponds to the first step towards the study of spontaneous symmetry breaking and thermal phase transitions in the non-perturbative framework of the boundary effective theory.
Attractor black holes and quantum distribution functions
Energy Technology Data Exchange (ETDEWEB)
Montanez, S. [Instituto de Fisica Teorica CSIC-UAM, Modulo C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Gomez, C. [Instituto de Fisica Teorica CSIC-UAM, Modulo C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Theory Group, Physics Department, CERN, 1211 Geneva 23 (Switzerland)
2007-05-15
Using the attractor mechanism and the wavefunction interpretation of the topological string partition function on a Calabi Yau threefold M we study the relation between the Bekenstein-Hawking-Wald entropy of BPS Calabi-Yau black holes and quantum distribution functions defined on H{sup 3}(M). We discuss the OSV conjecture in this context. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
On the Potts Model Partition Function in an External Field
McDonald, Leslie M.; Moffatt, Iain
2012-03-01
We study the partition function of the Potts model in an external (magnetic) field, and its connections with the zero-field Potts model partition function. Using a deletion-contraction formulation for the partition function Z for this model, we show that it can be expanded in terms of the zero-field partition function. We also show that Z can be written as a sum over the spanning trees, and the spanning forests, of a graph G. Our results extend to Z the well-known spanning tree expansion for the zero-field partition function that arises though its connections with the Tutte polynomial.
Surface defects and instanton partition functions
Gaiotto, Davide; Kim, Hee-Cheol
2016-10-01
We study the superconformal index of five-dimensional SCFTs and the sphere partition function of four-dimensional gauge theories with eight supercharges in the presence of co-dimension two half-BPS defects. We derive a prescription which is valid for defects which can be given a "vortex construction", i.e. can be defined by RG flow from vortex configurations in a larger theory. We test the prescription against known results and expected dualities. We employ our prescription to develop a general computational strategy for defects defined by coupling the bulk degrees of freedom to a Gauged Linear Sigma Model living in co-dimension two.
Generalised partition functions: inferences on phase space distributions
Treumann, Rudolf A.; Baumjohann, Wolfgang
2016-06-01
It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs-Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1/|q - 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel-Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs-Boltzmann partition function is fundamental not only to Gibbs-Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.
Modular properties of full 5D SYM partition function
Qiu, Jian; Winding, Jacob; Zabzine, Maxim
2015-01-01
We study properties of the full partition function for the $U(1)$ 5D $\\mathcal{N}=2^*$ gauge theory with adjoint hypermultiplet of mass $M$. This theory is ultimately related to abelian 6D (2,0) theory. We construct the full non-perturbative partition function on toric Sasaki-Einstein manifolds by gluing flat copies of the Nekrasov partition function and we express the full partition function in terms of the generalized double elliptic gamma function $G_2^C$ associated with a certain moment map cone $C$. The answer exhibits a curious $SL(4,\\mathbb{Z})$ modular property. Finally, we propose a set of rules to construct the partition function that resembles the calculation of 5D supersymmetric partition function with the insertion of defects of various co-dimensions.
Modular properties of full 5D SYM partition function
Qiu, Jian; Tizzano, Luigi; Winding, Jacob; Zabzine, Maxim
2016-03-01
We study properties of the full partition function for the U(1) 5D N = {2}^{ast } gauge theory with adjoint hypermultiplet of mass M . This theory is ultimately related to abelian 6D (2,0) theory. We construct the full non-perturbative partition function on toric Sasaki-Einstein manifolds by gluing flat copies of the Nekrasov partition function and we express the full partition function in terms of the generalized double elliptic gamma function G 2 C associated with a certain moment map cone C. The answer exhibits a curious SL(4 , ℤ) modular property. Finally, we propose a set of rules to construct the partition function that resembles the calculation of 5d supersymmetric partition function with the insert ion of defects of various co-dimensions.
S^3/Z_n partition function and dualities
Imamura, Yosuke
2012-01-01
We investigate S^3/Z_n partition function of N = 2 supersymmetric gauge theories. A gauge theory on the orbifold has degenerate vacua specified by the holonomy. The partition function is obtained by summing up the contributions of saddle points with different holonomies. An appropriate choice of the phase of each contribution is essential to obtain the partition function. We determine the relative phases in the holonomy sum in a few examples by using duality to non-gauge theories. In the case of odd n the phase factors can be absorbed by modifying a single function appearing in the partition function.
Partition function of nearest neighbour Ising models: Some new insights
Indian Academy of Sciences (India)
G Nandhini; M V Sangaranarayanan
2009-09-01
The partition function for one-dimensional nearest neighbour Ising models is estimated by summing all the energy terms in the Hamiltonian for N sites. The algebraic expression for the partition function is then employed to deduce the eigenvalues of the basic 2 × 2 matrix and the corresponding Hermitian Toeplitz matrix is derived using the Discrete Fourier Transform. A new recurrence relation pertaining to the partition function for two-dimensional Ising models in zero magnetic field is also proposed.
Matrix models for β-ensembles from Nekrasov partition functions
Sułkowski, P.
2010-01-01
We relate Nekrasov partition functions, with arbitrary values of ∊ 1, ∊ 2 parameters, to matrix models for β-ensembles. We find matrix models encoding the instanton part of Nekrasov partition functions, whose measure, to the leading order in ∊ 2 expansion, is given by the Vandermonde determinant to
Superconformal indices and partition functions for supersymmetric field theories
Energy Technology Data Exchange (ETDEWEB)
Gahramanov, I.B. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Vartanov, G.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-12-15
Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions using localization method. Here we discuss a connection of 4d superconformal indices and 3d partition functions using a particular example of supersymmetric theories with matter in antisymmetric representation.
A partition function approximation using elementary symmetric functions.
Directory of Open Access Journals (Sweden)
Ramu Anandakrishnan
Full Text Available In statistical mechanics, the canonical partition function [Formula: see text] can be used to compute equilibrium properties of a physical system. Calculating [Formula: see text] however, is in general computationally intractable, since the computation scales exponentially with the number of particles [Formula: see text] in the system. A commonly used method for approximating equilibrium properties, is the Monte Carlo (MC method. For some problems the MC method converges slowly, requiring a very large number of MC steps. For such problems the computational cost of the Monte Carlo method can be prohibitive. Presented here is a deterministic algorithm - the direct interaction algorithm (DIA - for approximating the canonical partition function [Formula: see text] in [Formula: see text] operations. The DIA approximates the partition function as a combinatorial sum of products known as elementary symmetric functions (ESFs, which can be computed in [Formula: see text] operations. The DIA was used to compute equilibrium properties for the isotropic 2D Ising model, and the accuracy of the DIA was compared to that of the basic Metropolis Monte Carlo method. Our results show that the DIA may be a practical alternative for some problems where the Monte Carlo method converge slowly, and computational speed is a critical constraint, such as for very large systems or web-based applications.
Congruences involving F-partition functions
Directory of Open Access Journals (Sweden)
James Sellers
1994-01-01
Full Text Available The primary goal of this note is to prove the congruence ϕ3(3n+2≡0(mod3, where ϕ3(n denotes the number of F-partitions of n with at most 3 repetitions. Secondarily, we conjecture a new family of congruences involving cϕ2(n, the number of F-partitions of n with 2 colors.
The Kostant partition functions for twisted Kac-Moody algebras
Directory of Open Access Journals (Sweden)
Ranabir Chakrabarti
2000-01-01
Full Text Available Employing the method of generating functions and making use of some infinite product identities like Euler, Jacobi's triple product and pentagon identities we derive recursion relations for Kostant's partition functions for the twisted Kac-Moody algebras.
The Kostant partition functions for twisted Kac-Moody algebras
Ranabir Chakrabarti; Santhanam, Thalanayar S.
2000-01-01
Employing the method of generating functions and making use of some infinite product identities like Euler, Jacobi's triple product and pentagon identities we derive recursion relations for Kostant's partition functions for the twisted Kac-Moody algebras.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Based on theoretical linear solvation energy relationship and quantum chemical descriptors computed by AM1 Hamiltonian, a new model is developed to predict the partitioning of some volatile organic compounds between the plant cuticular matrix and air.
Bosonic Partition Functions at Nonzero (Imaginary) Chemical Potential
Kellerstein, M
2016-01-01
We consider bosonic random matrix partition functions at nonzero chemical potential and compare the chiral condensate, the baryon number density and the baryon number susceptibility to the result of the corresponding fermionic partition function. We find that as long as results are finite, the phase transition of the fermionic theory persists in the bosonic theory. However, in case that bosonic partition function diverges and has to be regularized, the phase transition of the fermionic theory does not occur in the bosonic theory, and the bosonic theory is always in the broken phase.
Approximating the partition function of the ferromagnetic Potts model
Goldberg, Leslie Ann
2010-01-01
We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic q-state Potts model when q>2. Specifically we show that the partition function is hard for the complexity class #RHPi_1 under approximation-preserving reducibility. Thus, it is as hard to approximate the partition function as it is to find approximate solutions to a wide range of counting problems, including that of determining the number of independent sets in a bipartite graph. Our proof exploits the second order phase transition of the "random cluster" model, which is a probability distribution on graphs that is closely related to the q-state Potts
Exact partition functions for gauge theories on Rλ3
Directory of Open Access Journals (Sweden)
Jean-Christophe Wallet
2016-11-01
Full Text Available The noncommutative space Rλ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of Rλ3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.
Exact partition functions for gauge theories on Rλ3
Wallet, Jean-Christophe
2016-11-01
The noncommutative space R,SUB>λ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of R&x03bb;3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.
Quantum iterated function systems.
Łoziński, Artur; Zyczkowski, Karol; Słomczyński, Wojciech
2003-10-01
An iterated function system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum IFS (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting, a QIFS consists of completely positive maps acting in the space of density operators. This formalism is designed to describe certain problems of nonunitary quantum dynamics. We present exemplary classical IFSs, the invariant measure of which exhibits fractal structure, and study properties of the corresponding QIFSs and their invariant states.
Subsets of configurations and canonical partition functions
DEFF Research Database (Denmark)
Bloch, J.; Bruckmann, F.; Kieburg, M.;
2013-01-01
We explain the physical nature of the subset solution to the sign problem in chiral random matrix theory: the subset sum over configurations is shown to project out the canonical determinant with zero quark charge from a given configuration. As the grand canonical chiral random matrix partition...
String partition functions in Rindler space and maximal acceleration
Mertens, Thomas G; Zakharov, Valentin I
2015-01-01
We revisit non-interacting string partition functions in Rindler space by summing over fields in the spectrum. Using recent results of JHEP 1505 (2015) 106, this construction, first done by Emparan, can be put on much firmer ground. For open strings, we demonstrate that surface contributions to the higher spin fields correspond to open strings piercing the Rindler origin, unifying the higher spin surface contributions in string language. We generalize the construction of these partition functions to type II and heterotic superstrings and demonstrate modular invariance for the resulting partition functions. Also, explicit signs of spacetime supersymmetry are visible. All of these exhibit an IR divergence that can be interpreted as a maximal acceleration with $T_{\\text{crit}} = T_{H}/\\pi$ close to the black hole horizon. Ultimately, these partition functions are not physical, and divergences here should not be viewed as a failure of string theory: maximal acceleration is a feature of a faulty treatment of the h...
Factorization of S^3/Z_n partition function
Imamura, Yosuke; Yokoyama, Daisuke
2013-01-01
We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field theories. In a gauge theory the partition function is the sum of the contributions of sectors specified by holonomies, and we should carefully choose the relative signs among the contributions. We argue that the factorization to holomorphic blocks is a useful criterion to determine the signs and propose a formula for them. We show that the orbifold partition function of a general non-gauge theory is correctly factorized provided that we take appropriate relative signs. We also present a few examples of gauge theories. We point out that the sign factor for the orbifold partition function is closely related to a similar sign factor in the lens space index and the 3d index.
Dominant partition method. [based on a wave function formalism
Dixon, R. M.; Redish, E. F.
1979-01-01
By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails.
Energy Technology Data Exchange (ETDEWEB)
Dominicis, C. de [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires
1961-07-01
The grand partition function Z ({alpha},{beta}) of a quantum system is studied, using diagrammatic representations of the perturbation expansion. For a fermions system, it is possible to show, by proper resummation, without approximations but under some 'regularity hypothesis', that Log Z ({alpha},{beta}) takes a form where, besides trivial dependences, {alpha} and {beta} only appear through a statistical factor F{sub k}{sup -} = [1 + e{sup -{alpha}}{sup +{beta}}{sup {epsilon}{sub k}{sup 0}}{sup -{beta}}{sup W{sub k}}]{sup -1}. W{sub k} is a (real) self-consistent potential, generalized to all orders and can be defined by a stationary condition on Log Z ({alpha},{beta}) under variations of F{sub k}{sup -}. The thermodynamical quantities take a form analogous to the expressions Landau introduced for the Fermi liquids. The zero temperature limit (for isotropic systems) gives back Goldstone expressions for the ground state of a system. (author) [French] La grande fonction de partition Z ({alpha},{beta}) d'un systeme quantique est etudiee en utilisant des representations diagrammatiques du developpement en serie des perturbations. Pour un systeme de fermions on peut, par des resommations adequates, sans approximations mais sous reserve d'une 'hypothese de regularite', mettre Log Z ({alpha},{beta}) sous une forme ou, en dehors de dependances triviales, {alpha} et {beta} n'interviennent que par l'intermediaire d'un facteur statistique F{sub k}{sup -} = [1 + e{sup -{alpha}}{sup +{beta}}{sup {epsilon}{sub k}{sup 0}}{sup -{beta}}{sup W{sub k}}]{sup -1}. W{sub k} est ici un potentiel self-consistant (reel) generalise a tous les ordres et peut etre defini par une condition de stationnarite de Log Z ({alpha},{beta}) pour des variations de F{sub k}{sup -}. Les grandeurs thermodynamiques prennent une forme analogue aux expressions que LANDAU a introduites pour les liquides de FERMI. A la limite de la temperature nulle (et pour un
A brief history of partitions of numbers, partition functions and their modern applications
Debnath, Lokenath
2016-04-01
'Number rules the universe.' The Pythagoras 'If you wish to forsee the future of mathematics our course is to study the history and present conditions of the science.' Henri Poincaré 'The primary source (Urqell) of all mathematics are integers.' Hermann Minkowski This paper is written to commemorate the centennial anniversary of the Mathematical Association of America. It deals with a short history of different kinds of natural numbers including triangular, square, pentagonal, hexagonal and k-gonal numbers, and their simple properties and their geometrical representations. Included are Euclid's and Pythagorean's main contributions to elementary number theory with the main contents of the Euclid Elements of the 13-volume masterpiece of mathematical work. This is followed by Euler's new discovery of the additive number theory based on partitions of numbers. Special attention is given to many examples, Euler's theorems on partitions of numbers with geometrical representations of Ferrers' graphs, Young's diagrams, Lagrange's four-square theorem and the celebrated Waring problem. Included are Euler's generating functions for the partitions of numbers, Euler's pentagonal number theorem, Gauss' triangular and square number theorems and the Jacobi triple product identity. Applications of the theory of partitions of numbers to different statistics such as the Bose- Einstein, Fermi- Dirac, Gentile, and Maxwell- Boltzmann statistics are briefly discussed. Special attention is given to pedagogical information through historical approach to number theory so that students and teachers at the school, college and university levels can become familiar with the basic concepts of partitions of numbers, partition functions and their modern applications, and can pursue advanced study and research in analytical and computational number theory.
Quantum Iterated Function Systems
Lozinski, A; Slomczynski, W; Lozinski, Artur; Zyczkowski, Karol; Slomczynski, Wojciech
2003-01-01
Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on the initial point. In an analogous way, we define quantum iterated functions system (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting a QIFS consists of completely positive maps acting in the space of density operators. We present exemplary classical IFSs, the invariant measure of which exhibits fractal structure, and study properties of the corresponding QIFSs and their invariant state.
Entanglement resonances of driven multi-partite quantum systems
Sauer, Simeon; Buchleitner, Andreas
2011-01-01
We show that periodic driving of a weakly interacting set of qubits can generate strongly entangled multi-partite dressed states. Floquet theory allows to predict, from single particle dynamics only, the driving parameters at which such "entanglement resonances" occur.
Energy levels in hydrogen plasmas and the Planck-Larkin partition function - A comment
Ebeling, W.; Kraeft, W. D.; Kremp, D.; Roepke, G.
1985-03-01
Attention is given to the objections raised by Rouse (1983) against the use of the Planck-Larkin partition function (PLPF) in the description of the ionization equilibrium. It is presently noted that, in an up-to-date version of the quantum statistics of Coulomb systems with bound states, the discrete energy states of the Bethe-Salpeter equation have to be introduced into the PLPF. The latter then becomes both temperature- and density-dependent.
Asymptotics of a singularly perturbed GUE partition function
Mezzadri, F
2010-01-01
We study the double scaling asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble with weight exp(-z^2/2x^2 + t/x - x^2/2). We derive the asymptotics of the partition function when z and t are of O(N^(-1/2)). Our results are obtained using the Deift-Zhou steepest descent method and are expressed in terms of a solution of a fourth order nonlinear differential equation. We also compute the asymptotic limit of such a solution when zN^(1/2) -> 0. The behavior of this solution, together with fact that the partition function is an odd function in the variable t, allows us to reduce such a fourth order differential equation into a second order nonlinear ODE.
Discord as a quantum resource for bi-partite communication
Energy Technology Data Exchange (ETDEWEB)
Chrzanowski, Helen M.; Assad, Syed M.; Symul, Thomas; Lam, Ping Koy [Centre for Quantum Computation and Communication Technology, Department of Quantum Science, The Australian National University (Australia); Gu, Mile; Modi, Kavan; Vedral, Vlatko [Centre for Quantum Technologies, National University of Singapore (Singapore); Ralph, Timothy C. [Centre for Quantum Computation and Communication Technology, Department of Physics, University of Queensland (Australia)
2014-12-04
Coherent interactions that generate negligible entanglement can still exhibit unique quantum behaviour. This observation has motivated a search beyond entanglement for a complete description of all quantum correlations. Quantum discord is a promising candidate. Here, we experimentally demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interactions. The inability to access this information by any other means allows us to use discord to directly quantify this ‘quantum advantage’.
Partition function of massless scalar field in Schwarzschild background
Sanyal, Abhik Kumar
2014-01-01
Using thermal value of zeta function instead of zero temperature, the partition function of quantized fields in arbitrary stationary backgrounds was found to be independent of undetermined regularization constant in even-dimension and the long drawn problem associated with the trace anomaly effect had been removed. Here, we explicitly calculate the expression for the coincidence limit so that the technique may be applied in some specific problems. A particular problem dealt with here is to calculate the partition function of massless scalar field in Schwarzschild background.
On matrix model partition functions for QCD with chemical potential
Akemann, G; Vernizzi, G
2004-01-01
Partition functions of two different matrix models for QCD with chemical potential are computed for an arbitrary number of quark and complex conjugate anti-quark flavors. In the large-N limit of weak nonhermiticity complete agreement is found between the two models. This supports the universality of such fermionic partition functions, that is of products of characteristic polynomials in the complex plane. In the strong nonhermiticity limit agreement is found for an equal number of quark and conjugate flavours. For a general flavor content the equality of partition functions holds only for small chemical potential. The chiral phase transition is analyzed for an arbitrary number of quarks, where the free energy presents a discontinuity of first order at a critical chemical potential. In the case of nondegenerate flavors there is first order phase transition for each separate mass scale.
Partition function zeros of an Ising spin glass
Damgaard, P H
1995-01-01
We study the pattern of zeros emerging from exact partition function evaluations of Ising spin glasses on conventional finite lattices of varying sizes. A large number of random bond configurations are probed in the framework of quenched averages. This study is motivated by the relationship between hierarchical lattice models whose partition function zeros fall on Julia sets and chaotic renormalization flows in such models with frustration, and by the possible connection of the latter with spin glass behaviour. In any finite volume, the simultaneous distribution of the zeros of all partition functions can be viewed as part of the more general problem of finding the location of all the zeros of a certain class of random polynomials with positive integer coefficients. Some aspects of this problem have been studied in various branches of mathematics, and we show how polynomial mappings which are used in graph theory to classify graphs, may help in characterizing the distribution of zeros. We finally discuss the ...
Revisiting noninteracting string partition functions in Rindler space
Mertens, Thomas G.; Verschelde, Henri; Zakharov, Valentin I.
2016-05-01
We revisit noninteracting string partition functions in Rindler space by summing over fields in the spectrum. In field theory, the total partition function splits in a natural way into a piece that does not contain surface terms and a piece consisting of solely the so-called edge states. For open strings, we illustrate that surface contributions to the higher-spin fields correspond to open strings piercing the Rindler origin, unifying the higher-spin surface contributions in string language. For closed strings, we demonstrate that the string partition function is not quite the same as the sum over the partition functions of the fields in the spectrum: an infinite overcounting is present for the latter. Next we study the partition functions obtained by excluding the surface terms. Using recent results of He et al. [J. High Energy Phys. 05 (2015) 106], this construction, first done by Emparan [arXiv:hep-th/9412003], can be put on much firmer ground. We generalize to type II and heterotic superstrings and demonstrate modular invariance. All of these exhibit an IR divergence that can be interpreted as a maximal acceleration close to the black hole horizon. Ultimately, since these partition functions are only part of the full story, divergences here should not be viewed as a failure of string theory: maximal acceleration is a feature of a faulty treatment of the higher-spin fields in the string spectrum. We comment on the relevance of this to Solodukhin's recent proposal [Phys. Rev. D 91, 084028 (2015)]. A possible link with the firewall paradox is apparent.
Distribution of a Certain Partition Function Modulo Powers of Primes
Institute of Scientific and Technical Information of China (English)
Hei-Chi CHAN
2011-01-01
In this paper, we study a certain partition function a(n) defined by Σn≥0 a(n)qn :=∏n=1(1-qn)-1(1-q2n)-1.We prove that given a positive integer j≥1 and a prime m≥5,there are infinitely many congruences of the type a(An + B)≡0 (mod mj). This work is inspired by Ono's ground breaking result in the study of the distribution of the partition function p(n).
Popovas, Andrius
2016-01-01
Aims. In this work we rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition function. These errors carry on to calculations of thermodynamic quantities. Therefore a more complicated approach has to be taken. Methods. Seven possible simplifications of various complexity are described, together with advantages and disadvantages of direct summation of experimental values. These were compared to what we consider the most accurate and most complete treatment (case 8). Dunham coefficients were determined from experimental and theoretical energy levels of a number of electronically excited states of H$_2$ . Both equilibrium and normal hydrogen was taken into consideration. Results. Various shortcomings in existing calculations are demonstrated, and the reasons for them are explained. New partition functions for equilibrium, normal, and ortho and para hyd...
Partition function and astronomical observation of interstellar isomers: Is there a link?
Etim, Emmanuel E.; Arunan, Elangannan
2017-02-01
The unsuccessful astronomical searches for some important astrophysical and astrobiological molecules have been linked to the large partition function of these molecules. This letter reports an extensive investigation of the relationship between partition function and astronomical observation of interstellar isomers using high level quantum chemical calculations. 120 molecules from 30 different isomeric groups have been considered. Partition function and thermodynamic stabilities are determined for each set of isomeric species. From the results, there is no direct correlation between partition function and astronomical observation of the same isomeric species. Though interstellar formations processes are generally controlled by factors like kinetics, thermodynamics, formation and destruction pathways. However, the observation of the isomers seems to correlate well with thermodynamics. For instance, in all the groups considered, the astronomically detected isomers are the thermodynamically most stable molecules in their respective isomeric groups. The implications of these results in accounting for the limited number of known cyclic interstellar molecules, unsuccessful searches for amino acid and the possible molecules for astronomical observations are discussed.
A functional quantum programming language
Altenkirch, T; Altenkirch, Thorsten; Grattage, Jonathan
2004-01-01
We introduce the language QML, a functional language for quantum computations on finite types. Its design is guided by its categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations, which provides a constructive semantics of irreversible quantum computations realizable as quantum gates. QML integrates reversible and irreversible quantum computations in one language, using first order strict linear logic to make weakenings explicit. Strict programs are free of decoherence and hence preserve entanglement which is essential for quantum parallelism.
Partition function for the eigenvalues of the Wilson line
Gocksch, A
1993-01-01
In a gauge theory at nonzero temperature the eigenvalues of the Wilson line form a set of gauge invariant observables. By constructing the corresponding partition function for the phases of these eigenvalues, we prove that the trivial vacuum, where the phases vanish, is a minimum of the free energy.
Zeta Function Expression of Spin Partition Functions on Thermal AdS3
Directory of Open Access Journals (Sweden)
Floyd L.Williams
2015-07-01
Full Text Available We find a Selberg zeta function expression of certain one-loop spin partition functions on three-dimensional thermal anti-de Sitter space. Of particular interest is the partition function of higher spin fermionic particles. We also set up, in the presence of spin, a Patterson-type formula involving the logarithmic derivative of zeta.
Zeros of the Partition Function in the Randomized Riemann Gas
Dueñas, J G
2014-01-01
An arithmetic gas is a second quantized mechanical system where the partition function is a Dirichlet series of a given arithmetic function. One example of such system is known as the bosonic Riemann gas. We assume that the hamiltonian of the bosonic Riemann gas has a random variable with some probability distribution over an ensemble of hamiltonians. We discuss the singularity structure for the average free energy density of this arithmetic gas in the complex $\\beta$ plane. First, assuming the Riemann hypothesis, there is a clustering of singular points along the imaginary axis coming from the non-trivial zeros of the Riemann zeta function on the critical line. This singularity structure associated to the zeros of the partition functions of the ensemble in the complex $\\beta$ plane are the Fisher zeros. Second, there are also logarithmic singularities due to the poles of the Riemann zeta functions associated to the ensemble of hamiltonians. Finally we present the average energy density of the system.
5D partition functions, q-Virasoro systems and integrable spin-chains
Nieri, Fabrizio; Passerini, Filippo; Torrielli, Alessandro
2013-01-01
We analyze N = 1 theories on S5 and S4 x S1, showing how their partition functions can be written in terms of a set of fundamental 5d holomorphic blocks. We demonstrate that, when the 5d mass parameters are analytically continued to suitable values, the S5 and S4 x S1 partition functions degenerate to those for S3 and S2 x S1. We explain this mechanism via the recently proposed correspondence between 5d partition functions and correlators with underlying q-Virasoro symmetry. From the q-Virasoro 3-point functions, we axiomatically derive a set of associated reflection coefficients, and show they can be geometrically interpreted in terms of Harish-Chandra c-functions for quantum symmetric spaces. We then link these particular c-functions to the types appearing in the Jost functions encoding the asymptotics of the scattering in integrable spin chains, obtained taking different limits of the XYZ model to XXZ-type.
A non-commuting twist in the partition function
Govindarajan, Suresh
2012-01-01
We compute a twisted index for an orbifold theory when the twist generating group does not commute with the orbifold group. The twisted index requires the theory to be defined on moduli spaces that are compatible with the twist. This is carried out for CHL models at special points in the moduli space where they admit dihedral symmetries. The commutator subgroup of the dihedral groups are cyclic groups that are used to construct the CHL orbifolds. The residual reflection symmetry is chosen to act as a `twist' on the partition function. The reflection symmetries do not commute with the orbifolding group and hence we refer to this as a non-commuting twist. We count the degeneracy of half-BPS states using the twisted partition function and find that the contribution comes mainly from the untwisted sector. We show that the generating function for these twisted BPS states are related to the Mathieu group M_{24}.
$q$-Virasoro modular double and 3d partition functions
Nedelin, Anton; Zabzine, Maxim
2016-01-01
We study partition functions of 3d $\\mathcal{N}=2$ U(N) gauge theories on compact manifolds which are $S^1$ fibrations over $S^2$. We show that the partition functions are free field correlators of vertex operators and screening charges of the $q$-Virasoro modular double, which we define. The inclusion of supersymmetric Wilson loops in arbitrary representations allows us to show that the generating functions of Wilson loop vacuum expectation values satisfy two SL(2,$\\mathbb{Z}$)-related commuting sets of $q$-Virasoro constraints. We generalize our construction to 3d $\\mathcal{N}=2$ unitary quiver gauge theories and as an example we give the free boson realization of the ABJ(M) model.
Computing black hole partition functions from quasinormal modes
Arnold, Peter; Vaman, Diana
2016-01-01
We propose a method of computing one-loop determinants in black hole spacetimes (with emphasis on asymptotically anti-de Sitter black holes) that may be used for numerics when completely-analytic results are unattainable. The method utilizes the expression for one-loop determinants in terms of quasinormal frequencies determined by Denef, Hartnoll and Sachdev in [1]. A necessary ingredient is a refined regularization scheme to regulate the contributions of individual fixed-momentum sectors to the partition function. To this end, we formulate an effective two-dimensional problem in which a natural refinement of standard heat kernel techniques can be used to account for contributions to the partition function at fixed momentum. We test our method in a concrete case by reproducing the scalar one-loop determinant in the BTZ black hole background. We then discuss the application of such techniques to more complicated spacetimes.
Unified approach to partition functions of RNA secondary structures.
Bundschuh, Ralf
2014-11-01
RNA secondary structure formation is a field of considerable biological interest as well as a model system for understanding generic properties of heteropolymer folding. This system is particularly attractive because the partition function and thus all thermodynamic properties of RNA secondary structure ensembles can be calculated numerically in polynomial time for arbitrary sequences and homopolymer models admit analytical solutions. Such solutions for many different aspects of the combinatorics of RNA secondary structure formation share the property that the final solution depends on differences of statistical weights rather than on the weights alone. Here, we present a unified approach to a large class of problems in the field of RNA secondary structure formation. We prove a generic theorem for the calculation of RNA folding partition functions. Then, we show that this approach can be applied to the study of the molten-native transition, denaturation of RNA molecules, as well as to studies of the glass phase of random RNA sequences.
Rotating higher spin partition functions and extended BMS symmetries
Energy Technology Data Exchange (ETDEWEB)
Campoleoni, A.; Gonzalez, H.A. [Université Libre de Bruxelles and International Solvay Institutes,ULB-Campus Plaine CP231, 1050 Brussels (Belgium); Oblak, B. [Université Libre de Bruxelles and International Solvay Institutes,ULB-Campus Plaine CP231, 1050 Brussels (Belgium); DAMTP, Centre for Mathematical Sciences, University of Cambridge,Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Riegler, M. [Institute for Theoretical Physics, Vienna University of Technology,Wiedner Hauptstrasse 8-10, A-1040 Vienna (Austria)
2016-04-06
We evaluate one-loop partition functions of higher-spin fields in thermal flat space with angular potentials; this computation is performed in arbitrary space-time dimension, and the result is a simple combination of Poincaré characters. We then focus on dimension three, showing that suitable products of one-loop partition functions coincide with vacuum characters of higher-spin asymptotic symmetry algebras at null infinity. These are extensions of the bms{sub 3} algebra that emerges in pure gravity, and we propose a way to build their unitary representations and to compute the associated characters. We also extend our investigations to supergravity and to a class of gauge theories involving higher-spin fermionic fields.
Potts model partition functions on two families of fractal lattices
Gong, Helin; Jin, Xian'an
2014-11-01
The partition function of q-state Potts model, or equivalently the Tutte polynomial, is computationally intractable for regular lattices. The purpose of this paper is to compute partition functions of q-state Potts model on two families of fractal lattices. Based on their self-similar structures and by applying the subgraph-decomposition method, we divide their Tutte polynomials into two summands, and for each summand we obtain a recursive formula involving the other summand. As a result, the number of spanning trees and their asymptotic growth constants, and a lower bound of the number of connected spanning subgraphs or acyclic root-connected orientations for each of such two lattices are obtained.
Institute of Scientific and Technical Information of China (English)
LINGNeng-xiang; DUXue-qiao
2005-01-01
In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; partitioning estimation; strong convergence;φ-mixing sequences.
The partition function of a ferromagnet up to three loops
Energy Technology Data Exchange (ETDEWEB)
Hofmann, C P, E-mail: christoph@ucol.mx [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima 28045 (Mexico)
2011-04-01
The low-temperature behavior of ferromagnets with a spontaneously broken symmetry O(3) {yields} O(2) is analyzed within the perspective of effective Lagrangians. The leading coefficients of the low-temperature expansion for the partition function are calculated up to three loops and the manifestation of the spin-wave interaction in this series is discussed. The effective field theory method has the virtue of being completely systematic and model-independent.
Gauge Fields on Torus and Partition Function of Strings
Nakamula, Atsushi
2014-01-01
In this paper we consider the interrelation between compactified string theories on torus and gauge fields on it. We start from open string theories with background gauge fields and derive partition functions by path integral. Since the effects of background fields and compactification correlate only through string zero modes, we investigate these zero modes. From this point of view, we discuss the Wilson loop mechanism at finite temperature. For the closed string, only a few comments are mentioned.
Product Representation of Dyon Partition Function in CHL Models
David, J R; Sen, A; David, Justin R.; Jatkar, Dileep P.; Sen, Ashoke
2006-01-01
A formula for the exact partition function of 1/4 BPS dyons in a class of CHL models has been proposed earlier. The formula involves inverse of Siegel modular forms of subgroups of Sp(2,Z). In this paper we propose product formulae for these modular forms. This generalizes the result of Gritsenko and Nikulin for the weight 10 cusp form of the full Sp(2,Z) group.
Product representation of dyon partition function in CHL models
David, Justin R.; Jatkar, Dileep P.; Sen, Ashoke
2006-06-01
A formula for the exact partition function of 1/4 BPS dyons in a class of CHL models has been proposed earlier. The formula involves inverse of Siegel modular forms of subgroups of Sp(2,Bbb Z). In this paper we propose product formulae for these modular forms. This generalizes the result of Borcherds and Gritsenko and Nikulin for the weight 10 cusp form of the full Sp(2,Bbb Z) group.
Factorized domain wall partition functions in trigonometric vertex models
Foda, O; Zuparic, M
2007-01-01
We obtain factorized domain wall partition functions for two sets of trigonometric vertex models: 1. The N-state Deguchi-Akutsu models, for N = {2, 3, 4} (and conjecture the result for all N >= 5), and 2. The sl(r+1|s+1) Perk-Schultz models, for {r, s = \\N}, where (given the symmetries of these models) the result is independent of {r, s}.
Institute of Scientific and Technical Information of China (English)
Zhang Xiu-Xing; LiFu-Li
2011-01-01
The correlation dynamics are investigated for various bi-partitions of a composite quantum system consisting of two qubits and two independent and non-identical noisy environments.The two qubits have no direct interaction with each other and locally interact with their environments.Classical and quantum correlations including the entanglement are initially prepared only between the two qubits.We find that contrary to the identical noisy environment case,the quantum correlation transfer direction can be controlled by combining different noisy environments.The amplitudedamping environment determines whether there exists the entanglement transfer among bi-partitions of the system.When one qubit is coupled to an amplitude-damping environment and the other one to a bit-flip one,we find a very interesting result that all the quantum and the classical correlations,and even the entanglement,originally existing between the qubits,can be completely transferred without any loss to the qubit coupled to the bit-flit environment and the amplitude-damping environment.We also notice that it is possible to distinguish the quantum correlation from the classical correlation and the entanglement by combining different noisy environments.
Partitioning of Behavioral Descriptions with Exploiting Function-Level Parallelism
Hara, Yuko; Tomiyama, Hiroyuki; Honda, Shinya; Takada, Hiroaki
A novel method to efficiently synthesize hardware from a large behavioral description in behavioral synthesis is proposed. For a program with functions executable in parallel, this proposed method determines a behavioral partitioning which simultaneously minimizes the overall datapath area and the complexity of the controller while maximizing performance of a synthesized circuit by fully exploiting function-level parallelism of a behavioral description. This method is formulated as an integer programming problem. Experimental results demonstrate that this method leads to a shift of the explorable design space so that superior solutions which could not be explored by earlier work are included, showing the effectiveness of our proposed method.
Asymptotic expansion of a partition function related to the sinh-model
Borot, Gaëtan; Kozlowski, Karol K
2016-01-01
This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integra...
Partition of unity finite element method for quantum mechanical materials calculations
Pask, John E
2016-01-01
The current state of the art for large-scale quantum-mechanical simulations is the planewave (PW) pseudopotential method, as implemented in codes such as VASP, ABINIT, and many others. However, since the PW method uses a global Fourier basis, with strictly uniform resolution at all points in space, it suffers from substantial inefficiencies in calculations involving atoms with localized states, such as first-row and transition-metal atoms, and requires significant nonlocal communications, which limit parallel efficiency. Real-space methods such as finite-differences and finite-elements have partially addressed both resolution and parallel-communications issues but have been plagued by one key disadvantage relative to PW: excessive number of degrees of freedom needed to achieve the required accuracies. We present a real-space partition of unity finite element (PUFE) method to solve the Kohn-Sham equations of density functional theory. In the PUFE method, we build the known atomic physics into the solution proc...
Popovas, A.; Jørgensen, U. G.
2016-11-01
Context. Hydrogen is the most abundant molecule in the Universe. Its thermodynamic quantities dominate the physical conditions in molecular clouds, protoplanetary disks, etc. It is also of high interest in plasma physics. Therefore thermodynamic data for molecular hydrogen have to be as accurate as possible in a wide temperature range. Aims: We here rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition function. These errors carry on to calculations of thermodynamic quantities. Therefore a more complicated approach has to be taken. Methods: Seven possible simplifications of various complexity are described, together with advantages and disadvantages of direct summation of experimental values. These were compared to what we consider the most accurate and most complete treatment (case 8). Dunham coefficients were determined from experimental and theoretical energy levels of a number of electronically excited states of H2. Both equilibrium and normal hydrogen was taken into consideration. Results: Various shortcomings in existing calculations are demonstrated, and the reasons for them are explained. New partition functions for equilibrium, normal, and ortho and para hydrogen are calculated and thermodynamic quantities are reported for the temperature range 1-20 000 K. Our results are compared to previous estimates in the literature. The calculations are not limited to the ground electronic state, but include all bound and quasi-bound levels of excited electronic states. Dunham coefficients of these states of H2 are also reported. Conclusions: For most of the relevant astrophysical cases it is strongly advised to avoid using simplifications, such as a harmonic oscillator and rigid rotor or ad hoc summation limits of the eigenstates to estimate accurate partition functions and to be particularly careful when
Holographic partition functions and phases for higher genus Riemann surfaces
Maxfield, Henry; Ross, Simon F.; Way, Benson
2016-06-01
We describe a numerical method to compute the action of Euclidean saddle points for the partition function of a two-dimensional holographic CFT on a Riemann surface of arbitrary genus, with constant curvature metric. We explicitly evaluate the action for the saddles for genus two and map out the phase structure of dominant bulk saddles in a two-dimensional subspace of the moduli space. We discuss spontaneous breaking of discrete symmetries, and show that the handlebody bulk saddles always dominate over certain non-handlebody solutions.
Ratios of partition functions for the log-gamma polymer
Georgiou, Nicos; Rassoul-Agha, Firas; Seppalainen, Timo; Yilmaz, Atilla
2015-01-01
The Annals of Probability 2015, Vol. 43, No. 5, 2282–2331 DOI: 10.1214/14-AOP933 © Institute of Mathematical Statistics, 2015 RATIOS OF PARTITION FUNCTIONS FOR THE LOG-GAMMA POLYMER BY NICOS GEORGIOU1, FIRAS RASSOUL-AGHA1, TIMO SEPPÄLÄINEN2 AND ATILLA YILMAZ3 University of Sussex, University of Utah, University of Wisconsin–Madison and Bo˘gaziçi University We introduce a random walk in random environment associated to an underlying directed polymer model in 1 ...
Non-perturbative Nekrasov partition function from string theory
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, I., E-mail: ignatios.antoniadis@cern.ch [Department of Physics, CERN – Theory Division, CH-1211 Geneva 23 (Switzerland); Florakis, I., E-mail: florakis@mppmu.mpg.de [Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München (Germany); Hohenegger, S., E-mail: stefan.hohenegger@cern.ch [Department of Physics, CERN – Theory Division, CH-1211 Geneva 23 (Switzerland); Narain, K.S., E-mail: narain@ictp.trieste.it [High Energy Section, The Abdus Salam International Center for Theoretical Physics, Strada Costiera, 11-34014 Trieste (Italy); Zein Assi, A., E-mail: zeinassi@cern.ch [Department of Physics, CERN – Theory Division, CH-1211 Geneva 23 (Switzerland); Centre de Physique Théorique (UMR CNRS 7644), Ecole Polytechnique, 91128 Palaiseau (France)
2014-03-15
We calculate gauge instanton corrections to a class of higher derivative string effective couplings introduced in [1]. We work in Type I string theory compactified on K3×T{sup 2} and realise gauge instantons in terms of D5-branes wrapping the internal space. In the field theory limit we reproduce the deformed ADHM action on a general Ω-background from which one can compute the non-perturbative gauge theory partition function using localisation. This is a non-perturbative extension of [1] and provides further evidence for our proposal of a string theory realisation of the Ω-background.
Holographic partition functions and phases for higher genus Riemann surfaces
Maxfield, Henry; Way, Benson
2016-01-01
We describe a numerical method to compute the action of Euclidean saddlepoints for the partition function of a two-dimensional holographic CFT on a Riemann surface of arbitrary genus, with constant curvature metric. We explicitly evaluate the action for the saddles for genus two and map out the phase structure of dominant bulk saddles in a two-dimensional subspace of the moduli space. We discuss spontaneous breaking of discrete symmetries, and show that the handlebody bulk saddles always dominate over certain non-handlebody solutions.
