BOOK REVIEW: Path Integrals in Field Theory: An Introduction
Ryder, Lewis
2004-06-01
In the 1960s Feynman was known to particle physicists as one of the people who solved the major problems of quantum electrodynamics, his contribution famously introducing what are now called Feynman diagrams. To other physicists he gained a reputation as the author of the Feynman Lectures on Physics; in addition some people were aware of his work on the path integral formulation of quantum theory, and a very few knew about his work on gravitation and Yang--Mills theories, which made use of path integral methods. Forty years later the scene is rather different. Many of the problems of high energy physics are solved; and the standard model incorporates Feynman's path integral method as a way of proving the renormalisability of the gauge (Yang--Mills) theories involved. Gravitation is proving a much harder nut to crack, but here also questions of renormalisability are couched in path-integral language. What is more, theoretical studies of condensed matter physics now also appeal to this technique for quantisation, so the path integral method is becoming part of the standard apparatus of theoretical physics. Chapters on it appear in a number of recent books, and a few books have appeared devoted to this topic alone; the book under review is a very recent one. Path integral techniques have the advantage of enormous conceptual appeal and the great disadvantage of mathematical complexity, this being partly the result of messy integrals but more fundamentally due to the notions of functional differentiation and integration which are involved in the method. All in all this subject is not such an easy ride. Mosel's book, described as an introduction, is aimed at graduate students and research workers in particle physics. It assumes a background knowledge of quantum mechanics, both non-relativistic and relativistic. After three chapters on the path integral formulation of non-relativistic quantum mechanics there are eight chapters on scalar and spinor field theory, followed
Stochastic quantisation: theme and variation
International Nuclear Information System (INIS)
Klauder, J.R.; Kyoto Univ.
1987-01-01
The paper on stochastic quantisation is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. Stochastic quantisation reformulates Euclidean quantum field theory in the language of Langevin equations. The generalised free field is discussed from the viewpoint of stochastic quantisation. An artificial family of highly singular model theories wherein the space-time derivatives are dropped altogether is also examined. Finally a modified form of stochastic quantisation is considered. (U.K.)
Are the gravitational waves quantised?
International Nuclear Information System (INIS)
Lovas, Istvan
1997-01-01
If the gravitational waves are classical objects then the value of their correlation function is 1. If they are quantised, then there exist two possibilities: the gravitational waves are either completely coherent, then their correlation function is again 1, or they are only partially coherent, then their correlation function is expected to deviate from 1. Unfortunately such a deviation is not a sufficient proof for the quantised character of the gravitational waves. If the gravitational waves are quantised and generated by the change of the background metrical then they can be in a squeezed state. In a squeezed state there is a chance for the correlation between the phase of the wave and the quantum fluctuations. The observation of such a correlation would be a genuine proof of the quantised character of the gravitational wave
The Dirac quantisation condition for fluxes on four-manifolds
International Nuclear Information System (INIS)
Alvarez, M.; Olive, D.I.
2000-01-01
A systematic treatment is given of the Dirac quantisation condition for electromagnetic fluxes through two-cycles on a four-manifold space-time which can be very complicated topologically, provided only that it is connected, compact, oriented and smooth. This is sufficient for the quantised Maxwell theory on it to satisfy electromagnetic duality properties. The results depend upon whether the complex wave function needed for the argument is scalar or spinorial in nature. An essential step is the derivation of a ''quantum Stokes' theorem'' for the integral of the gauge potential around a closed loop on the manifold. This can only be done for an exponentiated version of the line integral (the ''Wilson loop'') and the result again depends on the nature of the complex wave functions, through the appearance of what is known as a Stiefel-Whitney cohomology class in the spinor case. A nice picture emerges providing a physical interpretation, in terms of quantised fluxes and wave-functions, of mathematical concepts such as spin structures, spin C structures, the Stiefel-Whitney class and Wu's formula. Relations appear between these, electromagnetic duality and the Atiyah-Singer index theorem. Possible generalisation to higher dimensions of space-time in the presence of branes are mentioned. (orig.)
BRST Quantisation of Histories Electrodynamics
Noltingk, D.