Minimal models on Riemann surfaces: The partition functions
Energy Technology Data Exchange (ETDEWEB)
Foda, O. (Katholieke Univ. Nijmegen (Netherlands). Inst. voor Theoretische Fysica)
1990-06-04
The Coulomb gas representation of the A{sub n} series of c=1-6/(m(m+1)), m{ge}3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius){sup 2} of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.).
Holonomy spin foam models: Asymptotic geometry of the partition function
Hellmann, Frank
2013-01-01
We study the asymptotic geometry of the spin foam partition function for a large class of models, including the models of Barrett and Crane, Engle, Pereira, Rovelli and Livine, and, Freidel and Krasnov. The asymptotics is taken with respect to the boundary spins only, no assumption of large spins is made in the interior. We give a sufficient criterion for the existence of the partition function. We find that geometric boundary data is suppressed unless its interior continuation satisfies certain accidental curvature constraints. This means in particular that most Regge manifolds are suppressed in the asymptotic regime. We discuss this explicitly for the case of the configurations arising in the 3-3 Pachner move. We identify the origin of these accidental curvature constraints as an incorrect twisting of the face amplitude upon introduction of the Immirzi parameter and propose a way to resolve this problem, albeit at the price of losing the connection to the SU(2) boundary Hilbert space. The key methodological...
Colour-independent partition functions in coloured vertex models
Energy Technology Data Exchange (ETDEWEB)
Foda, O., E-mail: omar.foda@unimelb.edu.au [Dept. of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010 (Australia); Wheeler, M., E-mail: mwheeler@lpthe.jussieu.fr [Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589 (France); Université Pierre et Marie Curie – Paris 6, 4 place Jussieu, 75252 Paris cedex 05 (France)
2013-06-11
We study lattice configurations related to S{sub n}, the scalar product of an off-shell state and an on-shell state in rational A{sub n} integrable vertex models, n∈{1,2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric A{sub n} models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S{sub 2} (Caetano and Vieira, 2012, [1], Wheeler, (arXiv:1204.2089), [2]). Namely, 1.S{sub 2}, which depends on two sets of Bethe roots, {b_1} and {b_2}, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit {b_1}→∞, and/or {b_2}→∞, into a product of determinants, 2. Each of the latter determinants is an A{sub 1} vertex-model partition function.
The grand partition function of dilute biregular solutions
Nagamori, Meguru; Ito, Kimihisa; Tokuda, Motonori
1994-10-01
It has been demonstrated that the grand partition function (GPF) of biregular solutions contains in one single equation such thermodynamic principles as Henry's law, Raoult's law, the Gibbs-Duhem relation, Raoultian activity coefficients and their finite power series, Wagner's rec-iprocity, Schenck-Frohberg-Steinmetz's interchange, Lupis-Elliott's additivity, Mori-Morooka's disparity, and Darken's quadratic formalism. The logarithm of the Raoultian activity coefficient of species i, In γi should not be expressed by the Taylor series expansion, lest its truncation infringe the Gibbs-Duhem equation. The GPF methodology establishes that In γi, is not a vector but a scalar point function, free from any path dependence. While Darken's quadratic formalism employs three parameters to describe a ternary solution, the present biregularity approximation offers an alternative using seven empirical parameters, in case better accuracy is needed.
A Graphical representation of the grand canonical partition function
Smii, Boubaker
2010-01-01
In this paper we consider a stochastic partial differential equation defined on a Lattice $L_\\delta$ with coefficients of non-linearity with degree $p$. An analytic solution in the sense of formal power series is given. The obtained series can be re-expressed in terms of rooted trees with two types of leaves. Under the use of the so-called Cole-Hopf transformation and for the particular case $p=2$, one thus get the generalized Burger equation. A graphical representation of the solution and its logarithm is done in this paper. A discussion of the summability of the previous formal solutions is done in this paper using Borel sum. A graphical calculus of the correlation function is given. The special case when the noise is of L\\'evy type gives a simplified representations of the solution of the generalized Burger equation. From the previous results we recall a graphical representation of the grand canonical partition function.
On open superstring partition function in inhomogeneous rolling tachyon background
Fotopoulos, A
2003-01-01
We consider open superstring partition function Z on the disc in time-dependent tachyon background T= f(x_i) e^{m x_0} where the profile function f depends on spatial coordinates. We compute Z to second order in derivatives of f and compare the result with some previously suggested effective actions depending only on the first derivatives of the tachyon field. We also compute the target-space stress-energy tensor in this background and demonstrate its conservation in the ``on-shell'' case of the linear profile f= f_0 + q_i x_i corresponding to a marginal perturbation. We comment on the role of the rolling tachyon with linear spatial profile in the decay of an unstable D-brane.
Exact Potts model partition functions on ladder graphs
Shrock, Robert
2000-08-01
We present exact calculations of the partition function Z of the q-state Potts model and its generalization to real q, for arbitrary temperature on n-vertex ladder graphs, i.e., strips of the square lattice with width Ly=2 and arbitrary length Lx, with free, cyclic, and Möbius longitudinal boundary conditions. These partition functions are equivalent to Tutte/Whitney polynomials for these graphs. The free energy is calculated exactly for the infinite-length limit of these ladder graphs and the thermodynamics is discussed. By comparison with strip graphs of other widths, we analyze how the singularities at the zero-temperature critical point of the ferromagnet on infinite-length, finite-width strips depend on the width. We point out and study the following noncommutativity at certain special values q s: lim n→∞ limq→q s Z 1/n≠ limq→q s limn→∞ Z 1/n. It is shown that the Potts antiferromagnet on both the infinite-length line and ladder graphs with cyclic or Möbius boundary conditions exhibits a phase transition at finite temperature if 0< q<2, but with unphysical properties, including negative specific heat and non-existence, in the low-temperature phase, of an n→∞ limit for thermodynamic functions that is independent of boundary conditions. Considering the full generalization to arbitrary complex q and temperature, we determine the singular locus B in the corresponding C2 space, arising as the accumulation set of partition function zeros as n→∞. In particular, we study the connection with the T=0 limit of the Potts antiferromagnet where B reduces to the accumulation set of chromatic zeros. Certain properties of the complex-temperature phase diagrams are shown to exhibit close connections with those of the model on the square lattice, showing that exact solutions on infinite-length strips provide a way of gaining insight into these complex-temperature phase diagrams.
Modular invariant partition function of critical dense polymers
Energy Technology Data Exchange (ETDEWEB)
Morin-Duchesne, Alexi, E-mail: a.morinduchesne@uq.edu.au [School of Mathematics and Physics, University of Queensland, St Lucia, Brisbane, Queensland 4072 (Australia); Pearce, Paul A., E-mail: p.pearce@ms.unimelb.edu.au [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia); Rasmussen, Jørgen, E-mail: j.rasmussen@uq.edu.au [School of Mathematics and Physics, University of Queensland, St Lucia, Brisbane, Queensland 4072 (Australia)
2013-09-01
A lattice model of critical dense polymers is solved exactly for arbitrary system size on the torus. More generally, an infinite family of lattice loop models is studied on the torus and related to the corresponding Fortuin–Kasteleyn random cluster models. Starting with a cylinder, the commuting periodic single-row transfer matrices are built from the periodic Temperley–Lieb algebra extended by the shift operators Ω{sup ±1}. In this enlarged algebra, the non-contractible loop fugacity is α and the contractible loop fugacity is β. The torus is formed by gluing the top and bottom of the cylinder. This gives rise to a variety of non-contractible loops winding around the torus. Because of their nonlocal nature, the standard matrix trace does not produce the proper geometric torus. Instead, we introduce a modified matrix trace for this purpose. This is achieved by using a representation of the enlarged periodic Temperley–Lieb algebra with a parameter v that keeps track of the winding of defects on the cylinder. The transfer matrix representatives and their eigenvalues thus depend on v. The modified trace is constructed as a linear functional on planar connectivity diagrams in terms of matrix traces Tr{sub d} (with a fixed number of defects d) and Chebyshev polynomials of the first kind. For critical dense polymers, where β=0, the transfer matrix eigenvalues are obtained by solving a functional equation in the form of an inversion identity. The solution depends on d and is subject to selection rules which we prove. Simplifications occur if all non-contractible loop fugacities are set to α=2 in which case the traces are evaluated at v=1. In the continuum scaling limit, the corresponding conformal torus partition function obtained from finite-size corrections agrees with the known modular invariant partition function of symplectic fermions.
Thermal partition function of photons and gravitons in a Rindler wedge
Iellici, D; Iellici, Devis; Moretti, Valter
1996-01-01
The thermal partition function of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local zeta-function regularization approach. The correct Planckian leading order temperature dependence T^4 is obtained in both cases. For the photons, it is confirmed the existence of a surface term giving a negative contribution to the entropy, as earlier obtained by D.Kabat, but this term is shown to be gauge-dependent in the four dimensional case and therefore discarded. It is argued that similar terms could appear dealing with any integer spin s\\geq 1 in the massless case and in more general manifolds. Our conjecture is checked in the case of a graviton in the harmonic gauge, where different surface terms also appear, and physically consistent results arise dropping these terms. The results are discussed in relation to the quantum corrections to the black-hole entropy.
Quantum Digital Signature based on quantum one-way functions
Lü, X; L\\"u, Xin; Feng, Deng-Guo
2004-01-01
A quantum digital signature protocol based on quantum mechanics is proposed in this paper. The security of the protocol relies on the existence of quantum one-way functions by quantum information theorem. This protocol involves a so-called arbitrator who validates and authenticates the signed message. In this protocol, we use privacy key algorithm to ensure the security of quantum information on channel and use quantum public keys to sign message. To guarantee the authenticity of the message, a family of quantum stabilizer codes are employed. Our protocol presents a novel method to construct ultimately secure digital system in future secure communication.
Characterisations of Partition of Unities Generated by Entire Functions in Cd
DEFF Research Database (Denmark)
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2017-01-01
Collections of functions forming a partition of unity play an important role in analysis. In this paper we characterise for any N∈N the entire functions P for which the partition of unity condition ∑n∈ZdP(x+n)χ[0,N]d(x+n)=1 holds for all x∈Rd. The general characterisation leads to various easy ways...... such that the functions in the partition of unity belong to the Feichtinger algebra....
Gauge Invariance of Resummation Schemes The QCD Partition Function
Achhammer, M; Leupold, S; Wiedemann, Urs Achim; Achhammer, Marc; Heinz, Ulrich; Leupold, Stefan; Wiedemann, Urs Achim
1996-01-01
We pick up a method originally developed by Cheng and Tsai for vacuum perturbation theory which allows to test the consistency of different sets of Feynman rules on a purely diagrammatic level, making explicit loop calculations superfluous. We generalize it to perturbative calculations in thermal field theory and we show that it can be adapted to check the gauge invariance of physical quantities calculated in improved perturbation schemes. Specifically, we extend this diagrammatic technique to a simple resummation scheme in imaginary time perturbation theory. As an application, we check up to O(g^4) in general covariant gauge the gauge invariance of the result for the QCD partition function which was recently obtained in Feynman gauge.
Twists of Pl\\"ucker coordinates as dimer partition functions
Scott, Jeanne
2013-01-01
The homogeneous coordinate ring of the Grassmannian Gr(k,n) has a cluster structure defined in terms of planar diagrams known as Postnikov diagrams. The cluster corresponding to such a diagram consists entirely of Pl\\"ucker coordinates. We introduce a twist map on Gr(k,n) related to the BZ-twist, and give an explicit Laurent expansion for the twist of an arbitrary Pl\\"ucker coordinate, in terms of the cluster variables associated with a fixed Postnikov diagram. The expansion arises as a (scaled) dimer partition function of a weighted version of the bipartite graph dual to the Postnikov diagram, modified by a boundary condition determined by the Pl\\"ucker coordinate.
Partition Function of 1-, 2-, and 3-D Monatomic Ideal Gas (a Simple and Comprehensive Review)
Khotimah, Siti Nurul
2011-01-01
This article discusses partition function of monatomic ideal gas which is given in Statistical Physisc at Physics Department, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia. Students in general are not familiar with partition function. This unfamiliarness was detected at a problem of partition function which was re-given in an examination in other dimensions that had been previously given in the lecture. Based on this observation, the need of a simple but comprehensive article about partition function in one-, two-, and three-dimensions is a must. For simplicity, a monatomic ideal gas is chosen.
Pal, S P; Kumar, S; Pal, Sudebkumar Prasant; Singh, Sudhir Kumar; Kumar, Somesh
2003-01-01
In this paper we show that sufficient multi-partite quantum entanglement helps in fair and unbiased election of a leader in a distributed network of processors with only linear classical communication complexity. We show that a total of $O(log n)$ distinct multi-partite maximally entanglement sets (ebits) are capable of supporting such a protocol in the presence of nodes that may lie and thus be biased. Here, $n$ is the number of nodes in the network. We also demonstrate the difficulty of performing unbiased and fair election of a leader with linear classical communication complexity in the absence of quantum entanglement even if all nodes have perfect random bit generators. We show that the presence of a sufficient number $O(n/log n)$ of biased agents leads to a non-zero limiting probability of biased election of the leader, whereas, the presence of a smaller number $O(log n)$ of biased agents matters little. We define two new related complexity classes motivated by the our leader election problem and discus...
Elliptic solid-on-solid model's partition function as a single determinant
Galleas, W
2016-01-01
In this work we express the partition function of the integrable elliptic solid-on-solid model with domain-wall boundary conditions as a single determinant. This representation appears naturally as the solution of a system of functional equations governing the model's partition function.
Smoothed analysis of partitioning algorithms for Euclidean functionals
Bläser, Markus; Manthey, Bodo; Rao, B.V. Raghavendra
2013-01-01
Euclidean optimization problems such as TSP and minimum-length matching admit fast partitioning algorithms that compute near-optimal solutions on typical instances. In order to explain this performance, we develop a general framework for the application of smoothed analysis to partitioning algorithm
Smoothed analysis of partitioning algorithms for Euclidean functionals
Bläser, Markus; Manthey, Bodo; Rao, B.V. Raghavendra; Dehne, F.; Iacono, J.; Sack, J.-R.
2011-01-01
Euclidean optimization problems such as TSP and minimum-length matching admit fast partitioning algorithms that compute near-optimal solutions on typical instances. We develop a general framework for the application of smoothed analysis to partitioning algorithms for Euclidean optimization problems.
Partition function and base pairing probabilities of RNA heterodimers
Directory of Open Access Journals (Sweden)
Stadler Peter F
2006-03-01
Full Text Available Abstract Background RNA has been recognized as a key player in cellular regulation in recent years. In many cases, non-coding RNAs exert their function by binding to other nucleic acids, as in the case of microRNAs and snoRNAs. The specificity of these interactions derives from the stability of inter-molecular base pairing. The accurate computational treatment of RNA-RNA binding therefore lies at the heart of target prediction algorithms. Methods The standard dynamic programming algorithms for computing secondary structures of linear single-stranded RNA molecules are extended to the co-folding of two interacting RNAs. Results We present a program, RNAcofold, that computes the hybridization energy and base pairing pattern of a pair of interacting RNA molecules. In contrast to earlier approaches, complex internal structures in both RNAs are fully taken into account. RNAcofold supports the calculation of the minimum energy structure and of a complete set of suboptimal structures in an energy band above the ground state. Furthermore, it provides an extension of McCaskill's partition function algorithm to compute base pairing probabilities, realistic interaction energies, and equilibrium concentrations of duplex structures. Availability RNAcofold is distributed as part of the Vienna RNA Package, http://www.tbi.univie.ac.at/RNA/. Contact Stephan H. Bernhart – berni@tbi.univie.ac.at
A simplified approach to calculate atomic partition functions in plasmas
Energy Technology Data Exchange (ETDEWEB)
D' Ammando, Giuliano [Dipartimento di Chimica, Universita di Bari, Via Orabona 4, 70125 Bari (Italy); Colonna, Gianpiero [CNR-IMIP, Via Amendola 122/D, 70126 Bari (Italy); Capitelli, Mario [Dipartimento di Chimica, Universita di Bari, Via Orabona 4, 70125 Bari (Italy); CNR-IMIP, Via Amendola 122/D, 70126 Bari (Italy)
2013-03-15
A simplified method to calculate the electronic partition functions and the corresponding thermodynamic properties of atomic species is presented and applied to C(I) up to C(VI) ions. The method consists in reducing the complex structure of an atom to three lumped levels. The ground level of the lumped model describes the ground term of the real atom, while the second lumped level represents the low lying states and the last one groups all the other atomic levels. It is also shown that for the purpose of thermodynamic function calculation, the energy and the statistical weight of the upper lumped level, describing high-lying excited atomic states, can be satisfactorily approximated by an analytic hydrogenlike formula. The results of the simplified method are in good agreement with those obtained by direct summation over a complete set (i.e., including all possible terms and configurations below a given cutoff energy) of atomic energy levels. The method can be generalized to include more lumped levels in order to improve the accuracy.
Dualities and Curved Space Partition Functions of Supersymmetric Theories
Agarwal, Prarit
In this dissertation we discuss some conjectured dualities in supersymmetric field theories and provide non-trivial checks for these conjectures. A quick review of supersymmetry and related topics is provided in chapter 1. In chapter 2, we develop a method to identify the so called BPS states in the Hilbert space of a supersymmetric field theory (that preserves at least two real supercharges) on a generic curved space. As an application we obtain the superconformal index (SCI) of 4d theories. The large N SCI of quiver gauge theories has been previously noticed to factorize over the set of extremal BPS mesonic operators. In chapter 3, we reformulate this factorization in terms of the zigzag paths in the dimer model associated to the quiver and extend the factorization theorem of the index to include theories obtained from D-branes probing orbifold singularities. In chapter 4, we consider the dualities in two classes of 3 dimensional theories. The first class consist of dualities of certain necklace type Chern-Simons (CS) quiver gauge theories. A non trivial check of these dualities is provided by matching their squashed sphere partition functions. The second class consists of theories whose duals are described by a collection of free fields. In such cases, due to mixing between the superconformal R-symmetry and accidental symmetries, the matching of electric and magnetic partition functions is not straightforward. We provide a prescription to rectify this mismatch. In chapter 5, we consider some the N = 1 4d theories with orthogonal and symplectic gauge groups, arising from N = 1 preserving reduction of 6d theories on a Riemann surface. This construction allows us to dual descriptions of 4d theories. Some of the dual frames have no known Lagrangian description. We check the dualities by computing the anomaly coefficients and the superconformal indices. We also give a prescription to write the index of the theory obtained by reduction of 6d theories on a three
A characterization of edge reflection positive partition functions of vertex coloring models
G. Regts (Guus)
2013-01-01
htmlabstractSzegedy (B. Szegedy, Edge coloring models and reflection positivity, Journal of the American Mathematical Society 20, 2007, 969-988.) showed that the partition function of any vertex coloring model is equal to the partition function of a complex edge coloring model. Using some results in
A characterization of edge-reflection positive partition functions of vertex-coloring models
G. Regts (Guus); J. Nešetřil (Jaroslav); M Pellegrini
2013-01-01
htmlabstractSzegedy (B. Szegedy, Edge coloring models and reflection positivity, Journal of the American Mathematical Society 20, 2007, 969-988.) showed that the partition function of any vertex coloring model is equal to the partition function of a complex edge coloring model. Using some results in
Research of partition function on optical properties and temperature diagnosis of air plasma
Qiu, Dechuan; Gao, Guoqiang; Wei, Wenfu; Hu, Haixing; Li, Chunmao; Wu, Guangning
2017-08-01
The relationship between partition function, particle density, refractive index, and temperature for atmospheric plasma is calculated based on thermodynamics and chemical equilibrium. Taking into account the contribution of hydrogen-like levels to the atomic partition function, a compact method to calculate the atomic partition function is first used with the Eindhoven model to deduce the plasma's refractive index. Results calculated by the new approach and two other traditional simplified methods are compared and analyzed. For a better understanding on the temperature measurement accuracy deduced by different partition function disposal approaches, moiré deflectometry is employed as the experimental scheme to acquire the refractive index-position curve. Finally, applicability of different partition function disposal approaches are discussed, and results indicate that the optical properties deduced in this paper are well suited for the refractive index-based plasma diagnosis.
2D CFT partition functions at late times
Dyer, Ethan; Gur-Ari, Guy
2017-08-01
We consider the late time behavior of the analytically continued partition function Z( β + it) Z( β - it) in holographic 2 d CFTs. This is a probe of information loss in such theories and in their holographic duals. We show that each Virasoro character decays in time, and so information is not restored at the level of individual characters. We identify a universal decaying contribution at late times, and conjecture that it describes the behavior of generic chaotic 2 d CFTs out to times that are exponentially large in the central charge. It was recently suggested that at sufficiently late times one expects a crossover to random matrix behavior. We estimate an upper bound on the crossover time, which suggests that the decay is followed by a parametrically long period of late time growth. Finally, we discuss gravitationally-motivated integrable theories and show how information is restored at late times by a series of characters. This hints at a possible bulk mechanism, where information is restored by an infinite sum over non-perturbative saddles.
Polymer quantization and the saddle point approximation of partition functions
Técotl, Hugo A Morales; Rastgoo, Saeed
2015-01-01
The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method can not be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with by adding a counter-term to the classical action, which is a solution of the corresponding Hamilton-Jacobi equation. In this work we study the effects of polymer quantization on a mechanical model presenting the aforementioned difficulties and contrast it with the above counter-term method. This type of quantization for mechanical models is motivated by the loop quantization of gravity which is known to play a role in the thermodynamics of black holes systems. The model we consider is a non relativistic particle in an i...
2D CFT Partition Functions at Late Times
Dyer, Ethan
2016-01-01
We consider the late time behavior of the analytically continued partition function $Z(\\beta + it) Z(\\beta - it)$ in holographic $2d$ CFTs. This is a probe of information loss in such theories and in their holographic duals. We show that each Virasoro character decays in time, and so information is not restored at the level of individual characters. We identify a universal decaying contribution at late times, and conjecture that it describes the behavior of generic chaotic $2d$ CFTs out to times that are exponentially large in the central charge. It was recently suggested that at sufficiently late times one expects a crossover to random matrix behavior. We estimate an upper bound on the crossover time, which suggests that the decay is followed by a parametrically long period of late time growth. Finally, we discuss integrable theories and show how information is restored at late times by a series of characters. This hints at a possible bulk mechanism, where information is restored by an infinite sum over non-...
Colour-independent partition functions in coloured vertex models
Foda, O
2013-01-01
We study lattice configurations related to S_n, the scalar product of an off-shell state and an on-shell state in rational A_n integrable vertex models, n = {1, 2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric A_n models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S_2 [1, 2]. Namely, 1. S_2 which depends on two sets of Bethe roots, b_1 and b_2, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit b_1 -> infinity, and/or b_2 -> infinity, into a product of determinants, 2. Each of the la...
Quantum algorithms for testing Boolean functions
Erika Andersson; Floess, Dominik F.; Mark Hillery
2010-01-01
We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same quantum algorithm can also be used to learn which input variables other types of Boolean functions...
Adiabatic quantum gates and Boolean functions
Energy Technology Data Exchange (ETDEWEB)
Andrecut, M; Ali, M K [Department of Physics, University of Lethbridge, Lethbridge, AB, T1K 3M4 (Canada)
2004-06-25
We discuss the logical implementation of quantum gates and Boolean functions in the framework of quantum adiabatic method, which uses the language of ground states, spectral gaps and Hamiltonians instead of the standard unitary transformation language. (letter to the editor)
Polymer quantization and the saddle point approximation of partition functions
Morales-Técotl, Hugo A.; Orozco-Borunda, Daniel H.; Rastgoo, Saeed
2015-11-01
The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method cannot be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with by adding a counterterm to the classical action, which is a solution of the corresponding Hamilton-Jacobi equation. In this work we study the effects of polymer quantization on a mechanical model presenting the aforementioned difficulties and contrast it with the above counterterm method. This type of quantization for mechanical models is motivated by the loop quantization of gravity, which is known to play a role in the thermodynamics of black hole systems. The model we consider is a nonrelativistic particle in an inverse square potential, and we analyze two polarizations of the polymer quantization in which either the position or the momentum is discrete. In the former case, Thiemann's regularization is applied to represent the inverse power potential, but we still need to incorporate the Hamilton-Jacobi counterterm, which is now modified by polymer corrections. In the latter, momentum discrete case, however, such regularization could not be implemented. Yet, remarkably, owing to the fact that the position is bounded, we do not need a Hamilton-Jacobi counterterm in order to have a well-defined saddle point approximation. Further developments and extensions are commented upon in the discussion.
Computing the partition function for kinetically trapped RNA secondary structures.
Directory of Open Access Journals (Sweden)
William A Lorenz
Full Text Available An RNA secondary structure is locally optimal if there is no lower energy structure that can be obtained by the addition or removal of a single base pair, where energy is defined according to the widely accepted Turner nearest neighbor model. Locally optimal structures form kinetic traps, since any evolution away from a locally optimal structure must involve energetically unfavorable folding steps. Here, we present a novel, efficient algorithm to compute the partition function over all locally optimal secondary structures of a given RNA sequence. Our software, RNAlocopt runs in O(n3 time and O(n2 space. Additionally, RNAlocopt samples a user-specified number of structures from the Boltzmann subensemble of all locally optimal structures. We apply RNAlocopt to show that (1 the number of locally optimal structures is far fewer than the total number of structures--indeed, the number of locally optimal structures approximately equal to the square root of the number of all structures, (2 the structural diversity of this subensemble may be either similar to or quite different from the structural diversity of the entire Boltzmann ensemble, a situation that depends on the type of input RNA, (3 the (modified maximum expected accuracy structure, computed by taking into account base pairing frequencies of locally optimal structures, is a more accurate prediction of the native structure than other current thermodynamics-based methods. The software RNAlocopt constitutes a technical breakthrough in our study of the folding landscape for RNA secondary structures. For the first time, locally optimal structures (kinetic traps in the Turner energy model can be rapidly generated for long RNA sequences, previously impossible with methods that involved exhaustive enumeration. Use of locally optimal structure leads to state-of-the-art secondary structure prediction, as benchmarked against methods involving the computation of minimum free energy and of maximum expected
Fermi and Coulomb correlation effects upon the interacting quantum atoms energy partition
Ruiz, Isela; Holguín-Gallego, Fernando José; Francisco, Evelio; Pendás, Ángel Martín; Rocha-Rinza, Tomás
2016-01-01
The Interacting Quantum Atoms (IQA) electronic energy partition is an important method in the field of quantum chemical topology which has given important insights of different systems and processes in physical chemistry. There have been several attempts to include Electron Correlation (EC) in the IQA approach, for example, through DFT and Hartree-Fock/Coupled-Cluster (HF/CC) transition densities. This work addresses the separation of EC in Fermi and Coulomb correlation and its effect upon the IQA analysis by taking into account spin-dependent one- and two-electron matrices $D^{\\mathrm{HF/CC}}_{p\\sigma q \\sigma}$ and $d^{\\mathrm{HF/CC}}_{p\\sigma q\\sigma r\\tau s\\tau}$ wherein $\\sigma$ and $\\tau$ represent either of the $\\alpha$ and $\\beta$ spin projections. We illustrate this approach by considering BeH$_2$,BH, CN$^-$, HF, LiF, NO$^+$, LiH, H$_2$O$\\cdots$H$_2$O and C$_2$H$_2$, which comprise non-polar covalent, polar covalent, ionic and hydrogen bonded systems. The same and different spin contributions to ($i$...
On entire functions restricted to intervals, partition of unities, and dual Gabor frames
DEFF Research Database (Denmark)
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2014-01-01
Partition of unities appears in many places in analysis. Typically it is generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire functions restricted to finite intervals. We characterize the entire...... functions that lead to a partition of unity in this way, and we provide characterizations of the “cut-off” entire functions, considered as functions of a real variable, to have desired regularity. In particular we obtain partition of unities generated by functions with small support and desired regularity....... Applied to Gabor analysis this leads to constructions of dual pairs of Gabor frames with low redundancy, generated by trigonometric polynomials with small support and desired regularity....
Partition and Correlation Functions of a Freely Crossed Network Using Ising Model-Type Interactions
Saito, Akira
2016-01-01
We set out to determine the partition and correlation functions of a network under the assumption that its elements are freely connected, with an Ising model-type interaction energy associated with each connection. The partition function is obtained from all combinations of loops on the free network, while the correlation function between two elements is obtained based on all combinations of routes between these points, as well as all loops on the network. These functions allow measurement of the dynamics over the whole of any network, regardless of its form. Furthermore, even as parts are added to the network, the partition and correlation functions can still be obtained. As an example, we obtain the partition and correlation functions in a crystal system under the repeated addition of fixed parts.
Quantum mechanics without potential function
Energy Technology Data Exchange (ETDEWEB)
Alhaidari, A. D., E-mail: haidari@sctp.org.sa [Saudi Center for Theoretical Physics, P.O. Box 32741, Jeddah 21438 (Saudi Arabia); Ismail, M. E. H. [Department of Mathematics, University of Central Florida, Orlando, Florida 32816 (United States)
2015-07-15
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrödinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.
Partitioning heritability by functional category using GWAS summary statistics
DEFF Research Database (Denmark)
Finucane, Hilary K.; Bulik-Sullivan, Brendan; Gusev, Alexander
2015-01-01
in genome-wide association studies (GWAS) of 17 complex diseases and traits with an average sample size of 73,599. To enable this analysis, we introduce a new method, stratified LD score regression, for partitioning heritability from GWAS summary statistics while accounting for linked markers. This new...
Functional quantum biology in photosynthesis and magnetoreception
Lambert, Neill; Cheng, Yuan-Chung; Li, Che-Ming; Chen, Guang-Yin; Nori, Franco
2012-01-01
Is there a functional role for quantum mechanics or coherent quantum effects in biological processes? While this question is as old as quantum theory, only recently have measurements on biological systems on ultra-fast time-scales shed light on a possible answer. In this review we give an overview of the two main candidates for biological systems which may harness such functional quantum effects: photosynthesis and magnetoreception. We discuss some of the latest evidence both for and against room temperature quantum coherence, and consider whether there is truly a functional role for coherence in these biological mechanisms. Finally, we give a brief overview of some more speculative examples of functional quantum biology including the sense of smell, long-range quantum tunneling in proteins, biological photoreceptors, and the flow of ions across a cell membrane.
2d partition function in Ω-background and vortex/instanton correspondence
Energy Technology Data Exchange (ETDEWEB)
Fujimori, Toshiaki; Kimura, Taro; Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences, Keio University,Hiyoshi 4-1-1, Kanagawa 223-8521 (Japan); Ohashi, Keisuke [Department of Physics, “E. Fermi”, University of Pisa,and INFN, Sezione di Pisa,Largo Pontecorvo, 3, 56127 Pisa (Italy)
2015-12-16
We derive the exact vortex partition function in 2d N=(2,2) gauge theory on the Ω-background, applying the localization scheme in the Higgs phase. We show that the partition function at a finite Ω-deformation parameter ϵ satisfies a system of differential equations, which can be interpreted as a quantized version of the twisted F-term equations characterizing the SUSY vacua. Using the differential equations derived in this paper, we show the correspondence between the partition function of the two-dimensional vortex string worldsheet theory and the Nekrasov partition function at the root of Higgs branch of the four-dimensional N=2 theory with two Ω-deformation parameters (ϵ{sub 1},ϵ{sub 2}).
Refined partition functions for open superstrings with 4, 8 and 16 supercharges
Energy Technology Data Exchange (ETDEWEB)
Lüst, Dieter, E-mail: dieter.luest@lmu.de [Arnold-Sommerfeld-Center für Theoretische Physik, Department für Physik, Ludwig-Maximilians-Universität München, Theresienstraße 37, 80333 München (Germany); Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München (Germany); CERN, Theory Group, 1211 Geneva 23 (Switzerland); Mekareeya, Noppadol, E-mail: noppadol@mpp.mpg.de [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München (Germany); Schlotterer, Oliver, E-mail: oliver.schlotterer@aei.mpg.de [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, 14476 Golm (Germany); Thomson, Andrew, E-mail: andrew.thomson09@imperial.ac.uk [Theoretical Physics Group, The Blackett Laboratory, Imperial College London, SW7 2AZ (United Kingdom)
2013-11-01
We analyze the perturbative massive open string spectrum of even-dimensional superstring compactifications with four, eight and sixteen supercharges. In each of such cases, we focus on universal states that exist independently on the internal geometry and other compatification details. We analytically compute refined partition functions that count these states at each mass level. Such refined partition functions are written in a super-Poincaré covariant form, providing information on how supermultiplets transform under the little group and the R symmetry. Various asymptotic limits of the partition functions and their associated quantities, such as the leading and subleading Regge trajectories, are studied empirically and analytically. In the phenomenologically relevant case of four supercharges, the partition function can be cast into the most compact form and the asymptotic formula in the large spin limit is derived explicitly.
Algebraic method for exact solution of canonical partition function in nuclear multifragmentation
Parvan, A S
2002-01-01
An algebraic method for the exact recursion formula for the calculation of canonical partition function of non-interaction finite systems of particles obeying Bose-Einstein, Fermi-Dirac, Maxwell-Boltzmann statistics or parastatistics is derived. A new exactly solvable multifragmentation model with baryon and electric charge conservation laws is developed. Recursion relations for this model are presented that allow exact calculation of canonical partition function for any statistics.
The partition function of a multi-component Coulomb gas on a circle
Energy Technology Data Exchange (ETDEWEB)
Jokela, Niko; Keski-Vakkuri, Esko [Helsinki Institute of Physics, University of Helsinki, PO Box 64, FIN-00014 (Finland); Jaervinen, Matti [University of Southern Denmark, Campusvej 55, DK-5230 Odense M (Denmark)], E-mail: niko.jokela@helsinki.fi, E-mail: mjarvine@ifk.sdu.dk, E-mail: esko.keski-vakkuri@helsinki.fi
2008-04-11
We study a two-dimensional Coulomb gas consisting of a mixture of particles carrying various positive multiple integer charges, confined on a unit circle. We consider the system in the canonical and grand canonical ensembles, and attempt to calculate the partition functions analytically, using Toeplitz and confluent Vandermonde determinants. Just like in the simple one-component system (Dyson gas), the partition functions simplify at special temperature {beta} = 2, allowing us to find compact expressions for them.
Karandashev, Yakov M
2016-01-01
In this paper we propose and realize (the code is publicly available at https://github.com/Thrawn1985/2D-Partition-Function) an algorithm for exact calculation of partition function for planar graph models with binary spins. The complexity of the algorithm is O(N^2). Test experiments shows good agreement with Onsager's analytical solution for two-dimensional Ising model of infinite size.
One loop partition function of six dimensional conformal gravity using heat kernel on AdS
Energy Technology Data Exchange (ETDEWEB)
Lovreković, Iva [Institute for Theoretical Physics, Technische Universität Wien,Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria)
2016-10-13
We compute the heat kernel for the Laplacians of symmetric transverse traceless fields of arbitrary spin on the AdS background in even number of dimensions using the group theoretic approach introduced in http://dx.doi.org/10.1007/JHEP11(2011)010 and apply it on the partition function of six dimensional conformal gravity. The obtained partition function consists of the Einstein gravity, conformal ghost and two modes that contain mass.
A paradox in the electronic partition function or how to be cautious with mathematics
Energy Technology Data Exchange (ETDEWEB)
Miranda, E.N. [CRICYT - CONICET, Mendoza (Argentina); Departamento de Fisica, Universidad Nacional de San Luis, San Luis (Argentina)
2001-09-01
When the electronic partition functions of atoms or molecules are evaluated in textbooks, only the contribution of the ground state is considered. The excited states' contribution is argued to be negligible. However, a closer look shows that the partition function diverges if such states are taken into account. This paper shows that the blind use of mathematics is the reason behind this odd behaviour. (author)
Directory of Open Access Journals (Sweden)
Jonathan Witztum
Full Text Available The availability of many complete, annotated proteomes enables the systematic study of the relationships between protein conservation and functionality. We explore this question based solely on the presence or absence of protein homologues (a.k.a. conservation profiles. We study 18 metazoans, from two distinct points of view: the human's and the fly's. Using the GOrilla gene ontology (GO analysis tool, we explore functional enrichment of the "universal proteins", those with homologues in all 17 other species, and of the "non-universal proteins". A large number of GO terms are strongly enriched in both human and fly universal proteins. Most of these functions are known to be essential. A smaller number of GO terms, exhibiting markedly different properties, are enriched in both human and fly non-universal proteins. We further explore the non-universal proteins, whose conservation profiles are consistent with the "tree of life" (TOL consistent, as well as the TOL inconsistent proteins. Finally, we applied Quantum Clustering to the conservation profiles of the TOL consistent proteins. Each cluster is strongly associated with one or a small number of specific monophyletic clades in the tree of life. The proteins in many of these clusters exhibit strong functional enrichment associated with the "life style" of the related clades. Most previous approaches for studying function and conservation are "bottom up", studying protein families one by one, and separately assessing the conservation of each. By way of contrast, our approach is "top down". We globally partition the set of all proteins hierarchically, as described above, and then identify protein families enriched within different subdivisions. While supporting previous findings, our approach also provides a tool for discovering novel relations between protein conservation profiles, functionality, and evolutionary history as represented by the tree of life.
Szilard engine reversibility as quantum gate function
Mihelic, F. Matthew
2012-06-01
A quantum gate is a logically and thermodynamically reversible situation that effects a unitary transformation of qubits of superimposed information, and essentially constitutes a situation for a reversible quantum decision. A quantum decision is a symmetry break, and the effect of the function of a Szilard engine is a symmetry break. A quantum gate is a situation in which a reversible quantum decision can be made, and so if a logically and thermodynamically reversible Szilard engine can be theoretically constructed then it would function as a quantum gate. While the traditionally theorized Szilard engine is not thermodynamically reversible, if one of the bounding walls of a Szilard engine were to be constructed out of the physical information by which it functions in such a manner as to make that information available to both sides of the wall simultaneously, then such a Szilard engine would be both logically and thermodynamically reversible, and thus capable of function as a quantum gate. A theoretical model of the special case of a reversible Szilard engine functioning as a quantum gate is presented and discussed, and since a quantum decision is made when the shutter of a Szilard engine closes, the coherence of linked reversible Szilard engines should be considered as a state during which all of the shutters of linked Szilard engines are open simultaneously.
Density functional theory in quantum chemistry
Tsuneda, Takao
2014-01-01
This book examines density functional theory based on the foundation of quantum chemistry. Unconventional in approach, it reviews basic concepts, then describes the physical meanings of state-of-the-art exchange-correlation functionals and their corrections.
3d and 5d gauge theory partition functions as q-deformed CFT correlators
Nieri, Fabrizio; Passerini, Filippo
2015-01-01
3d N=2 partition functions on the squashed three-sphere and on the twisted product S2xS1 have been shown to factorize into sums of squares of solid tori partition functions, the so-called holomorphic blocks. The same set of holomorphic blocks realizes squashed three-sphere and S2xS1 partition functions but the two cases involve different inner products, the S-pairing and the id-pairing respectively. We define a class of q-deformed CFT correlators where conformal blocks are controlled by a deformation of Virasoro symmetry and are paired by S-pairing and id-pairing respectively. Applying the bootstrap approach to a class of degenerate correlators we are able to derive three-point functions. We show that degenerate correlators can be mapped to 3d partition functions while the crossing symmetry of CFT correlators corresponds to the flop symmetry of 3d gauge theories. We explore how non-degenerate q-deformed correlators are related to 5d partition functions. We argue that id-pairing correlators are associated to t...
Coexistence via resource partitioning fails to generate an increase in community function.
Directory of Open Access Journals (Sweden)
John P DeLong
Full Text Available Classic ecological theory suggests that resource partitioning facilitates the coexistence of species by reducing inter-specific competition. A byproduct of this process is an increase in overall community function, because a greater spectrum of resources can be used. In contrast, coexistence facilitated by neutral mechanisms is not expected to increase function. We studied coexistence in laboratory microcosms of the bactivorous ciliates Paramecium aurelia and Colpidium striatum to understand the relationship between function and coexistence mechanism. We quantified population and community-level function (biomass and oxygen consumption, competitive interactions, and resource partitioning. The two ciliates partitioned their bacterial resource along a size axis, with the larger ciliate consuming larger bacteria than the smaller ciliate. Despite this, there was no gain in function at the community level for either biomass or oxygen consumption, and competitive effects were symmetrical within and between species. Because other potential coexistence mechanisms can be ruled out, it is likely that inter-specific interference competition diminished the expected gain in function generated by resource partitioning, leading to a system that appeared competitively neutral even when structured by niche partitioning. We also analyzed several previous studies where two species of protists coexisted and found that the two-species communities showed a broad range of biomass levels relative to the single-species states.
Quantum algorithms for testing Boolean functions
Directory of Open Access Journals (Sweden)
Erika Andersson
2010-06-01
Full Text Available We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same quantum algorithm can also be used to learn which input variables other types of Boolean functions depend on, with a success probability that depends on the form of the Boolean function that is tested, but does not depend on the total number of input variables. We also outline a procedure to futher amplify the success probability, based on another quantum algorithm, the Grover search.
Nagesh, Jayashree; Brumer, Paul; Izmaylov, Artur F
2016-01-01
We extend the localized operator partitioning method (LOPM) [J. Nagesh, A.F. Izmaylov, and P. Brumer, J. Chem. Phys. 142, 084114 (2015)] to the time-dependent density functional theory (TD-DFT) framework to partition molecular electronic energies of excited states in a rigorous manner. A molecular fragment is defined as a collection of atoms using Stratman-Scuseria-Frisch atomic partitioning. A numerically efficient scheme for evaluating the fragment excitation energy is derived employing a resolution of the identity to preserve standard one- and two-electron integrals in the final expressions. The utility of this partitioning approach is demonstrated by examining several excited states of two bichromophoric compounds: 9-((1-naphthyl)-methyl)-anthracene and 4-((2-naphthyl)-methyl)-benzaldehyde. The LOPM is found to provide nontrivial insights into the nature of electronic energy localization that are not accessible using simple density difference analysis.
Partition functions of 3d $\\hat D$-quivers and their mirror duals from 1d free fermions
Assel, Benjamin; Felix, Jan
2015-01-01
We study the matrix models calculating the sphere partition functions of 3d gauge theories with $\\mathcal{N}=4$ supersymmetry and a quiver structure of a $\\hat D$ Dynkin diagram (where each node is a unitary gauge group). As in the case of necklace ($\\hat A $) quivers, we can map the problem to that of free fermion quantum mechanics whose complicated Hamiltonian we find explicitly. Many of these theories are conjectured to be dual under mirror symmetry to certain unitary linear quivers with extra Sp nodes or antisymmetric hypermultiplets. We show that the free fermion formulations of such mirror pairs are related by a linear symplectic transformation. We then study the large N expansion of the partition function, which as in the case of the $\\hat A$-quivers is given to all orders in 1/N by an Airy function. We simplify the algorithm to calculate the numerical coefficients appearing in the Airy function and evaluate them for a wide class of $\\hat D$-quiver theories.
Partition and generating function zeros in adsorbing self-avoiding walks
Janse van Rensburg, E. J.
2017-03-01
The Lee–Yang theory of adsorbing self-avoiding walks is presented. It is shown that Lee–Yang zeros of the generating function of this model asymptotically accumulate uniformly on a circle in the complex plane, and that Fisher zeros of the partition function distribute in the complex plane such that a positive fraction are located in annular regions centred at the origin. These results are examined in a numerical study of adsorbing self-avoiding walks in the square and cubic lattices. The numerical data are consistent with the rigorous results; for example, Lee–Yang zeros are found to accumulate on a circle in the complex plane and a positive fraction of partition function zeros appear to accumulate on a critical circle. The radial and angular distributions of partition function zeros are also examined and it is found to be consistent with the rigorous results.
Energy Technology Data Exchange (ETDEWEB)
Pask, J E; Sukumar, N; Guney, M; Hu, W
2011-02-28
Over the course of the past two decades, quantum mechanical calculations have emerged as a key component of modern materials research. However, the solution of the required quantum mechanical equations is a formidable task and this has severely limited the range of materials systems which can be investigated by such accurate, quantum mechanical means. The current state of the art for large-scale quantum simulations is the planewave (PW) method, as implemented in now ubiquitous VASP, ABINIT, and QBox codes, among many others. However, since the PW method uses a global Fourier basis, with strictly uniform resolution at all points in space, and in which every basis function overlaps every other at every point, it suffers from substantial inefficiencies in calculations involving atoms with localized states, such as first-row and transition-metal atoms, and requires substantial nonlocal communications in parallel implementations, placing critical limits on scalability. In recent years, real-space methods such as finite-differences (FD) and finite-elements (FE) have been developed to address these deficiencies by reformulating the required quantum mechanical equations in a strictly local representation. However, while addressing both resolution and parallel-communications problems, such local real-space approaches have been plagued by one key disadvantage relative to planewaves: excessive degrees of freedom (grid points, basis functions) needed to achieve the required accuracies. And so, despite critical limitations, the PW method remains the standard today. In this work, we show for the first time that this key remaining disadvantage of real-space methods can in fact be overcome: by building known atomic physics into the solution process using modern partition-of-unity (PU) techniques in finite element analysis. Indeed, our results show order-of-magnitude reductions in basis size relative to state-of-the-art planewave based methods. The method developed here is
Directory of Open Access Journals (Sweden)
O.V.Patsahan
2006-01-01
Full Text Available Based on the method of collective variables (CV with a reference system, the exact expression for the functional of the grand partition function of a m-component ionic model with charge and size asymmetry is found. Particular attention is paid to the n-th particle correlation functions of the reference system which is presented as a m-component system of "colour" hard spheres of the same diameter. A two-component model is considered in more detail. In this case the recurrence formulas for the correlation functions are found. A general case of a m-component inhomogeneous system of the "colour" hard spheres is also analysed.
Liu, Qian; Chen, Yi-Ping Phoebe; Li, Jinyan
2014-01-07
Many studies are aimed at identifying dense clusters/subgraphs from protein-protein interaction (PPI) networks for protein function prediction. However, the prediction performance based on the dense clusters is actually worse than a simple guilt-by-association method using neighbor counting ideas. This indicates that the local topological structures and properties of PPI networks are still open to new theoretical investigation and empirical exploration. We introduce a novel topological structure called k-partite cliques of protein interactions-a functionally coherent but not-necessarily dense subgraph topology in PPI networks-to study PPI networks. A k-partite protein clique is a maximal k-partite clique comprising two or more nonoverlapping protein subsets between any two of which full interactions are exhibited. In the detection of PPI's maximal k-partite cliques, we propose to transform PPI networks into induced K-partite graphs where edges exist only between the partites. Then, we present a maximal k-partite clique mining (MaCMik) algorithm to enumerate maximal k-partite cliques from K-partite graphs. Our MaCMik algorithm is then applied to a yeast PPI network. We observed interesting and unusually high functional coherence in k-partite protein cliques-the majority of the proteins in k-partite protein cliques, especially those in the same partites, share the same functions, although k-partite protein cliques are not restricted to be dense compared with dense subgraph patterns or (quasi-)cliques. The idea of k-partite protein cliques provides a novel approach of characterizing PPI networks, and so it will help function prediction for unknown proteins.
Exact Partition Function for the Random Walk of an Electrostatic Field
Directory of Open Access Journals (Sweden)
Gabriel González
2017-01-01
Full Text Available The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either ±σ is obtained. We find the electrostatic energy of the system and show that it can be analyzed through generalized Dyck paths. The relation between the electrostatic field and generalized Dyck paths allows us to sum overall possible electrostatic field configurations and is used for obtaining the partition function of the system. We illustrate our results with one example.
Some exact results on the Potts model partition function in a magnetic field
Energy Technology Data Exchange (ETDEWEB)
Chang, S-C [Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan (China); Shrock, Robert [C N Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794 (United States)], E-mail: scchang@mail.ncku.edu.tw, E-mail: robert.shrock@stonybrook.edu
2009-09-25
We consider the Potts model in a magnetic field on an arbitrary graph G. Using a formula by F Y Wu for the partition function Z of this model as a sum over spanning subgraphs of G, we prove some properties of Z concerning factorization, monotonicity and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context, we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for Z for cyclic strip graphs.
Some exact results on the Potts model partition function in a magnetic field
Chang, Shu-Chiuan; Shrock, Robert
2009-09-01
We consider the Potts model in a magnetic field on an arbitrary graph G. Using a formula by F Y Wu for the partition function Z of this model as a sum over spanning subgraphs of G, we prove some properties of Z concerning factorization, monotonicity and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context, we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for Z for cyclic strip graphs.
On the measurability of quantum correlation functions
Energy Technology Data Exchange (ETDEWEB)
Lima Bernardo, Bertúlio de, E-mail: bertulio.fisica@gmail.com; Azevedo, Sérgio; Rosas, Alexandre
2015-05-15
The concept of correlation function is widely used in classical statistical mechanics to characterize how two or more variables depend on each other. In quantum mechanics, on the other hand, there are observables that cannot be measured at the same time; the so-called incompatible observables. This prospect imposes a limitation on the definition of a quantum analog for the correlation function in terms of a sequence of measurements. Here, based on the notion of sequential weak measurements, we circumvent this limitation by introducing a framework to measure general quantum correlation functions, in principle, independently of the state of the system and the operators involved. To illustrate, we propose an experimental configuration to obtain explicitly the quantum correlation function between two Pauli operators, in which the input state is an arbitrary mixed qubit state encoded on the polarization of photons.
The partition function of two-dimensional string theory
Dijkgraaf, Robbert; Moore, Gregory; Plesser, Ronen
1993-04-01
We derive a compact and explicit expression for the generating functional of all correlation functions of tachyon operators in two-dimensional string theory. This expression makes manifest relations of the c = 1 system to KP flow nd W 1 + ∞ constraints. Moreover we derive a Kontsevich-Penner integral representation of this generating functional.
The partition function of 2d string theory
Dijkgraaf, R; Plesser, R
1993-01-01
We derive a compact and explicit expression for the generating functional of all correlation functions of tachyon operators in 2D string theory. This expression makes manifest relations of the $c=1$ system to KP flow and $W_{1+\\infty}$ constraints. Moreover we derive a Kontsevich-Penner integral representation of this generating functional.
Directory of Open Access Journals (Sweden)
Mihai V. Putz
2009-11-01
Full Text Available The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving many-electronic systems.
The partition function of two-dimensional string theory
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, R. (School of Natural Sciences, Inst. for Advanced Study, Princeton, NJ (United States) Dept. of Mathematics, Univ. Amsterdam (Netherlands)); Moore, G.; Plesser, R. (Dept. of Physics, Yale Univ., New Haven, CT (United States))
1993-04-12
We derive a compact and explicit expression for the generating functional of all correlation functions of tachyon operators in two-dimensional string theory. This expression makes manifest relations of the c=1 system to KP flow and W[sub 1+[infinity
Mean Spherical Approximation-Based Partitioned Density Functional Theory
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi
2003-01-01
Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =ζ∫ dr4a(r4 - r1)a(r4 - r2)a(r4 - r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ζ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.
Mean Spherical Approximation-Based Partitioned Density Functional Theory
Institute of Scientific and Technical Information of China (English)
ZHOUShi-Qi
2003-01-01
Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =(∫dr4a(r4-r1)a(r4-r2)a(r4-r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ξ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.
How Incorrect Is the Classical Partition Function for the Ideal Gas?
Kroemer, Herbert
1980-01-01
Discussed is the classical partition function for the ideal gas and how it differs from the exact value for bosons or fermions in the classical regime. The differences in the two values are negligible hence the classical treatment leads in the end to correct answers for all observables. (Author/DS)
Exact Potts model partition function on strips of the triangular lattice
Chang, Shu-Chiuan; Shrock, Robert
2000-10-01
In this paper we present exact calculations of the partition function Z of the q-state Potts model and its generalization to real q, for arbitrary temperature on n-vertex strip graphs, of width Ly=2 and arbitrary length, of the triangular lattice with free, cyclic, and Möbius longitudinal boundary conditions. These partition functions are equivalent to Tutte/Whitney polynomials for these graphs. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. Considering the full generalization to arbitrary complex q and temperature, we determine the singular locus B in the corresponding C2 space, arising as the accumulation set of partition function zeros as n→∞. In particular, we study the connection with the T=0 limit of the Potts antiferromagnet where B reduces to the accumulation set of chromatic zeros. Comparisons are made with our previous exact calculation of Potts model partition functions for the corresponding strips of the square lattice. Our present calculations yield, as special cases, several quantities of graph-theoretic interest.
1999-01-01
A locus close to one end of the linear N15 prophage closely resembles the sop operon which governs partition of the F plasmid; the promoter region contains similar operator sites, and the two putative gene products have extensive amino acid identity with the SopA and -B proteins of F. Our aim was to ascertain whether the N15 sop homologue functions in partition, to identify the centromere site, and to examine possible interchangeability of function with the F Sop system. When expressed at a m...
Partitioning of Function in a Distributed Graphics System.
1985-03-01
clipping fo~r extents totally outside the area being drawn. -’- his is effectively die display processing unil. In a hiigher- performance... clipping and scaling. However, in the IRIS workstation these functions are provided in hardware by the Geometry Engilic [381. General’y, the IRIS provides...VIiv.., ] VIO VlO VlO +VIO VIO VGTS VOTS BSP VGTS rCP fexecute PUP Telnet iptn Internal a) VAX-IKP b) PUP Telnet c) IP Telnet Figure 6-2: Server host
A Partitioned Correlation Function Interaction approach for describing electron correlation in atoms
Verdebout, S; Jönsson, P; Gaigalas, G; Fischer, C Froese; Godefroid, M
2013-01-01
Traditional multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis (OB). For atoms with complicated shell structures, a large OB is needed to saturate all the electron correlation effects. The large OB leads to massive configuration state function (CSF) expansions that are difficult to handle. We show that it is possible to relax the orthonormality restriction on the OB and break down the originally large calculations to a set of smaller ones that can be run in parallel. Each calculation determines a partitioned correlation function (PCF) that accounts for a specific correlation effect. The PCFs are built on optimally localized orbital sets and are added to a zero-order multireference (MR) function to form a total wave function. The mixing coefficients of the PCFs are fixed from a small generalized eigenvalue problem. The required matrices are computed using a biorthonormal transformation technique. The new method, called partitioned c...
Optical Approach for the Thermal Partition Function of Photons
Moretti, V; Moretti, Valter; Iellici, Devis
1997-01-01
The optical manifold method to compute the one-loop effective action in a static space-time is extended from the massless scalar field to the Maxwell field in any Feynman-like covariant gauge. The method applied in the case of the Rindler space obtaining the same results as the point-splitting procedure. The result is free from Kabat's surface terms which instead affect the manifold containing conical singularities. The relation between the optical method and the direct $\\zeta$-function approach on the Euclidean Rindler manifold is discussed both in the scalar and the photon case. Problems with the thermodynamic consistency of the results obtained from the point-splitting thermal stress tensor in the case of the Rindler space are pointed out.
Pendás, A Martín; Francisco, E; Blanco, M A
2007-01-01
We analyze the response of a quantum group within a molecule to charge transfer by using the interacting quantum atoms approach (IQA), an energy partitioning scheme within the quantum theory of atoms in molecules (QTAM). It is shown that this response lies at the core of the concept of the functional group. The manipulation of fractional electron populations is carried out by using distribution functions for the electron number within the quantum basins. Several test systems are studied to show that similar chemical potential groups are characterized by similar energetic behavior upon interaction with other groups. The origin of the empirical additivity rules for group energies in simple hydrocarbons is also investigated. It turns out to rest on the independent saturation of both the self-energies and the interaction energies of the groups as the size of the chain increases. We also show that our results are compatible with the standard group energies of the QTAM.
The Wave Function of Quantum de Sitter
Castro, Alejandra; Maloney, Alexander
2012-01-01
We consider quantum general relativity in three dimensions with a positive cosmological constant. The Hartle-Hawking wave function is computed as a function of metric data at asymptotic future infinity. The analytic continuation from Euclidean Anti-de Sitter space provides a natural integration contour in the space of metrics, allowing us -- with certain assumptions -- to compute the wave function exactly, including both perturbative and non-perturbative effects. The resulting wave function i...
Function Optimization Based on Quantum Genetic Algorithm
Directory of Open Access Journals (Sweden)
Ying Sun
2014-01-01
Full Text Available Optimization method is important in engineering design and application. Quantum genetic algorithm has the characteristics of good population diversity, rapid convergence and good global search capability and so on. It combines quantum algorithm with genetic algorithm. A novel quantum genetic algorithm is proposed, which is called Variable-boundary-coded Quantum Genetic Algorithm (vbQGA in which qubit chromosomes are collapsed into variable-boundary-coded chromosomes instead of binary-coded chromosomes. Therefore much shorter chromosome strings can be gained. The method of encoding and decoding of chromosome is first described before a new adaptive selection scheme for angle parameters used for rotation gate is put forward based on the core ideas and principles of quantum computation. Eight typical functions are selected to optimize to evaluate the effectiveness and performance of vbQGA against standard Genetic Algorithm (sGA and Genetic Quantum Algorithm (GQA. The simulation results show that vbQGA is significantly superior to sGA in all aspects and outperforms GQA in robustness and solving velocity, especially for multidimensional and complicated functions.
Semenov, Alexander; Zaikin, Oleg
2016-01-01
In this paper we propose an approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance one can construct different partitionings, each of them is a set of simplified versions of the original SAT instance. The effectiveness of an arbitrary partitioning is determined by the total time of solving of all SAT instances from it. We suggest the approach, based on the Monte Carlo method, for estimating time of processing of an arbitrary partitioning. With each partitioning we associate a point in the special finite search space. The estimation of effectiveness of the particular partitioning is the value of predictive function in the corresponding point of this space. The problem of search for an effective partitioning can be formulated as a problem of optimization of the predictive function. We use metaheuristic algorithms (simulated annealing and tabu search) to move from point to point in the search space. In our computational experiments we found partitionings for SAT instances encoding problems of inversion of some cryptographic functions. Several of these SAT instances with realistic predicted solving time were successfully solved on a computing cluster and in the volunteer computing project SAT@home. The solving time agrees well with estimations obtained by the proposed method.
Soucek, Jiri
2010-01-01
In the paper the basic concepts of extended probability theory are introduced. The basic idea: the concept of an event as a subset of \\Omega is replaced with the concept of an event as a partition. The partition is any set of disjoint non-empty subsets of \\Omega (i.e. partition=subset+its decomposition). Interpretation: elements inside certain part are indistinguishable, while elements from different parts are distinguishable. There are incompatible events, e.g {{e1},{e2}} and {{e1,e2}}. This is logical incompatibility analogical to the impossibility to have and simultaneously not to have the which-way information in the given experiment. The context is the maximal set of mutually compatible events. Each experiment has associated its context. In each context the extended probability is reduced to classical probability. Then the quadratic representation of events, partitions and probability measures is developed. At the end the central concept of quadratic probability spaces (which extend Kolmogorov probabilit...
DEFF Research Database (Denmark)
Bessenrodt, Christine; Olsson, Jørn Børling; Sellers, James A.
2013-01-01
We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions.......We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions....
Watanabe, Hiroshi C; Kubillus, Maximilian; Kubař, Tomáš; Stach, Robert; Mizaikoff, Boris; Ishikita, Hiroshi
2017-07-21
In the condensed phase, quantum chemical properties such as many-body effects and intermolecular charge fluctuations are critical determinants of the solvation structure and dynamics. Thus, a quantum mechanical (QM) molecular description is required for both solute and solvent to incorporate these properties. However, it is challenging to conduct molecular dynamics (MD) simulations for condensed systems of sufficient scale when adapting QM potentials. To overcome this problem, we recently developed the size-consistent multi-partitioning (SCMP) quantum mechanics/molecular mechanics (QM/MM) method and realized stable and accurate MD simulations, using the QM potential to a benchmark system. In the present study, as the first application of the SCMP method, we have investigated the structures and dynamics of Na(+), K(+), and Ca(2+) solutions based on nanosecond-scale sampling, a sampling 100-times longer than that of conventional QM-based samplings. Furthermore, we have evaluated two dynamic properties, the diffusion coefficient and difference spectra, with high statistical certainty. Furthermore the calculation of these properties has not previously been possible within the conventional QM/MM framework. Based on our analysis, we have quantitatively evaluated the quantum chemical solvation effects, which show distinct differences between the cations.
Supersymmetric partition functions and the three-dimensional A-twist arXiv
Closset, Cyril; Willett, Brian
We study three-dimensional $\\mathcal{N}=2$ supersymmetric gauge theories on $\\mathcal{M}_{g,p}$, an oriented circle bundle of degree $p$ over a closed Riemann surface, $\\Sigma_g$. We compute the $\\mathcal{M}_{g,p}$ supersymmetric partition function and correlation functions of supersymmetric loop operators. This uncovers interesting relations between observables on manifolds of different topologies. In particular, the familiar supersymmetric partition function on the round $S^3$ can be understood as the expectation value of a so-called "fibering operator" on $S^2 \\times S^1$ with a topological twist. More generally, we show that the 3d $\\mathcal{N}=2$ supersymmetric partition functions (and supersymmetric Wilson loop correlation functions) on $\\mathcal{M}_{g,p}$ are fully determined by the two-dimensional A-twisted topological field theory obtained by compactifying the 3d theory on a circle. We give two complementary derivations of the result. We also discuss applications to F-maximization and to three-dimens...
Automated quantum conductance calculations using maximally-localised Wannier functions
Shelley, Matthew; Mostofi, Arash A; Marzari, Nicola
2011-01-01
A robust, user-friendly, and automated method to determine quantum conductance in disordered quasi-one-dimensional systems is presented. The scheme relies upon an initial density- functional theory calculation in a specific geometry after which the ground-state eigenfunctions are transformed to a maximally-localised Wannier function (MLWF) basis. In this basis, our novel algorithms manipulate and partition the Hamiltonian for the calculation of coherent electronic transport properties within the Landauer-Buttiker formalism. Furthermore, we describe how short- ranged Hamiltonians in the MLWF basis can be combined to build model Hamiltonians of large (>10,000 atom) disordered systems without loss of accuracy. These automated algorithms have been implemented in the Wannier90 code[Mostofi et al, Comput. Phys. Commun. 178, 685 (2008)], which is interfaced to a number of electronic structure codes such as Quantum-ESPRESSO, AbInit, Wien2k, SIESTA and FLEUR. We apply our methods to an Al atomic chain with a Na defect...
Functional determinants, index theorems, and exact quantum black hole entropy
Murthy, Sameer; Reys, Valentin
2015-12-01
The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the QV operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around Q-invariant off-shell configurations in four-dimensional N=2 supergravity with AdS 2 × S 2 boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in N=2 supergravity. We explain cancellations concerning 1/8 -BPS black holes in N=8 supergravity that were observed in arXiv:1111.1161. We also make comments about the interpretation of a logarithmic term in the topological string partition function in the low energy supergravity theory.
Energy Technology Data Exchange (ETDEWEB)
Ladrem, M.; Ait-El-Djoudi, A. [Ecole Normale Superieure-Kouba, Laboratoire de Physique des Particules et Physique Statistique, B.P. 92, Vieux-Kouba, Algiers (Algeria)
2005-10-01
We study the finite-size effects for the thermal quantum chromodynamics (QCD) deconfinement phase transition, and use a numerical finite-size scaling analysis to extract the scaling exponents characterizing its scaling behavior when approaching the thermodynamic limit (V{yields}{infinity}). For this, we use a simple model of coexistence of hadronic gas and color-singlet quark gluon plasma (QGP) phases in a finite volume. The color-singlet partition function of the QGP cannot be exactly calculated and is usually derived within the saddle-point approximation. When we try to do calculations with such an approximate color-singlet partition function, a problem arises in the limit of small temperatures and/or volumes VT{sup 3}<<1, requiring additional approximations if we want to carry out calculations. We propose in this work a method for an accurate calculation of any quantity of the finite system, without any approximation. By probing the behavior of some useful thermodynamic response functions on the whole range of temperature, it turns out that, in a finite-size system, all singularities in the thermodynamic limit are smeared out and the transition point is shifted away. A numerical finite-size scaling (FSS) analysis of the obtained data allows us to determine the scaling exponents of the QCD deconfinement phase transition. Our results expressing the equality between their values and the space dimensionality is a consequence of the singularity characterizing a first-order phase transition and agree very well with the predictions of other FSS theoretical approaches to a first-order phase transition and with the results of calculations using Monte Carlo methods in both lattice QCD and statistical physics models. (orig.)
Relation between the 4d superconformal index and the S^3 partition function
Imamura, Yosuke
2011-01-01
A relation between the 4d superconformal index and the S^3 partition function is studied with focus on the 4d and 3d actions used in localization. In the case of vanishing Chern-Simons levels and round S^3 we explicitly show that the 3d action is obtained from the 4d action by dimensional reduction up to terms which do not affect the exact results. By combining this fact and a recent proposal concerning a squashing of S^3 and SU(2) Wilson line, we obtain a formula which gives the partition function depending on the Weyl weight of chiral multiplets, real mass parameters, FI parameters, and a squashing parameter as a limit of the index of a parent 4d theory.
Barklem, Paul S
2016-01-01
Partition functions and dissociation equilibrium constants are presented for 291 diatomic molecules for temperatures in the range from near absolute zero to 10000 K, thus providing data for many diatomic molecules of astrophysical interest at low temperature. The calculations are based on molecular spectroscopic data from the book of Huber and Herzberg with significant improvements from the literature, especially updated data for ground states of many of the most important molecules by Irikura. Dissociation energies are collated from compilations of experimental and theoretical values. Partition functions for 284 species of atoms for all elements from H to U are also presented based on data collected at NIST. The calculated data are expected to be useful for modelling a range of low density astrophysical environments, especially star-forming regions, protoplanetary disks, the interstellar medium, and planetary and cool stellar atmospheres. The input data, which will be made available electronically, also prov...
One-Loop Partition Functions in Deformed $\\mathcal{N}=4$ SYM Theory
Fokken, Jan
2014-01-01
We study the thermodynamic behaviour of the real $\\beta$- and $\\gamma_i$-deformation of $\\mathcal{N}=4$ Super Yang-Mills theory on $\\mathbb{R}\\times S^3$ in the planar limit. These theories were shown to be the most general asymptotically integrable supersymmetric and non-supersymmetric field-theory deformations of $\\mathcal{N}=4$ Super Yang-Mills theory, respectively. We calculate the first loop correction to their partition functions using an extension of the dilatation-operator and P\\'{o}lya-counting approach. In particular, we account for the one-loop finite-size effects which occur for operators of length one and two. Remarkably, we find that the $\\mathcal{O}(\\lambda)$ correction to the Hagedorn temperature is independent of the deformation parameters, although the partition function depends on them in a non-trivial way.
Density functional theory with quantum nuclei
Requist, Ryan
2016-01-01
It is proved that the ground state energy of an electron-nuclear system is a variational functional of the conditional electronic density n_R(r), the nuclear wavefunction \\chi(R) and the quantum geometric tensor of the conditional electronic wavefunction $T_{\\mu\
An efficient algorithm for upper bound on the partition function of nucleic acids.
Chitsaz, Hamidreza; Forouzmand, Elmirasadat; Haffari, Gholamreza
2013-07-01
It has been shown that minimum free-energy structure for RNAs and RNA-RNA interaction is often incorrect due to inaccuracies in the energy parameters and inherent limitations of the energy model. In contrast, ensemble-based quantities such as melting temperature and equilibrium concentrations can be more reliably predicted. Even structure prediction by sampling from the ensemble and clustering those structures by Sfold has proven to be more reliable than minimum free energy structure prediction. The main obstacle for ensemble-based approaches is the computational complexity of the partition function and base-pairing probabilities. For instance, the space complexity of the partition function for RNA-RNA interaction is O(n4) and the time complexity is O(n6), which is prohibitively large. Our goal in this article is to present a fast algorithm, based on sparse folding, to calculate an upper bound on the partition function. Our work is based on the recent algorithm of Hazan and Jaakkola (2012). The space complexity of our algorithm is the same as that of sparse folding algorithms, and the time complexity of our algorithm is O(MFE(n)ℓ) for single RNA and O(MFE(m, n)ℓ) for RNA-RNA interaction in practice, in which MFE is the running time of sparse folding and ℓ≤n (ℓ≤n+m) is a sequence-dependent parameter.
Faribault, Alexandre; Tschirhart, Hugo; Muller, Nicolas
2016-05-01
In this work we present a determinant expression for the domain-wall boundary condition partition function of rational (XXX) Richardson-Gaudin models which, in addition to N-1 spins \\frac{1}{2}, contains one arbitrarily large spin S. The proposed determinant representation is written in terms of a set of variables which, from previous work, are known to define eigenstates of the quantum integrable models belonging to this class as solutions to quadratic Bethe equations. Such a determinant can be useful numerically since systems of quadratic equations are much simpler to solve than the usual highly nonlinear Bethe equations. It can therefore offer significant gains in stability and computation speed.
Spectral determinants and quantum theta functions
Grassi, Alba
2016-12-01
It has been recently conjectured that the spectral determinants of operators associated to mirror curves can be expressed in terms of a generalization of theta functions, called quantum theta functions. In this paper we study the symplectic properties of these spectral determinants by expanding them around the point {\\hslash }=2π , where the quantum theta functions become conventional theta functions. We find that they are modular invariant, order by order, and we give explicit expressions for the very first terms of the expansion. Our derivation requires a detailed understanding of the modular properties of topological string free energies in the Nekrasov-Shatashvili limit. We derive these properties in a diagrammatic form. Finally, we use our results to provide a new test of the duality between topological strings and spectral theory.
Rovibrational energies, partition functions and equilibrium fractionation of the CO2 isotopologues
Cerezo, J.; Bastida, A.; Requena, A.; Zúñiga, J.
2014-11-01
Rovibrational energy levels, partition functions and relative abundances of the stable isotopologues of CO2 in gas phase at equilibrium are calculated using an empirical Morse-cosine potential energy surface (PES) refined by fitting to the updated pure (l2 = 0) vibrational frequencies observed for the main 12C16O2 isotopologue. The rovibrational energy levels are calculated variationally using a system of optimized hyperspherical normal coordinates, and from these the vibrational terms Gv and rotational constants Bv of the isotopologues are determined. The refined potential surface is shown to be clearly superior to the original potential surface, with the former reproducing the observed values of the spectroscopic constants Gv and Bv with accuracies of about 0.1 cm-1 and 0.00020 cm-1, respectively, for levels with l2 ≥ 0 up to 10,000 cm-1 above the ground state. The internal partition functions of the isotopologues are calculated by approximated direct summation over the rovibrational energies and compared with both previous partition sums and values obtained from analytical expressions based on the harmonic oscillator and rigid rotor models. The partition functions calculated by approximated direct summation are then used to determine the abundances of the CO2 isotopologues at thermodynamic equilibrium using the method developed by Wang et al. [74]. Significant variations in the relative abundances of some of the CO2 multiple substituted isotopologues at terrestrial temperatures with respect to those provided by the classical harmonic-based Urey theory are found, which may be of relevance in geochemical processes.
Inverse theta functions as quantum modular forms
Bringmann, Kathrin; Rolen, Larry
2014-01-01
In this paper, we consider the Fourier coefficients of a special class of meromorphic Jaocbi forms of negative index. Much recent work has been done on the Fourier coefficients of meromorphic Jacobi forms of positive index, but almost nothing is known for Jacobi forms of negative index. Here we show from two different perspectives that their Fourier coefficients have a simple decomposition in terms of partial theta functions. The first perspective uses the language of Lie super algebras, and the second applies the theory of elliptic functions. In particular, we find a new infinite family of rank-crank type PDEs generalizing the famous example of Atkin and Garvan. We then describe the modularity properties of these coefficients, showing that they are \\emph{mixed quantum modular forms}, along the way determining a new class of quantum modular partial theta functions.
VizieR Online Data Catalog: Partition functions for molecules and atoms (Barklem+, 2016)
Barklem, P. S.; Collet, R.
2016-02-01
The results and input data are presented in the following files. Table 1 contains dissociation energies from the literature, and final adopted values, for 291 molecules. The literature values are from the compilations of Huber & Herzberg (1979, Constants of Diatomic Molecules (Van Nostrand Reinhold), Luo (2007, Comprehensive Handbook of Chemical Bond Energies (CRC Press)) and G2 theory calculations of Curtiss et al. (1991, J. Chem. Phys., 94, 7221). Table 2 contains the input data for the molecular calculations including adopted dissociation energy, nuclear spins, molecular spectroscopic constants and their sources. There are 291 files, one for each molecule, labelled by the molecule name. The various molecular spectroscopic constants are as defined in the paper. Table 4 contains the first, second and third ionisation energies for all chemical elements from H to U. The data comes from the CRC Handbook of Chemistry and Physics (Haynes, W.M. 2010, CRC Handbook of Chemistry and Physics, 91st edn. (CRC Press, Taylor and Francis Group)). Table 5a contains a list of keys to bibliographic references for the atomic energy level data that was extracted from NIST Atomic Spectra Database and used in the present work to compute atomic partition functions. The citation keys are abbreviations of the full bibliographic references which are made available in Table 5b in BibTeX format. Table 5b contains the full bibliographic references for the atomic energy level data that was extracted from the NIST Atomic Spectra Database. Table 6 contains tabulated partition function data as a function of temperature for 291 molecules. Table 7 contains tabulated equilibrium constant data as a function of temperature for 291 molecules. Table 8 contains tabulated partition function data as a function of temperature for 284 atoms and ions. The paper should be consulted for further details. (10 data files).
On modular invariant partition functions of conformal field theories with logarithmic operators
Flohr, M A
1995-01-01
We extend the definitions of characters and partition functions to the case of conformal field theories which contain operators with logarithmic correlation functions. As an example we consider the theories with central charge c = c(p,1) = 13-6(p+1/p), the ``border'' of the discrete minimal series. We show that there is a slightly generalized form of the property of rationality for such logarithmic theories. In particular, we obtain a classification of theories with c = c(p,1) which is similar to the A-D-E classification of c = 1 models.
Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM
Aguilera-Damia, Jeremías; Correa, Diego H.; Silva, Guillermo A.
2015-03-01
We compute the 1-loop partition function for strings in , whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.
Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM
Aguilera-Damia, Jeremias; Silva, Guillermo A
2014-01-01
We compute the 1-loop partition function for strings in $AdS_4\\times\\mathbb{CP}^3$, whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.
Bornyakov, V G; Goy, V A; Molochkov, A V; Nakamura, Atsushi; Nikolaev, A A; Zakharov, V I
2016-01-01
We propose and test a new approach to computation of canonical partition functions in lattice QCD at finite density. We suggest a few steps procedure. We first compute numerically the quark number density for imaginary chemical potential $i\\mu_{qI}$. Then we restore the grand canonical partition function for imaginary chemical potential using fitting procedure for the quark number density. Finally we compute the canonical partition functions using high precision numerical Fourier transformation. Additionally we compute the canonical partition functions using known method of the hopping parameter expansion and compare results obtained by two methods in the deconfining as well as in the confining phases. The agreement between two methods indicates the validity of the new method. Our numerical results are obtained in two flavor lattice QCD with clover improved Wilson fermions.
A novel brain partition highlights the modular skeleton shared by structure and function.
Diez, Ibai; Bonifazi, Paolo; Escudero, Iñaki; Mateos, Beatriz; Muñoz, Miguel A; Stramaglia, Sebastiano; Cortes, Jesus M
2015-01-01
Elucidating the intricate relationship between brain structure and function, both in healthy and pathological conditions, is a key challenge for modern neuroscience. Recent progress in neuroimaging has helped advance our understanding of this important issue, with diffusion images providing information about structural connectivity (SC) and functional magnetic resonance imaging shedding light on resting state functional connectivity (rsFC). Here, we adopt a systems approach, relying on modular hierarchical clustering, to study together SC and rsFC datasets gathered independently from healthy human subjects. Our novel approach allows us to find a common skeleton shared by structure and function from which a new, optimal, brain partition can be extracted. We describe the emerging common structure-function modules (SFMs) in detail and compare them with commonly employed anatomical or functional parcellations. Our results underline the strong correspondence between brain structure and resting-state dynamics as well as the emerging coherent organization of the human brain.
Parrish, Robert M; Parker, Trent M; Sherrill, C David
2014-10-14
Recently, we introduced an effective atom-pairwise partition of the many-body symmetry-adapted perturbation theory (SAPT) interaction energy decomposition, producing a method known as atomic SAPT (A-SAPT) [Parrish, R. M.; Sherrill, C. D. J. Chem. Phys. 2014, 141, 044115]. A-SAPT provides ab initio atom-pair potentials for force field development and also automatic visualizations of the spatial contributions of noncovalent interactions, but often has difficulty producing chemically useful partitions of the electrostatic energy, due to the buildup of oscillating partial charges on adjacent functional groups. In this work, we substitute chemical functional groups in place of atoms as the relevant local quasiparticles in the partition, resulting in a functional-group-pairwise partition denoted as functional-group SAPT (F-SAPT). F-SAPT assigns integral sets of local occupied electronic orbitals and protons to chemical functional groups and linking σ bonds. Link-bond contributions can be further assigned to chemical functional groups to simplify the analysis. This approach yields a SAPT partition between pairs of functional groups with integral charge (usually neutral), preventing oscillations in the electrostatic partition. F-SAPT qualitatively matches chemical intuition and the cut-and-cap fragmentation technique but additionally yields the quantitative many-body SAPT interaction energy. The conceptual simplicity, chemical utility, and computational efficiency of F-SAPT is demonstrated in the context of phenol dimer, proflavine(+)-DNA intercalation, and a cucurbituril host-guest inclusion complex.
Investigating energy partitioning during photosynthesis using an expanded quantum yield convention
Ahn, Tae Kyu; Avenson, Thomas J.; Peers, Graham; Li, Zhirong; Dall'Osto, Luca; Bassi, Roberto; Niyogi, Krishna K.; Fleming, Graham R.
2009-02-01
In higher plants, regulation of excess absorbed light is essential for their survival and fitness, as it enables avoidance of a build up of singlet oxygen and other reactive oxygen species. Regulation processes (known as non-photochemical quenching; NPQ) can be monitored by steady-state fluorescence on intact plant leaves. Pulse amplitude modulated (PAM) measurements of chlorophyll a fluorescence have been used for over 20 years to evaluate the amount of NPQ and photochemistry (PC). Recently, a quantum yield representation of NPQ ( ΦNPQ), which incorporates a variable fraction of open reaction centers, was proposed by Hendrickson et al. [L. Hendrickson, R.T. Furbank, W.S. Chow, Photosynth. Res. 82 (2004) 73]. In this work we extend the quantum yield approach to describe the yields of reversible energy-dependent quenching ( ΦqE), state transitions to balance PC between photosystems II and I ( ΦqT), and photoinhibition quenching associated with damaged reaction centers ( ΦqI). We showed the additivity of the various quantum yield components of NPQ through experiments on wild-type and npq1 strains of Arabidopsis thaliana. The quantum yield approach enables comparison of ΦqE with data from a variety of techniques used to investigate the mechanism of qE. We showed that ΦqE for a series of A. thaliana genotypes scales linearly with the magnitude of zeaxanthin cation formation, suggesting that charge-transfer quenching is largely responsible for qE in plants.
Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end
Yang, Wen-Li; Feng, Jun; Hao, Kun; Shi, Kang-Jie; Sun, Cheng-Yi; Yang, Zhan-Ying; Zhang, Yao-Zhong
2011-01-01
With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex SOS model, we obtain the explicit determinant expression of the partition function of the eight-vertex model with a generic non-diagonal reflecting end and domain wall boundary condition. Our result shows that, contrary to the eight-vertex model without a reflection end, the partition function can be expressed as a single determinant.
Investigating energy partitioning during photosynthesis using an expanded quantum yield convention
Energy Technology Data Exchange (ETDEWEB)
Ahn, Tae Kyu [Department of Chemistry, Hildebrand B77, University of California, Berkeley, CA 94720-1460 (United States); Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Avenson, Thomas J. [Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Department of Plant and Microbial Biology, 111 Koshland Hall, University of California, Berkeley, CA 94720-3102 (United States); Peers, Graham; Li Zhirong [Department of Plant and Microbial Biology, 111 Koshland Hall, University of California, Berkeley, CA 94720-3102 (United States); Dall' Osto, Luca; Bassi, Roberto [Department of Science and Technology, University of Verona, Verona 37134 (Italy); Niyogi, Krishna K. [Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Department of Plant and Microbial Biology, 111 Koshland Hall, University of California, Berkeley, CA 94720-3102 (United States)], E-mail: niyogi@nature.berkeley.edu; Fleming, Graham R. [Department of Chemistry, Hildebrand B77, University of California, Berkeley, CA 94720-1460 (United States); Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)], E-mail: GRFleming@lbl.gov
2009-02-23
In higher plants, regulation of excess absorbed light is essential for their survival and fitness, as it enables avoidance of a build up of singlet oxygen and other reactive oxygen species. Regulation processes (known as non-photochemical quenching; NPQ) can be monitored by steady-state fluorescence on intact plant leaves. Pulse amplitude modulated (PAM) measurements of chlorophyll a fluorescence have been used for over 20 years to evaluate the amount of NPQ and photochemistry (PC). Recently, a quantum yield representation of NPQ ({phi}{sub NPQ}), which incorporates a variable fraction of open reaction centers, was proposed by Hendrickson et al. [L. Hendrickson, R.T. Furbank, W.S. Chow, Photosynth. Res. 82 (2004) 73]. In this work we extend the quantum yield approach to describe the yields of reversible energy-dependent quenching ({phi}{sub qE}), state transitions to balance PC between photosystems II and I ({phi}{sub qT}), and photoinhibition quenching associated with damaged reaction centers ({phi}{sub qI}). We showed the additivity of the various quantum yield components of NPQ through experiments on wild-type and npq1 strains of Arabidopsis thaliana. The quantum yield approach enables comparison of {phi}{sub qE} with data from a variety of techniques used to investigate the mechanism of qE. We showed that {phi}{sub qE} for a series of A. thaliana genotypes scales linearly with the magnitude of zeaxanthin cation formation, suggesting that charge-transfer quenching is largely responsible for qE in plants.
The Wave Function and Quantum Reality
Gao, Shan
2011-01-01
We investigate the meaning of the wave function by analyzing the mass and charge density distribution of a quantum system. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, and it is formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion is not continuous but discontinuous and random. This result suggests a new interpretation of the wave function, according to which the wave function is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations. It is shown that the suggested interpretation of the wave function disfavors the de Broglie-Bohm theory and the many-worlds interpretation but favors the dynamical collapse theories, and the rando...
Inner products of Bethe states as partial domain wall partition functions
Kostov, Ivan
2012-01-01
We study the inner product of Bethe states in the inhomogeneous periodic XXX spin-1/2 chain of length L, which is given by the Slavnov determinant formula. We show that the inner product of an on-shell M-magnon state with a generic M-magnon state is given by the same expression as the inner product of a 2M-magnon state with a vacuum descendent. The second inner product is proportional to the partition function of the six-vertex model on a rectangular Lx2M grid, with partial domain-wall boundary conditions.