2001-01-01
This paper is a continuation of earlier work where a classical history theory of pure electrodynamics was developed in which the the history fields have \\emph{five} components. The extra component is associated with an extra constraint, thus enlarging the gauge group of histories electrodynamics. In this paper we quantise the classical theory developed previously by two methods. Firstly we quantise the reduced classical history space, to obtain a reduced quantum history theory. Secondly we qu...
Understanding the Quantum Computational Speed-up via De-quantisation
Directory of Open Access Journals (Sweden)
Cristian S. Calude
2010-06-01
Full Text Available While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating the ability to de-quantise quantum algorithms into classical simulations of the algorithms which are as efficient in both time and space as the original quantum algorithms. The process of de-quantisation helps formulate conditions to determine if a quantum algorithm provides a real speed-up over classical algorithms. These conditions can be used to develop new quantum algorithms more effectively (by avoiding features that could allow the algorithm to be efficiently classically simulated, as well as providing the potential to create new classical algorithms (by using features which have proved valuable for quantum algorithms. Results on many different methods of de-quantisations are presented, as well as a general formal definition of de-quantisation. De-quantisations employing higher-dimensional classical bits, as well as those using matrix-simulations, put emphasis on entanglement in quantum algorithms; a key result is that any algorithm in which the entanglement is bounded is de-quantisable. These methods are contrasted with the stabiliser formalism de-quantisations due to the Gottesman-Knill Theorem, as well as those which take advantage of the topology of the circuit for a quantum algorithm. The benefits of the different methods are contrasted, and the importance of a range of techniques is emphasised. We further discuss some features of quantum algorithms which current de-quantisation methods do not cover.
The quantisation and measurement of momentum observables
International Nuclear Information System (INIS)
Wan, K.K.; McFarlane, K.
1980-01-01
Mackey's scheme for the quantisation of classical momenta generating complete vector fields (complete momenta) is introduced, the differential operators corresponding to these momenta are introduced and discussed, and an isomorphism is shown to exist between the subclass of first-order self-adjoint differential operators, whose symmetric restrictions are essentially self-adjoint, and the complete classical momenta. Difficulties in the quantisation of incomplete momenta are discussed, and a critique given. Finally, in an attempt to relate the concept of completeness to measurability concepts of classical and quantum global measurability are introduced, and shown to require completeness. These results afford strong physical insight into the nature of complete momenta, and leads us to suggest a quantisability condition based upon global measurability. (author)
Testing quantised inertia on emdrives with dielectrics
McCulloch, M. E.
2017-05-01
Truncated-cone-shaped cavities with microwaves resonating within them (emdrives) move slightly towards their narrow ends, in contradiction to standard physics. This effect has been predicted by a model called quantised inertia (MiHsC) which assumes that the inertia of the microwaves is caused by Unruh radiation, more of which is allowed at the wide end. Therefore, photons going towards the wide end gain inertia, and to conserve momentum the cavity must move towards its narrow end, as observed. A previous analysis with quantised inertia predicted a controversial photon acceleration, which is shown here to be unnecessary. The previous analysis also mispredicted the thrust in those emdrives with dielectrics. It is shown here that having a dielectric at one end of the cavity is equivalent to widening the cavity at that end, and when dielectrics are considered, then quantised inertia predicts these results as well as the others, except for Shawyer's first test where the thrust is predicted to be the right size but in the wrong direction. As a further test, quantised inertia predicts that an emdrive's thrust can be enhanced by using a dielectric at the wide end.
Projective flatness in the quantisation of bosons and fermions
Wu, Siye
2015-07-01
We compare the quantisation of linear systems of bosons and fermions. We recall the appearance of projectively flat connection and results on parallel transport in the quantisation of bosons. We then discuss pre-quantisation and quantisation of fermions using the calculus of fermionic variables. We define a natural connection on the bundle of Hilbert spaces and show that it is projectively flat. This identifies, up to a phase, equivalent spinor representations constructed by various polarisations. We introduce the concept of metaplectic correction for fermions and show that the bundle of corrected Hilbert spaces is naturally flat. We then show that the parallel transport in the bundle of Hilbert spaces along a geodesic is a rescaled projection provided that the geodesic lies within the complement of a cut locus. Finally, we study the bundle of Hilbert spaces when there is a symmetry.