Airy Equation for the Topological String Partition Function in a Scaling Limit
Alim, Murad; Yau, Shing-Tung; Zhou, Jie
2016-06-01
We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi-Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.
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.
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.
Role of Wigner function in studying quantum correlations
Siyouri, F.; El Baz, M.; Hassouni, Y.
2016-09-01
In this paper, we investigate the possibility to use the Wigner function to detect and quantify quantum correlations in general. We study these quantum correlations for two quasi-Werner states formed with two general bipartite superposed squeezed states. We find then that the Wigner function is not sensitive to all kinds of quantum correlations but it only witnesses entanglement.
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.
Exact Partition Functions of Interacting Self-Avoiding Walks on Lattices
Directory of Open Access Journals (Sweden)
Hsieh Yu-Hsin
2016-01-01
Full Text Available Ideas and methods of statistical physics have been shown to be useful for understanding some interesting problems in physical systems, e.g. universality and scaling in critical systems. The interacting self-avoiding walk (ISAW on a lattice is the simplest model for homopolymers and serves as the framework of simple models for biopolymers, such as DNA, RNA, and protein, which are important components in complex systems in biology. In this paper, we briefly review our recent work on exact partition functions of ISAW. Based on zeros of these exact partition functions, we have developed a novel method in which both loci of zeros and thermodynamic functions associated with them are considered. With this method, the first zeros can be identified clearly without ambiguity. The critical point of a small system can then be defined as the peak position of the heat capacity component associated with the first zeros. For the system with two phase transitions, two pairs of first zeros corresponding to two phase transitions can be identified and overlapping Cυ can be well separated. ISAW on the simple cubic lattice is such a system where in addition to a standard collapse transition, there is another freezing transition occurring at a lower temperature. Our approach can give a clear scenario for the collapse and the freezing transitions.
Quasi-Modular instanton partition function and elliptic solution of KdV equations
He, Wei
2014-01-01
Four dimensional N=2 supersymmetric gauge theories are related to some solvable quantum mechanics models. For SU(2) theory with an adjoint matter, or with 4 fundamental matters, if the mass of matter takes special value then the potential of quantum model is the elliptic solution of KdV equations. We show that the prepotential of the gauge theory can be obtained from the average densities of the conserved charges of classical KdV solution, the UV gauge coupling dependence is assembled into Eisenstein series. The Eisenstein series come from integration of elliptic functions in KdV Hamiltonians. The gauge theory with adjoint mass is taken as the example.
Energy Technology Data Exchange (ETDEWEB)
Akemann, G. [Department of Mathematical Sciences and BURSt Research Centre, School of Information Systems, Computing and Mathematics, Brunel University West London, Uxbridge UB8 3PH (United Kingdom)]. E-mail: gernot.akemann@brunel.ac.uk; Basile, F. [Department of Mathematical Sciences and BURSt Research Centre, School of Information Systems, Computing and Mathematics, Brunel University West London, Uxbridge UB8 3PH (United Kingdom); Dipartimento di Fisica dell' Universita di Pisa and INFN, Via Buonarroti, 56127 Pisa (Italy)
2007-03-26
We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are valid for general weight functions without degeneracies of the mass parameters. The expressions we derive are given in terms of the Pfaffian of skew orthogonal polynomials in the complex plane and their kernel. They are much simpler than the corresponding expressions for symplectic matrix models with real eigenvalues, and we explicitly show how to recover these in the Hermitean limit. This explains the appearance of three different kernels as quaternion matrix elements there in terms of derivatives of a single kernel here.
Response functions after a quantum quench
Marcuzzi, Matteo; Gambassi, Andrea
2014-04-01
The response of physical systems to external perturbations can be used to probe both their equilibrium and nonequilibrium dynamics. While response and correlation functions are related in equilibrium by fluctuation-dissipation theorems, out of equilibrium they provide complementary information on the dynamics. In the past years, a method has been devised to map the quantum dynamics of an isolated extended system after a quench onto a static theory with boundaries in imaginary time; up to now, however, the focus was entirely on symmetrized correlation functions. Here we provide a prescription which, in principle, allows one to retrieve the whole set of relevant dynamical quantities characterizing the evolution, including linear response functions. We illustrate this construction with some relevant examples, showing in the process the emergence of light-cone effects similar to those observed in correlation functions.
Sabour, Mohammad Reza; Moftakhari Anasori Movahed, Saman
2017-02-01
The soil sorption partition coefficient logKoc is an indispensable parameter that can be used in assessing the environmental risk of organic chemicals. In order to predict soil sorption partition coefficient for different and even unknown compounds in a fast and accurate manner, a radial basis function neural network (RBFNN) model was developed. Eight topological descriptors of 800 organic compounds were used as inputs of the model. These 800 organic compounds were chosen from a large and very diverse data set. Generalized Regression Neural Network (GRNN) was utilized as the function in this neural network model due to its capability to adapt very quickly. Hence, it can be used to predict logKoc for new chemicals, as well. Out of total data set, 560 organic compounds were used for training and 240 to test efficiency of the model. The obtained results indicate that the model performance is very well. The correlation coefficients (R2) for training and test sets were 0.995 and 0.933, respectively. The root-mean square errors (RMSE) were 0.2321 for training set and 0.413 for test set. As the results for both training and test set are extremely satisfactory, the proposed neural network model can be employed not only to predict logKoc of known compounds, but also to be adaptive for prediction of this value precisely for new products that enter the market each year. Copyright © 2016 Elsevier Ltd. All rights reserved.
Gupta, Rajesh Kumar; Jeon, Imtak
2015-01-01
We use the techniques of supersymmetric localization to compute the BPS black hole entropy in N=2 supergravity. We focus on the n_v+1 vector multiplets on the black hole near horizon background which is AdS_2 x S^2 space. We find the localizing saddle point of the vector multiplets by solving the localization equations, and compute the exact one loop partition function on the saddle point. Furthermore, we propose the appropriate functional integration measure. Through this measure, the one loop determinant is written in terms of the radius of the physical metric, which depends on the localizing saddle point value of the vector multiplets. The result for the one loop determinant is consistent with the logarithmic corrections to the BPS black hole entropy from vector multiplets.
New enumeration formulas for alternating sign matrices and square ice partition functions
Ayyer, Arvind
2012-01-01
The refined enumeration of alternating sign matrices (ASMs) of given order having prescribed behavior near one or more of their boundary edges has been the subject of extensive study, starting with the Refined Alternating Sign Matrix Conjecture of Mills-Robbins-Rumsey, its proof by Zeilberger, and more recent work on doubly-refined and triply-refined enumeration by several authors. In this paper we extend the previously known results on this problem by deriving explicit enumeration formulas for the "top-left-bottom" (triply-refined) and "top-left-bottom-right" (quadruply-refined) enumerations. The latter case solves the problem of computing the full boundary correlation function for ASMs. The enumeration formulas are proved by deriving new representations, which are of independent interest, for the partition function of the square ice model with domain wall boundary conditions at the "combinatorial point" two pi over three.
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.
Conformal partition functions of critical percolation from D 3 thermodynamic Bethe Ansatz equations
Morin-Duchesne, Alexi; Klümper, Andreas; Pearce, Paul A.
2017-08-01
Using the planar Temperley-Lieb algebra, critical bond percolation on the square lattice can be reformulated as a loop model. In this form, it is incorporated as {{ L}}{{ M}}(2, 3) in the Yang-Baxter integrable family of logarithmic minimal models {{ L}}{{ M}}( p, p\\prime) . We consider this model of percolation in the presence of boundaries and with periodic boundary conditions. Inspired by Kuniba, Sakai and Suzuki, we rewrite the recently obtained infinite Y-system of functional equations. In this way, we obtain nonlinear integral equations in the form of a closed finite set of TBA equations described by a D 3 Dynkin diagram. Following the methods of Klümper and Pearce, we solve the TBA equations for the conformal finite-size corrections. For the ground states of the standard modules on the strip, these agree with the known central charge c = 0 and conformal weights Δ1, s for \\renewcommand≥≥slant} s\\in {{ Z}≥slant 1} with Δr, s=\\big((3r-2s){\\hspace{0pt}}^2-1\\big)/24 . For the periodic case, the finite-size corrections agree with the conformal weights Δ0, s , Δ1, s with \\renewcommand{≥{≥slant} s\\in\\frac{1}{2}{{ Z}≥slant 0} . These are obtained analytically using Rogers dilogarithm identities. We incorporate all finite excitations by formulating empirical selection rules for the patterns of zeros of all the eigenvalues of the standard modules. We thus obtain the conformal partition functions on the cylinder and the modular invariant partition function (MIPF) on the torus. By applying q-binomial and q-Narayana identities, it is shown that our refined finitized characters on the strip agree with those of Pearce, Rasmussen and Zuber. For percolation on the torus, the MIPF is a non-diagonal sesquilinear form in affine u(1) characters given by the u(1) partition function Z2, 3(q)=Z2, 3{Circ}(q) . The u(1) operator content is {{ N}}Δ, \\barΔ=1 for Δ=\\barΔ=-\\frac{1}{24}, \\frac{35}{24} and {{ N}}Δ, \\barΔ=2 for
Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence
Cheon, Sangmo; Kim, Nakwoo
2011-01-01
We test the AdS/CFT correspondence by computing the partition function of some $\\cN=2$ quiver Chern-Simons-matter theories on three-sphere. The M-theory backgrounds are of the Freund-Rubin type with the seven-dimensional internal space given as Sasaki-Einstein manifolds $Q^{1,1,1}$ or $V^{5,2}$. Localization technique reduces the exact path integral to a matrix model, and we study the large-N behavior of the partition function. For simplicity we consider only non-chiral models which have a real-valued partition function. The result is in full agreement with the prediction of the gravity duals, i.e. the free energy is proportional to $N^{3/2}$ and the coefficient matches correctly the volume of $Q^{1,1,1}$ and $V^{5,2}$.
Energy Technology Data Exchange (ETDEWEB)
Rocha, Thiago Lopes [CIMA, Faculty of Science and Technology, University of Algarve, Campus de Gambelas, 8005-139 Faro (Portugal); Gomes, Tânia [CIMA, Faculty of Science and Technology, University of Algarve, Campus de Gambelas, 8005-139 Faro (Portugal); Norwegian Institute for Water Research (NIVA), Gaustadalléen 21, NO-0349 Oslo (Norway); Durigon, Emerson Giuliani [CIMA, Faculty of Science and Technology, University of Algarve, Campus de Gambelas, 8005-139 Faro (Portugal); Bebianno, Maria João, E-mail: mbebian@ualg.pt [CIMA, Faculty of Science and Technology, University of Algarve, Campus de Gambelas, 8005-139 Faro (Portugal)
2016-06-01
The environmental health impact of metal-based nanomaterials is of emerging concern, but their metabolism and detoxification pathways in marine bioindicator species remain unclear. This study investigated the role of subcellular partitioning kinetics, metallothioneins (MTs) response and oxidative damage (lipid peroxidation – LPO) in the marine mussel Mytilus galloprovincialis exposed to CdTe quantum dots (QDs) in comparison with its dissolved counterpart. Mussels were exposed to QDs and dissolved Cd for 21 days at 10 μg Cd L{sup −1} followed by a 50 days depuration. Higher Cd concentrations were detected in fractions containing mitochondria, nucleus and lysosomes, suggesting potential subcellular targets of QDs toxicity in mussel tissues. Tissue specific metabolism patterns were observed in mussels exposed to both Cd forms. Although MT levels were directly associated with Cd in both forms, QDs subcellular partitioning is linked to biologically active metal (BAM), but no increase in LPO occurred, while in the case of dissolved Cd levels are in the biologically detoxified metal (BDM) form, indicating nano-specific effects. Mussel gills showed lower detoxification capability of QDs, while the digestive gland is the major tissue for storage and detoxification of both Cd forms. Both mussel tissues were unable to completely eliminate the Cd accumulated in the QDs form (estimated half-life time > 50 days), highlighting the potential source of Cd and QDs toxicity for human and environmental health. Results indicate tissue specific metabolism patterns and nano-specific effects in marine mussel exposed to QDs. - Highlights: • Subcellular partitioning and MT response are Cd form, tissue and time dependent. • Tissue specific metabolism of Cd-based quantum dots (QDs) in marine mussels. • QDs are slower biologically detoxified when compared to dissolved Cd. • Subcellular partitioning and biomarker responses indicate nano-specific effects. • Subcellular
The star-triangle relation, lens partition function, and hypergeometric sum/integrals
Gahramanov, Ilmar
2016-01-01
The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic sum/integral identity obtained from this limit, has two important physical applications in the context of the so-called gauge/YBE correspondence. For statistical mechanics, this identity is equivalent to a new solution of the star-triangle relation form of the Yang-Baxter equation, that directly generalises the Faddeev-Volkov models to the case of discrete and continuous spin variables. On the gauge theory side, this identity represents the duality of lens ($S_b^3/\\mathbb{Z}_r$) partition functions, for certain three-dimensional $\\mathcal N = 2$ supersymmetric gauge theories.
The star-triangle relation, lens partition function, and hypergeometric sum/integrals
Gahramanov, Ilmar; Kels, Andrew P.
2017-02-01
The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic sum/integral identity obtained from this limit, has two important physical applications in the context of the so-called gauge/YBE correspondence. For statistical mechanics, this identity is equivalent to a new solution of the star-triangle relation form of the Yang-Baxter equation, that directly generalises the Faddeev-Volkov models to the case of discrete and continuous spin variables. On the gauge theory side, this identity represents the duality of lens ({S}_b^3/{Z}_r) partition functions, for certain three-dimensional N=2 supersymmetric gauge theories.
Rigorous Calculation of the Partition Function for the Finite Number of Ising Spins
Peretyatko, Alexey A; Kapitan, Vitaliy Yu; Kirienko, Yury V; Nefedev, Konstantin V; Belokon, Valery I
2011-01-01
The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing Interface and massive parallel instructions. The algorithm can be used for the research of the interacting spin systems in the Ising models of 2D and 3D. The processing power and scalability is analyzed for different parallel and distributed systems. Different methods of the speed up measuring allow obtain the super-linear speeding up for the small number of processes. Program code could be useful also for research by exact method of different Ising spin systems, e.g. system with competition interactions.
The Low Level Modular Invariant Partition Functions of Rank-Two Algebras
Gannon, T; Gannon, Terry
1994-01-01
Using the self-dual lattice method, we make a systematic search for modular invariant partition functions of the affine algebras $g\\*{(1)}$ of $g=A_2$, $A_1+A_1$, $G_2$, and $C_2$. Unlike previous computer searches, this method is necessarily complete. We succeed in finding all physical invariants for $A_2$ at levels $\\le 32$, for $G_2$ at levels $\\le 31$, for $C_2$ at levels $\\le 26$, and for $A_1+A_1$ at levels $k_1=k_2\\le 21$. This work thus completes a recent $A_2$ classification proof, where the levels $k=3,5,6,9,12,15,21$ had been left out. We also compute the dimension of the (Weyl-folded) commutant for these algebras and levels.
Correlation Functions in Open Quantum-Classical Systems
Directory of Open Access Journals (Sweden)
Chang-Yu Hsieh
2013-12-01
Full Text Available Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantum-classical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of the quantum-classical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation and connections to other approximate quantum dynamical methods.
Institute of Scientific and Technical Information of China (English)
QIAN Shang-Wu; GU Zhi-Yu
2001-01-01
Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution PnL for the winding number n and the partition function PL of the entangled system around a ribbon segment chain. We find that when the width of the ribbon segment chain 2a increases,the partition function exponentially decreases, whereas the free energy increases an amount, which is proportional to the square of the width. When the width tends to zero we obtain the same results as those of a single chain with one singular point.
Hydrodynamic transport functions from quantum kinetic theory
Calzetta, E A; Ramsey, S
2000-01-01
Starting from the quantum kinetic field theory [E. Calzetta and B. L. Hu, Phys. Rev. D37, 2878 (1988)] constructed from the closed-time-path (CTP), two-particle-irreducible (2PI) effective action we show how to compute from first principles the shear and bulk viscosity functions in the hydrodynamic-thermodynamic regime. For a real scalar field with $\\lambda \\Phi ^{4}$ self-interaction we need to include 4 loop graphs in the equation of motion. This work provides a microscopic field-theoretical basis to the ``effective kinetic theory'' proposed by Jeon and Yaffe [S. Jeon and L. G. Yaffe, Phys. Rev. D53, 5799 (1996)], while our result for the bulk viscosity reproduces their expression derived from linear response theory and the imaginary-time formalism of thermal field theory. Though unavoidably involved in calculations of this sort, we feel that the approach using fundamental quantum kinetic field theory is conceptually clearer and methodically simpler than the effective kinetic theory approach, as the success...
Function Optimization Based on Quantum Genetic Algorithm
Ying Sun; Hegen Xiong
2014-01-01
Optimization method is important in engineering design and application. Quantum genetic algorithm has the characteristics of good population diversity, rapid convergence and good global search capability and so on. It combines quantum algorithm with genetic algorithm. A novel quantum genetic algorithm is proposed, which is called Variable-boundary-coded Quantum Genetic Algorithm (vbQGA) in which qubit chromosomes are collapsed into variable-boundary-coded chromosomes instead of binary-coded c...
Function Optimization Based on Quantum Genetic Algorithm
Ying Sun; Yuesheng Gu; Hegen Xiong
2013-01-01
Quantum genetic algorithm has the characteristics of good population diversity, rapid convergence and good global search capability and so on.It combines quantum algorithm with genetic algorithm. A novel quantum genetic algorithm is proposed ,which is called variable-boundary-coded quantum genetic algorithm (vbQGA) in which qubit chromosomes are collapsed into variableboundary- coded chromosomes instead of binary-coded chromosomes. Therefore much shorter chromosome strings can be gained.The m...
Niklas, Karl J
2006-01-01
Biomass-partitioning patterns influence the functioning of aquatic and terrestrial vegetation at all levels, ranging from individual growth and reproduction to the flow of mass and energy through entire communities. For this reason, leaf, stem and root dry biomass-partitioning patterns across taxonomically and ecologically diverse seed plants (spermatophytes) have been intensively investigated, both empirically and theoretically. By contrast, phyletically disparate plants (e.g. green and brown algal macrophytes, mosses and pteridophytes) have not been examined to determine whether the partitioning of their body parts into 'leaf', 'stem' and 'root' analogs accords with that of spermatophytes. In this review, the biomass-partitioning patterns of siphonous and brown algal macrophytes, mosses and pteridophytes were compared allometrically with those of spermatophytes and were shown to be largely in statistical accordance (thus lending support to the hypothesis that a single scaling relationship exists across eukaryotic photoautotrophs). This concordance is argued to support the hypothesis of functional equivalence across analogous, but developmentally different, body parts, a feature that permits the use of simpler biological model systems with which to derive analytical explanations for the biomass-partitioning patterns reported for more complex seed plants.
Performance of the density matrix functional theory in the quantum theory of atoms in molecules.
García-Revilla, Marco; Francisco, E; Costales, A; Martín Pendás, A
2012-02-02
The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.
Fixing the quantum three-point function
Energy Technology Data Exchange (ETDEWEB)
Jiang, Yunfeng; Kostov, Ivan [Institut de Physique Théorique, DSM, CEA, URA2306 CNRS,Saclay, F-91191 Gif-sur-Yvette (France); Loebbert, Florian [School of Natural Sciences, Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540 (United States); Niels Bohr International Academy & Discovery Center, Niels Bohr Institute,Blegdamsvej 17, 2100 Copenhagen (Denmark); Serban, Didina [Institut de Physique Théorique, DSM, CEA, URA2306 CNRS,Saclay, F-91191 Gif-sur-Yvette (France)
2014-04-03
We propose a new method for the computation of quantum three-point functions for operators in su(2) sectors of N=4 super Yang-Mills theory. The method is based on the existence of a unitary transformation relating inhomogeneous and long-range spin chains. This transformation can be traced back to a combination of boost operators and an inhomogeneous version of Baxter’s corner transfer matrix. We reproduce the existing results for the one-loop structure constants in a simplified form and indicate how to use the method at higher loop orders. Then we evaluate the one-loop structure constants in the quasiclassical limit and compare them with the recent strong coupling computation.
Transfer functions for solid solution partitioning of cadmium for Australian soils
Vries, de W.; Mc Laughlin, M.J.; Groenenberg, J.E.
2011-01-01
To assess transport and ecotoxicological risks of metals, such as cadmium (Cd) in soils, models are needed for partitioning and speciation. We derived regression-based “partition-relations” based on adsorption and desorption experiments for main Australian soil types. First, batch adsorption experim
On quantum mechanical phase-space wave functions
DEFF Research Database (Denmark)
Wlodarz, Joachim J.
1994-01-01
An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...
Mutygullina, A. A.; Khamadeev, M. A.; Blum, D. O.; Shirdelhavar, A. H.
2017-06-01
Influence of quantum fluctuations in a system consisting of a quantum dot and the reservoir of acoustic phonons on processes in which the quantum dot takes part is investigated. Under some conditions this influence is shown to be very strong. We find a contribution from the quantum fluctuations to the self-energy function of the exciton coupled to the quantum dot.
Do, Hainam; Wheatley, Richard J.
2016-08-01
A robust and model free Monte Carlo simulation method is proposed to address the challenge in computing the classical density of states and partition function of solids. Starting from the minimum configurational energy, the algorithm partitions the entire energy range in the increasing energy direction ("upward") into subdivisions whose integrated density of states is known. When combined with the density of states computed from the "downward" energy partitioning approach [H. Do, J. D. Hirst, and R. J. Wheatley, J. Chem. Phys. 135, 174105 (2011)], the equilibrium thermodynamic properties can be evaluated at any temperature and in any phase. The method is illustrated in the context of the Lennard-Jones system and can readily be extended to other molecular systems and clusters for which the structures are known.
Goldstone bosons in a finite volume the partition function to three loops
Bietenholz, W
1994-01-01
A system of Goldstone bosons - stemming from a symmetry breaking $O(N) \\to O(N-1)$ - in a finite volume at finite temperature is considered. In the framework of dimensional regularization, the partition function is calculated to 3 loops for 3 and 4 dimensions, where Polyakov's measure for the functional integration is applied. Although the underlying theory is the non-linear $\\sigma $ model, the 3 loop result turns out to be renormalizable in the sense that all the singularities can be absorbed by the couplings occuring so far. In finite volume, this property is highly non trivial and confirms the method for the measure. We also show that the result coincides with the one obtained using the Faddeev- Popov measure. This is also true for the maximal generalization of Polyakov's measure: none of the additional invariant terms that can be added contributes to the dimensionally regularized system. Our phenomenological Lagrangian describes e.g. 2 flavor chiral QCD as well as the classical Heisenberg model, but ther...
Exact partition functions for the $\\Omega$-deformed $\\mathcal N=2^{*}$ $SU(2)$ gauge theory
Beccaria, Matteo
2016-01-01
We study the low energy effective action of the $\\Omega$-deformed $\\mathcal N =2^{*}$ $SU(2) $ gauge theory. It depends on the deformation parameters $\\epsilon_{1},\\epsilon_{2}$, the scalar field expectation value $a$, and the hypermultiplet mass $m$. We explore the plane $(\\frac{m}{\\epsilon_{1}}, \\frac{\\epsilon_{2}}{\\epsilon_{1}})$ looking for special features in the multi-instanton contributions to the prepotential, motivated by what happens in the Nekrasov-Shatashvili limit $\\epsilon_{2}\\to 0$. We propose a simple condition on the structure of poles of the $k$-instanton prepotential and show that it is admissible at a finite set of points in the above plane. At these special points, the prepotential has poles at fixed positions independent on the instanton number. Besides and remarkably, both the instanton partition function and the full prepotential, including the perturbative contribution, may be given in closed form as functions of the scalar expectation value $a$ and the modular parameter $q$ appearing...
Pattern-Driven Architectural Partitioning. Balancing Functional and Non-functional Requirements
Harrison, Neil; Avgeriou, Paris
2007-01-01
One of the vexing challenges of software architecture is the problem of satisfying the functional specifications of the system to be created while at the same time meeting its non-functional needs. In this work we focus on the early stages of the software architecture process, when initial
Chang, Shu-Chiuan; Shrock, Robert
2001-07-01
The q-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width Ly and arbitrary length Lx has the form Z(G,q,v)=∑ j=1N Z,G,λ c Z,G,j(λ Z,G,j) L x, where v is a temperature-dependent variable. The special case of the zero-temperature antiferromagnet ( v=-1) is the chromatic polynomial P( G, q). Using coloring and transfer matrix methods, we give general formulas for C X,G=∑ j=1N X,G,λ c X,G,j for X= Z, P on cyclic and Möbius strip graphs of the square and triangular lattice. Combining these with a general expression for the (unique) coefficient cZ, G, j of degree d in q: c (d)=U 2d( q/2) , where Un( x) is the Chebyshev polynomial of the second kind, we determine the number of λZ, G, j's with coefficient c( d) in Z( G, q, v) for these cyclic strips of width Ly to be n Z(L y,d)=(2d+1)(L y+d+1) -1{2L y}/{L y-d } for 0⩽ d⩽ Ly and zero otherwise. For both cyclic and Möbius strips of these lattices, the total number of distinct eigenvalues λZ, G, j is calculated to be N Z,L y,λ = {2L y}/{L y}. Results are also presented for the analogous numbers nP( Ly, d) and NP, Ly, λ for P( G, q). We find that nP( Ly,0)= nP( Ly-1,1)= MLy-1 (Motzkin number), nZ( Ly,0)= CLy (the Catalan number), and give an exact expression for NP, Ly, λ. Our results for NZ, Ly, λ and NP, Ly, λ apply for both the cyclic and Möbius strips of both the square and triangular lattices; we also point out the interesting relations NZ, Ly, λ=2 NDA, tri, Ly and NP, Ly, λ=2 NDA, sq, Ly, where NDA, Λ, n denotes the number of directed lattice animals on the lattice Λ. We find the asymptotic growths NZ, Ly, λ∼ Ly-1/24 Ly and NP, Ly, λ∼ Ly-1/23 Ly as Ly→∞. Some general geometric identities for Potts model partition functions are also presented.
2008-01-01
The exact partition function of the two-dimensional nearest neighbour Ising model pertaining to square lattices is derived for N sites in the case of a non-vanishing magnetic field.When the magnetic field is zero,the partition functions estimated from the present analysis are identical with those arising from Onsager's exact solution.
Consistent histories, quantum truth functionals, and hidden variables
Griffiths, Robert B.
2000-01-01
A central principle of consistent histories quantum theory, the requirement that quantum descriptions be based upon a single framework (or family), is employed to show that there is no conflict between consistent histories and a no-hidden-variables theorem of Bell, and Kochen and Specker, contrary to a recent claim by Bassi and Ghirardi. The argument makes use of `truth functionals' defined on a Boolean algebra of classical or quantum properties.
Consistent histories, quantum truth functionals, and hidden variables
Griffiths, R B
1999-01-01
A central principle of consistent histories quantum theory, the requirement that quantum descriptions be based upon a single framework (or family), is employed to show that there is no conflict between consistent histories and a no-hidden-variables theorem of Bell, and Kochen and Specker, contrary to a recent claim by Bassi and Ghirardi. The argument makes use of ``truth functionals'' defined on a Boolean algebra of classical or quantum properties.
Biological diversity can be divided into: alpha (α, local), beta (β, difference in assemblage composition among locals), and gamma (γ, total diversity). We assessed the partitioning of taxonomic diversity of Ephemeroptera, Plecoptera and Trichoptera (EPT) and of ...
Kamarchik, Eugene; Jasper, Ahren W.
2013-05-01
An algorithm is presented for calculating fully anharmonic vibrational state counts, state densities, and partition functions for molecules using Monte Carlo integration of classical phase space. The algorithm includes numerical evaluations of the elements of the Jacobian and is general enough to allow for sampling in arbitrary curvilinear or rectilinear coordinate systems. Invariance to the choice of coordinate system is demonstrated for vibrational state densities of methane, where we find comparable sampling efficiency when using curvilinear z-matrix and rectilinear Cartesian normal mode coordinates. In agreement with past work, we find that anharmonicity increases the vibrational state density of methane by a factor of ˜2 at its dissociation threshold. For the vinyl radical, we find a significant (˜10×) improvement in sampling efficiency when using curvilinear z-matrix coordinates relative to Cartesian normal mode coordinates. We attribute this improved efficiency, in part, to a more natural curvilinear coordinate description of the double well associated with the H2C-C-H wagging motion. The anharmonicity correction for the vinyl radical state density is ˜1.4 at its dissociation threshold. Finally, we demonstrate that with trivial parallelizations of the Monte Carlo step, tractable calculations can be made for the vinyl radical using direct ab initio potential energy surface evaluations and a composite QCISD(T)/MP2 method.
Exact partition functions for deformed N=2 theories with N{sub f}=4 flavours
Energy Technology Data Exchange (ETDEWEB)
Beccaria, Matteo; Fachechi, Alberto; Macorini, Guido; Martina, Luigi [Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento,Via Arnesano, 73100 Lecce (Italy); INFN, Via Arnesano, 73100 Lecce (Italy)
2016-12-07
We consider the Ω-deformed N=2SU(2) gauge theory in four dimensions with N{sub f}=4 massive fundamental hypermultiplets. The low energy effective action depends on the deformation parameters ε{sub 1},ε{sub 2}, the scalar field expectation value a, and the hypermultiplet masses m=(m{sub 1},m{sub 2},m{sub 3},m{sub 4}). Motivated by recent findings in the N=2{sup ∗} theory, we explore the theories that are characterized by special fixed ratios ε{sub 2}/ε{sub 1} and m/ε{sub 1} and propose a simple condition on the structure of the multi-instanton contributions to the prepotential determining the effective action. This condition determines a finite set Π{sub N} of special points such that the prepotential has N poles at fixed positions independent on the instanton number. In analogy with what happens in the N=2{sup ∗} gauge theory, the full prepotential of the Π{sub N} theories may be given in closed form as an explicit function of a and the modular parameter q appearing in special combinations of Eisenstein series and Jacobi theta functions with well defined modular properties. The resulting finite pole partition functions are related by AGT correspondence to special 4-point spherical conformal blocks of the Virasoro algebra. We examine in full details special cases where the closed expression of the block is known and confirms our Ansatz. We systematically study the special features of Zamolodchikov’s recursion for the Π{sub N} conformal blocks. As a result, we provide a novel effective recursion relation that can be exactly solved and allows to prove the conjectured closed expressions analytically in the case of the Π{sub 1} and Π{sub 2} conformal blocks.
Exact partition functions for deformed N=2 theories with N_f=4 flavours
Beccaria, Matteo; Fachechi, Alberto; Macorini, Guido; Martina, Luigi
2016-12-01
We consider the Ω-deformed N=2 SU(2) gauge theory in four dimensions with N f = 4 massive fundamental hypermultiplets. The low energy effective action depends on the deformation parameters ɛ 1 , ɛ 2, the scalar field expectation value a, and the hypermultiplet masses m = ( m 1 , m 2 , m 3 , m 4). Motivated by recent findings in the N={2}^{*} theory, we explore the theories that are characterized by special fixed ratios ɛ 2 /ɛ 1 and m /ɛ 1 and propose a simple condition on the structure of the multi-instanton contributions to the prepotential determining the effective action. This condition determines a finite set Π N of special points such that the prepotential has N poles at fixed positions independent on the instanton number. In analogy with what happens in the N={2}^{*} gauge theory, the full prepotential of the Π N theories may be given in closed form as an explicit function of a and the modular parameter q appearing in special combinations of Eisenstein series and Jacobi theta functions with well defined modular properties. The resulting finite pole partition functions are related by AGT correspondence to special 4-point spherical conformal blocks of the Virasoro algebra. We examine in full details special cases where the closed expression of the block is known and confirms our Ansatz. We systematically study the special features of Zamolodchikov's recursion for the Π N conformal blocks. As a result, we provide a novel effective recursion relation that can be exactly solved and allows to prove the conjectured closed expressions analytically in the case of the Π1 and Π2 conformal blocks.
Functional evolution of quantum cylindrical waves
Cho, D H J; Cho, Demian H.J.; Varadarajan, Madhavan
2006-01-01
Kucha{\\v{r}} showed that the quantum dynamics of (1 polarization) cylindrical wave solutions to vacuum general relativity is determined by that of a free axially-symmetric scalar field along arbitrary axially-symmetric foliations of a fixed flat 2+1 dimensional spacetime. We investigate if such a dynamics can be defined {\\em unitarily} within the standard Fock space quantization of the scalar field. Evolution between two arbitrary slices of an arbitrary foliation of the flat spacetime can be built out of a restricted class of evolutions (and their inverses). The restricted evolution is from an initial flat slice to an arbitrary (in general, curved) slice of the flat spacetime and can be decomposed into (i) `time' evolution in which the spatial Minkowskian coordinates serve as spatial coordinates on the initial and the final slice, followed by (ii) the action of a spatial diffeomorphism of the final slice on the data obtained from (i). We show that although the functional evolution of (i) is unitarily implemen...
Functional renormalization group methods in quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Braun, J.
2006-12-18
We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)
The wave function essays on the metaphysics of quantum mechanics
Albert, David Z
2013-01-01
This is a new volume of original essays on the metaphysics of quantum mechanics. The essays address questions such as: What fundamental metaphysics is best motivated by quantum mechanics? What is the ontological status of the wave function? Does quantum mechanics support the existence of any other fundamental entities, e.g. particles? What is the nature of the fundamental space (or space-time manifold) of quantum mechanics? What is the relationship between the fundamental ontology of quantum mechanics and ordinary, macroscopic objects like tables, chairs, and persons? This collection includes a comprehensive introduction with a history of quantum mechanics and the debate over its metaphysical interpretation focusing especially on the main realist alternatives.
Directory of Open Access Journals (Sweden)
GUILHERME MALLMANN
2014-12-01
Full Text Available Subduction zone or arc magmas are known to display a characteristic depletion of High Field Strength Elements (HFSE relative to other similarly incompatible elements, which can be attributed to the presence of the accessory mineral rutile (TiO2 in the residual slab. Here we show that the partitioning behavior of vanadium between rutile and silicate melt varies from incompatible (∼0.1 to compatible (∼18 as a function of oxygen fugacity. We also confirm that the HFSE are compatible in rutile, with D(Ta> D(Nb>> (D(Hf>/∼ D(Zr, but that the level of compatibility is strongly dependent on melt composition, with partition coefficients increasing about one order of magnitude with increasing melt polymerization (or decreasing basicity. Our partitioning results also indicate that residual rutile may fractionate U from Th due to the contrasting (over 2 orders of magnitude partitioning between these two elements. We confirm that, in addition to the HFSE, Cr, Cu, Zn and W are compatible in rutile at all oxygen fugacity conditions.
Tempel, David G; Aspuru-Guzik, Alán
2012-01-01
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.
Quantum groups and functional relations for lower rank
Nirov, Kh. S.; Razumov, A. V.
2017-02-01
A detailed construction of the universal integrability objects related to the integrable systems associated with the quantum loop algebra Uq(L(sl2)) is given. The full proof of the functional relations in the form independent of the representation of the quantum loop algebra on the quantum space is presented. The case of the general gradation and general twisting is treated. The specialization of the universal functional relations to the case when the quantum space is the state space of a discrete spin chain is described. This is a digression of the corresponding consideration for the case of the quantum loop algebra Uq(L(sl3)) with an extension to the higher spin case.
Mielke, Steven L; Truhlar, Donald G
2016-01-21
Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.
Estimates on Functional Integrals of Quantum Mechanics and Non-relativistic Quantum Field Theory
Bley, Gonzalo A.; Thomas, Lawrence E.
2017-01-01
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form {E[{exp}(A_T)]} , the (effective) action {A_T} being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schrödinger operator with {1/|x|^2} potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
Carter, Stuart; Sharma, Amit R; Bowman, Joel M
2012-10-21
Large-scale, rovibrational variational calculations are performed for ethylene, using the potential energy surface published by Avila and Carrington [J. Chem. Phys. 135, 064101 (2011)]. Energies for J = 0 are in very good agreement with their benchmark results. Corresponding energies for J = 1 and J = 2 are also given. Calculations with a slightly reduced basis permit energies to J = 40, allowing a reliable determination of the partition function at 296 K. Using a new ab initio dipole moment surface, reported here, the infrared spectra of five dipole-allowed fundamentals are calculated. Both the partition function and infrared spectra are shown to be in excellent agreement with those in the experimental HITRAN database, with the exception of one band, which we believe is partially mis-assigned in HITRAN.
Effect of partition board color on mood and autonomic nervous function.
Sakuragi, Sokichi; Sugiyama, Yoshiki
2011-12-01
The purpose of this study was to evaluate the effects of the presence or absence (control) of a partition board and its color (red, yellow, blue) on subjective mood ratings and changes in autonomic nervous system indicators induced by a video game task. The increase in the mean Profile of Mood States (POMS) Fatigue score and mean Oppressive feeling rating after the task was lowest with the blue partition board. Multiple-regression analysis identified oppressive feeling and error scores on the second half of the task as statistically significant contributors to Fatigue. While explanatory variables were limited to the physiological indices, multiple-regression analysis identified a significant contribution of autonomic reactivity (assessed by heart rate variability) to Fatigue. These results suggest that a blue partition board would reduce task-induced subjective fatigue, in part by lowering the oppressive feeling of being enclosed during the task, possibly by increasing autonomic reactivity.
Ruelle-Lanford functions for quantum spin systems
Ogata, Yoshiko
2010-01-01
We prove a large deviation principle for the expectation of macroscopic observables in quantum (and classical) Gibbs states. Our proof is based on Ruelle-Lanford functions and direct subadditivity arguments, as in the classical case, instead of relying on G\\"artner-Ellis theorem, and cluster expansion or transfer operators as done in the quantum case. In this approach we recover, expand, and unify quantum (and classical) large deviation results for lattice Gibbs states. In the companion paper \\cite{OR} we discuss the characterization of rate functions in terms of relative entropies.
2013-01-01
The Tibetan Plateau (TP) is predicted to experience increases in air temperature, increases in snowfall, and decreases in monsoon rains; however, there is currently a paucity of data that examine the ecological responses to such climate changes. In this study, we examined the effects of increased air temperature and snowfall on: 1) water use partitioning by different plant functional groups, and 2) ecosystem CO2 fluxes throughout the growing season. At the individual plant scale, we used stab...
Shrock, Robert; Xu, Yan
2010-12-01
We present exact results on the partition function of the q-state Potts model on various families of graphs G in a generalized external magnetic field that favors or disfavors spin values in a subset I s ={1,…, s} of the total set of possible spin values, Z( G, q, s, v, w), where v and w are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial Ph( G, q, s, w) that counts the number of colorings of the vertices of G subject to the condition that colors of adjacent vertices are different, with a weighting w that favors or disfavors colors in the interval I s . We derive powerful new upper and lower bounds on Z( G, q, s, v, w) for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for Z( G, q, s, v, w) on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.
Odabasi, Mustafa; Cetin, Eylem; Sofuoglu, Aysun
Octanol-air partition coefficients ( KOA) for 14 polycyclic aromatic hydrocarbons (PAHs) were determined as a function of temperature using the gas chromatographic retention time method. log KOA values at 25° ranged over six orders of magnitude, between 6.34 (acenaphthylene) and 12.59 (dibenz[ a,h]anthracene). The determined KOA values were within factor of 0.7 (dibenz[ a,h]anthracene) to 15.1 (benz[ a]anthracene) of values calculated as the ratio of octanol-water partition coefficient to dimensionless Henry's law constant. Supercooled liquid vapor pressures ( PL) of 13 PAHs were also determined using the gas chromatographic retention time technique. Activity coefficients in octanol calculated using KOA and PL ranged between 3.2 and 6.2 indicating near-ideal solution behavior. Atmospheric concentrations measured in this study in Izmir, Turkey were used to investigate the partitioning of PAHs between particle and gas-phases. Experimental gas-particle partition coefficients ( Kp) were compared to the predictions of KOA absorption and KSA (soot-air partition coefficient) models. Octanol-based absorptive partitioning model predicted lower partition coefficients especially for relatively volatile PAHs. Ratios of measured/modeled partition coefficients ranged between 1.1 and 15.5 (4.5±6.0, average±SD) for KOA model. KSA model predictions were relatively better and measured to modeled ratios ranged between 0.6 and 5.6 (2.3±2.7, average±SD).
On partitions avoiding right crossings
Yan, Sherry H F
2011-01-01
Recently, Chen et al. derived the generating function for partitions avoiding right nestings and posed the problem of finding the generating function for partitions avoiding right crossings. In this paper, we derive the generating function for partitions avoiding right crossings via an intermediate structure of partial matchings avoiding 2-right crossings and right nestings. We show that there is a bijection between partial matchings avoiding 2-right crossing and right nestings and partitions avoiding right crossings.
Institute of Scientific and Technical Information of China (English)
Serena Morigi; Fiorella Sgallari
2009-01-01
This paper introduces the use of partition of unity method for the develop-ment of a high order finite volume discretization scheme on unstructured grids for solv-ing diffusion models based on partial differential equations. The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions. The methodology proposed is applied to the noise removal prob-lem in functional surfaces and images. Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.
How many functions can be distinguished with k quantum queries?
Farhi, E; Gutmann, S; Sipser, M
1999-01-01
Suppose an oracle is known to hold one of a given set of D two-valued functions. To successfully identify which function the oracle holds with k classical queries, it must be the case that D is at most 2^k. In this paper we derive a bound for how many functions can be distinguished with k quantum queries.
On Quantum Field Theories in Operator and Functional Integral Formalisms
Teleki, A; Noga, Milan; Teleki, Aba
2006-01-01
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional integral in quantum field theory cannot be regarded as a Newton-Lebesgue integral but rather as a formal object to which one associates distinct numerical values for different processes of its integration. By choosing an appropriate method for the integration of a given functional integral, one can select a single representation out of infinitely many inequivalent representations for an operator whose trace is expressed by the corresponding functional integral. These properties are demonstrated with two exactly solvable examples.
Wigner function and the probability representation of quantum states
Directory of Open Access Journals (Sweden)
Man’ko Margarita A.
2014-01-01
Full Text Available The relation of theWigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics with the integral Radon transform of the Wigner quasidistribution is discussed. The Wigner–Moyal equation for the Wigner function is presented in the form of kinetic equation for the tomographic probability distribution both in quantum mechanics and in the classical limit of the Liouville equation. The calculation of moments of physical observables in terms of integrals with the state tomographic probability distributions is constructed having a standard form of averaging in the probability theory. New uncertainty relations for the position and momentum are written in terms of optical tomograms suitable for directexperimental check. Some recent experiments on checking the uncertainty relations including the entropic uncertainty relations are discussed.
Anatomy of quantum critical wave functions in dissipative impurity problems
Blunden-Codd, Zach; Bera, Soumya; Bruognolo, Benedikt; Linden, Nils-Oliver; Chin, Alex W.; von Delft, Jan; Nazir, Ahsan; Florens, Serge
2017-02-01
Quantum phase transitions reflect singular changes taking place in a many-body ground state; however, computing and analyzing large-scale critical wave functions constitutes a formidable challenge. Physical insights into the sub-Ohmic spin-boson model are provided by the coherent-state expansion (CSE), which represents the wave function by a linear combination of classically displaced configurations. We find that the distribution of low-energy displacements displays an emergent symmetry in the absence of spontaneous symmetry breaking while experiencing strong fluctuations of the order parameter near the quantum critical point. Quantum criticality provides two strong fingerprints in critical low-energy modes: an algebraic decay of the average displacement and a constant universal average squeezing amplitude. These observations, confirmed by extensive variational matrix-product-state (VMPS) simulations and field theory arguments, offer precious clues into the microscopics of critical many-body states in quantum impurity models.
Ding, J; Ding, Jintai; Feigin, Boris
1996-01-01
We construct a commutative current operator $\\bar x^+(z)$ inside $U_q(\\hat{\\frak sl}(2))$. With this operator and the condition of quantum integrability on the quantum current of $U_q(\\hat{\\frak sl}(2))$, we derive the quantization of the semi-infinite construction of integrable modules of The quantization of the functional models for $\\hat{\\frak sl}(2)$ are also given.
On Partition of Unities Generated by Entire Functions and Gabor Frames in L2(Rd) and ℓ2(Zd)
DEFF Research Database (Denmark)
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2016-01-01
We characterize the entire functions P of d variables, d≥2, for which the Zd-translates of Pχ[0,N]d satisfy the partition of unity for some N∈N. In contrast to the one-dimensional case, these entire functions are not necessarily periodic. In the case where P is a trigonometric polynomial, we char...... of matrix-generated Gabor frames in L2(Rd), with small support and high smoothness. By sampling this yields dual pairs of finite Gabor frames in ℓ2(Zd)....
Marine microalgae growth and carbon partitioning as a function of nutrient availability.
Fernandes, Tomásia; Fernandes, Igor; Andrade, Carlos A P; Cordeiro, Nereida
2016-08-01
To understand in which way the structural differences of three marine microalgae (Nannochloropsis gaditana, Rhodomonas marina and Isochrysis sp.) affect their carbon partitioning, growth and applicability; a stoichiometric imbalance was imposed by steady carbon and other nutrients variation. Towards high nutrients concentrations/low carbon availability a decrease of 12-51% in C/N microalgae ratio was observed and maximum cell densities were achieved. Moreover, linear correlation between the nutrient input and microalgae protein content were observed. The macromolecular ratios pointed that carbohydrate was the main contributor for the C/N decrement. Although lipid content in R. marina remained constant throughout the experiment, a rise of 37-107% in N. gaditana and Isochrysis sp. was verified. Lipid fractions revealed high percentages of glycolipids in all microalgae (57-73% of total lipids). The present study shows an easy way to understand and modulate microalgae carbon partitioning relying on the field of application.
Operators versus functions: from quantum dynamical semigroups to tomographic semigroups
Aniello, Paolo
2013-11-01
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the so-called generalized Wigner functions or (group-covariant) tomograms, obtained by means of group-theoretical methods. A typical problem arising in this context is to express the evolution of a quantum system in terms of tomograms. In the case of a (suitable) open quantum system, the dynamics can be described by means of a quantum dynamical semigroup 'in disguise', namely, by a semigroup of operators acting on tomograms rather than on density operators. We focus on a special class of quantum dynamical semigroups, the twirling semigroups, that have interesting applications, e.g., in quantum information science. The 'disguised counterparts' of the twirling semigroups, i.e., the corresponding semigroups acting on tomograms, form a class of semigroups of operators that we call tomographic semigroups. We show that the twirling semigroups and the tomographic semigroups can be encompassed in a unique theoretical framework, a class of semigroups of operators including also the probability semigroups of classical probability theory, so achieving a deeper insight into both the mathematical and the physical aspects of the problem.
Instantons on ALE spaces and orbifold partitions
Dijkgraaf, Robbert; Sułkowski, Piotr
2008-03-01
We consider Script N = 4 theories on ALE spaces of Ak-1 type. As is well known, their partition functions coincide with Ak-1 affine characters. We show that these partition functions are equal to the generating functions of some peculiar classes of partitions which we introduce under the name 'orbifold partitions'. These orbifold partitions turn out to be related to the generalized Frobenius partitions introduced by G. E. Andrews some years ago. We relate the orbifold partitions to the blended partitions and interpret explicitly in terms of a free fermion system.
Instantons on ALE spaces and orbifold partitions
Dijkgraaf, Robbert
2008-01-01
We consider N=4 theories on ALE spaces of $A_{k-1}$ type. As is well known, their partition functions coincide with $A_{k-1}$ affine characters. We show that these partition functions are equal to the generating functions of some peculiar classes of partitions which we introduce under the name 'orbifold partitions'. These orbifold partitions turn out to be related to the generalized Frobenius partitions introduced by G. E. Andrews some years ago. We relate the orbifold partitions to the blended partitions and interpret explicitly in terms of a free fermion system.
Directory of Open Access Journals (Sweden)
Fabio Burderi
2007-05-01
Full Text Available Motivated by the study of decipherability conditions for codes weaker than Unique Decipherability (UD, we introduce the notion of coding partition. Such a notion generalizes that of UD code and, for codes that are not UD, allows to recover the ``unique decipherability" at the level of the classes of the partition. By tacking into account the natural order between the partitions, we define the characteristic partition of a code X as the finest coding partition of X. This leads to introduce the canonical decomposition of a code in at most one unambiguouscomponent and other (if any totally ambiguouscomponents. In the case the code is finite, we give an algorithm for computing its canonical partition. This, in particular, allows to decide whether a given partition of a finite code X is a coding partition. This last problem is then approached in the case the code is a rational set. We prove its decidability under the hypothesis that the partition contains a finite number of classes and each class is a rational set. Moreover we conjecture that the canonical partition satisfies such a hypothesis. Finally we consider also some relationships between coding partitions and varieties of codes.
Classical-Quantum Correspondence and Functional Relations for Painleve Equations
Zabrodin, A
2012-01-01
In the light of the Quantum Painleve-Calogero Correspondence established in our previous papers [1,2], we investigate the inverse problem. We imply that this type of the correspondence (Classical-Quantum Correspondence) holds true and find out what kind of potentials arise from the compatibility conditions of the related linear problems. The latter conditions are written as functional equations for the potentials depending on a choice of a single function - the left-upper element of the Lax connection. The conditions of the Correspondence impose restrictions on this function. In particular, it satisfies the heat equation. It is shown that all natural choices of this function (rational, hyperbolic and elliptic) reproduce exactly the Painleve list of equations. In this sense the Classical-Quantum Correspondence can be regarded as an alternative definition of the Painleve equations.
Rocha, Thiago Lopes; Gomes, Tânia; Durigon, Emerson Giuliani; Bebianno, Maria João
2016-06-01
The environmental health impact of metal-based nanomaterials is of emerging concern, but their metabolism and detoxification pathways in marine bioindicator species remain unclear. This study investigated the role of subcellular partitioning kinetics, metallothioneins (MTs) response and oxidative damage (lipid peroxidation - LPO) in the marine mussel Mytilus galloprovincialis exposed to CdTe quantum dots (QDs) in comparison with its dissolved counterpart. Mussels were exposed to QDs and dissolved Cd for 21 days at 10 μg Cd L(-1) followed by a 50 days depuration. Higher Cd concentrations were detected in fractions containing mitochondria, nucleus and lysosomes, suggesting potential subcellular targets of QDs toxicity in mussel tissues. Tissue specific metabolism patterns were observed in mussels exposed to both Cd forms. Although MT levels were directly associated with Cd in both forms, QDs subcellular partitioning is linked to biologically active metal (BAM), but no increase in LPO occurred, while in the case of dissolved Cd levels are in the biologically detoxified metal (BDM) form, indicating nano-specific effects. Mussel gills showed lower detoxification capability of QDs, while the digestive gland is the major tissue for storage and detoxification of both Cd forms. Both mussel tissues were unable to completely eliminate the Cd accumulated in the QDs form (estimated half-life time>50 days), highlighting the potential source of Cd and QDs toxicity for human and environmental health. Results indicate tissue specific metabolism patterns and nano-specific effects in marine mussel exposed to QDs.
Green's functions in perturbative quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Upadhyay, Sudhaker [Indian Institute of Technology Kanpur, Department of Physics, Kanpur (India); Mandal, Bhabani Prasad [Banaras Hindu University, Department of Physics, Varanasi (India)
2015-07-15
We show that the Green's functions in a non-linear gauge in the theory of perturbative quantum gravity is expressed as a series in terms of those in linear gauges. This formulation also holds for operator Green's functions. We further derive the explicit relation between the Green's functions in the theory of perturbative quantum gravity in a pair of arbitrary gauges. This process involves some sort of modified FFBRST transformations which are derivable from infinitesimal field-dependent BRST transformations. (orig.)
Green’s functions in perturbative quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Upadhyay, Sudhaker, E-mail: sudhakerupadhyay@gmail.com [Department of Physics, Indian Institute of Technology Kanpur, 208016, Kanpur (India); Mandal, Bhabani Prasad, E-mail: bhabani.mandal@gmail.com [Department of Physics, Banaras Hindu University, 221005, Varanasi (India)
2015-07-17
We show that the Green’s functions in a non-linear gauge in the theory of perturbative quantum gravity is expressed as a series in terms of those in linear gauges. This formulation also holds for operator Green’s functions. We further derive the explicit relation between the Green’s functions in the theory of perturbative quantum gravity in a pair of arbitrary gauges. This process involves some sort of modified FFBRST transformations which are derivable from infinitesimal field-dependent BRST transformations.
Garvan, F G
2010-01-01
New congruences are found for Andrews' smallest parts partition function spt(n). The generating function for spt(n) is related to the holomorphic part alpha(24z) of a certain weak Maass form M(z) of weight 3/2. We show that a normalized form of the generating function for spt(n) is an eigenform modulo 72 for the Hecke operators T(p^2) for primes p > 3, and an eigenform modulo t for t = 5, 7 or 13 provided that (t, 6p) = 1. The result for the modulus 3 was observed earlier by the author and considered by Ono and Folsom. Similar congruences for higher powers of t (namely 5^6, 7^4 and 13^2) occur for the coefficients of the function alpha(z). Analogous results for the partition function were found by Atkin in 1966. Our results depend on the recent result of Ono that M[p](z/24) is a weakly holomorphic modular form of weight 3/2 for the full modular group where M[p](z) = M(z)|T(p^2) - chi(p)(1 + p)M(z).
Cavallo, A; Cosenza, F; De Cesare, L
2008-05-01
We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multiplier representation, the q -spectral properties and the methods for a direct calculation of the two-time q Green's functions and the related q -spectral density ( q measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive (q=1) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the q -induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the q -induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the q grand-partition function.
Efficient wave-function matching approach for quantum transport calculations
DEFF Research Database (Denmark)
Sørensen, Hans Henrik Brandenborg; Hansen, Per Christian; Petersen, Dan Erik;
2009-01-01
The wave-function matching (WFM) technique has recently been developed for the calculation of electronic transport in quantum two-probe systems. In terms of efficiency it is comparable to the widely used Green's function approach. The WFM formalism presented so far requires the evaluation of all ...
Energy Technology Data Exchange (ETDEWEB)
Salini, K. [School of Physics, IISER TVM, CET Campus, Thiruvananthapuram, Kerala 695 016 (India); Prabhu, R.; Sen, Aditi [Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019 (India); Sen, Ujjwal, E-mail: ujjwal@hri.res.in [Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019 (India)
2014-09-15
Monogamy of quantum correlation measures puts restrictions on the sharability of quantum correlations in multiparty quantum states. Multiparty quantum states can satisfy or violate monogamy relations with respect to given quantum correlations. We show that all multiparty quantum states can be made monogamous with respect to all measures. More precisely, given any quantum correlation measure that is non-monogamic for a multiparty quantum state, it is always possible to find a monotonically increasing function of the measure that is monogamous for the same state. The statement holds for all quantum states, whether pure or mixed, in all finite dimensions and for an arbitrary number of parties. The monotonically increasing function of the quantum correlation measure satisfies all the properties that are expected for quantum correlations to follow. We illustrate the concepts by considering a thermodynamic measure of quantum correlation, called the quantum work deficit.
Efficient quantum algorithm for computing n-time correlation functions.
Pedernales, J S; Di Candia, R; Egusquiza, I L; Casanova, J; Solano, E
2014-07-11
We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.
Quantum modular forms, mock modular forms, and partial theta functions
Kimport, Susanna
Defined by Zagier in 2010, quantum modular forms have been the subject of an explosion of recent research. Many of these results are aimed at discovering examples of these functions, which are defined on the rational numbers and have "nice" modularity properties. Though the subject is in its early stages, numerous results (including Zagier's original examples) show these objects naturally arising from many areas of mathematics as limits of other modular-like functions. One such family of examples is due to Folsom, Ono, and Rhoades, who connected these new objects to partial theta functions (introduced by Rogers in 1917) and mock modular forms (about which there is a rich theory, whose origins date back to Ramanujan in 1920). In this thesis, we build off of the work of Folsom, Ono, and Rhoades by providing an infinite family of quantum modular forms of arbitrary positive half-integral weight. Further, this family of quantum modular forms "glues" mock modular forms to partial theta functions and is constructed from a so-called "universal" mock theta function by extending a method of Eichler and Zagier (originally defined for holomorphic Jacobi forms) into a non-holomorphic setting. In addition to the infinite family, we explore the weight 1/2 and 3/2 functions in more depth. For both of these weights, we are able to explicitly write down the quantum modular form, as well as the corresponding "errors to modularity," which can be shown to be Mordell integrals of specific theta functions and, as a consequence, are real-analytic functions. Finally, we turn our attention to the partial theta functions associated with these low weight examples. Berndt and Kim provide asymptotic expansions for a certain class of partial theta functions as q approaches 1 radially within the unit disk. Here, we extend this work to not only obtain asymptotic expansions for this class of functions as q approaches any root of unity, but also for a certain class of derivatives of these functions
Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min
2016-01-29
Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.
Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min
2016-01-01
Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.
Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min
2016-01-01
Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information. PMID:26823196
Functional methods underlying classical mechanics, relativity and quantum theory
Kryukov, A.
2013-04-01
The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is "made" of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space submanifold) yields the Born rule for transitions between arbitrary quantum states.
Partitive descriptions in Korean
Directory of Open Access Journals (Sweden)
Keun Young Shin
2017-02-01
Full Text Available This paper examines Korean partitive constructions to investigate the typology of the partitive structure. In Korean, a quantifier precedes the nominal in a non-partitive, but it follows the nominal in a partitive. The relative order between a quantifier and its associated nominal indicates that a quantifier in Korean partitive does not function as a NP adjunct but takes a DP as its argument. I argue that Korean postnominal (floating quantifier constructions can be interpreted as partitives or pseudo-partitives/quantitatives because a postnominal (floating quantifier denoting a part-of relation can occur with a kind-denoting DP as well as a definite DP. I also propose that a quantifier denoting a part-of relation is associated with the argument of a verb via composition with a verbal predicate in the floating quantifier construction. This approach can provide an account for several idiosyncratic properties of floating quantifier constructions, which are difficult to capture under the assumption that a floating quantifier construction is derived by moving a quantifier away from its associated nominal. This article is part of the Special Collection: Partitives
Chen, Y. F.; Tung, J. C.; Tuan, P. H.; Yu, Y. T.; Liang, H. C.; Huang, K. F.
2017-01-01
A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.
Generating Functionals for Quantum Field Theories with Random Potentials
Jain, Mudit
2015-01-01
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include condensed matter systems with quenched disorder (e.g. spin glass) or cosmological systems in context of the string theory landscape (e.g. cosmic inflation). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out ...
Transfer matrices for the partition function of the Potts model on cyclic and Möbius lattice strips
Chang, Shu-Chiuan; Shrock, Robert
2005-03-01
We present a method for calculating transfer matrices for the q-state Potts model partition functions Z(G,q,v), for arbitrary q and temperature variable v, on cyclic and Möbius strip graphs G of the square (sq), triangular (tri), and honeycomb (hc) lattices of width Ly vertices and of arbitrarily great length Lx vertices. For the cyclic case we express the partition function as Z(Λ,Ly×Lx,q,v)=∑d=0Ly c Tr[(T)m], where Λ denotes lattice type, c are specified polynomials of degree d in q, T is the transfer matrix in the degree- d subspace, and m=Lx (Lx/2) for Λ=sq, tri ( hc), respectively. An analogous formula is given for Möbius strips. We exhibit a method for calculating T for arbitrary Ly. Explicit results for arbitrary Ly are given for T with d=Ly and Ly-1. In particular, we find very simple formulas the determinant det(T), and trace Tr(T). Corresponding results are given for the equivalent Tutte polynomials for these lattice strips and illustrative examples are included. We also present formulas for self-dual cyclic strips of the square lattice.
Directory of Open Access Journals (Sweden)
Keith A Hultman
2007-01-01
Full Text Available The retention of particular genes after the whole genome duplication in zebrafish has given insights into how genes may evolve through partitioning of ancestral functions. We examine the partitioning of expression patterns and functions of two zebrafish kit ligands, kit ligand a (kitla and kit ligand b (kitlb, and discuss their possible coevolution with the duplicated zebrafish kit receptors (kita and kitb. In situ hybridizations show that kitla mRNA is expressed in the trunk adjacent to the notochord in the middle of each somite during stages of melanocyte migration and later expressed in the skin, when the receptor is required for melanocyte survival. kitla is also expressed in other regions complementary to kita receptor expression, including the pineal gland, tail bud, and ear. In contrast, kitlb mRNA is expressed in brain ventricles, ear, and cardinal vein plexus, in regions generally not complementary to either zebrafish kit receptor ortholog. However, like kitla, kitlb is expressed in the skin during stages consistent with melanocyte survival. Thus, it appears that kita and kitla have maintained congruent expression patterns, while kitb and kitlb have evolved divergent expression patterns. We demonstrate the interaction of kita and kitla by morpholino knockdown analysis. kitla morphants, but not kitlb morphants, phenocopy the null allele of kita, with defects for both melanocyte migration and survival. Furthermore, kitla morpholino, but not kitlb morpholino, interacts genetically with a sensitized allele of kita, confirming that kitla is the functional ligand to kita. Last, we examine kitla overexpression in embryos, which results in hyperpigmentation caused by an increase in the number and size of melanocytes. This hyperpigmentation is dependent on kita function. We conclude that following genome duplication, kita and kitla have maintained their receptor-ligand relationship, coevolved complementary expression patterns, and that
Ravin, Nikolai V.; Rech, Jérôme; Lane, David
2008-01-01
The mitotic stability of the linear plasmid-prophage N15 of Escherichia coli depends on a partition system closely related to that of the F plasmid SopABC. The two Sop systems are distinguished mainly by the arrangement of their centromeric SopB-binding sites, clustered in F (sopC) and dispersed in N15 (IR1 to IR4). Because two of the N15 inverted repeat (IR) sites are located close to elements presumed (by analogy with phage λ) to regulate late gene expression during the lytic growth of N15, we asked whether Sop partition functions play a role in this process. In N15, a putative Q antiterminator gene is located 6 kb upstream of the probable major late promoter and two intrinsic terminator-like sequences, in contrast to λ, where the Q gene is adjacent to the late promoter. Northern hybridization and lacZ reporter activity confirmed the identity of the N15 late promoter (p52), demonstrated antiterminator activity of the Q analogue, and located terminator sequences between p52 and the first open reading frame. Following prophage induction, N15 mutated in IR2 (downstream from gene Q) or IR3 (upstream of p52) showed a pronounced delay in lysis relative to that for wild-type N15. Expression of ir3−-p52::lacZ during N15 wild-type lytic growth was strongly reduced relative to the equivalent ir3+ fusion. The provision of Q protein and the IR2 and SopAB proteins in trans to ir3+-p52::lacZ increased expression beyond that seen in the absence of any one of these factors. These results indicate that the N15 Sop system has a dual role: partition and regulation of late gene transcription during lytic growth. PMID:18359814
Directory of Open Access Journals (Sweden)
Jia Hu
Full Text Available The Tibetan Plateau (TP is predicted to experience increases in air temperature, increases in snowfall, and decreases in monsoon rains; however, there is currently a paucity of data that examine the ecological responses to such climate changes. In this study, we examined the effects of increased air temperature and snowfall on: 1 water use partitioning by different plant functional groups, and 2 ecosystem CO2 fluxes throughout the growing season. At the individual plant scale, we used stable hydrogen isotopes (δD to partition water use between shallow- and deep-rooted species. Prior to the arrival of summer precipitation (typically mid-July, snowmelt was the main water source in the soils. During this time, shallow and deep-rooted species partitioned water use by accessing water from shallow and deep soils, respectively. However, once the monsoon rains arrived, all plants used rainwater from the upper soils as the main water source. Snow addition did not result in increased snowmelt use throughout the growing season; instead, snowmelt water was pushed down into deeper soils when the rains arrived. At the larger plot scale, CO2 flux measurements demonstrated that rain was the main driver for net ecosystem productivity (NEP. NEP rates were low during June and July and reached a maximum during the monsoon season in August. Warming decreased NEP through a reduction in gross primary productivity (GPP, and snow additions did not mitigate the negative effects of warming by increasing NEP or GPP. Both the isotope and CO2 flux results suggest that rain drives productivity in the Nam Tso region on the TP. This also suggests that the effects of warming-induced drought on the TP may not be mitigated by increased snowfall. Further decreases in summer monsoon rains may affect ecosystem productivity, with large implications for livestock-based livelihoods.
Ravin, Nikolai V; Rech, Jérôme; Lane, David
2008-05-01
The mitotic stability of the linear plasmid-prophage N15 of Escherichia coli depends on a partition system closely related to that of the F plasmid SopABC. The two Sop systems are distinguished mainly by the arrangement of their centromeric SopB-binding sites, clustered in F (sopC) and dispersed in N15 (IR1 to IR4). Because two of the N15 inverted repeat (IR) sites are located close to elements presumed (by analogy with phage lambda) to regulate late gene expression during the lytic growth of N15, we asked whether Sop partition functions play a role in this process. In N15, a putative Q antiterminator gene is located 6 kb upstream of the probable major late promoter and two intrinsic terminator-like sequences, in contrast to lambda, where the Q gene is adjacent to the late promoter. Northern hybridization and lacZ reporter activity confirmed the identity of the N15 late promoter (p52), demonstrated antiterminator activity of the Q analogue, and located terminator sequences between p52 and the first open reading frame. Following prophage induction, N15 mutated in IR2 (downstream from gene Q) or IR3 (upstream of p52) showed a pronounced delay in lysis relative to that for wild-type N15. Expression of ir3(-)-p52::lacZ during N15 wild-type lytic growth was strongly reduced relative to the equivalent ir3(+) fusion. The provision of Q protein and the IR2 and SopAB proteins in trans to ir3(+)-p52::lacZ increased expression beyond that seen in the absence of any one of these factors. These results indicate that the N15 Sop system has a dual role: partition and regulation of late gene transcription during lytic growth.
Discrete Wigner functions and quantum computational speed-up
Galvão, E F
2004-01-01
In quant-ph/0401155 Wootters and colaborators defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize a set C_d of states having non-negative W simultaneously in all definitions of W in this class. For d<6 I show C_d is the convex hull of stabilizer states. This supports the conjecture that negativity of W is necessary for exponential speed-up in pure-state quantum computation.
Geometry of q-Hypergeometric Functions, Quantum Affine Algebras and Elliptic Quantum Groups
Tarasov, V; Tarasov, Vitaly; Varchenko, Alexander
1997-01-01
The trigonometric quantized Knizhnik-Zamolodchikov equation (qKZ equation) associated with the quantum group $U_q(sl_2)$ is a system of linear difference equations with values in a tensor product of $U_q(sl_2)$ Verma modules. We solve the equation in terms of multidimensional $q$-hypergeometric functions and define a natural isomorphism between the space of solutions and the tensor product of the corresponding evaluation Verma modules over the elliptic quantum group $E_{\\rho,\\gamma}(sl_2)$, where parameters $\\rho$ and $\\gamma$ are related to the parameter $q$ of the quantum group $U_q(sl_2)$ and the step $p$ of the qKZ equation via $p=e^{2\\pii\\rho}$ and $q=e^{-2\\pii\\gamma}$. We construct asymptotic solutions associated with suitable asymptotic zones and compute the transition functions between the asymptotic solutions in terms of the dynamical elliptic $R$-matrices. This description of the transition functions gives a connection between representation theories of the quantum loop algebra $U_q(\\widetilde{gl}_2...
Functional methods underlying classical mechanics, relativity and quantum theory
Kryukov, Alexey A.
2013-01-01
The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is "made" of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accou...
A classical one-way function to confound quantum adversaries
Moore, Cristopher; Vazirani, U; Moore, Cristopher; Russell, Alexander; Vazirani, Umesh
2007-01-01
The promise of quantum computation and its consequences for complexity-theoretic cryptography motivates an immediate search for cryptosystems which can be implemented with current technology, but which remain secure even in the presence of quantum computers. Inspired by recent negative results pertaining to the nonabelian hidden subgroup problem, we present here a classical algebraic function $f_V(M)$ of a matrix $M$ which we believe is a one-way function secure against quantum attacks. Specifically, inverting $f_V$ reduces naturally to solving a hidden subgroup problem over the general linear group (which is at least as hard as the hidden subgroup problem over the symmetric group). We also demonstrate a reduction from Graph Isomorphism to the problem of inverting $f_V$; unlike Graph Isomorphism, however, the function $f_V$ is random self-reducible and therefore uniformly hard. These results suggest that, unlike Shor's algorithm for the discrete logarithm--which is, so far, the only successful quantum attack ...
Two-point functions in (loop) quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca; Gielen, Steffen; Oriti, Daniele, E-mail: calcagni@aei.mpg.de, E-mail: gielen@aei.mpg.de, E-mail: doriti@aei.mpg.de [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany)
2011-06-21
The path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions is discussed, with particular but non-exclusive reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.
Two-point functions in (loop) quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca; Oriti, Daniele [Max-Planck-Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany); Gielen, Steffen [Max-Planck-Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm (Germany); DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2011-07-01
We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions, with particular but non-exclusive reference to loop quantum cosmology (LQC). Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.
Multi-Determinant Wave-functions in Quantum Monte Carlo
Morales, M A; Clark, B K; Kim, J; Scuseria, G; 10.1021/ct3003404
2013-01-01
Quantum Monte Carlo (QMC) methods have received considerable attention over the last decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling with number of particles, QMC methods present a compelling competitive alternative for the accurate study of large molecular systems and solid state calculations. In spite of such promise, the method has not permeated the quantum chemistry community broadly, mainly because of the fixed-node error, which can be large and whose control is difficult. In this Perspective, we present a systematic application of large scale multi-determinant expansions in QMC, and report on its impressive performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of this strategy for systematically reducing the fixed-node error in the wave function and for achieving chemical accuracy in energy predictions. When compared to traditional quantum chemistr...
Combinatorics of set partitions
Mansour, Toufik
2012-01-01
Focusing on a very active area of mathematical research in the last decade, Combinatorics of Set Partitions presents methods used in the combinatorics of pattern avoidance and pattern enumeration in set partitions. Designed for students and researchers in discrete mathematics, the book is a one-stop reference on the results and research activities of set partitions from 1500 A.D. to today. Each chapter gives historical perspectives and contrasts different approaches, including generating functions, kernel method, block decomposition method, generating tree, and Wilf equivalences. Methods and d
Modelling of multidimensional quantum systems by the numerical functional integration
Energy Technology Data Exchange (ETDEWEB)
Lobanov, Yu.Yu.; Zhidkov, E.P. (Joint Inst. for Nuclear Research, Dubna (USSR)); Shahbagian, R.R. (Yerevan Physics Inst., Erevan (USSR))
1990-01-01
The employment of the numerical functional integration for the description of multidimensional systems in quantum and statistical physics is considered. For the multiple functional integrals with respect to Gaussian measures in the full separable metric spaces the new approximation formulas exact on a class of polynomial functionals of a given summary degree are constructed. The use of the formulas is demonstrated on example of computation of the Green function and the ground state energy in multidimensional Calogero model. The comparison of numerical results with the data obtained by the other authors which used the Monte Carlo method combined with iterative algorithms indicates that our formulas provide the higher efficiency of computations.
Path integrals and quantum processes
Swanson, Marc S
1992-01-01
In a clearly written and systematic presentation, Path Integrals and Quantum Processes covers all concepts necessary to understand the path integral approach to calculating transition elements, partition functions, and source functionals. The book, which assumes only a familiarity with quantum mechanics, is ideal for use as a supplemental textbook in quantum mechanics and quantum field theory courses. Graduate and post-graduate students who are unfamiliar with the path integral will also benefit from this contemporary text. Exercise sets are interspersed throughout the text to facilitate self-
What Density Functional Theory could do for Quantum Information
Mattsson, Ann
2015-03-01
The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Quantum anharmonic oscillator: The airy function approach
Energy Technology Data Exchange (ETDEWEB)
Maiz, F., E-mail: fethimaiz@gmail.com [King Khalid University, Faculty of Science, Physics Department, PO Box 9004, Abha 61413, Asseer (Saudi Arabia); University of Cartage, Nabeul Engineering Preparatory Institute, Merazka, 8000 Nabeul (Tunisia); AlFaify, S. [King Khalid University, Faculty of Science, Physics Department, PO Box 9004, Abha 61413, Asseer (Saudi Arabia)
2014-05-15
New and simple numerical method is being reported to solve anharmonic oscillator problems. The method is setup to approach the real potential V(x) of the anharmonic oscillator system as a piecewise linear potential u(x) and to solve the Schrödinger equation of the system using the Airy function. Then, solutions continuity conditions lead to the energy quantification condition, and consequently, the energy eigenvalues. For testing purpose, the method was applied on the sextic and octic oscillators systems. The proposed method is found to be realistic, computationally simple, and having high degrees of accuracy. In addition, it can be applied to any form of potential. The results obtained by the proposed method were seen closely agreeing with results reached by other complicated methods.
Maji, Jaya; Bhattacharjee, Somendra M
2012-10-01
We study the melting of three-stranded DNA by using the real-space renormalization group and exact recursion relations. The prediction of an unusual Efimov-analog three-chain bound state, that appears at the critical melting of two-chain DNA, is corroborated by the zeros of the partition function. The distribution of the zeros has been studied in detail for various situations. We show that the Efimov DNA can occur even if the three-chain (i.e., three-monomer) interaction is repulsive in nature. In higher dimensions, a striking result that emerged in this repulsive zone is a continuous transition from the critical state to the Efimov DNA.
On Complex Zeros of the q-Potts Partition Function for a Self-dual Family of Graphs
Billiot, J.-M.; Corset, F.; Fontenas, E.
2010-06-01
This paper deals with the location of the complex zeros of q-Potts partition function for a class of self-dual graphs. For this class of graphs, as the form of the eigenvalues is known, the regions of the complex plane can be focused on the sets where there is only one dominant eigenvalue in particular containing the positive half plane. Thus, in these regions, the analyticity of the free energy per site can be derived easily. Next, some examples of graphs with their Tutte polynomial having few eigenvalues are given. The case of the cycle with an edge having a high order of multiplicity is presented in detail. In particular, we show that the well known conjecture of Chen et al. is false in the finite case. Furthermore we obtain a sequence of self-dual graphs for which the unit circle does not belong to the accumulation sets of the zeros.
Lee, Jae Hwan; Kim, Seung-Yeon; Lee, Julian
2013-05-01
We study distributions of the partition function zeros in the complex temperature plane for a square-lattice homopolymer with nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions. The dependence of distributions on the ratio of NN and NNN interaction strengths R is examined. The finite-size scaling of the zeros is performed to obtain the crossover exponent, which is shown to be independent of R within error bars, suggesting that all of these models belong to the same universality class. The transition temperatures are also computed by the zeros to obtain the phase diagram, and the results confirm that the model with stronger NNN interaction exhibits stronger effects of cooperativity.
Rocha, J. C. S.; Mól, L. A. S.; Costa, B. V.
2016-12-01
Using the two dimensional XY -(S(O(3))) model as a test case, we show that analysis of the Fisher zeros of the canonical partition function can provide signatures of a transition in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. Studying the internal border of zeros in the complex temperature plane, we found a scenario in complete agreement with theoretical expectations which allow one to uniquely classify a phase transition as in the BKT class of universality. We obtain TBKT in excellent accordance with previous results. A careful analysis of the behavior of the zeros for both regions Re(T) ≤TBKT and Re(T) >TBKT in the thermodynamic limit shows that Im(T) goes to zero in the former case and is finite in the last one.
On the interpretation of wave function overlaps in quantum dots
DEFF Research Database (Denmark)
Stobbe, Søren; Hvam, Jørn Märcher; Lodahl, Peter
2011-01-01
that the electron and the hole are located at the same point or region in space, i.e., they must coincide spatially to recombine. Here, we show that this interpretation is not correct even loosely speaking. By general mathematical considerations we compare the envelope wave function overlap, the exchange overlap......The spontaneous emission rate of excitons strongly confined in quantum dots (QDs) is proportional to the overlap integral of electron and hole envelope wave functions. A common and intuitive interpretation of this result is that the spontaneous emission rate is proportional to the probability...... compare our qualitative predictions with recent measurements of the wave function overlap and find good agreement....
Quantum Dynamics in Classical Time Evolution of Correlation Functions
Wetterich, C
1997-01-01
The time-dependence of correlation functions under the influence of cla= ssical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show that this fixed point is not universally stable, since infinitely many conserved correlation functions obstruct the approach to equilibrium. Equilibrium can therefore be reached at most for suitably av= eraged quantities or for subsystems, similar to quantum statistics. The classica= l time evolution of correlation functions shows many dynamical features of quant= um mechanics.
External Source Method for Kubo-Transformed Quantum Correlation Functions
Horikoshi, Atsushi
2014-01-01
We revisit the external source method for Kubo-transformed quantum correlation functions recently proposed by Krishna and Voth. We derive an exact formula and show that the Krishna-Voth formula can be derived as an approximation of our formula. Some properties of this approximation are clarified through a model calculation of the position autocorrelation function for a one-dimensional harmonic oscillator. A key observation is that the Krishna-Voth correlation function has a term which behaves as the secular term in perturbation theory.
Schwenke, David W.; Truhlar, Donald G.
1990-01-01
The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.
Experimental energy levels and partition function of the $^{12}$C$_2$ molecule
Furtenbacher, Tibor; Csaszar, Attila G; Bernath, Peter F; Yurchenko, Sergei N; Tennyson, Jonathan
2016-01-01
The carbon dimer, the $^{12}$C$_2$ molecule, is ubiquitous in astronomical environments. Experimental-quality rovibronic energy levels are reported for $^{12}$C$_2$, based on rovibronic transitions measured for and among its singlet, triplet, and quintet electronic states, reported in 42 publications. The determination utilizes the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The 23,343 transitions measured experimentally and validated within this study determine 5,699 rovibronic energy levels, 1,325, 4,309, and 65 levels for the singlet, triplet, and quintet states investigated, respectively. The MARVEL analysis provides rovibronic energies for six singlet, six triplet, and two quintet electronic states. For example, the lowest measurable energy level of the \\astate\\ state, corresponding to the $J=2$ total angular momentum quantum number and the $F_1$ spin-multiplet component, is 603.817(5) \\cm. This well-determined energy difference should facilitate observations of singlet--trip...
Horizon Wave-Function and the Quantum Cosmic Censorship
Casadio, Roberto; Stojkovic, Dejan
2015-01-01
We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superxtremal case (with charge-to-mass ratio $\\alpha>1$), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for $\\alpha^2 2$, and the uncertainty in the location of the horizon blows up at $\\alpha^2=2$, signalling that such an object is no more well-defined. This perhaps implies that a {\\em quantum\\/} Cosmic Censorhip might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of $\\sqrt{2}$) can exist.
Horizon wave-function and the quantum cosmic censorship
Directory of Open Access Journals (Sweden)
Roberto Casadio
2015-07-01
Full Text Available We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superextremal case (with charge-to-mass ratio α>1, which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for α22, and the uncertainty in the location of the horizon blows up at α2=2, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorship might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of 2 can exist.
Sugisaki, Kenji; Yamamoto, Satoru; Nakazawa, Shigeaki; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji
2016-08-18
Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.
The quantum Ising model: finite sums and hyperbolic functions
Damski, Bogdan
2015-10-01
We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and Products.
The quantum Ising model: finite sums and hyperbolic functions
Bogdan Damski
2015-01-01
We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn...
Theory of brain function, quantum mechanics and superstrings
Nanopoulos, Dimitri V.
1995-01-01
Recent developments/efforts to understand aspects of the brain function at the {\\em sub-neural} level are discussed. MicroTubules (MTs) participate in a wide variety of dynamical processes in the cell especially in bioinformation processes such as learning and memory, by possessing a well-known binary error-correcting code with 64 words. In fact, MTs and DNA/RNA are unique cell structures that possess a code system. It seems that the MTs' code system is strongly related to a kind of ``Mental Code" in the following sense. The MTs' periodic paracrystalline structure make them able to support a superposition of coherent quantum states, as it has been recently conjectured by Hameroff and Penrose, representing an external or mental order, for sufficient time needed for efficient quantum computing. Then the quantum superposition collapses spontaneously/dynamically through a new, string-derived mechanism for collapse proposed recently by Ellis, Mavromatos, and myself. At the moment of collapse, organized quantum exo...
Characteristic functions based on a quantum jump trajectory
Liu, Fei; Xi, Jingyi
2016-12-01
Characteristic functions (CFs) provide a very efficient method for evaluating the probability density functions of stochastic thermodynamic quantities and investigating their statistical features in quantum master equations (QMEs). A conventional procedure for obtaining these functions is to resort to a first-principles approach; namely, the evolution equations of the CFs of the combined system and its environment are obtained and then projected into the degrees of freedom of the system. However, the QMEs can be unraveled by a quantum jump trajectory. Thermodynamic quantities such as the heat, work, and entropy production can be well defined along a trajectory. Hence, on the basis of the notion of a trajectory, can we straightforwardly derive these CFs, e.g., their evolution equations? This is essential to establish the self-contained stochastic thermodynamics of a QME. In this paper, we show that it is indeed plausible and also simple. Particularly, these equations are fully consistent with those obtained by the first-principles method. Our results have practical significance; they indicate that the quantum fluctuation relations could be verified by more realistic photocounting experiments.
Lectin functionalized quantum dots for recognition of mammary tumors
Santos, Beate S.; de Farias, Patricia M. A.; de Menezes, Frederico D.; de C. Ferreira, Ricardo; Júnior, Severino A.; Figueiredo, Regina C. B. Q.; Beltrão, Eduardo I. C.
2006-02-01
In this study we use CdS/Cd(OH) II quantum dots functionalized with concanavalin-A (Con-A) lectin, specific to glucose/mannose residues, to investigate cell alterations regarding carbohydrate profile in human mammary tissues diagnosed as fibroadenoma (benign tumor). These particles were functionalized with glutaraldehyde and Con-A and incubated with tissue sections of normal and to Fibroadenoma, a benign type of mammary tumor. The tissue sections were deparafinized, hydrated in graded alcohol and treated with a solution of Evans Blue in order to avoid autofluorescence. The fluorescence intensity of QD-Con-A stained tissues showed different patterns, which reflect the carbohydrate expression of glucose/mannose in fibroadenoma when compared to the detection of the normal carbohydrate expression. The pattern of unspecific labeling of the tissues with glutaraldehyde functionalized CdS/Cd(OH) II quantum dots is compared to the targeting driven by the Con-A lectin. The preliminary findings reported here support the use of CdS/Cd(OH) II quantum dots as specific probes of cellular alterations and their use in diagnostics.