Are the gravitational waves quantised?
International Nuclear Information System (INIS)
Lovas, I.
1998-01-01
The question whether gravitational waves are quantised or not can be investigated by the help of correlation measurements. If the gravitational waves are classical objects then the value of their correlation function is 1. However, if they are quantised, then there exist two possibilities: the gravitational waves are either completely coherent, then the correlation function is again 1, or they are partially coherent, then the correlation function is expected to deviate from 1. If the gravitational waves are generated by the change of the background metrics then they can be in a squeezed state. In a squeezed state there is a chance for the correlation between the phase of the wave and the quantum fluctuations. (author)
Alternative to dead reckoning for model state quantisation when migrating to a quantised discrete
CSIR Research Space (South Africa)
Duvenhage, A
2008-06-01
Full Text Available Some progress has recently been made on migrating an existing distributed parallel discrete time simulator to a quantised discrete event architecture. The migration is done to increase the scale of the real-time simulations supported...
Self-organised fractional quantisation in a hole quantum wire
Gul, Y.; Holmes, S. N.; Myronov, M.; Kumar, S.; Pepper, M.
2018-03-01
We have investigated hole transport in quantum wires formed by electrostatic confinement in strained germanium two-dimensional layers. The ballistic conductance characteristics show the regular staircase of quantum levels with plateaux at n2e 2/h, where n is an integer, e is the fundamental unit of charge and h is Planck’s constant. However as the carrier concentration is reduced, the quantised levels show a behaviour that is indicative of the formation of a zig-zag structure and new quantised plateaux appear at low temperatures. In units of 2e 2/h the new quantised levels correspond to values of n = 1/4 reducing to 1/8 in the presence of a strong parallel magnetic field which lifts the spin degeneracy but does not quantise the wavefunction. A further plateau is observed corresponding to n = 1/32 which does not change in the presence of a parallel magnetic field. These values indicate that the system is behaving as if charge was fractionalised with values e/2 and e/4, possible mechanisms are discussed.
DEFF Research Database (Denmark)
Jensen, Tom Nørgaard; Wisniewski, Rafal
2013-01-01
a set of decentralised, logarithmic quantised and constrained control actions with properly designed quantisation parameters. That is, an attractor set with a compact basin of attraction exists. Subsequently, the basin can be increased by increasing the control gains. In our work, this result...... is extended by showing that an attractor set with a global basin of attraction exists for arbitrary values of positive control gains, given that the upper level of the quantiser is properly designed. Furthermore, the proof is given for general monotone quantisation maps. Since the basin of attraction...
Gauge symmetries, topology, and quantisation
International Nuclear Information System (INIS)
Balachandran, A.P.
1994-01-01
The following two loosely connected sets of topics are reviewed in these lecture notes: (1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall effect. (2) Quantisation on multiply connected spaces and a topological proof the spin-statistics theorem which avoids quantum field theory and relativity. Under (1), after explaining the meaning of gauge invariance and the theory of constraints, we discuss boundary conditions on gauge transformations and the definition of internal symmetries in gauge field theories. We then show how the edge states in the quantum Hall effect can be derived from the Chern-Simons action using the preceding ideas. Under (2), after explaining the significance of fibre bundles for quantum physics, we review quantisation on multiply connected spaces in detail, explaining also mathematical ideas such as those of the universal covering space and the fundamental group. These ideas are then used to prove the aforementioned topological spin-statistics theorem
Hybrid 3D Fractal Coding with Neighbourhood Vector Quantisation
Directory of Open Access Journals (Sweden)
Zhen Yao
2004-12-01
Full Text Available A hybrid 3D compression scheme which combines fractal coding with neighbourhood vector quantisation for video and volume data is reported. While fractal coding exploits the redundancy present in different scales, neighbourhood vector quantisation, as a generalisation of translational motion compensation, is a useful method for removing both intra- and inter-frame coherences. The hybrid coder outperforms most of the fractal coders published to date while the algorithm complexity is kept relatively low.