Institute of Scientific and Technical Information of China (English)
Xiao-Gang Ruan; Jin-Lian Wang; Jian-Geng Li
2006-01-01
Computational analysis is essential for transforming the masses of microarray data into a mechanistic understanding of cancer. Here we present a method for finding gene functional modules of cancer from microarray data and have applied it to colon cancer. First, a colon cancer gene network and a normal colon tissue gene network were constructed using correlations between the genes. Then the modules that tended to have a homogeneous functional composition were identified by splitting up the network. Analysis of both networks revealed that they are scale-free.Comparison of the gene functional modules for colon cancer and normal tissues showed that the modules' functions changed with their structures.
Quantum Computational Complexity of Spin Glasses
2011-03-19
canonical problem of classical statistical mechanics: computation of the classical partition function. We have approached this problem using the Potts...enumerator polynomial from coding theory and Z and exploited the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in...computational complexity of the canonical problem of classical statistical mechanics: computation of the classical partition function. We have approached this
Modelling graphene quantum dot functionalization via ethylene-dinitrobenzoyl
Energy Technology Data Exchange (ETDEWEB)
Noori, Keian; Giustino, Feliciano [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Hübener, Hannes [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC & DIPC, Av. Tolosa 72, 20018 San Sebastián (Spain); Kymakis, Emmanuel [Center of Materials Technology and Photonics & Electrical Engineering Department, Technological Educational Institute (TEI) of Crete, Heraklion, 71004 Crete (Greece)
2016-03-21
Ethylene-dinitrobenzoyl (EDNB) linked to graphene oxide has been shown to improve the performance of graphene/polymer organic photovoltaics. Its binding conformation on graphene, however, is not yet clear, nor have its effects on work function and optical absorption been explored more generally for graphene quantum dots. In this report, we clarify the linkage of EDNB to GQDs from first principles and show that the binding of the molecule increases the work function of graphene, while simultaneously modifying its absorption in the ultraviolet region.
Water-solubilization and functionalization of semiconductor quantum dots.
Tyrakowski, Christina M; Isovic, Adela; Snee, Preston T
2013-01-01
Semiconductor quantum dots (QDs) are highly fluorescent nanocrystals that have abundant potential for uses in biological imaging and sensing. However, the best materials are synthesized in hydrophobic surfactants that prevent direct aqueous solubilization. While several methods have been developed to impart water-solubility, an aqueous QD dispersion has no inherent useful purpose and must be functionalized further. Due to the colloidal nature of QD dispersions, traditional methods of chemical conjugation in water either have low yields or cause irreversible precipitation of the sample. Here, we describe several methods to water-solubilize QDs and further functionalize the materials with chemical and/or biological vectors.
Quantum power functional theory for many-body dynamics
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Matthias, E-mail: Matthias.Schmidt@uni-bayreuth.de [Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth (Germany)
2015-11-07
We construct a one-body variational theory for the time evolution of nonrelativistic quantum many-body systems. The position- and time-dependent one-body density, particle current, and time derivative of the current act as three variational fields. The generating (power rate) functional is minimized by the true current time derivative. The corresponding Euler-Lagrange equation, together with the continuity equation for the density, forms a closed set of one-body equations of motion. Space- and time-nonlocal one-body forces are generated by the superadiabatic contribution to the functional. The theory applies to many-electron systems.
Adam, Thomas C; Kelley, Megan; Ruttenberg, Benjamin I; Burkepile, Deron E
2015-12-01
The recent loss of key consumers to exploitation and habitat degradation has significantly altered community dynamics and ecosystem function across many ecosystems worldwide. Predicting the impacts of consumer losses requires knowing the level of functional diversity that exists within a consumer assemblage. In this study, we document functional diversity among nine species of parrotfishes on Caribbean coral reefs. Parrotfishes are key herbivores that facilitate the maintenance and recovery of coral-dominated reefs by controlling algae and provisioning space for the recruitment of corals. We observed large functional differences among two genera of parrotfishes that were driven by differences in diet. Fishes in the genus Scarus targeted filamentous algal turf assemblages, crustose coralline algae, and endolithic algae and avoided macroalgae, while fishes in the genus Sparisoma preferentially targeted macroalgae. However, species with similar diets were dissimilar in other attributes, including the habitats they frequented, the types of substrate they fed from, and the spatial scale at which they foraged. These differences indicate that species that appear to be functionally redundant when looking at diet alone exhibit high levels of complementarity when we consider multiple functional traits. By identifying key functional differences among parrotfishes, we provide critical information needed to manage parrotfishes to enhance the resilience of coral-dominated reefs and reverse phase shifts on algal-dominated reefs throughout the wider Caribbean. Further, our study provides a framework for predicting the impacts of consumer losses in other species rich ecosystems.
Exact partition functions for the Ω-deformed N=2{sup ∗}SU(2) gauge theory
Energy Technology Data Exchange (ETDEWEB)
Beccaria, Matteo; Macorini, Guido [Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento,Via Arnesano, 73100 Lecce (Italy); INFN,Via Arnesano, 73100 Lecce (Italy)
2016-07-12
We study the low energy effective action of the Ω-deformed N=2{sup ∗}SU(2) gauge theory. It depends on the deformation parameters ϵ{sub 1},ϵ{sub 2}, the scalar field expectation value a, and the hypermultiplet mass m. We explore the plane ((m/(ϵ{sub 1})),((ϵ{sub 2})/(ϵ{sub 1}))) looking for special features in the multi-instanton contributions to the prepotential, motivated by what happens in the Nekrasov-Shatashvili limit ϵ{sub 2}→0. We propose a simple condition on the structure of poles of the k-instanton prepotential and show that it is admissible at a finite set of points in the above plane. At these special points, the prepotential has poles at fixed positions independent on the instanton number. Besides and remarkably, both the instanton partition function and the full prepotential, including the perturbative contribution, may be given in closed form as functions of the scalar expectation value a and the modular parameter q appearing in special combinations of Eisenstein series and Dedekind η function. As a byproduct, the modular anomaly equation can be tested at all orders at these points. We discuss these special features from the point of view of the AGT correspondence and provide explicit toroidal 1-blocks in non-trivial closed form. The full list of solutions with 1, 2, 3, and 4 poles is determined and described in details.
A fast quantum algorithm for the affine Boolean function identification
Younes, Ahmed
2015-02-01
Bernstein-Vazirani algorithm (the one-query algorithm) can identify a completely specified linear Boolean function using a single query to the oracle with certainty. The first aim of the paper is to show that if the provided Boolean function is affine, then one more query to the oracle (the two-query algorithm) is required to identify the affinity of the function with certainty. The second aim of the paper is to show that if the provided Boolean function is incompletely defined, then the one-query and the two-query algorithms can be used as bounded-error quantum polynomial algorithms to identify certain classes of incompletely defined linear and affine Boolean functions respectively with probability of success at least 2/3.
Symmetric polynomials, quantum Jacobi-Trudi identities and \\tau-functions
Harnad, J
2013-01-01
An element [\\Phi] of the Grassmannian of n-dimensional subspaces of the Hardy space H^2, extended over the field C(x_1,..., x_n), may be associated to any polynomial basis {\\phi} for C(x). The Pl\\"ucker coordinates S^\\phi_{\\lambda,n}(x_1,..., x_n) of \\Phi, labelled by partitions \\lambda, provide an analog of Jacobi's bi-alternant formula, defining a generalization of Schur polynomials. Applying the recursion relations satisfied by the polynomial system to the analog of the complete symmetric functions generates a doubly infinite matrix of symmetric polynomials that determine an element [H] of the Grasmannian. This is shown to coincide with [\\Phi], implying a set of {\\it quantum Jacobi-Trudi identities} that generalize a result obtained by Sergeev and Veselov for the case of orthogonal polynomials. The symmetric polynomials S^\\phi_{\\lambda,n}(x_1,..., x_n) are shown to be KP (Kadomtsev-Petviashvili) tau-functions in terms of the monomial sums in the parameters x_a, viewed as KP flow variables. A fermionic oper...
Time-dependent density functional theory for quantum transport.
Zheng, Xiao; Chen, GuanHua; Mo, Yan; Koo, SiuKong; Tian, Heng; Yam, ChiYung; Yan, YiJing
2010-09-21
Based on our earlier works [X. Zheng et al., Phys. Rev. B 75, 195127 (2007); J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)], we propose a rigorous and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The proposed approach combines time-dependent density functional theory with quantum dissipation theory, and results in a useful tool for studying transient dynamics of electronic systems. Within the proposed exact theoretical framework, we construct a number of practical schemes for simulating realistic systems such as nanoscopic electronic devices. Computational cost of each scheme is analyzed, with the expected level of accuracy discussed. As a demonstration, a simulation based on the adiabatic wide-band limit approximation scheme is carried out to characterize the transient current response of a carbon nanotube based electronic device under time-dependent external voltages.
Minimum uncertainty states for the quantum group SU{sub q}(2) and quantum Wigner d-functions
Energy Technology Data Exchange (ETDEWEB)
Mann, A.; Parthasarathy, R. [Institute of Mathematical Sciences, Madras (India)
1996-01-21
Minimum uncertainty angular momentum states for the quantum group SU{sub q}(2) are constructed. They involve the eigenvalues of J{sub 1} which are q-numbers and the quantum group analogue of the Wigner d-functions for {theta}={pi}/2. The result is generalized for all values of {theta} and a formula for the quantum Wigner d-function is derived. The case of q=1 is discussed and compared with the well known results for the Wigner d-functions. (author)
Distinct functional constraints partition sequence conservation in a cis-regulatory element.
Directory of Open Access Journals (Sweden)
Antoine Barrière
2011-06-01
Full Text Available Different functional constraints contribute to different evolutionary rates across genomes. To understand why some sequences evolve faster than others in a single cis-regulatory locus, we investigated function and evolutionary dynamics of the promoter of the Caenorhabditis elegans unc-47 gene. We found that this promoter consists of two distinct domains. The proximal promoter is conserved and is largely sufficient to direct appropriate spatial expression. The distal promoter displays little if any conservation between several closely related nematodes. Despite this divergence, sequences from all species confer robustness of expression, arguing that this function does not require substantial sequence conservation. We showed that even unrelated sequences have the ability to promote robust expression. A prominent feature shared by all of these robustness-promoting sequences is an AT-enriched nucleotide composition consistent with nucleosome depletion. Because general sequence composition can be maintained despite sequence turnover, our results explain how different functional constraints can lead to vastly disparate rates of sequence divergence within a promoter.
Predicting functional associations from metabolism using bi-partite network algorithms
Directory of Open Access Journals (Sweden)
Veeramani Balaji
2010-07-01
Full Text Available Abstract Background Metabolic reconstructions contain detailed information about metabolic enzymes and their reactants and products. These networks can be used to infer functional associations between metabolic enzymes. Many methods are based on the number of metabolites shared by two enzymes, or the shortest path between two enzymes. Metabolite sharing can miss associations between non-consecutive enzymes in a serial pathway, and shortest-path algorithms are sensitive to high-degree metabolites such as water and ATP that create connections between enzymes with little functional similarity. Results We present new, fast methods to infer functional associations in metabolic networks. A local method, the degree-corrected Poisson score, is based only on the metabolites shared by two enzymes, but uses the known metabolite degree distribution. A global method, based on graph diffusion kernels, predicts associations between enzymes that do not share metabolites. Both methods are robust to high-degree metabolites. They out-perform previous methods in predicting shared Gene Ontology (GO annotations and in predicting experimentally observed synthetic lethal genetic interactions. Including cellular compartment information improves GO annotation predictions but degrades synthetic lethal interaction prediction. These new methods perform nearly as well as computationally demanding methods based on flux balance analysis. Conclusions We present fast, accurate methods to predict functional associations from metabolic networks. Biological significance is demonstrated by identifying enzymes whose strong metabolic correlations are missed by conventional annotations in GO, most often enzymes involved in transport vs. synthesis of the same metabolite or other enzyme pairs that share a metabolite but are separated by conventional pathway boundaries. More generally, the methods described here may be valuable for analyzing other types of networks with long-tailed degree
Predicting functional associations from metabolism using bi-partite network algorithms.
Veeramani, Balaji; Bader, Joel S
2010-07-14
Metabolic reconstructions contain detailed information about metabolic enzymes and their reactants and products. These networks can be used to infer functional associations between metabolic enzymes. Many methods are based on the number of metabolites shared by two enzymes, or the shortest path between two enzymes. Metabolite sharing can miss associations between non-consecutive enzymes in a serial pathway, and shortest-path algorithms are sensitive to high-degree metabolites such as water and ATP that create connections between enzymes with little functional similarity. We present new, fast methods to infer functional associations in metabolic networks. A local method, the degree-corrected Poisson score, is based only on the metabolites shared by two enzymes, but uses the known metabolite degree distribution. A global method, based on graph diffusion kernels, predicts associations between enzymes that do not share metabolites. Both methods are robust to high-degree metabolites. They out-perform previous methods in predicting shared Gene Ontology (GO) annotations and in predicting experimentally observed synthetic lethal genetic interactions. Including cellular compartment information improves GO annotation predictions but degrades synthetic lethal interaction prediction. These new methods perform nearly as well as computationally demanding methods based on flux balance analysis. We present fast, accurate methods to predict functional associations from metabolic networks. Biological significance is demonstrated by identifying enzymes whose strong metabolic correlations are missed by conventional annotations in GO, most often enzymes involved in transport vs. synthesis of the same metabolite or other enzyme pairs that share a metabolite but are separated by conventional pathway boundaries. More generally, the methods described here may be valuable for analyzing other types of networks with long-tailed degree distributions and high-degree hubs.
Nonperturbative Studies of Quantum Gravity
Beirl, W; Riedler, J; Beirl, Wolfgang; Markum, Harald; Riedler, Juergen
1993-01-01
We investigate quantum gravity in the path integral formulation using the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin system with higher couplings on a Kagome lattice. Various measures acting as external field were considered. Extensions to matter fields and higher dimensions are discussed.
On the Convergence to Ergodic Behaviour of Quantum Wave Functions
Jacquod, P; Jacquod, Ph.
1996-01-01
We study the decrease of fluctuations of diagonal matrix elements of observables and of Husimi densities of quantum mechanical wave functions around their mean value upon approaching the semi-classical regime ($\\hbar strongly chaotic regime. We show that the fluctuations are Gaussian distributed, with a width $\\sigma^2$ decreasing as the square root of Planck's constant. This is consistent with Random Matrix Theory (RMT) predictions, and previous studies on these fluctuations. We further study the width of the probability distribution of $\\hbar$-dependent fluctuations and compare it to the Gaussian Orthogonal Ensemble (GOE) of RMT.
Functional analysis and quantum mechanics: an introduction for physicists
Energy Technology Data Exchange (ETDEWEB)
Ranade, Kedar S. [Ulm Univ. (Germany). Inst. fuer Quantenphysik and Center for Integrated Quantum Science and Technology (IQST)
2015-09-15
We give an introduction to certain topics from functional analysis which are relevant for physics in general and in particular for quantum mechanics. Starting from some examples, we discuss the theory of Hilbert spaces, spectral theory of unbounded operators, distributions and their applications and present some facts from operator algebras. We do not give proofs, but present examples and analogies from physics which should be useful to get a feeling for the topics considered. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
A Comment on Quantum Distribution Functions and the OSV Conjecture
Gómez, C; Gomez, Cesar; Montanez, Sergio
2006-01-01
Using the attractor mechanism and the relation between the quantization of $H^{3}(M)$ and topological strings on a Calabi Yau threefold $M$ we define a map from BPS black holes into coherent states. This map allows us to represent the Bekenstein-Hawking-Wald entropy as a quantum distribution function on the phase space $H^{3}(M)$. This distribution function is a mixed Husimi/anti-Husimi distribution corresponding to the different normal ordering prescriptions for the string coupling and deviations of the complex structure moduli. From the integral representation of this distribution function in terms of the Wigner distribution we recover the Ooguri-Strominger-Vafa (OSV) conjecture in the region "at infinity" of the complex structure moduli space. The physical meaning of the OSV corrections are briefly discussed in this limit.
A comment on quantum distribution functions and the OSV conjecture
Energy Technology Data Exchange (ETDEWEB)
Gomez, Cesar [Instituto de Fisica Teorica CSIC/UAM, C-XVI Universidad Autonoma, E-28049 Madrid (Spain); Montanez, Sergio [Instituto de Fisica Teorica CSIC/UAM, C-XVI Universidad Autonoma, E-28049 Madrid (Spain)
2006-12-15
Using the attractor mechanism and the relation between the quantization of H{sup 3}(M) and topological strings on a Calabi Yau threefold M we define a map from BPS black holes into coherent states. This map allows us to represent the Bekenstein-Hawking-Wald entropy as a quantum distribution function on the phase space H{sup 3}(M). This distribution function is a mixed Husimi/anti-Husimi distribution corresponding to the different normal ordering prescriptions for the string coupling and deviations of the complex structure moduli. From the integral representation of this distribution function in terms of the Wigner distribution we recover the Ooguri-Strominger-Vafa (OSV) conjecture in the region 'at infinity' of the complex structure moduli space. The physical meaning of the OSV corrections are briefly discussed in this limit.
New useful special function in quantum optics theory
Chen, Feng; Fan, Hong-Yi
2016-08-01
By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-series and Hermite polynomials, i.e., By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators (IWOP) we derive its generating function. The circumstance in which this new special function appears and is applicable is considered. Project supported by the Natural Science Fund of Education Department of Anhui Province, China (Grant No. KJ2016A590), the Talent Foundation of Hefei University, China (Grant No. 15RC11), and the National Natural Science Foundation of China (Grant Nos. 11247009 and 11574295).
Directory of Open Access Journals (Sweden)
J. Park
2010-06-01
Full Text Available An energy-conservative metric based on the discrete wavelet transform is applied to assess the relative energy distribution of extreme sea level events across different temporal scales. The metric is applied to coastal events at Key West and Pensacola Florida as a function of two Atlantic Multidecadal Oscillation (AMO regimes. Under AMO warm conditions there is a small but significant redistribution of event energy from nearly static into more dynamic (shorter duration timescales at Key West, while at Pensacola the AMO-dependent changes in temporal event behaviour are less pronounced. Extreme events with increased temporal dynamics might be consistent with an increase in total energy of event forcings which may be a reflection of more energetic storm events during AMO warm phases. As dynamical models mature to the point of providing regional climate index predictability, coastal planners may be able to consider such temporal change metrics in planning scenarios.
Directory of Open Access Journals (Sweden)
J. Park
2010-03-01
Full Text Available An energy-conservative metric based on the discrete wavelet transform is applied to assess the relative energy distribution of non-stationary extreme sea level events across different temporal scales. The metric is applied to coastal events at Key West and Pensacola Florida as a function of two Atlantic Multidecadal Oscillation (AMO regimes. Under AMO warm conditions there is a small but significant redistribution of event energy from nearly static into more dynamic timescales at Key West, while at Pensacola the AMO-dependent changes in temporal event behaviour are less pronounced. Extreme events with increased temporal dynamics are consistent with an increase in total energy of event forcings which may be a reflection of more energetic storm events during AMO warm phases. As dynamical models mature to the point of providing regional climate index predictability, coastal planners may be able to consider such temporal change metrics in planning scenarios.
Optimized Local Trigonometric Bases with Nonuniform Partitions
Institute of Scientific and Technical Information of China (English)
Qiao Fang LIAN; Yong Ge WANG; Dun Yan YAN
2006-01-01
The authors provide optimized local trigonometric bases with nonuniform partitions which efficiently compress trigonometric functions. Numerical examples demonstrate that in many cases the proposed bases provide better compression than the optimized bases with uniform partitions obtained by Matviyenko.
Chuang, William Huanshan
2015-01-01
The goals of this note are twofold: First, to revisit a mechanism proposed by Ho\\v{r}ava and Minic\\cite{Horava:2000fk} which generates a zero cosmological constant to the Universe based on Boltzmann probability distribution and the Holographic principle, a comparison between the zero cosmological constant and recent observation results is given. Secondly, in order to investigate the possibility of phase-transition phenomena of the Universe, a further study on an exponential class of the partition function of the Universe, which is given by Shaw and Barrow \\cite{Shaw:2011ij,Barrow:2011bs} was provided by investigating the distribution of Lee-Yang zeros are given. The contribution of this paper is that after applying the fundamental theorem of algebra to one action chosen from the exponential class that derived from the Shaw and Barrow's works, the Lee-Yang theorem can be applied to the selected action, meaning that critical phenomena might involve the growth of large-scale structure of the Universe, and the ph...
Phinney, W. C.
1992-01-01
As a prelude to determinations of the content of total iron as FeO(T) in melts in equilibrium with calcic anorthosites, the partition coefficients (Ds) for FeO(T) between calcic plagioclase and basaltic melt were determined, as a function of oxygen fugacity (f(O2)), for a basaltic composition that occurs as matrices for plagioclase megacrysts. Results showed that, at the liquidus conditions, the value of D for FeO(T) between calcic plagioclase and tholeiitic basalt changed little (from 0.030 to 0.044) between the very low f(O2) of the iron-wustite buffer and that of the quartz-fayalite-magnetite (QFM) buffer. At fugacities above QFM, the value for D increased rapidly to 0.14 at the magnetite-hematite buffer and to 0.33 in air. The increase in D results from the fact that, at f(O2) below QFM, nearly all of the Fe is in the Fe(2+) state; above QFM, the Fe(3+)/Fe(2+) ratio in the melt increases rapidly, causing more Fe to enter the plagioclase which accepts Fe(3+) more readily than Fe(2+).
Choy, Jaeyoo
2016-08-01
Let K be the compact Lie group USp(N / 2) or SO(N , R) . Let MnK be the moduli space of framed K-instantons over S4 with the instanton number n. By Donaldson (1984), MnK is endowed with a natural scheme structure. It is a Zariski open subset of a GIT quotient of μ-1(0) , where μ is a holomorphic moment map such that μ-1(0) consists of the ADHM data. The purpose of the paper is to study the geometric properties of μ-1(0) and its GIT quotient, such as complete intersection, irreducibility, reducedness and normality. If K = USp(N / 2) then μ is flat and μ-1(0) is an irreducible normal variety for any n and even N. If K = SO(N , R) the similar results are proven for low n and N. As an application one can obtain a mathematical interpretation of the K-theoretic Nekrasov partition function of Nekrasov and Shadchin (2004).
Quantum speedup of Monte Carlo methods.
Montanaro, Ashley
2015-09-08
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.
Partitions with Initial Repetitions
Institute of Scientific and Technical Information of China (English)
George E. ANDREWS
2009-01-01
A variety of interesting connections with modular forms, mock theta functions and Rogers-Ramanujan type identities arise in consideration of partitions in which the smaller integers are repeated as summands more often than the larger summands. In particular, this concept leads to new interpre-tations of the Rogers-Selberg identities and Bailey's modulus 9 identities.
Quantum canonical tensor model and an exact wave function
Sasakura, Naoki
2013-01-01
Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class constraints. The Poisson algebra of the first-class constraints has structure functions, and provides an algebraically consistent way of discretizing the Dirac first-class constraint algebra for general relativity. This paper successfully formulates the Wheeler-DeWitt scheme of quantization of the canonical tensor model; the ordering of operators in the constraints is determined without ambiguity by imposing Hermiticity and covariance on the constraints, and the commutation algebra of constraints takes essentially the same from as the classical Poisson algebra, i.e. is first-class. Thus one could consistently obtain, at least locally in the configuration space, wave functions of "universe" by solving the partial differential equations representing the constraints, i.e. the Wheeler...
Huang, Chen; Muñoz-García, Ana Belén; Pavone, Michele
2016-12-01
Density-functional embedding theory provides a general way to perform multi-physics quantum mechanics simulations of large-scale materials by dividing the total system's electron density into a cluster's density and its environment's density. It is then possible to compute the accurate local electronic structures and energetics of the embedded cluster with high-level methods, meanwhile retaining a low-level description of the environment. The prerequisite step in the density-functional embedding theory is the cluster definition. In covalent systems, cutting across the covalent bonds that connect the cluster and its environment leads to dangling bonds (unpaired electrons). These represent a major obstacle for the application of density-functional embedding theory to study extended covalent systems. In this work, we developed a simple scheme to define the cluster in covalent systems. Instead of cutting covalent bonds, we directly split the boundary atoms for maintaining the valency of the cluster. With this new covalent embedding scheme, we compute the dehydrogenation energies of several different molecules, as well as the binding energy of a cobalt atom on graphene. Well localized cluster densities are observed, which can facilitate the use of localized basis sets in high-level calculations. The results are found to converge faster with the embedding method than the other multi-physics approach ONIOM. This work paves the way to perform the density-functional embedding simulations of heterogeneous systems in which different types of chemical bonds are present.
Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions
Chuang, Wu-Yen; Jafferis, Daniel Louis
2009-11-01
In this paper we study the relation between pyramid partitions with a general empty room configuration (ERC) and the BPS states of D-branes on the resolved conifold. We find that the generating function for pyramid partitions with a length n ERC is exactly the same as the D6/D2/D0 BPS partition function on the resolved conifold in particular Kähler chambers. We define a new type of pyramid partition with a finite ERC that counts the BPS degeneracies in certain other chambers. The D6/D2/D0 partition functions in different chambers were obtained by applying the wall crossing formula. On the other hand, the pyramid partitions describe T 3 fixed points of the moduli space of a quiver quantum mechanics. This quiver arises after we apply Seiberg dualities to the D6/D2/D0 system on the conifold and choose a particular set of FI parameters. The arrow structure of the dual quiver is confirmed by computation of the Ext group between the sheaves. We show that the superpotential and the stability condition of the dual quiver with this choice of the FI parameters give rise to the rules specifying pyramid partitions with length n ERC.
Energy Technology Data Exchange (ETDEWEB)
Mielke, Steven L., E-mail: slmielke@gmail.com, E-mail: truhlar@umn.edu; Truhlar, Donald G., E-mail: slmielke@gmail.com, E-mail: truhlar@umn.edu [Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant St. S.E., Minneapolis, Minnesota 55455-0431 (United States)
2015-01-28
We present an improved version of our “path-by-path” enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P{sup −6}) to O(P{sup −12}), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational–rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan–Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ∼1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300–3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.
Mielke, Steven L; Truhlar, Donald G
2015-01-28
We present an improved version of our "path-by-path" enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P(-6)) to O(P(-12)), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational-rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan-Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ∼1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300-3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.
Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator's Wave Functions
Institute of Scientific and Technical Information of China (English)
LU Hai-Liang; FAN Hong-Yi
2007-01-01
We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator's wave functions.The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S(r)Hm,n(μa1+, μa2+)|00〉, which is the minimum uncertainty state for sum squeezing, in 〈η| representation is calculated.
Functional determinants, index theorems, and exact quantum black hole entropy
Murthy, Sameer
2015-01-01
The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the $Q\\mathcal{V}$ operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around $Q$-invariant off-shell configurations in four-dimensional $\\mathcal{N}=2$ supergravity with $AdS_{2} \\times S^{2}$ boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in $\\mathcal{N}=2$ supergravity. We explain cancellations concerning $\\frac18$-BPS black holes in $\\mathcal{N}=8$ supergravity that were observed previously. We also make comments about the interpretation of...
Directory of Open Access Journals (Sweden)
Ali Meftah
2017-06-01
Full Text Available In an attempt to improve U II analysis, the lowest configurations of both parities have been interpreted by means of the Racah-Slater parametric method, using Cowan codes. In the odd parity, including the ground state, 253 levels of the interacting configurations 5 f 3 7 s 2 + 5 f 3 6 d 7 s + 5 f 3 6 d 2 + 5 f 4 7 p + 5 f 5 are interpreted by 24 free parameters and 64 constrained ones, with a root mean square (rms deviation of 60 cm − 1 . In the even parity, the four known configurations 5 f 4 7 s , 5 f 4 6 d , 5 f 2 6 d 2 7 s , 5 f 2 6 d 7 s 2 and the unknown 5 f 2 6 d 3 form a basis for interpreting 125 levels with a rms deviation of 84 cm − 1 . Due to perturbations, the theoretical description of the higher configurations 5 f 3 7 s 7 p + 5 f 3 6 d 7 p remains unsatisfactory. The known and predicted levels of U II are used for a determination of the partition function. The parametric study led us to a re-investigation of high resolution ultraviolet spectrum of uranium recorded at the Meudon Observatory in the late eighties, of which the analysis was unachieved. In the course of the present study, a number of 451 lines of U II has been classified in the region 2344 –2955 Å. One new level has been established as 5 f 3 6 d 7 p ( 4 I 6 K ( J = 5.5 at 39113.98 ± 0.1 cm − 1 .
Quantum arrival-time distributions from intensity functions
DEFF Research Database (Denmark)
Wlodarz, Joachim
2002-01-01
The quantum time-of-arrival problem is discussed within the standard formulation of nonrelativistic quantum mechanics with parametric time. It is shown that a general class of arrival-time probability distributions results from the assumption that the arrival process of a quantum particle...
2007-01-01
An explicit expression for the partition function of two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived by a systematic enumeration of all the spin configurations pertaining to a square lattice of sixteen sites. The critical temperature is shown to be in excellent agreement with the reported values while the corresponding dimensionless magnetic field is obtained as 0.004.
The Partition Ensemble Fallacy Fallacy
Nemoto, K; Nemoto, Kae; Braunstein, Samuel L.
2002-01-01
The Partition Ensemble Fallacy was recently applied to claim no quantum coherence exists in coherent states produced by lasers. We show that this claim relies on an untestable belief of a particular prior distribution of absolute phase. One's choice for the prior distribution for an unobservable quantity is a matter of `religion'. We call this principle the Partition Ensemble Fallacy Fallacy. Further, we show an alternative approach to construct a relative-quantity Hilbert subspace where unobservability of certain quantities is guaranteed by global conservation laws. This approach is applied to coherent states and constructs an approximate relative-phase Hilbert subspace.
The realization of the wave function collapse in the linguistic interpretation of quantum mechanics
Ishikawa, Shiro
2015-01-01
Recently I proposed the linguistic interpretation of quantum mechanics, which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. This turn from physics to language does not only extend quantum theory to classical theory but also yield the quantum mechanical world view. Although the wave function collapse is prohibited in the linguistic interpretation, in this paper I show that the phenomenon like wave function collapse can be realized in the linguistic interpretation. And furthermore, I propose the justification of the von Neumann-L\\"uders projection postulate. After all, I conclude that the wave function collapse should not be adopted in the Copenhagen interpretation.
The negativity of Wigner function as a measure of quantum correlations
Siyouri, F.; El Baz, M.; Hassouni, Y.
2016-10-01
In this paper, we study comparatively the behaviors of Wigner function and quantum correlations for two quasi-Werner states formed with two general bipartite superposed coherent states. We show that the Wigner function can be used to detect and quantify the quantum correlations. However, we show that it is in fact not sensitive to all kinds of quantum correlations but only to entanglement. Then, we analyze the measure of non-classicality of quantum states based on the volume occupied by the negative part of the Wigner function.
Zeta function zeros, powers of primes, and quantum chaos.
Sakhr, Jamal; Bhaduri, Rajat K; van Zyl, Brandon P
2003-08-01
We present a numerical study of Riemann's formula for the oscillating part of the density of the primes and their integer powers. The formula consists of an infinite series of oscillatory terms, one for each zero of the zeta function on the critical line, and was derived by Riemann in his paper on primes, assuming the Riemann hypothesis. We show that high-resolution spectral lines can be generated by the truncated series at all integer powers of primes and demonstrate explicitly that the relative line intensities are correct. We then derive a Gaussian sum rule for Riemann's formula. This is used to analyze the numerical convergence of the truncated series. The connections to quantum chaos and semiclassical physics are discussed.
Conservation Laws in Quantum-Correlation-Function Dynamics
Directory of Open Access Journals (Sweden)
Wei Wang
2010-01-01
Full Text Available For a complete and lucid discussion of quantum correlation, we introduced two new first-order correlation tensors defined as linear combinations of the general coherence tensors of the quantized fields and derived the associated coherence potentials governing the propagation of quantum correlation. On the basis of these quantum optical coherence tensors, we further introduced new concepts of scalar, vector and tensor densities and presented some related properties, such as conservation laws and the wave-particle duality for quantum correlation, which provide new insights into photon statistics and quantum correlation.
Software Partitioning Technologies
2001-05-29
1 Software Partitioning Technologies Tim Skutt Smiths Aerospace 3290 Patterson Ave. SE Grand Rapids, MI 49512-1991 (616) 241-8645 skutt_timothy...Limitation of Abstract UU Number of Pages 12 2 Agenda n Software Partitioning Overview n Smiths Software Partitioning Technology n Software Partitioning...Partition Level OS Core Module Level OS Timers MMU I/O API Layer Partitioning Services 6 Smiths Software Partitioning Technology n Smiths has developed
Synthesis of Reversible Functions Beyond Gate Count and Quantum Cost
Wille, Robert; Drechsler, Rolf
2010-01-01
Many synthesis approaches for reversible and quantum logic have been proposed so far. However, most of them generate circuits with respect to simple metrics, i.e. gate count or quantum cost. On the other hand, to physically realize reversible and quantum hardware, additional constraints exist. In this paper, we describe cost metrics beyond gate count and quantum cost that should be considered while synthesizing reversible and quantum logic for the respective target technologies. We show that the evaluation of a synthesis approach may differ if additional costs are applied. In addition, a new cost metric, namely Nearest Neighbor Cost (NNC) which is imposed by realistic physical quantum architectures, is considered in detail. We discuss how existing synthesis flows can be extended to generate optimal circuits with respect to NNC while still keeping the quantum cost small.
HPAM: Hirshfeld partitioned atomic multipoles
Elking, Dennis M.; Perera, Lalith; Pedersen, Lee G.
2012-02-01
molecular charge density ρ(r) is partitioned into Hirshfeld (HD) and Hirshfeld-Iterated (HD-I) atomic charge densities ρ(r) on a grid. Atomic charges q and multipoles Qlma are calculated from the partitioned atomic charge densities ρ(r) by numerical integration. Solution method: Molecular and isolated atomic grids are generated for the molecule of interest. The ab initio density matrix P and basis functions χ(r) are read in from 'formatted checkpoint' files obtained from the Gaussian 03 or 09 quantum chemistry programs. The ab initio density is evaluated for the molecule and the isolated atoms/atomic ions on grids and used to construct Hirshfeld (HD) and Hirshfeld-I (HD-I) partitioned atomic charges densities ρ(r), which are used to calculate atomic charges q and atomic multipoles Qlma by integration. Restrictions: The ab initio density matrix can be calculated at the HF, DFT, MP2, or CCSD levels with ab initio Gaussian basis sets that include up to s, p, d, f, g functions for either closed shell or open shell molecules. Running time: The running time varies with the size of the molecule, the size of the ab initio basis set, and the coarseness of the desired grid. The run time can range from a minute or less for water to ˜15 minutes for neopentane.
Sapra, Karan; Gupta, Saurabh; Atchley, Scott; Anantharaj, Valentine; Miller, Ross; Vazhkudai, Sudharshan
2016-04-01
Efficient resource utilization is critical for improved end-to-end computing and workflow of scientific applications. Heterogeneous node architectures, such as the GPU-enabled Titan supercomputer at the Oak Ridge Leadership Computing Facility (OLCF), present us with further challenges. In many HPC applications on Titan, the accelerators are the primary compute engines while the CPUs orchestrate the offloading of work onto the accelerators, and moving the output back to the main memory. On the other hand, applications that do not exploit GPUs, the CPU usage is dominant while the GPUs idle. We utilized Heterogenous Functional Partitioning (HFP) runtime framework that can optimize usage of resources on a compute node to expedite an application's end-to-end workflow. This approach is different from existing techniques for in-situ analyses in that it provides a framework for on-the-fly analysis on-node by dynamically exploiting under-utilized resources therein. We have implemented in the Community Earth System Model (CESM) a new concurrent diagnostic processing capability enabled by the HFP framework. Various single variate statistics, such as means and distributions, are computed in-situ by launching HFP tasks on the GPU via the node local HFP daemon. Since our current configuration of CESM does not use GPU resources heavily, we can move these tasks to GPU using the HFP framework. Each rank running the atmospheric model in CESM pushes the variables of of interest via HFP function calls to the HFP daemon. This node local daemon is responsible for receiving the data from main program and launching the designated analytics tasks on the GPU. We have implemented these analytics tasks in C and use OpenACC directives to enable GPU acceleration. This methodology is also advantageous while executing GPU-enabled configurations of CESM when the CPUs will be idle during portions of the runtime. In our implementation results, we demonstrate that it is more efficient to use HFP
Banik, S K; Ray, D S; Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar
2002-01-01
Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {\\it exact} quantum analogues of their classical counterparts. The present work is {\\it independent} of path integral techniques. The theory as developed here is a natural ext...
Gentile statistics and restricted partitions
Indian Academy of Sciences (India)
C S Srivatsan; M V N Murthy; R K Bhaduri
2006-03-01
In a recent paper (Tran et al, Ann. Phys. 311, 204 (2004)), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We generalise these results to obtain an asymptotic formula for the restricted or coloured partitions $p_{k}^{s} (n)$, which is the number of partitions of an integer into the summand of th powers of integers such that each power of a given integer may occur utmost times. While the method is not rigorous, it reproduces the well-known asymptotic results for = 1 apart from yielding more general results for arbitrary values of .
Exact quantum algorithm to distinguish Boolean functions of different weights
Energy Technology Data Exchange (ETDEWEB)
Braunstein, Samuel L [Computer Science, University of York, York YO10 5DD (United Kingdom); Choi, Byung-Soo [Computer Science, University of York, York YO10 5DD (United Kingdom); Ghosh, Subhroshekhar [Indian Statistical Institute, Kolkata 700 108 (India); Maitra, Subhamoy [Applied Statistics Unit, Indian Statistical Institute, Kolkata 700 108 (India)
2007-07-20
In this work, we exploit the Grover operator for the weight analysis of a Boolean function, specifically to solve the weight-decision problem. The weight w is the fraction of all possible inputs for which the output is 1. The goal of the weight-decision problem is to find the exact weight w from the given two weights w{sub 1} and w{sub 2} satisfying a general weight condition as w{sub 1} + w{sub 2} = 1 and 0 < w{sub 1} < w{sub 2} < 1. First, we propose a limited weight-decision algorithm where the function has another constraint: a weight is in {l_brace} W{sub 1} = sin{sup 2}(k/(2k+1) {pi}/2), w{sub 2} = cos{sup 2}(k/(2k+1) {pi}/2){r_brace} for integer k. Second, by changing the phases in the last two Grover iterations, we propose a general weight-decision algorithm which is free from the above constraint. Finally, we show that when our algorithm requires O(k) queries to find w with a unit success probability, any classical algorithm requires at least {omega}(k{sup 2}) queries for a unit success probability. In addition, we show that our algorithm requires fewer queries to solve this problem compared with the quantum counting algorithm.
Design of Biotin-Functionalized Luminescent Quantum Dots
Directory of Open Access Journals (Sweden)
Kimihiro Susumu
2007-01-01
Full Text Available We report the design and synthesis of a tetraethylene glycol- (TEG- based bidentate ligand functionalized with dihydrolipoic acid (DHLA and biotin (DHLA—TEG—biotin to promote biocompatibility of luminescent quantum dots (QD's. This new ligand readily binds to CdSe—ZnS core-shell QDs via surface ligand exchange. QDs capped with a mixture of DHLA and DHLA—TEG—biotin or polyethylene glycol- (PEG- (molecular weight average ∼600 modified DHLA (DHLA—PEG600 and DHLA—TEG—biotin are easily dispersed in aqueous buffer solutions. In particular, homogeneous buffer solutions of QDs capped with a mixture of DHLA—PEG600 and DHLA—TEG—biotin that are stable over broad pH range have been prepared. QDs coated with mixtures of DHLA/DHLA—TEG—biotin and with DHLA—PEG600/DHLA—TEG—biotin were tested in surface binding assays and the results indicate that biotin groups on the QD surface interact specifically with NeutrAvidin-functionalized microtiter well plates.
Breuer, H P; Petruccione, F; Breuer, Heinz-Peter; Kappler, Bernd; Petruccione, Francesco
1997-01-01
Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open quantum system coupled to an environment consisting of an ensemble of harmonic oscillators in arbitrary pure or mixed states. It is shown that matrix elements of reduced Heisenberg picture operators and general time-ordered correlation functions can be expressed by time-symmetric expectation values of extended operators in a doubled Hilbert space. This representation allows the construction of a stochastic process in the doubled Hilbert space which enables the determination of arbitrary matrix elements and correlation functions. The numerical efficiency of the resulting stochastic simulation algorithm is investigated and compared with an alternative Monte Carlo wave function method proposed first by Dalibard et al. [Phys. Rev. Lett. {\\bf 68}, 580 (1992)]. By means of a stan...
The meaning of the wave function in search of the ontology of quantum mechanics
Gao, Shan
2017-01-01
At the heart of quantum mechanics lies the wave function, a powerful but mysterious mathematical object which has been a hot topic of debate from its earliest stages. Covering much of the recent debate and providing a comprehensive and critical review of competing approaches, this ambitious text provides new, decisive proof of the reality of the wave function. Aiming to make sense of the wave function in quantum mechanics and to find the ontological content of the theory, this book explores new ontological interpretations of the wave function in terms of random discontinuous motion of particles. Finally, the book investigates whether the suggested quantum ontology is complete in solving the measurement problem and if it should be revised in the relativistic domain. A timely addition to the literature on the foundations of quantum mechanics, this book is of value to students and researchers with an interest in the philosophy of physics. Presents a concise introduction to quantum mechanics, including the c...
Energy Technology Data Exchange (ETDEWEB)
Foda, Omar; Wheeler, Michael [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia)
2007-01-15
Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h columns, h > 0, an h-path, then 1. Every h-path can assume one of two possible colours. 2. There is a unique way to move along an h-path from any column to another.
Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals
Hamilton, I. P.; Mosna, Ricardo A.; Site, L. Delle
2006-01-01
We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson's stochastic approach to quant...
Functional Approach to Quantum Decoherence and the Classical Final Limit
Castagnino, M A; Castagnino, Mario; Laura, Roberto
2000-01-01
For a wide set of quantum systems it is demonstrated that the quantum regime can be considered as the transient phase while the final classical statistical regime is a permanent state. A basis where exact matrix decoherence appears for these final states is found. The relation with the decoherence of histories formalism is studied. A set of final intrinsically consistent histories is found.
Jayatilaka, Dylan; Dittrich, Birger
2008-05-01
An approach is outlined for X-ray structure refinement using atomic density fragments obtained by Hirshfeld partitioning of quantum-mechanical density fragments. Results are presented for crystal structure refinements of urea and benzene using these 'Hirshfeld atoms'. Using this procedure, the quantum-mechanical non-spherical electron density is taken into account in the structural model based on the conformation found in the crystal. Contrary to current consensus in structure refinement, the anisotropic displacement parameters of H atoms can be reproduced from neutron diffraction measurements simply from a least-squares fit using the Hirshfeld atoms derived from the BLYP level of theory and including a simple point-charge model to treat the crystal environment.
Directory of Open Access Journals (Sweden)
Amin Qorbani
2011-12-01
Full Text Available Fractal Image Compression is a well-known problem which is in the class of NP-Hard problems.Quantum Evolutionary Algorithm is a novel optimization algorithm which uses a probabilisticrepresentation for solutions and is highly suitable for combinatorial problems like Knapsack problem.Genetic algorithms are widely used for fractal image compression problems, but QEA is not used for thiskind of problems yet. This paper improves QEA whit change population size and used it in fractal imagecompression. Utilizing the self-similarity property of a natural image, the partitioned iterated functionsystem (PIFS will be found to encode an image through Quantum Evolutionary Algorithm (QEA methodExperimental results show that our method has a better performance than GA and conventional fractalimage compression algorithms.
Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions
Chuang, Wu-yen
2008-01-01
In this paper we study the relation between pyramid partitions with a general empty room configuration (ERC) and the BPS states of D-branes on the resolved conifold. We find that the generating function for pyramid partitions with a length n ERC is exactly the same as the D6/D2/D0 BPS partition function on the resolved conifold in particular Kaehler chambers. We define a new type of pyramid partition with a finite ERC that counts the BPS degeneracies in certain other chambers. The D6/D2/D0 partition functions in different chambers were obtained by applying the wall crossing formula. On the other hand, the pyramid partitions describe $T^3$ fixed points of the moduli space of a quiver quantum mechanics. This quiver arises after we apply Seiberg dualities to the D6/D2/D0 system on the conifold and choose a particular set of FI parameters. The arrow structure of the dual quiver is confirmed by computation of the Ext group between the sheaves. We show that the superpotential and the stability condition of the dual...
From quantum Schubert polynomials to k-Schur functions via the Toda lattice
Lam, Thomas
2010-01-01
We show that Lapointe-Lascoux-Morse k-Schur functions (at t=1) and Fomin-Gelfand-Postnikov quantum Schubert polynomials can be obtained from each other by a rational substitution. This is based upon Kostant's solution of the Toda lattice and Peterson's work on quantum Schubert calculus.
Constraints on Airy function zeros from quantum-mechanical sum rules
Belloni, M
2010-01-01
We derive new constraints on the zeros of Airy functions by using the so-called quantum bouncer system to evaluate quantum-mechanical sum rules and perform perturbation theory calculations for the Stark effect. Using commutation and completeness relations, we show how to systematically evaluate sums of the form $S_{p}(n) = \\sum_{k \
Green's functions technique for calculating the emission spectrum in a quantum dot-cavity system
Directory of Open Access Journals (Sweden)
Edgar Arturo Gómez
2016-12-01
Full Text Available We introduce the Green's functions technique as an alternative theory to the quantum regression theorem formalism for calculating the two-time correlation functions in open quantum systems at the steady state. In order to investigate the potential of this theoretical approach, we consider a dissipative system composed of a single quantum dot inside a semiconductor cavity and the emission spectrum is computed due to the quantum dot as well as the cavity. We propose an algorithm based on the Green's functions technique for computing the emission spectrum that can easily be adapted to more complex open quantum systems. We found that the numerical results based on the Green's functions technique are in perfect agreement with the quantum regression theorem formalism. Moreover, it allows overcoming the inherent theoretical difficulties associated with the direct application of the quantum regression theorem in open quantum systems. Received: 6 September 2016, Accepted: 5 November 2016; Edited by: J. P. Paz; DOI: http://dx.doi.org/10.4279/PIP.080008 Cite as: E A Gómez, J D Hernández-Rivero, H Vinck-Posada, Papers in Physics 8, 080008 (2016
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; WANG Yong
2006-01-01
In Phys. Lett. A 313 (2003) 343 we have found that the self-reciprocal Hankel transformation (HT) is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations' transformation in quantum mechanics.
Cao, Hujia; Ma, Junliang; Huang, Lin; Qin, Haiyan; Meng, Renyang; Li, Yang; Peng, Xiaogang
2016-12-07
Single-molecular spectroscopy reveals that photoluminescence (PL) of a single quantum dot blinks, randomly switching between bright and dim/dark states under constant photoexcitation, and quantum dots photobleach readily. These facts cast great doubts on potential applications of these promising emitters. After ∼20 years of efforts, synthesis of nonblinking quantum dots is still challenging, with nonblinking quantum dots only available in red-emitting window. Here we report synthesis of nonblinking quantum dots covering most part of the visible window using a new synthetic strategy, i.e., confining the excited-state wave functions of the core/shell quantum dots within the core quantum dot and its inner shells (≤ ∼5 monolayers). For the red-emitting ones, the new synthetic strategy yields nonblinking quantum dots with small sizes (∼8 nm in diameter) and improved nonblinking properties. These new nonblinking quantum dots are found to be antibleaching. Results further imply that the PL blinking and photobleaching of quantum dots are likely related to each other.
The Fibonacci partition triangles
Fahr, Philipp
2011-01-01
In two previous papers we have presented partition formulae for the Fibonacci numbers motivated by the appearance of the Fibonacci numbers in the representation theory of the 3-Kronecker quiver and its universal cover, the 3-regular tree. Here we show that the basic information can be rearranged in two triangles. They are quite similar to the Pascal triangle of the binomial coefficients, but in contrast to the additivity rule for the Pascal triangle, we now deal with additivity along hooks, or, equivalently, with additive functions for valued translation quivers. As for the Pascal triangle, we see that the numbers in these Fibonacci partition triangles are given by evaluating polynomials. We show that the two triangles can be obtained from each other by looking at differences of numbers, it is sufficient to take differences along arrows and knight's moves.
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.
The properties of Q-deformed hyperbolic and trigonometric functions in quantum deformation
Energy Technology Data Exchange (ETDEWEB)
Deta, U. A., E-mail: utamaalan@yahoo.co.id, E-mail: utamadeta@unesa.ac.id [Department of Physics, the State University of Surabaya (Unesa), Jl. Ketintang, Surabaya 60231 (Indonesia); Suparmi [Departmet of Physics, Sebelas Maret University, Jl. Ir. Sutami 36A Kentingan, Surakarta 57126 (Indonesia)
2015-09-30
Quantum deformation has been studied due to its relation with applications in nuclear physics, conformal field theory, and statistical-quantum theory. The q-deformation of hyperbolic function was introduced by Arai. The application of q-deformed functions has been widely used in quantum mechanics. The properties of this two kinds of system explained in this paper including their derivative. The graph of q-deformed functions presented using Matlab. The special case is given for modified Poschl-Teller plus q-deformed Scarf II trigonometry potentials.
Rocha, Julio C S; Landau, David P; Bachmann, Michael
2014-01-01
For the estimation of transition points of finite elastic, flexible polymers with chain lengths from $13$ to $309$ monomers, we compare systematically transition temperatures obtained by the Fisher partition function zeros approach with recent results from microcanonical inflection-point analysis. These methods rely on accurate numerical estimates of the density of states, which have been obtained by advanced multicanonical Monte Carlo sampling techniques. Both the Fisher zeros method and microcanonical inflection-point analysis yield very similar results and enable the unique identification of transition points in finite systems, which is typically impossible in the conventional canonical analysis of thermodynamic quantities.
Quantum Drude friction for time-dependent density functional theory
Neuhauser, Daniel; Lopata, Kenneth
2008-10-01
Friction is a desired property in quantum dynamics as it allows for localization, prevents backscattering, and is essential in the description of multistage transfer. Practical approaches for friction generally involve memory functionals or interactions with system baths. Here, we start by requiring that a friction term will always reduce the energy of the system; we show that this is automatically true once the Hamiltonian is augmented by a term of the form ∫a(q ;n0)[∂j(q,t)/∂t]ṡJ(q)dq, which includes the current operator times the derivative of its expectation value with respect to time, times a local coefficient; the local coefficient will be fitted to experiment, to more sophisticated theories of electron-electron interaction and interaction with nuclear vibrations and the nuclear background, or alternately, will be artificially constructed to prevent backscattering of energy. We relate this term to previous results and to optimal control studies, and generalize it to further operators, i.e., any operator of the form ∫a(q ;n0)[∂c(q,t)/∂t]ṡC(q)dq (or a discrete sum) will yield friction. Simulations of a small jellium cluster, both in the linear and highly nonlinear excitation regime, demonstrate that the friction always reduces energy. The energy damping is essentially double exponential; the long-time decay is almost an order of magnitude slower than the rapid short-time decay. The friction term stabilizes the propagation (split-operator propagator here), therefore increasing the time-step needed for convergence, i.e., reducing the overall computational cost. The local friction also allows the simulation of a metal cluster in a uniform jellium as the energy loss in the excitation due to the underlying corrugation is accounted for by the friction. We also relate the friction to models of coupling to damped harmonic oscillators, which can be used for a more sophisticated description of the coupling, and to memory functionals. Our results open the
Moretti, Valter
2016-01-01
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of so-called frame functions, introduced by A.M. Gleason to prove his celebrated theorem. In particular, the problem of associating quantum state with positive Liouville densities is tackled from an axiomatic point of view, proving a theorem classifying all possible correspondences. A similar result is established for classical observables representing quantum ones. These correspondences turn out to be encoded in a one-parameter class and, in both cases, the classical objects representing quantum ones result to be frame functions. The requirements of $U(n)$ covariance and (convex) linearity play a central r\\^ole in the proof of those theorems. A new characterization of classical observables describing quantum observables is presented, together with a geometric description of the ...
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.
Papike, J. J.; Le, L.; Burger, P. V.; Shearer, C. K.; Bell, A. S.; Jones, J.
2013-01-01
Our research on valence state partitioning began in 2005 with a review of Cr, Fe, Ti, and V partitioning among crystallographic sites in olivine, pyroxene, and spinel [1]. That paper was followed by several on QUE94201 melt composition and specifically on Cr, V, and Eu partitioning between pyroxene and melt [2-5]. This paper represents the continuation of our examination of the partitioning of multivalent V between olivine, spinel, and melt in martian olivine-phyric basalts of Y980459 composition [6, 7]. Here we introduce a new, potentially powerful oxybarometer, V partitioning between spinel and olivine, which can be used when no melt is preserved in the meteorite. The bulk composition of QUE94201 was ideal for our study of martian pyroxene-phyric basalts and specifically the partitioning between pyroxene-melt for Cr, V, and Eu. Likewise, bulk composition Y980459 is ideal for the study of martian olivine-phyric basalts and specifically for olivine-melt, spinel-melt, and spinel-olivine partitioning of V as a function of oxygen fugacity.
On the Green's function and iterative solutions of Loop Quantum Cosmology
Shojai, F.; Shojai, A.
2006-01-01
Here we shall find the Green’s function of the difference equation of loop quantum cosmology. To illustrate how to use it, we shall obtain an iterative solution for closed model and evaluate its corresponding Bohmian trajectory.
Quantum scalar fields in the half-line. A heat kernel/zeta function approach
Mateos Guilarte, Juan; Muñoz-Castañeda, Jose María; Senosiaín Aramendía, María Jesús
2009-01-01
[EN]In this paper we shall study vacuum fluctuations of a single scalar field with Dirichlet boundary conditions in a finite but very long line. The spectral heat kernel, the heat partition function and the spectral zeta function are calculated in terms of Riemann Theta functions, the error function, and hypergeometric PFQ functions. [ES]En este artículo vamos a estudiar las fluctuaciones en el vacío de un campo escalar con las condiciones de contorno de Dirichlet en una línea finita pero muy...
Implementation of transmission functions for an optimized three-terminal quantum dot heat engine
Schiegg, Christian H.; Dzierzawa, Michael; Eckern, Ulrich
2017-03-01
We consider two modifications of a recently proposed three-terminal quantum dot heat engine. First, we investigate the necessity of the thermalization assumption, namely that electrons are always thermalized by inelastic processes when traveling across the cavity where the heat is supplied. Second, we analyze various arrangements of tunneling-coupled quantum dots in order to implement a transmission function that is superior to the Lorentzian transmission function of a single quantum dot. We show that the maximum power of the heat engine can be improved by about a factor of two, even for a small number of dots, by choosing an optimal structure.
Accelerating Wave Function Convergence in Interactive Quantum Chemical Reactivity Studies
Mühlbach, Adrian H; Reiher, Markus
2015-01-01
The inherently high computational cost of iterative self-consistent-field (SCF) methods proves to be a critical issue delaying visual and haptic feedback in real-time quantum chemistry. In this work, we introduce two schemes for SCF acceleration. They provide a guess for the initial density matrix of the SCF procedure generated by extrapolation techniques. SCF optimizations then converge in fewer iterations, which decreases the execution time of the SCF optimization procedure. To benchmark the proposed propagation schemes, we developed a test bed for performing quantum chemical calculations on sequences of molecular structures mimicking real-time quantum chemical explorations. Explorations of a set of six model reactions employing the semi-empirical methods PM6 and DFTB3 in this testing environment showed that the proposed propagation schemes achieved speedups of up to thirty percent as a consequence of a reduced number of SCF iterations.
Sanoubar, Rabab; Orsini, Francesco; Gianquinto, Giorgio
2013-11-01
Vegetable grafting is commonly claimed to improve crop's tolerance to biotic and abiotic stresses, including salinity. Although the use of inter-specific graftings is relatively common, whether the improved salt tolerance should be attributed to the genotypic background rather than the grafting per se is a matter of discussion among scientists. It is clear that most of published research has to date overlooked the issue, with the mutual presence of self-grafted and non-grafted controls resulting to be quite rare within experimental evidences. It was recently demonstrated that the genotype of the rootstock and grafting per se are responsible respectively for the differential ion accumulation and partitioning as well as to the stomatal adaptation to the stress. The present paper contributes to the ongoing discussion with further data on the differences associated to salinity response in a range of grafted melon combinations.
Zhang, Xiaomeng; Ding, Shushu; Cao, Sumei; Zhu, Anwei; Shi, Guoyue
2016-06-15
Selective and sensitive detection of extracellular lactate is of fundamental significance for studying the metabolic alterations in tumor progression. Here we report the rational design and synthesis of a quantum-dot-hydrogel-based fluorescent probe for biosensing and bioimaging the extracellular lactate. By surface engineering the destabilized quantum dot sol with Nile Blue, the destabilized Nile-Blue-functionalized quantum dot sol cannot only self-assemble forming quantum dot hydrogel but also monitor lactate in the presence of nicotinamide adenine dinucleotide cofactor and lactate dehydrogenase through fluorescence resonance energy transfer. Notably, the surface engineered quantum dot hydrogel show high selectivity toward lactate over common metal ions, amino acids and other small molecules that widely coexist in biological system. Moreover, the destabilized Nile-Blue-functionalized quantum dots can encapsulate isolated cancer cells when self-assembled into a hydrogel and thus specifically detect and image the extracellular lactate metabolism. By virtue of these properties, the functionalized quantum dot hydrogel was further successfully applied to monitor the effect of metabolic agents.
Monitoring Ion Channel Function In Real Time Through Quantum Decoherence
Hall, L T; Cole, J H; Städler, B; Caruso, F; Mulvaney, P; Wrachtrup, J; Hollenberg, L C L
2009-01-01
In drug discovery research there is a clear and urgent need for non-invasive detection of cell membrane ion channel operation with wide-field capability. Existing techniques are generally invasive, require specialized nano structures, or are only applicable to certain ion channel species. We show that quantum nanotechnology has enormous potential to provide a novel solution to this problem. The nitrogen-vacancy (NV) centre in nano-diamond is currently of great interest as a novel single atom quantum probe for nanoscale processes. However, until now, beyond the use of diamond nanocrystals as fluorescence markers, nothing was known about the quantum behaviour of a NV probe in the complex room temperature extra-cellular environment. For the first time we explore in detail the quantum dynamics of a NV probe in proximity to the ion channel, lipid bilayer and surrounding aqueous environment. Our theoretical results indicate that real-time detection of ion channel operation at millisecond resolution is possible by d...
Classical Ising model test for quantum circuits
Geraci, Joseph; Lidar, Daniel A.
2010-07-01
We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model partition function in terms of quadratically signed weight enumerators (QWGTs), which are polynomials that arise naturally in an expansion of quantum circuits in terms of rotations involving Pauli matrices. We combine this expression with a known efficient classical algorithm for the Ising partition function of any planar graph in the absence of an external magnetic field, and the Robertson-Seymour theorem from graph theory. We give as an example a set of quantum circuits with a small number of non-nearest-neighbor gates which admit an efficient classical simulation.
Directory of Open Access Journals (Sweden)
Parnaíba-da Silva Antenor J.
2006-01-01
Full Text Available RHF and MP2 ab initio molecular orbital calculations using the 4-31G**, 6-311G** and cc-pVTZ basis sets have revealed that the Green's function matrix element (G D,A values show a good correlation with the amount of intermolecular transferred charges obtained from different charge partitioning schemes for the CNH?CNH, NCH?CNH, CNH?NCH and NCH?NCH hydrogen bonded complexes. This is evident specially when the hydrogen bond distance is progressively increased from the equilibrium position until 4.5 Å. However, G D,A values show a better linear correlation with deltaQ values using corrected Mülliken charges, which are obtained from the charge-charge flux-overlap (CCFO model for infrared intensities. In this case, both G D,A and deltaQcorr form two practically superposed exponential curves. On the other hand, G D,A values show a smaller agreement with deltaQ values obtained from atomic charges derived from natural bonding orbitals. This is clearly verified when considering the first order exponential decay rate of G D,A versus deltaQ obtained from different charge partitioning schemes.
Energy Technology Data Exchange (ETDEWEB)
Anas, M. M.; Othman, A. P.; Gopir, G. [School of Applied Physics, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600, Bangi, Selangor (Malaysia)
2014-09-03
Density functional theory (DFT), as a first-principle approach has successfully been implemented to study nanoscale material. Here, DFT by numerical basis-set was used to study the quantum confinement effect as well as electronic properties of silicon quantum dots (Si-QDs) in ground state condition. Selection of quantum dot models were studied intensively before choosing the right structure for simulation. Next, the computational result were used to examine and deduce the electronic properties and its density of state (DOS) for 14 spherical Si-QDs ranging in size up to ∼ 2 nm in diameter. The energy gap was also deduced from the HOMO-LUMO results. The atomistic model of each silicon QDs was constructed by repeating its crystal unit cell of face-centered cubic (FCC) structure, and reconstructed until the spherical shape obtained. The core structure shows tetrahedral (T{sub d}) symmetry structure. It was found that the model need to be passivated, and hence it was noticed that the confinement effect was more pronounced. The model was optimized using Quasi-Newton method for each size of Si-QDs to get relaxed structure before it was simulated. In this model the exchange-correlation potential (V{sub xc}) of the electrons was treated by Local Density Approximation (LDA) functional and Perdew-Zunger (PZ) functional.
The Fractional Statistics of Generalized Haldane Wave Function in 4D Quantum Hall Effect
Institute of Scientific and Technical Information of China (English)
WANGKe-Lin; WANShao-Long; CHENQing; XUFei
2003-01-01
Recently, a generalization of Laughlin's wave function expressed in Haldane's spherical geometry is con-structed in 4D quantum Hall effect. In fact, it is a membrane wave function in CP3 space. In this article, we use non-Abelian Berry phase to anaJyze the statistics of this membrane wave function. Our results show that the membrane wave function obeys fractional statistics. It is the rare example to realize fractional statistics in higher-dimensiona space than 2D. And, it will help to make clear the unresolved problems in 4D quantum Hall effect.
The Fractional Statistics of Generalized Haldane Wave Function in 4D Quantum Hall Effect
Institute of Scientific and Technical Information of China (English)
XU Fei; WANG Ke-Lin; WAN Shao-Long; CHEN Qing
2003-01-01
Recently, a generalization of Laughlin's wave function expressed in Haldane's spherical geometry is con-structed in 4D quantum Hall effect. In fact, it is a membrane wave function in CP3 space. In this article, we usenon-Abelian Berry phase to analyze the statistics of this membrane wave function. Our results show that the membranewave function obeys fractional statistics. It is the rare example to realize fractional statistics in higher-dimensional spacethan 2D. And, it will help to make clear the unresolved problems in 4D quantum Hall effect.
2D quantum gravity at three loops: a counterterm investigation
Leduc, Laetitia
2015-01-01
We analyse the divergences of the three-loop partition function at fixed area in 2D quantum gravity. Considering the Liouville action in the Kahler formalism, we extract the coefficient of the leading divergence in $\\sim A\\Lambda^2 (\\ln A\\Lambda^2)^2$. This coefficient is non-vanishing. We discuss the counterterms one can and must add and compute their precise contribution to the partition function. This allows us to conclude that every local and non-local divergence in the partition function can be balanced by local counterterms, with the only exception of the maximally non-local divergence $(\\ln A\\Lambda^2)^3$. Yet, this latter is computed and does cancel between the different three-loop diagrams. Thus, requiring locality of the counterterms is enough to renormalize the partition function. Finally, the structure of the new counterterms strongly suggests that they can be understood as a renormalization of the measure action.
2D quantum gravity at three loops: A counterterm investigation
Directory of Open Access Journals (Sweden)
Lætitia Leduc
2016-02-01
Full Text Available We analyze the divergences of the three-loop partition function at fixed area in 2D quantum gravity. Considering the Liouville action in the Kähler formalism, we extract the coefficient of the leading divergence ∼AΛ2(lnAΛ22. This coefficient is non-vanishing. We discuss the counterterms one can and must add and compute their precise contribution to the partition function. This allows us to conclude that every local and non-local divergence in the partition function can be balanced by local counterterms, with the only exception of the maximally non-local divergence (lnAΛ23. Yet, this latter is computed and does cancel between the different three-loop diagrams. Thus, requiring locality of the counterterms is enough to renormalize the partition function. Finally, the structure of the new counterterms strongly suggests that they can be understood as a renormalization of the measure action.
Functional Basis for Efficient Physical Layer Classical Control in Quantum Processors
Ball, Harrison; Nguyen, Trung; Leong, Philip H. W.; Biercuk, Michael J.
2016-12-01
The rapid progress seen in the development of quantum-coherent devices for information processing has motivated serious consideration of quantum computer architecture and organization. One topic which remains open for investigation and optimization relates to the design of the classical-quantum interface, where control operations on individual qubits are applied according to higher-level algorithms; accommodating competing demands on performance and scalability remains a major outstanding challenge. In this work, we present a resource-efficient, scalable framework for the implementation of embedded physical layer classical controllers for quantum-information systems. Design drivers and key functionalities are introduced, leading to the selection of Walsh functions as an effective functional basis for both programing and controller hardware implementation. This approach leverages the simplicity of real-time Walsh-function generation in classical digital hardware, and the fact that a wide variety of physical layer controls, such as dynamic error suppression, are known to fall within the Walsh family. We experimentally implement a real-time field-programmable-gate-array-based Walsh controller producing Walsh timing signals and Walsh-synthesized analog waveforms appropriate for critical tasks in error-resistant quantum control and noise characterization. These demonstrations represent the first step towards a unified framework for the realization of physical layer controls compatible with large-scale quantum-information processing.
Tunable quantum beam splitters for coherent manipulation of a solid-state tripartite qubit system
Sun, Guozhu; Wen, Xueda; Mao, Bo; Chen, Jian; Yu, Yang; Wu, Peiheng; Han, Siyuan
2010-01-01
Coherent control of quantum states is at the heart of implementing solid-state quantum processors and testing quantum mechanics at the macroscopic level. Despite significant progress made in recent years in controlling single- and bi-partite quantum systems, coherent control of quantum wave function in multipartite systems involving artificial solid-state qubits has been hampered due to the relatively short decoherence time and lack of precise control methods. Here we report the creation and coherent manipulation of quantum states in a tripartite quantum system, which is formed by a superconducting qubit coupled to two microscopic two-level systems (TLSs). The avoided crossings in the system's energy-level spectrum due to the qubit–TLS interaction act as tunable quantum beam splitters of wave functions. Our result shows that the Landau–Zener–Stückelberg interference has great potential in precise control of the quantum states in the tripartite system. PMID:20975719
On the partition sum of the NS five-brane
Dijkgraaf, R; Vonk, M
2002-01-01
We study the Type IIA NS five-brane wrapped on a Calabi-Yau manifold X in a double-scaled decoupling limit. We calculate the euclidean partition function in the presence of a flat RR 3-form field. The classical contribution is given by a sum over fluxes of the self-dual tensor field which reduces to a theta-function. The quantum contributions are computed using a T-dual IIB background where the five-branes are replaced by an ALE singularity. Using the supergravity effective action we find that the loop corrections to the free energy are given by B-model topological string amplitudes. This seems to provide a direct link between the double-scaled little strings on the five-brane worldvolume and topological strings. Both the classical and quantum contributions to the partition function satisfy (conjugate) holomorphic anomaly equations, which explains an observation of Witten relating topological string theory to the quantization of three-form fields.
Institute of Scientific and Technical Information of China (English)
LIU Hong-Xia; WANG Zun-Yao; ZHAI Zhi-Cai; LIU Hong-Yan; WANG Lian-Sheng
2007-01-01
Optimized calculation of 35 dialkyl phenyl phosphate compounds (OPs) was carried out at the B3LYP/6-31G* level in Gaussian 98 program. Based on the theoretical linear solvation energy relationship (TLSER) model, the obtained parameters were taken as theoretical descriptors to establish the novel QSPR model for predicting n-octanol/water partition coefficients (IgKow) of OPs. The new model achieved in this work contains three variables, i.e., molecular volume (Vm),dipole moment of the molecules (μ) and enthalpy (H0). For this model, R2 = 0.9167 and SD = 0.31 at large t values. In addition, the variation inflation factors (VIF) of variables are all close to 1.0,suggesting high accuracy of the predicting model. And the results of cross-validation test (q2 =0.8993) and method validation also showed the model of this study exhibited optimum stability and better predictive power than that from semi-empirical method. The model achieved can be used to predict lgKow of congeneric compounds.
Photon reflection by a quantum mirror: a wave function approach
Corrêa, Raul
2016-01-01
We derive from first principles the momentum exchange between a photon and a quantum mirror upon reflection, by considering the boundary conditions imposed by the mirror surface on the photon wave equation. We show that the system generally ends up in an entangled state, unless the mirror position uncertainty is much smaller than the photon wavelength, when the mirror behaves classically. Our treatment leads us directly to the conclusion that the photon momentum has the known value hk/2{\\pi}. This implies that when the mirror is immersed in a dielectric medium the photon radiation pressure is proportional to the medium refractive index n. Our work thus contributes to the longstanding Abraham-Minkowski debate about the momentum of light in a medium. We interpret the result by associating the Minkowski momentum (which is proportional to n) with the canonical momentum of light, which appears naturally in quantum formulations.
Quantum optical coherence in cytoskeletal microtubules: implications for brain function.
Jibu, M; Hagan, S; Hameroff, S R; Pribram, K H; Yasue, K
1994-01-01
'Laser-like,' long-range coherent quantum phenomena may occur biologically within cytoskeletal microtubules. This paper presents a theoretical prediction of the occurrence in biological media of the phenomena which we term 'superradiance' and 'self-induced transparency'. Interactions between the electric dipole field of water molecules confined within the hollow core of microtubules and the quantized electromagnetic radiation field are considered, and microtubules are theorized to play the roles of non-linear coherent optical devices. Superradiance is a specific quantum mechanical ordering phenomenon with characteristic times much shorter than those of thermal interaction. Consequently, optical signalling (and computation) in microtubules would be free from both thermal noise and loss. Superradiant optical computing in networks of microtubules and other cytoskeletal structures may provide a basis for biomolecular cognition and a substrate for consciousness.
Innovative Ge Quantum Dot Functional Sensing/Metrology Devices
2015-05-20
on Fiber Optics and Photonics, Kharagpur, India , 13 - 16 December, 2014. (2) P. W. Li, (Invited Talk) 2014, “Designer germanium quantum dots for...disclosure/ Patent (title, date submitted): (1) “Method for manufacturing gate stack structure in insta-metal-oxide-semiconductor Field-effect-transistor...by Wei-Ting Lai, T. George, and P. W. Li, Taiwan and US patents , (Pending), Dec. 2014. (2) “Method For Forming a Thermoelectric Film Having a Micro
Constraints on Airy function zeros from quantum-mechanical sum rules
Belloni, M.; Robinett, R. W.
2009-02-01
We derive new constraints on the zeros of Airy functions by using the so-called quantum bouncer system to evaluate quantum-mechanical sum rules and perform perturbation theory calculations for the Stark effect. Using commutation and completeness relations, we show how to systematically evaluate sums of the form Sp(n) = ∑k≠n1/(ζk - ζn)p, for natural p > 1, where -ζn is the nth zero of Ai(ζ).
Classification algorithms using adaptive partitioning
Binev, Peter
2014-12-01
© 2014 Institute of Mathematical Statistics. Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set approximation to the Bayes set and thus fall into the general category of set estimators. In contrast with the most studied tree-based algorithms, which utilize piecewise constant approximation on the generated partition [IEEE Trans. Inform. Theory 52 (2006) 1335.1353; Mach. Learn. 66 (2007) 209.242], we consider decorated trees, which allow us to derive higher order methods. Convergence rates for these methods are derived in terms the parameter - of margin conditions and a rate s of best approximation of the Bayes set by decorated adaptive partitions. They can also be expressed in terms of the Besov smoothness β of the regression function that governs its approximability by piecewise polynomials on adaptive partition. The execution of the algorithms does not require knowledge of the smoothness or margin conditions. Besov smoothness conditions are weaker than the commonly used Holder conditions, which govern approximation by nonadaptive partitions, and therefore for a given regression function can result in a higher rate of convergence. This in turn mitigates the compatibility conflict between smoothness and margin parameters.
Exploring gravitational statistics not based on quantum dynamical assumptions
Mandrin, P A
2016-01-01
Despite considerable progress in several approaches to quantum gravity, there remain uncertainties on the conceptual level. One issue concerns the different roles played by space and time in the canonical quantum formalism. This issue occurs because the Hamilton-Jacobi dynamics is being quantised. The question then arises whether additional physically relevant states could exist which cannot be represented in the canonical form or as a partition function. For this reason, the author has explored a statistical approach (NDA) which is not based on quantum dynamical assumptions and does not require space-time splitting boundary conditions either. For dimension 3+1 and under thermal equilibrium, NDA simplifies to a path integral model. However, the general case of NDA cannot be written as a partition function. As a test of NDA, one recovers general relativity at low curvature and quantum field theory in the flat space-time approximation. Related paper: arxiv:1505.03719.
Reducibility of quantum representations of mapping class groups
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Fjelstad, Jens
2010-01-01
In this paper we provide a general condition for the reducibility of the Reshetikhin–Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove that the qu......In this paper we provide a general condition for the reducibility of the Reshetikhin–Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove...... that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture...
Energy Technology Data Exchange (ETDEWEB)
Pilla, Viviane, E-mail: vivianepilla@infis.ufu.br [Universidade Federal de Uberlandia (UFU), Instituto de Fisica (Brazil); Munin, Egberto [Universidade Camilo Castelo Branco (UNICASTELO), Centro de Engenharia Biomedica (Brazil)
2012-10-15
The thermo-optical parameters of cadmium selenide/zinc sulfide (CdSe/ZnS) core-shell quantum dots (QDs) suspended in aqueous solutions were measured using a Thermal Lens (TL) technique. TL transient measurements were performed using the mode-mismatched dual-beam (excitation and probe) configuration. A He-Ne laser at {lambda}{sub p} = 632.8 nm was used as the probe beam, and an Ar{sup +} laser (at {lambda}{sub e} = 514.5 nm) was used as the excitation beam to study the effect of the core sizes (2-4 nm) of CdSe/ZnS nanocrystals functionalized with amine (R-NH{sub 2}) or carboxyl (R-COOH) groups. The average values of the thermal diffusivity D = (1.48 {+-} 0.06) Multiplication-Sign 10{sup -3} cm{sup 2}/s obtained for QDs samples are in good agreement with the pure water solvent result. The fraction thermal load ({phi}) and radiative quantum efficiencies ({eta}) of the functionalized CdSe/ZnS QDs were determined and compared with non-functionalized CdSe/ZnS QDs. The obtained {eta} values for non-functionalized CdSe/ZnS are slightly higher than those for the QDs functionalized with amine or carboxyl groups.
Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr
2016-10-10
In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic-to-paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.
Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr
2016-10-01
In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic-to-paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.
Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere
Energy Technology Data Exchange (ETDEWEB)
Souza Batista, C.L. de [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Dingping Li [Perugia Univ. (Italy). Dipt. di Fisica
1996-07-01
We present a framework for the analytic calculations of the hierarchical wave functions and the composite fermion wave functions in the fractional quantum Hall effect on the sphere by using projective coordinates. Then we calculate the overlaps between these two wave functions at various fillings and small numbers of electrons. We find that the overlaps are most equal to one. This gives a further evidence that two theories of the fractional quantum Hall effect, the hierarchical theory, are physically equivalent. (author). 31 refs., 2 tabs.
Mezey, Paul G
2014-09-16
Conspectus Just as complete molecules have no boundaries and have "fuzzy" electron density clouds approaching zero density exponentially at large distances from the nearest nucleus, a physically justified choice for electron density fragments exhibits similar behavior. Whereas fuzzy electron densities, just as any fuzzy object, such as a thicker cloud on a foggy day, do not lend themselves to easy visualization, one may partially overcome this by using isocontours. Whereas a faithful representation of the complete fuzzy density would need infinitely many such isocontours, nevertheless, by choosing a selected few, one can still obtain a limited pictorial representation. Clearly, such images are of limited value, and one better relies on more complete mathematical representations, using, for example, density matrices of fuzzy fragment densities. A fuzzy density fragmentation can be obtained in an exactly additive way, using the output from any of the common quantum chemical computational techniques, such as Hartree-Fock, MP2, and various density functional approaches. Such "fuzzy" electron density fragments properly represented have proven to be useful in a rather wide range of applications, for example, (a) using them as additive building blocks leading to efficient linear scaling macromolecular quantum chemistry computational techniques, (b) the study of quantum chemical functional groups, (c) using approximate fuzzy fragment information as allowed by the holographic electron density theorem, (d) the study of correlations between local shape and activity, including through-bond and through-space components of interactions between parts of molecules and relations between local molecular shape and substituent effects, (e) using them as tools of density matrix extrapolation in conformational changes, (f) physically valid averaging and statistical distribution of several local electron densities of common stoichiometry, useful in electron density databank mining, for
Multiple-resonance local wave functions for accurate excited states in quantum Monte Carlo
Zulfikri, Habiburrahman; Amovilli, Claudio; Filippi, Claudia
2016-01-01
We introduce a novel class of local multideterminant Jastrow–Slater wave functions for the efficient and accurate treatment of excited states in quantum Monte Carlo. The wave function is expanded as a linear combination of excitations built from multiple sets of localized orbitals that correspond to
Directory of Open Access Journals (Sweden)
C. Wang
2017-06-01
Full Text Available Gas–particle partitioning governs the distribution, removal, and transport of organic compounds in the atmosphere and the formation of secondary organic aerosol (SOA. The large variety of atmospheric species and their wide range of properties make predicting this partitioning equilibrium challenging. Here we expand on earlier work and predict gas–organic and gas–aqueous phase partitioning coefficients for 3414 atmospherically relevant molecules using COSMOtherm, SPARC Performs Automated Reasoning in Chemistry (SPARC, and poly-parameter linear free-energy relationships. The Master Chemical Mechanism generated the structures by oxidizing primary emitted volatile organic compounds. Predictions for gas–organic phase partitioning coefficients (KWIOM/G by different methods are on average within 1 order of magnitude of each other, irrespective of the numbers of functional groups, except for predictions by COSMOtherm and SPARC for compounds with more than three functional groups, which have a slightly higher discrepancy. Discrepancies between predictions of gas–aqueous partitioning (KW/G are much larger and increase with the number of functional groups in the molecule. In particular, COSMOtherm often predicts much lower KW/G for highly functionalized compounds than the other methods. While the quantum-chemistry-based COSMOtherm accounts for the influence of intra-molecular interactions on conformation, highly functionalized molecules likely fall outside of the applicability domain of the other techniques, which at least in part rely on empirical data for calibration. Further analysis suggests that atmospheric phase distribution calculations are sensitive to the partitioning coefficient estimation method, in particular to the estimated value of KW/G. The large uncertainty in KW/G predictions for highly functionalized organic compounds needs to be resolved to improve the quantitative treatment of SOA formation.
Bok, Jan; Schauer, Petr
2014-01-01
In the paper, the SEM detector is evaluated by the modulation transfer function (MTF) which expresses the detector's influence on the SEM image contrast. This is a novel approach, since the MTF was used previously to describe only the area imaging detectors, or whole imaging systems. The measurement technique and calculation of the MTF for the SEM detector are presented. In addition, the measurement and calculation of the detective quantum efficiency (DQE) as a function of the spatial frequency for the SEM detector are described. In this technique, the time modulated e-beam is used in order to create well-defined input signal for the detector. The MTF and DQE measurements are demonstrated on the Everhart-Thornley scintillation detector. This detector was alternated using the YAG:Ce, YAP:Ce, and CRY18 single-crystal scintillators. The presented MTF and DQE characteristics show good imaging properties of the detectors with the YAP:Ce or CRY18 scintillator, especially for a specific type of the e-beam scan. The results demonstrate the great benefit of the description of SEM detectors using the MTF and DQE. In addition, point-by-point and continual-sweep e-beam scans in SEM were discussed and their influence on the image quality was revealed using the MTF.
Protsenko, V. S.; Katanin, A. A.
2017-06-01
We explore the effects of asymmetry of hopping parameters between double parallel quantum dots and the leads on the conductance and a possibility of local magnetic moment formation in this system using functional renormalization group approach with the counterterm. We demonstrate a possibility of a quantum phase transition to a local moment regime [so-called singular Fermi liquid (SFL) state] for various types of hopping asymmetries and discuss respective gate voltage dependencies of the conductance. We show that, depending on the type of the asymmetry, the system can demonstrate either a first-order quantum phase transition to an SFL state, accompanied by a discontinuous change of the conductance, similarly to the symmetric case, or the second-order quantum phase transition, in which the conductance is continuous and exhibits Fano-type asymmetric resonance near the transition point. A semianalytical explanation of these different types of conductance behavior is presented.
Twisted Conformal Algebra and Quantum Statistics of Harmonic Oscillators
Directory of Open Access Journals (Sweden)
J. Naji
2014-01-01
Full Text Available We consider noncommutative two-dimensional quantum harmonic oscillators and extend them to the case of twisted algebra. We obtained modified raising and lowering operators. Also we study statistical mechanics and thermodynamics and calculated partition function which yields the free energy of the system.
Observation of quantum oscillation of work function in ultrathin-metal/semiconductor junctions
Energy Technology Data Exchange (ETDEWEB)
Takhar, Kuldeep; Meer, Mudassar; Khachariya, Dolar; Ganguly, Swaroop; Saha, Dipankar, E-mail: dipankarsaha@iitb.ac.in [Applied Quantum Mechanics Laboratory, Centre of Excellence in Nanoelectronics, Department of Electrical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076 (India)
2015-09-15
Quantization in energy level due to confinement is generally observed for semiconductors. This property is used for various quantum devices, and it helps to improve the characteristics of conventional devices. Here, the authors have demonstrated the quantum size effects in ultrathin metal (Ni) layers sandwiched between two large band-gap materials. The metal work function is found to oscillate as a function of its thickness. The thermionic emission current bears the signature of the oscillating work function, which has a linear relationship with barrier heights. This methodology allows direct observation of quantum oscillations in metals at room temperature using a Schottky diode and electrical measurements using source-measure-units. The observed phenomena can provide additional mechanism to tune the barrier height of metal/semiconductor junctions, which are used for various electronic devices.
Farzanehpour, M.; Tokatly, I. V.
2016-05-01
We use analytic (current) density-potential maps of time-dependent (current) density-functional theory [TD(C)DFT] to inverse engineer analytically solvable time-dependent quantum problems. In this approach the driving potential (the control signal) and the corresponding solution of the Schrödinger equation are parametrized analytically in terms of the basic TD(C)DFT observables. We describe the general reconstruction strategy and illustrate it with a number of explicit examples. First we consider the real space one-particle dynamics driven by a time-dependent electromagnetic field and recover, from the general TDDFT reconstruction formulas, the known exact solution for a driven oscillator with a time-dependent frequency. Then we use analytic maps of the lattice TD(C)DFT to control quantum dynamics in a discrete space. As a first example we construct a time-dependent potential which generates prescribed dynamics on a tight-binding chain. Then our method is applied to the dynamics of spin-1/2 driven by a time-dependent magnetic field. We design an analytic control pulse that transfers the system from the ground to excited state and vice versa. This pulse generates the spin flip thus operating as a quantum not gate.