Edwards, James P.; Gerber, Urs; Schubert, Christian; Trejo, Maria Anabel; Weber, Axel
2018-04-01
We introduce two integral transforms of the quantum mechanical transition kernel that represent physical information about the path integral. These transforms can be interpreted as probability distributions on particle trajectories measuring respectively the relative contribution to the path integral from paths crossing a given spatial point (the hit function) and the likelihood of values of the line integral of the potential along a path in the ensemble (the path-averaged potential).
Do the SuperKamiokande atmospheric neutrino results explain electric charge quantisation?
International Nuclear Information System (INIS)
Foot, R.; Volkas, R.R.
1998-08-01
It is shown that the SuperKamiokande atmospheric neutrino results explain electric charge quantisation, provided that the oscillation mode is ν μ → ν τ and that the neutrino mass is of the Majorana type. It is emphasised that neutrino oscillation and neutrinoless double beta decay experiments provide important information regarding the seemingly unrelated issue of electric charge quantisation
Quantisation deforms w∞ to W∞ gravity
Bergshoeff, E.; Howe, P.S.; Pope, C.N.; Sezgin, E.; Shen, X.; Stelle, K.S.
1991-01-01
Quantising a classical theory of w∞ gravity requires the introduction of an infinite number of counterterms in order to remove matter-dependent anomalies. We show that these counterterms correspond precisely to a renormalisation of the classical w∞ currents to quantum W∞ currents.
International Nuclear Information System (INIS)
DeWitt-Morette, C.
1983-01-01
Much is expected of path integration as a quantization procedure. Much more is possible if one recognizes that path integration is at the crossroad of stochastic and differential calculus and uses the full power of both stochastic and differential calculus in setting up and computing path integrals. In contrast to differential calculus, stochastic calculus has only comparatively recently become an instrument of thought. It has nevertheless already been used in a variety of challenging problems, for instance in the quantization problem. The author presents some applications of the stochastic scheme. (Auth.)
Quantisation deforms w∞ to W∞ gravity
International Nuclear Information System (INIS)
Bergshoeff, E.; Howe, P.S.; State Univ. of New York, Stony Brook, NY; Pope, C.N.; Sezgin, E.; Shen, X.; Stelle, K.S.
1991-01-01
Quantising a classical theory of w ∞ gravity requires the introduction of an infinite number of counterterms in order to remove matter-dependent anomalies. We show that these counterterms correspond precisely to a renormalisation of the classical w ∞ currents to quantum w ∞ currents. (orig.)
Reparametrization in the path integral
International Nuclear Information System (INIS)
Storchak, S.N.
1983-01-01
The question of the invariance of a measure in the n-dimensional path integral under the path reparametrization is considered. The non-invariance of the measure through the jacobian is suggeste. After the path integral reparametrization the representatioq for the Green's function of the Hamilton operator in terms of the path integral with the classical Hamiltonian has been obtained
Twistor quantisation of open strings in three dimensions
International Nuclear Information System (INIS)
Shaw, W.T.
1987-01-01
The paper treats the first quantisation of loops in real four-dimensional twistor space. Such loops correspond to open strings in three-dimensional spacetime. The geometry and reality structures pertaining to twistors in three dimensions are reviewed and the twistor description of null geodesics is presented as a prototype for the discussion of null curves. The classical twistor structure of null curves is then described. The symplectic structure is exhibited and used to investigate the constraint algebra. Expressions for the momentum operators are found. The symplectic structure defines natural canonical variables for covariant twistor quantisation and the consequences of carrying this out are described. A twistor representation of the Virasoro algebra with central charge 2 is found and some solutions of the quantum constraints are exhibited. (author)
Feynman's path integrals and Bohm's particle paths
International Nuclear Information System (INIS)
Tumulka, Roderich
2005-01-01
Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schroedinger's equation, which is half of the defining equations of Bohmian mechanics. I try to give a clear and concise description of the various aspects of the situation. (letters and comments)
Stochastic Automata for Outdoor Semantic Mapping using Optimised Signal Quantisation
DEFF Research Database (Denmark)
Caponetti, Fabio; Blas, Morten Rufus; Blanke, Mogens
2011-01-01
Autonomous robots require many types of information to obtain intelligent and safe behaviours. For outdoor operations, semantic mapping is essential and this paper proposes a stochastic automaton to localise the robot within the semantic map. For correct modelling and classi¯cation under...... uncertainty, this paper suggests quantising robotic perceptual features, according to a probabilistic description, and then optimising the quantisation. The proposed method is compared with other state-of-the-art techniques that can assess the con¯dence of their classi¯cation. Data recorded on an autonomous...