Polynomial solution of quantum Grassmann matrices
Tierz, Miguel
2017-05-01
We study a model of quantum mechanical fermions with matrix-like index structure (with indices N and L) and quartic interactions, recently introduced by Anninos and Silva. We compute the partition function exactly with q-deformed orthogonal polynomials (Stieltjes-Wigert polynomials), for different values of L and arbitrary N. From the explicit evaluation of the thermal partition function, the energy levels and degeneracies are determined. For a given L, the number of states of different energy is quadratic in N, which implies an exponential degeneracy of the energy levels. We also show that at high-temperature we have a Gaussian matrix model, which implies a symmetry that swaps N and L, together with a Wick rotation of the spectral parameter. In this limit, we also write the partition function, for generic L and N, in terms of a single generalized Hermite polynomial.
Energy Technology Data Exchange (ETDEWEB)
Bushong, Neil; Di Ventra, Massimiliano [Department of Physics, University of California, San Diego, La Jolla, CA 92093-0319 (United States)], E-mail: diventra@physics.ucsd.edu
2008-10-01
Recently, time-dependent current-density-functional theory has been extended to include the dynamical interaction of quantum systems with external environments (Di Ventra and D'Agosta 2007 Phys. Rev. Lett. 98 226403). Here we show that such a theory allows us to study a fundamentally important class of phenomena previously inaccessible by standard density-functional methods: the decay of excited systems. As an example we study the decay of an ensemble of excited He atoms, and discuss these results in the context of quantum measurement theory.
Desgranges, Caroline; Delhommelle, Jerome
2016-03-28
We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%-15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si.
Quantum tests for the linearity and permutation invariance of Boolean functions
Energy Technology Data Exchange (ETDEWEB)
Hillery, Mark [Department of Physics, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10021 (United States); Andersson, Erika [SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)
2011-12-15
The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is {epsilon}-far from having that property. The performance of the algorithm is judged by how many calls need to be made to the black box in order to determine, with high probability, which of the two alternatives is the case. Here we present two quantum algorithms, the first to determine whether the function is linear and the second to determine whether it is symmetric (invariant under permutations of the arguments). Both require order {epsilon}{sup -2/3} calls to the oracle, which is better than known classical algorithms. In addition, in the case of linearity testing, if the function is linear, the quantum algorithm identifies which linear function it is. The linearity test combines the Bernstein-Vazirani algorithm and amplitude amplification, while the test to determine whether a function is symmetric uses projective measurements and amplitude amplification.
Green’s functions and energy eigenvalues for delta-perturbed space-fractional quantum systems
Energy Technology Data Exchange (ETDEWEB)
Nayga, M. M., E-mail: mnayga@nip.upd.edu.ph; Esguerra, J. P. [National Institute of Physics, University of the Philippines-Diliman, Quezon City (Philippines)
2016-02-15
Starting from the propagator, we introduced a time-ordered perturbation expansion and employed Wick rotation to obtain a general energy-dependent Green’s function expressions for space-fractional quantum systems with Dirac delta-function perturbation. We then obtained the Green’s functions and equations for the bound state energies for the space-fractional Schrödinger equation with single and double Dirac delta well potentials and the delta-perturbed infinite well.
Bourgine, Jean-Emile; Matsuo, Yutaka; Zhang, Hong; Zhu, Rui-Dong
2016-01-01
The instanton partition functions of $\\mathcal{N}=1$ 5d super Yang-Mills are built using elements of the representation theory of quantum $\\mathcal{W}_{1+\\infty}$ algebra: Gaiotto state, intertwiner, vertex operator. This algebra is also known under the names of Ding-Iohara-Miki and quantum toroidal $\\widehat{\\mathfrak{gl}}(1)$ algebra. Exploiting the explicit action of the algebra on the partition function, we prove the regularity of the 5d qq-characters. These characters provide a solution to the Schwinger-Dyson equations, and they can also be interpreted as a quantum version of the Seiberg-Witten curve.
Toutounji, Mohamad
2004-08-01
Optical linear response function of linearly and quadratically coupled mixed quantum-classical condensed phase systems is derived. The linear response function is derived using Kapral's formalism of statistical mechanics in mixed quantum-classical systems. Our mixed quantum-classical linear dipole moment correlation function J(t) is compared with the full quantum J(t) [Y. J. Yan and S. Mukamel, J. Chem. Phys. 85, 5908 (1986)] in the high temperature limit. Model calculations and discussion of our results are presented. Various formulas of Franck-Condon factors for both linear and quadratic coupling are discussed. (c) 2004 American Institute of Physics.
Quantum electronic stress: density-functional-theory formulation and physical manifestation.
Hu, Hao; Liu, Miao; Wang, Z F; Zhu, Junyi; Wu, Dangxin; Ding, Hepeng; Liu, Zheng; Liu, Feng
2012-08-01
The concept of quantum electronic stress (QES) is introduced and formulated within density functional theory to elucidate extrinsic electronic effects on the stress state of solids and thin films in the absence of lattice strain. A formal expression of QES (σ(QE)) is derived in relation to deformation potential of electronic states (Ξ) and variation of electron density (Δn), σ(QE) = ΞΔn as a quantum analog of classical Hooke's law. Two distinct QES manifestations are demonstrated quantitatively by density functional theory calculations: (1) in the form of bulk stress induced by charge carriers and (2) in the form of surface stress induced by quantum confinement. Implications of QES in some physical phenomena are discussed to underlie its importance.
Booth, George H; Chan, Garnet Kin-Lic
2012-11-21
In this communication, we propose a method for obtaining isolated excited states within the full configuration interaction quantum Monte Carlo framework. This method allows for stable sampling with respect to collapse to lower energy states and requires no uncontrolled approximations. In contrast with most previous methods to extract excited state information from quantum Monte Carlo methods, this results from a modification to the underlying propagator, and does not require explicit orthogonalization, analytic continuation, transient estimators, or restriction of the Hilbert space via a trial wavefunction. Furthermore, we show that the propagator can directly yield frequency-domain correlation functions and spectral functions such as the density of states which are difficult to obtain within a traditional quantum Monte Carlo framework. We demonstrate this approach with pilot applications to the neon atom and beryllium dimer.
Quantum Electronic Stress: Density-Functional-Theory Formulation and Physical Manifestation
Hu, Hao; Liu, Miao; Wang, Z. F.; Zhu, Junyi; Wu, Dangxin; Ding, Hepeng; Liu, Zheng; Liu, Feng
2012-08-01
The concept of quantum electronic stress (QES) is introduced and formulated within density functional theory to elucidate extrinsic electronic effects on the stress state of solids and thin films in the absence of lattice strain. A formal expression of QES (σQE) is derived in relation to deformation potential of electronic states (Ξ) and variation of electron density (Δn), σQE=ΞΔn as a quantum analog of classical Hooke’s law. Two distinct QES manifestations are demonstrated quantitatively by density functional theory calculations: (1) in the form of bulk stress induced by charge carriers and (2) in the form of surface stress induced by quantum confinement. Implications of QES in some physical phenomena are discussed to underlie its importance.
Research on Function Module Dynamic Partition for Product Innovation Design%面向产品创新设计的功能模块动态划分方法研究
Institute of Scientific and Technical Information of China (English)
陈继文; 张进生; 王志; 黄波; 王发凯
2013-01-01
针对面向产品创新设计的功能模块划分中没有考虑技术进化的问题,从客户需求、流、技术的角度出发,研究功能模块动态划分方法.以产品的功能结构为基础,建立了功能相关矩阵.基于模糊等价矩阵的动态聚类分析,动态划分产品的功能模块.以模块内平均聚合度和模块间平均分离度来评价不同模块划分结果.多绳金刚石串珠锯功能模块动态划分实例说明了该方法具有较强的分辨性,可以进行面向产品创新设计的功能模块动态划分.%Recently, technical evolution factors are not considered in function module partition for product innovation. From the point of customer demands, flow and technology, function module dynamic partition was researched. Function correlation matrix was established based on function structure. The dynamic cluster analysis of fuzzy equivalence matrix was used to dynamic parting function module. The function module partitions were evaluated by average polymerization degree in a module and average coupling degree among modules. Example of multi wire diamond saw shows the presented dynamic module partition method has strong distinguish ability and can be used to module dynamic partition for product innovation design.
Continuum quantum systems as limits of discrete quantum systems: II. State functions
Energy Technology Data Exchange (ETDEWEB)
Barker, Laurence [Department of Mathematics, Bilkent University, Bilkent, Ankara (Turkey)]. E-mail: barker@fen.bilkent.edu.tr
2001-06-08
In this second of four papers on the eponymous topic, pointwise convergence of a 'discrete' state function to a 'continuum' state function is shown to imply the algebraic criterion for convergence that was introduced in the prequel. As examples (and as a prerequisite for the sequels), the normal approximation theorem and the convergence of the Kravchuk functions to the Hermite-Gaussians are expressed in terms of the algebraic notion of convergence. (author)
Quantum Curves and $D$-Modules
Dijkgraaf, Robbert; Sulkowski, Piotr
2009-01-01
In this article we continue our study of chiral fermions on a quantum curve. This system is embedded in string theory as an I-brane configuration, which consists of D4 and D6-branes intersecting along a holomorphic curve in a complex surface, together with a B-field. Mathematically, it is described by a holonomic D-module. Here we focus on spectral curves, which play a prominant role in the theory of (quantum) integrable hierarchies. We show how to associate a quantum state to the I-brane system, and subsequently how to compute quantum invariants. As a first example, this yields an insightful formulation of (double scaled as well as general Hermitian) matrix models. Secondly, our formalism elegantly reconstructs the complete dual Nekrasov-Okounkov partition function from a quantum Seiberg-Witten curve.
Quantum curves and Script D-modules
Dijkgraaf, Robbert; Hollands, Lotte; Sułkowski, Piotr
2009-11-01
In this article we continue our study of chiral fermions on a quantum curve. This system is embedded in string theory as an I-brane configuration, which consists of D4 and D6-branes intersecting along a holomorphic curve in a complex surface, together with a B-field. Mathematically, it is described by a holonomic Script D-module. Here we focus on spectral curves, which play a prominent role in the theory of (quantum) integrable hierarchies. We show how to associate a quantum state to the I-brane system, and subsequently how to compute quantum invariants. As a first example, this yields an insightful formulation of (double scaled as well as general Hermitian) matrix models. Secondly, we formulate c = 1 string theory in this language. Finally, our formalism elegantly reconstructs the complete dual Nekrasov-Okounkov partition function from a quantum Seiberg-Witten curve.
Energy Technology Data Exchange (ETDEWEB)
Baur, H.
2006-07-01
In the first part of this work we extract the algebraic structure behind the method of the influence functional in the context of dissipative quantum mechanics. Special emphasis was put on the transition from a quantum mechanical description to a classical one, since it allows a deeper understanding of the measurement-process. This is tightly connected with the transition from a microscopic to a macroscopic world where the former one is described by the rules of quantum mechanics whereas the latter follows the rules of classical mechanics. In addition we show how the results of the influence functional method can be interpreted as a stochastical process, which in turn allows an easy comparison with the well known time development of a quantum mechanical system by use of the Schroedinger equation. In the following we examine the tight-binding approximation of models of which their hamiltionian shows discrete eigenstates in position space and where transitions between those states are suppressed so that propagation either is described by tunneling or by thermal activation. In the framework of dissipative quantum mechanics this leads to a tremendous simplification of the effective description of the system since instead of looking at the full history of all paths in the path integral description, we only have to look at all possible jump times and the possible corresponding set of weights for the jump direction, which is much easier to handle both analytically and numerically. In addition we deal with the mapping and the connection of dissipative quantum mechanical models with ones in quantum field theory and in particular models in statistical field theory. As an example we mention conformal invariance in two dimensions which always becomes relevant if a statistical system only has local interaction and is invariant under scaling. (orig.)
Quantum localization of Classical Mechanics
Batalin, Igor A
2016-01-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Quantum localization of classical mechanics
Batalin, Igor A.; Lavrov, Peter M.
2016-07-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Risser, Laurent; Vincent, Thomas; Ciuciu, Philippe; Idier, Jérôme
2009-01-01
In this paper, we present a fast numerical scheme to estimate Partition Functions (PF) of 3D Ising fields. Our strategy is applied to the context of the joint detection-estimation of brain activity from functional Magnetic Resonance Imaging (fMRI) data, where the goal is to automatically recover activated regions and estimate region-dependent hemodynamic filters. For any region, a specific binary Markov random field may embody spatial correlation over the hidden states of the voxels by modeling whether they are activated or not. To make this spatial regularization fully adaptive, our approach is first based upon a classical path-sampling method to approximate a small subset of reference PFs corresponding to prespecified regions. Then, the proposed extrapolation method allows us to approximate the PFs associated with the Ising fields defined over the remaining brain regions. In comparison with preexisting approaches, our method is robust to topological inhomogeneities in the definition of the reference regions. As a result, it strongly alleviates the computational burden and makes spatially adaptive regularization of whole brain fMRI datasets feasible.
Energy Technology Data Exchange (ETDEWEB)
Risser, L.; Vincent, T.; Ciuciu, Ph. [NeuroSpin CEA, F-91191 Gif sur Yvette (France); Risser, L.; Vincent, T. [Laboratoire de Neuroimagerie Assistee par Ordinateur (LNAO) CEA - DSV/I2BM/NEUROSPIN (France); Risser, L. [Institut de mecanique des fluides de Toulouse (IMFT), CNRS: UMR5502 - Universite Paul Sabatier - Toulouse III - Institut National Polytechnique de Toulouse - INPT (France); Idier, J. [Institut de Recherche en Communications et en Cybernetique de Nantes (IRCCyN) CNRS - UMR6597 - Universite de Nantes - ecole Centrale de Nantes - Ecole des Mines de Nantes - Ecole Polytechnique de l' Universite de Nantes (France)
2009-07-01
In this paper, we present a first numerical scheme to estimate Partition Functions (PF) of 3D Ising fields. Our strategy is applied to the context of the joint detection-estimation of brain activity from functional Magnetic Resonance Imaging (fMRI) data, where the goal is to automatically recover activated regions and estimate region-dependent, hemodynamic filters. For any region, a specific binary Markov random field may embody spatial correlation over the hidden states of the voxels by modeling whether they are activated or not. To make this spatial regularization fully adaptive, our approach is first based upon it, classical path-sampling method to approximate a small subset of reference PFs corresponding to pre-specified regions. Then, file proposed extrapolation method allows its to approximate the PFs associated with the Ising fields defined over the remaining brain regions. In comparison with preexisting approaches, our method is robust; to topological inhomogeneities in the definition of the reference regions. As a result, it strongly alleviates the computational burden and makes spatially adaptive regularization of whole brain fMRI datasets feasible. (authors)
Energy Technology Data Exchange (ETDEWEB)
Fewster, Christopher J [Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom); Sahlmann, Hanno [Spinoza Institute, Universiteit Utrecht (Netherlands)
2008-11-21
We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint.
Fewster, C.J.; Sahlmann, H.
2008-01-01
We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to giv
Quantum algorithm for identifying hidden polynomial function graphs
Decker, T.; Draisma, J.; Wocjan, P.
2009-01-01
We consider a natural generalization of an abelian Hidden Subgroup Problem where the subgroups and their cosets correspond to graphs of linear functions over a finite field F with d elements. The hidden functions of the generalized problem are not restricted to be linear but can also be m-variate po
On a c-number quantum $\\tau$-function
Mironov, A E; Vinet, L
1993-01-01
Review of the properties of conventional $\\tau$-functions of KP and Toda lattice hierarchies. Straightforward generalization is discussed, associated with transition from differential to finite-difference equations, but involving neither the concept of operator-valued $\\tau$-function, nor the one, associated with non-cartanian (level $k\
Real no-boundary wave function in Lorentzian quantum cosmology
Dorronsoro, J. Diaz; Halliwell, J. J.; Hartle, J. B.; Hertog, T.; Janssen, O.
2017-08-01
It is shown that the standard no-boundary wave function has a natural expression in terms of a Lorentzian path integral with its contour defined by Picard-Lefschetz theory. The wave function is real, satisfies the Wheeler-DeWitt equation and predicts an ensemble of asymptotically classical, inflationary universes with nearly-Gaussian fluctuations and with a smooth semiclassical origin.
Modern functional quantum field theory summing Feynman graphs
Fried, Herbert M
2013-01-01
A monograph, which can also be used as a textbook for graduate students, this book contains new and novel applications of Schwinger's well-known functional solutions, made possible by the use of Fradkin's little-known functional representations, together with recent research work of the author and his colleagues.
Quantum-kinetic equations for time correlation functions in higher-order perturbation theory
Leermakers, M.C.J.; Suttorp, L.G.
1981-01-01
The memory kernel of the kinetic equation for the time correlation function of a quantum fluid is determined both in third order of the interaction strength and in the low-density approximation. The results are obtained with the help of a diagram representation for the kernel. The connection with
Fracchia, F.; Filippi, C.; Amovilli, C.
2012-01-01
We propose a new class of multideterminantal Jastrow–Slater wave functions constructed with localized orbitals and designed to describe complex potential energy surfaces of molecular systems for use in quantum Monte Carlo (QMC). Inspired by the generalized valence bond formalism, we elaborate a coup
Quantum Graphs Whose Spectra Mimic the Zeros of the Riemann Zeta Function
Kuipers, Jack; Hummel, Quirin; Richter, Klaus
2014-02-01
One of the most famous problems in mathematics is the Riemann hypothesis: that the nontrivial zeros of the Riemann zeta function lie on a line in the complex plane. One way to prove the hypothesis would be to identify the zeros as eigenvalues of a Hermitian operator, many of whose properties can be derived through the analogy to quantum chaos. Using this, we construct a set of quantum graphs that have the same oscillating part of the density of states as the Riemann zeros, offering an explanation of the overall minus sign. The smooth part is completely different, and hence also the spectrum, but the graphs pick out the low-lying zeros.
Constraints on Airy function zeros from quantum-mechanical sum rules
Energy Technology Data Exchange (ETDEWEB)
Belloni, M [Physics Department, Davidson College, Davidson, NC 28035 (United States); Robinett, R W [Department of Physics, Pennsylvania State University, University Park, PA 16802 (United States)], E-mail: mabelloni@davidson.edu, E-mail: rick@phys.psu.edu
2009-02-20
We derive new constraints on the zeros of Airy functions by using the so-called quantum bouncer system to evaluate quantum-mechanical sum rules and perform perturbation theory calculations for the Stark effect. Using commutation and completeness relations, we show how to systematically evaluate sums of the form S{sub p}(n) = {sigma}{sub k{ne}}{sub n}1/({zeta}{sub k} - {zeta}{sub n}){sup p}, for natural p > 1, where -{zeta}{sub n} is the nth zero of Ai({zeta})
Quantum graphs whose spectra mimic the zeros of the Riemann zeta function.
Kuipers, Jack; Hummel, Quirin; Richter, Klaus
2014-02-21
One of the most famous problems in mathematics is the Riemann hypothesis: that the nontrivial zeros of the Riemann zeta function lie on a line in the complex plane. One way to prove the hypothesis would be to identify the zeros as eigenvalues of a Hermitian operator, many of whose properties can be derived through the analogy to quantum chaos. Using this, we construct a set of quantum graphs that have the same oscillating part of the density of states as the Riemann zeros, offering an explanation of the overall minus sign. The smooth part is completely different, and hence also the spectrum, but the graphs pick out the low-lying zeros.
On the nature of the change in the wave function in a measurement in quantum mechanics
Snyder, D M
1996-01-01
Generally a central role has been assigned to an unavoidable physical interaction between the measuring instrument and the physical entity measured in the change in the wave function that often occurs in measurement in quantum mechanics. A survey of textbooks on quantum mechanics by authors such as Dicke and Witke (1960), Eisberg and Resnick (1985), Gasiorowicz (1974), Goswami (1992), ift fur Physik, vol. 158, p. 417), supports these points. Work on electron shelving is reported by Dehmelt and his colleagues (Physical Review Letters, vol. 56, p. 2797), Wineland and his colleagues (Physical Review Letters, vol. 57, p. 1699), and Sauter, Neuhauser, Blatt, and Toschek (Physical Review Letters, vol. 57, p. 1696).
A spin-density-functional study of quantum dots and rings
Lin, J C
2002-01-01
We present a spin-density-functional theoretical (SDFT) study of the electronic states in GaAs quantum dots embedded in AlGaAs substrates. The SDFT allows for a systematic study of the joint effects of confinement, Coulomb interactions and spin for realistic systems. We model the system as electrons confined in a finite cylindrical dot. The screening due to the gate electrodes is also taken into account. The method predicts the electron addition energy spectra that are in agreement with experiments. We also apply the SDFT to GaAs quantum rings and find that they too show shell structures in the additional energy spectra.
Fox, R. J.; Bellwood, D. R.
2013-03-01
Niche theory predicts that coexisting species minimise competition by evolving morphological or behavioural specialisations that allow them to spread out along resource axes such as space, diet and temporal activity. These specialisations define how a species interacts with its environment and, by extension, determine its functional role. Here, we examine the feeding niche of three species of coral reef-dwelling rabbitfishes (Siganidae, Siganus). By comparing aspects of their feeding behaviour (bite location, bite rate, foraging distance) with that of representative species from two other abundant herbivorous fish families, the parrotfishes (Labridae, Scarus) and surgeonfishes (Acanthuridae, Acanthurus), we examine whether rabbitfishes have a feeding niche distinct from other members of the herbivore guild. Measurements of the penetration of the fishes' snouts and bodies into reef concavities when feeding revealed that rabbitfish fed to a greater degree from reef crevices and interstices than other herbivores. There was just a 40 % overlap in the penetration-depth niche between rabbitfish and surgeonfish and a 45 % overlap between rabbitfish and parrotfish, compared with the almost complete niche overlap (95 %) recorded for parrotfish and surgeonfish along this spatial niche axis. Aspects of the morphology of rabbitfish which may contribute to this niche segregation include a comparatively longer, narrower snout and narrower head. Our results suggest that sympatric coexistence of rabbitfish and other reef herbivores is facilitated by segregation along a spatial (and potentially dietary) axis. This segregation results in a unique functional role for rabbitfishes among roving herbivores that of "crevice-browser": a group that specifically feeds on crevice-dwelling algal or benthic organisms. This functional trait may have implications for reef ecosystem processes in terms of controlling the successional development of crevice-based algal communities, reducing their
Craig, Ian R; Manolopoulos, David E
2004-08-22
We propose an approximate method for calculating Kubo-transformed real-time correlation functions involving position-dependent operators, based on path integral (Parrinello-Rahman) molecular dynamics. The method gives the exact quantum mechanical correlation function at time zero, exactly satisfies the quantum mechanical detailed balance condition, and for correlation functions of the form C(Ax)(t) and C(xB)(t) it gives the exact result for a harmonic potential. It also works reasonably well at short times for more general potentials and correlation functions, as we illustrate with some example calculations. The method provides a consistent improvement over purely classical molecular dynamics that is most apparent in the low-temperature regime.
Quantum algorithm to solve function inversion with time-space trade-off
Wu, WanQing; Zhang, HuanGuo
2017-07-01
In general, it is a difficult problem to solve the inverse of any function. With the inverse implication operation, we present a quantum algorithm for solving the inversion of function via using time-space trade-off in this paper. The details are as follows. Let function f(x)=y have k solutions, where x\\in {0, 1}n, y\\in {0, 1}m for any integers n, m. We show that an iterative algorithm can be used to solve the inverse of function f( x) with successful probability 1-( 1-k/2n) L for L\\in Z+. The space complexity of proposed quantum iterative algorithm is O( Ln), where L is the number of iterations. The paper concludes that, via using time-space trade-off strategy, we improve the successful probability of algorithm.
Two-time Green's functions and spectral density method in nonextensive quantum statistical mechanics
Cavallo, A.; Cosenza, F.; De Cesare, L.
2007-01-01
We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multipliers representation, the $q$-spectral properties and the methods for a direct calculation of the two-time $q$% -Green's functions and the related $q$-spectral density ($q$ measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive ($q=1$) counterpart. Some emphasis is devoted to the...
2007-01-01
Recently, time-dependent current-density functional theory has been extended to include the dynamical interaction of quantum systems with external environments [Phys. Rev. Lett. {\\bf 98}, 226403 (2007)]. Here we show that such a theory allows us to study a fundamentally important class of phenomena previously inaccessible by standard density-functional methods: the decay of excited systems. As an example we study the decay of an ensemble of excited He atoms, and discuss these results in the c...
Functional renormalization group approach to the singlet-triplet transition in quantum dots.
Magnusson, E B; Hasselmann, N; Shelykh, I A
2012-09-12
We present a functional renormalization group approach to the zero bias transport properties of a quantum dot with two different orbitals and in the presence of Hund's coupling. Tuning the energy separation of the orbital states, the quantum dot can be driven through a singlet-triplet transition. Our approach, based on the approach by Karrasch et al (2006 Phys. Rev. B 73 235337), which we apply to spin-dependent interactions, recovers the key characteristics of the quantum dot transport properties with very little numerical effort. We present results on the conductance in the vicinity of the transition and compare our results both with previous numerical renormalization group results and with predictions of the perturbative renormalization group.
Delaney, J. S.; Sutton, S. R.; Newville, M.; Jones, J. H.; Hanson, B.; Dyar, M. D.; Schreiber, H.
2000-01-01
Oxidation state microanalyses for V in glass have been made by calibrating XANES spectral features with optical spectroscopic measurements. The oxidation state change with fugacity of O2 will strongly influence partitioning results.
Polymer as a function of monomer: Analytical quantum modeling
Nakhaee, Mohammad
2016-01-01
To identify an analytical relation between the properties of polymers and their's monomer a Metal-Molecule-Metal (MMM) junction has been presented as an interesting and widely used object of research in which the molecule is a polymer which is able to conduct charge. The method used in this study is based on the Green's function approach in the tight-binding approximation using basic properties of matrices. For a polymer base MMM system, transmission, density of states (DOS) and local density of states (LDOS) have been calculated as a function of the hamiltonian of the monomer. After that, we have obtained a frequency for LDOS variations in pass from a subunit to the next one which is a function of energy.
Characteristic operator functions for quantum input-plant-output models and coherent control
Gough, John E.
2015-01-01
We introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear input-plant-output systems to arbitrary quantum nonlinear Markovian input-output models. This is intended as a tool in the characterization of quantum feedback control systems that fits in with the general theory of networks. The definition exploits the linearity of noise differentials in both the plant Heisenberg equations of motion and the differential form of the input-output relations. Mathematically, the characteristic operator is a matrix of dimension equal to the number of outputs times the number of inputs (which must coincide), but with entries that are operators of the plant system. In this sense, the characteristic operator retains details of the effective plant dynamical structure and is an essentially quantum object. We illustrate the relevance to model reduction and simplification definition by showing that the convergence of the characteristic operator in adiabatic elimination limit models requires the same conditions and assumptions appearing in the work on limit quantum stochastic differential theorems of Bouten and Silberfarb [Commun. Math. Phys. 283, 491-505 (2008)]. This approach also shows in a natural way that the limit coefficients of the quantum stochastic differential equations in adiabatic elimination problems arise algebraically as Schur complements and amounts to a model reduction where the fast degrees of freedom are decoupled from the slow ones and eliminated.
Francisco, Ana Paula; Harner, Tom; Eng, Anita
2017-05-01
Polyurethane foam - air partition coefficients (KPUF-air) for 9 polycyclic aromatic hydrocarbons (PAHs), 10 alkyl-substituted PAHs, 4 organochlorine pesticides (OCPs) and dibenzothiophene were measured as a function of temperature over the range 5 °C-35 °C, using a generator column approach. Enthalpies of PUF-to-air transfer (ΔHPUF-air, kJ/mol) were determined from the slopes of log KPUF-air versus 1000/T (K), and have an average value of 81.2 ± 7.03 kJ/mol. The log KPUF-air values at 22 °C ranged from 4.99 to 7.25. A relationship for log KPUF-air versus log KOA was shown to agree with a previous relationship based on only polychlorinated biphenyls (PCBs) and derived from long-term indoor uptake study experiments. The results also confirm that the existing KOA-based model for predicting log KPUF-air values is accurate. This new information is important in the derivation of uptake profiles and effective air sampling volumes for PUF disk samplers so that results can be reported in units of concentration in air. Crown Copyright © 2017. Published by Elsevier Ltd. All rights reserved.
On Spectral Triples in Quantum Gravity I
DEFF Research Database (Denmark)
Aastrup, Johannes; M. Grimstrup, Jesper; Nest, Ryszard
2009-01-01
This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator....... The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly......, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations...
Whittaker vector, Wheeler-DeWitt equation, and the gravity dual of conformal quantum mechanics
Okazaki, Tadashi
2015-12-01
We study the energy representation of conformal quantum mechanics as the Whittaker vector without specifying the classical Lagrangian. We show that a generating function of expectation values among two excited states of the dilatation operator in conformal quantum mechanics is a solution to the Wheeler-DeWitt equation and it corresponds to the AdS2 partition function evaluated as the minisuperspace wave function in Liouville field theory. We also show that the dilatation expectation values in conformal quantum mechanics lead to the asymptotic smoothed counting function of the Riemann zeros.
Is Density Functional Theory adequate for quantum transport?
Burke, Kieron
2007-03-01
Density functional calculations for the electronic conductance of single molecules attached to leads are now common. I'll examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradient-corrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, XC corrections to the current are missed by the standard methodology. Finally, I will compare and contrast several new methodologies that go beyond the present standard approach of applying the Landauer formula to ground-state DFT. Self-interaction errors in density functional calculations of electronictransport, C. Toher, A. Filippetti, S. Sanvito, and K. Burke, Phys. Rev. Lett. 95, 146402 (2005) The Dramatic Role of the Exchange-Correlation Potential in ab initio Electron Transport Calculations, S-H. Ke, H.U. Baranger, and W. Yang, cond-mat/0609367. Zero-bias molecular electronics: Exchange-correlation corrections to Landauer's formula, M. Koentopp, K. Burke, and F. Evers, Phys. Rev. B Rapid Comm., 73, 121403 (2006). Density Functional Theory of the Electrical Conductivity of Molecular Devices, K. Burke, Roberto Car, and Ralph Gebauer, Phys. Rev. Lett. 94, 146803 (2005). Density functional calculations of nanoscale conductance, Connie Chang, Max Koentopp, Kieron Burke, and Roberto Car, in prep.
Hosur, Pavan; Roberts, Daniel A; Yoshida, Beni
2015-01-01
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.
Energy Technology Data Exchange (ETDEWEB)
Hosur, Pavan; Qi, Xiao-Liang [Department of Physics, Stanford University,476 Lomita Mall, Stanford, California 94305 (United States); Roberts, Daniel A. [Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology,77 Massachusetts Ave, Cambridge, Massachusetts 02139 (United States); Yoshida, Beni [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Walter Burke Institute for Theoretical Physics, California Institute of Technology,1200 E California Blvd, Pasadena CA 91125 (United States)
2016-02-01
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.
Zhang, Zengcui; Belcram, Harry; Gornicki, Piotr; Charles, Mathieu; Just, Jérémy; Huneau, Cécile; Magdelenat, Ghislaine; Couloux, Arnaud; Samain, Sylvie; Gill, Bikram S.; Rasmussen, Jack B.; Barbe, Valérie; Faris, Justin D.; Chalhoub, Boulos
2011-01-01
The Q gene encodes an AP2-like transcription factor that played an important role in domestication of polyploid wheat. The chromosome 5A Q alleles (5AQ and 5Aq) have been well studied, but much less is known about the q alleles on wheat homoeologous chromosomes 5B (5Bq) and 5D (5Dq). We investigated the organization, evolution, and function of the Q/q homoeoalleles in hexaploid wheat (Triticum aestivum L.). Q/q gene sequences are highly conserved within and among the A, B, and D genomes of hexaploid wheat, the A and B genomes of tetraploid wheat, and the A, S, and D genomes of the diploid progenitors, but the intergenic regions of the Q/q locus are highly divergent among homoeologous genomes. Duplication of the q gene 5.8 Mya was likely followed by selective loss of one of the copies from the A genome progenitor and the other copy from the B, D, and S genomes. A recent V329-to-I mutation in the A lineage is correlated with the Q phenotype. The 5Bq homoeoalleles became a pseudogene after allotetraploidization. Expression analysis indicated that the homoeoalleles are coregulated in a complex manner. Combined phenotypic and expression analysis indicated that, whereas 5AQ plays a major role in conferring domestication-related traits, 5Dq contributes directly and 5Bq indirectly to suppression of the speltoid phenotype. The evolution of the Q/q loci in polyploid wheat resulted in the hyperfunctionalization of 5AQ, pseudogenization of 5Bq, and subfunctionalization of 5Dq, all contributing to the domestication traits. PMID:22042872
Quantum kinematics on q-deformed quantum spaces II, Wave functions on position and momentum space
Wachter, H
2006-01-01
The aim of Part II of this paper is to try to describe wave functions on q-deformed versions of position and momentum space. This task is done within the framework developed in Part I of the paper. In order to make Part II self-contained the most important results of Part I are reviewed. Then it is shown that q-deformed exponentials and q-deformed delta functions play the role of momentum and position eigenfunctions, respectively. Their completeness and orthonormality relations are derived. For both bases of eigenfunctions matrix elements of position and momentum operators are calculated. A q-deformed version of the spectral decomposition of multiplication operators is discussed and q-analogs of Heaviside functions are proposed. Interpreting the results from the point of view provided by the concept of quasipoints gives the formalism a physical meaning. The definition of expectation values and the calculation of probability densities are explained in detail. Finally, it is outlined how the considerations so f...
Quantum transport: A unified approach via a multivariate hypergeometric generating function
Macedo-Junior, A. F.; Macêdo, A. M. S.
2014-07-01
We introduce a characteristic function method to describe charge-counting statistics (CCS) in phase coherent systems that directly connects the three most successful approaches to quantum transport: random-matrix theory (RMT), the nonlinear σ-model and the trajectory-based semiclassical method. The central idea is the construction of a generating function based on a multivariate hypergeometric function, which can be naturally represented in terms of quantities that are well-defined in each approach. We illustrate the power of our scheme by obtaining exact analytical results for the first four cumulants of CCS in a chaotic quantum dot coupled ideally to electron reservoirs via perfectly conducting leads with arbitrary number of open scattering channels.
Time-dependent density functional theory quantum transport simulation in non-orthogonal basis.
Kwok, Yan Ho; Xie, Hang; Yam, Chi Yung; Zheng, Xiao; Chen, Guan Hua
2013-12-14
Basing on the earlier works on the hierarchical equations of motion for quantum transport, we present in this paper a first principles scheme for time-dependent quantum transport by combining time-dependent density functional theory (TDDFT) and Keldysh's non-equilibrium Green's function formalism. This scheme is beyond the wide band limit approximation and is directly applicable to the case of non-orthogonal basis without the need of basis transformation. The overlap between the basis in the lead and the device region is treated properly by including it in the self-energy and it can be shown that this approach is equivalent to a lead-device orthogonalization. This scheme has been implemented at both TDDFT and density functional tight-binding level. Simulation results are presented to demonstrate our method and comparison with wide band limit approximation is made. Finally, the sparsity of the matrices and computational complexity of this method are analyzed.
Interacting relativistic quantum dynamics for multi-time wave functions
Directory of Open Access Journals (Sweden)
Lienert Matthias
2016-01-01
Full Text Available In this paper, we report on recent progress about a rigorous and manifestly covariant interacting model for two Dirac particles in 1+1 dimensions [9, 10]. It is formulated using the multi-time formalism of Dirac, Tomonaga and Schwinger. The mechanism of interaction is a relativistic generalization of contact interactions, and it is achieved going beyond the usual functional-analytic Hamiltonian method.
Interacting relativistic quantum dynamics for multi-time wave functions
Lienert, Matthias
2016-11-01
In this paper, we report on recent progress about a rigorous and manifestly covariant interacting model for two Dirac particles in 1+1 dimensions [9, 10]. It is formulated using the multi-time formalism of Dirac, Tomonaga and Schwinger. The mechanism of interaction is a relativistic generalization of contact interactions, and it is achieved going beyond the usual functional-analytic Hamiltonian method.
Institute of Scientific and Technical Information of China (English)
范志浩; 姜灿荣
2012-01-01
根据西藏的自然环境条件，结合林地保护管理现状，将全区林地划分为4个功能区，并就各区域林地的功能定位、差别化保护利用以及相应的管理措施进行探讨。%According to the natural environment, combining with forest land protection and management situa- tion ,Tibet was classified as four forest lands functional partition. In this paper, it discussed forest land function orientation, discrepant protection and utilization and appropriate management measures for each forest lands functional partition
Niels Bohr on the wave function and the classical/quantum divide
Zinkernagel, Henrik
2016-02-01
It is well known that Niels Bohr insisted on the necessity of classical concepts in the account of quantum phenomena. But there is little consensus concerning his reasons, and what he exactly meant by this. In this paper, I re-examine Bohr's interpretation of quantum mechanics, and argue that the necessity of the classical can be seen as part of his response to the measurement problem. More generally, I attempt to clarify Bohr's view on the classical/quantum divide, arguing that the relation between the two theories is that of mutual dependence. An important element in this clarification consists in distinguishing Bohr's idea of the wave function as symbolic from both a purely epistemic and an ontological interpretation. Together with new evidence concerning Bohr's conception of the wave function collapse, this sets his interpretation apart from both standard versions of the Copenhagen interpretation, and from some of the reconstructions of his view found in the literature. I conclude with a few remarks on how Bohr's ideas make much sense also when modern developments in quantum gravity and early universe cosmology are taken into account.
Protocol of Secure Key Distribution Using Hash Functions and Quantum Authenticated Channels (KDP-6DP
Directory of Open Access Journals (Sweden)
Mohammed M.A. Majeed
2010-01-01
Full Text Available Problem statement: In previous researches, we investigated the security of communication channels, which utilizes authentication, key distribution between two parties, error corrections and cost establishment. In the present work, we studied new concepts of Quantum Authentication (QA and sharing key according to previous points. Approach: This study presented a new protocol concept that allows the session and key generation on-site by independently applying a cascade of two hash functions on a random string of bits at the sender and receiver sides. This protocol however, required a reliable method of authentication. It employed an out-of-band authentication methodology based on quantum theory, which uses entangled pairs of photons. Results: The proposed quantum-authenticated channel is secure in the presence of eavesdropper who has access to both the classical and the quantum channels. Conclusion/Recommendations: The key distribution process using cascaded hash functions provides better security. The concepts presented by this protocol represent a valid approach to the communication security problem.
Environment-assisted quantum walks in excitonic energy transport
Mohseni, Masoud; Rebentrost, Patrick; Lloyd, Seth; Aspuru-Guzik, Alan
2010-03-01
Long-lived quantum coherence has recently been observed experimentally via ultrafast nonlinear spectroscopy in excitonic energy transfer within light-harvesting photosynthetic complexes, conjugated polymers, and marine alga even at room temperature. Here, we demonstrate that directed quantum walks lead to an enhancement of energy transfer efficiency in such systems. We introduce two complementary theoretical approaches, based on a Green's function method and energy transfer susceptibilities, to partition open quantum dynamics. We quantify the role of fundamental physical processes involved in energy transport. In particular, we examine the contributions of classical hopping, coherent excitonic Hamiltonian, and phonon-induced decoherence effects for pure dephasing, Markovian, and non-Markovian limits.
DEFF Research Database (Denmark)
Markussen, Troels; Kristensen, Philip Trøst; Tromborg, Bjarne
2006-01-01
Models of carrier dynamics in quantum dots rely strongly on adequate descriptions of the carrier wave functions. In this work we numerically solve the one-band effective mass Schrodinger equation to calculate the capture times of phonon-mediated carrier capture into self-assembled quantum dots...
Modeling on the size dependent properties of InP quantum dots: a hybrid functional study
Cho, Eunseog; Jang, Hyosook; Lee, Junho; Jang, Eunjoo
2013-05-01
Theoretical calculations based on density functional theory were performed to provide better understanding of the size dependent electronic properties of InP quantum dots (QDs). Using a hybrid functional approach, we suggest a reliable analytical equation to describe the change of energy band gap as a function of size. Synthesizing colloidal InP QDs with 2-4 nm diameter and measuring their optical properties was also carried out. It was found that the theoretical band gaps showed a linear dependence on the inverse size of QDs and gave energy band gaps almost identical to the experimental values.
Time-dependent density functional theory for open quantum systems with unitary propagation.
Yuen-Zhou, Joel; Tempel, David G; Rodríguez-Rosario, César A; Aspuru-Guzik, Alán
2010-01-29
We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) time-dependent density functional theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential. A Markovian bath functional inspired by the theory of nonlinear Schrödinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented.
The Meaning of the Wave Function: In Search of the Ontology of Quantum Mechanics
Gao, Shan
2016-01-01
The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of (incomplete) knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical state does it represent? In this book, I aim to make sense of the wave function in quantum mechanics and find the ontological content of the theory. The book can be divided into three parts. The first part addresses the question of the nature of the wave function (Chapters 1-5). After giving a comprehensive and critical review of the competing views of the wave function, I present a new argument for the ontic view in terms of protective measurements. In addition, I also analyze the origin of the wave function by derivin...