Exact quantisation of the relativistic Hopfield model
Energy Technology Data Exchange (ETDEWEB)
Belgiorno, F., E-mail: francesco.belgiorno@polimi.it [Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo 32, IT-20133 Milano (Italy); INdAM-GNFM (Italy); Cacciatori, S.L., E-mail: sergio.cacciatori@uninsubria.it [Department of Science and High Technology, Università dell’Insubria, Via Valleggio 11, IT-22100 Como (Italy); INFN sezione di Milano, via Celoria 16, IT-20133 Milano (Italy); Dalla Piazza, F., E-mail: f.dallapiazza@gmail.com [Università “La Sapienza”, Dipartimento di Matematica, Piazzale A. Moro 2, I-00185, Roma (Italy); Doronzo, M., E-mail: m.doronzo@uninsubria.it [Department of Science and High Technology, Università dell’Insubria, Via Valleggio 11, IT-22100 Como (Italy)
2016-11-15
We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields, represented by a mesoscopic polarisation field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalised Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.
Path integrals on curved manifolds
International Nuclear Information System (INIS)
Grosche, C.; Steiner, F.
1987-01-01
A general framework for treating path integrals on curved manifolds is presented. We also show how to perform general coordinate and space-time transformations in path integrals. The main result is that one has to subtract a quantum correction ΔV ∝ ℎ 2 from the classical Lagrangian L, i.e. the correct effective Lagrangian to be used in the path integral is L eff = L-ΔV. A general prescription for calculating the quantum correction ΔV is given. It is based on a canonical approach using Weyl-ordering and the Hamiltonian path integral defined by the midpoint prescription. The general framework is illustrated by several examples: The d-dimensional rotator, i.e. the motion on the sphere S d-1 , the path integral in d-dimensional polar coordinates, the exact treatment of the hydrogen atom in R 2 and R 3 by performing a Kustaanheimo-Stiefel transformation, the Langer transformation and the path integral for the Morse potential. (orig.)
Path integration in conical space
International Nuclear Information System (INIS)
Inomata, Akira; Junker, Georg
2012-01-01
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of the conical surface embedded in Euclidean space. The path integral calculation is compatible with the Schrödinger equation modified with the Gaussian and the mean curvature. -- Highlights: ► We study quantum mechanics on a cone by the path integral approach. ► The path integral depends only on the metric and the curvature effect is built in. ► The approach is consistent with the Schrödinger equation modified by an effective potential. ► The effective potential is found to be of the “Jensen–Koppe” and “da Costa” type.
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
The properties of path integrals associated with the allowance for nonstandard terms reflecting the operator nature of the canonical variables are considered. Rules for treating such terms (''equivalence rules'') are formulated. Problems with a boundary, the behavior of path integrals under canonical transformations, and the problem of quantization of dynamical systems with constraints are considered in the framework of the method
Factors Influencing Energy Quantisation | Adelabu | Global Journal ...
African Journals Online (AJOL)
Department of Physics, College of Science & Agriculture, University of Abuja, P. M. B. 117, Abuja FCT, Nigeria. Investigations of energy quantisation in a range of multiple quantum well (MQW) systems using effective mass band structure calculations including non-parabolicity in both the well and barrier layers are reported.
Quantisation of super Teichmueller theory
International Nuclear Information System (INIS)
Aghaei, Nezhla; Hamburg Univ.; Pawelkiewicz, Michal; Techner, Joerg
2015-12-01
We construct a quantisation of the Teichmueller spaces of super Riemann surfaces using coordinates associated to ideal triangulations of super Riemann surfaces. A new feature is the non-trivial dependence on the choice of a spin structure which can be encoded combinatorially in a certain refinement of the ideal triangulation. By constructing a projective unitary representation of the groupoid of changes of refined ideal triangulations we demonstrate that the dependence of the resulting quantum theory on the choice of a triangulation is inessential.
Energy Technology Data Exchange (ETDEWEB)
Mignemi, S., E-mail: smignemi@unica.it [Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Štrajn, R. [Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy)
2016-04-29
The definition of path integrals in one- and two-dimensional Snyder space is discussed in detail both in the traditional setting and in the first-order formalism of Faddeev and Jackiw. - Highlights: • The definition of the path integral in Snyder space is discussed using phase space methods. • The same result is obtained in the first-order formalism of Faddeev and Jackiw. • The path integral formulation of the two-dimensional Snyder harmonic oscillator is outlined.
International Nuclear Information System (INIS)
Mignemi, S.; Štrajn, R.
2016-01-01
The definition of path integrals in one- and two-dimensional Snyder space is discussed in detail both in the traditional setting and in the first-order formalism of Faddeev and Jackiw. - Highlights: • The definition of the path integral in Snyder space is discussed using phase space methods. • The same result is obtained in the first-order formalism of Faddeev and Jackiw. • The path integral formulation of the two-dimensional Snyder harmonic oscillator is outlined.
Path integrals and geometry of trajectories
International Nuclear Information System (INIS)
Blau, M.; Keski-Vakkuri, E.; Niemi, A.J.
1990-01-01
A geometrical interpretation of path integrals is developed in the space of trajectories. This yields a supersymmetric formulation of a generic path integral, with the supersymmetry resembling the BRST supersymmetry of a first class constrained system. If the classical equation of motion is a Killing vector field in the space of trajectories, the supersymmetry localizes the path integral to classical trajectories and the WKB approximation becomes exact. This can be viewed as a path integral generalization of the Duistermaat-Heckman theorem, which states the conditions for the exactness of the WKB approximation for integrals in a compact phase space. (orig.)
Techniques and applications of path integration
Schulman, L S
2005-01-01
A book of techniques and applications, this text defines the path integral and illustrates its uses by example. It is suitable for advanced undergraduates and graduate students in physics; its sole prerequisite is a first course in quantum mechanics. For applications requiring specialized knowledge, the author supplies background material.The first part of the book develops the techniques of path integration. Topics include probability amplitudes for paths and the correspondence limit for the path integral; vector potentials; the Ito integral and gauge transformations; free particle and quadra
On the quantisation of one-dimensional bags
International Nuclear Information System (INIS)
Fairley, G.T.; Squires, E.J.
1976-01-01
The quantisation of one-dimensional MIT bags by expanding the fields as a sum of classical modes and truncating the series after the first term is discussed. The lowest states of a bag in a world containing two scalar quark fields are obtained. Problems associated with the zero-point oscillations of the field are discussed. (Auth.)
Perfect discretization of path integrals
International Nuclear Information System (INIS)
Steinhaus, Sebastian
2012-01-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.
Perfect discretization of path integrals
Steinhaus, Sebastian
2012-05-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.
Path integrals for arbitrary canonical transformations
International Nuclear Information System (INIS)
Oliveira, L.A.R. de.
1980-01-01
Some aspects of the path integral formulation of quantum mechanics are studied. This formalism is generalized to arbitrary canonical transformations, by means of an association between path integral probalility amplitudes and classical generators of transformations, analogous to the usual Hamiltonian time development phase space expression. Such association turns out to be equivalent to the Weyl quantization rule, and it is also shown that this formalism furnishes a path integral representation for a Lie algebra of a given set of classical generators. Some physical considerations about the path integral quantization procedure and about the relationship between classical and quantum dynamical structures are also discussed. (Author) [pt
How to solve path integrals in quantum mechanics
International Nuclear Information System (INIS)
Grosche, C.
1994-10-01
A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last 15 years, including, of course, the main contributions since the invention of the path integral by Feynman in 1942. An outline of the general theory is given which will serve as a quick reference for solving path integrals. Explicit formulae for the so-called basic path integrals are presented on which our general scheme to classify and calculate path integrals in quantum mechanics is based. (orig.)
Path integration on hyperbolic spaces
Energy Technology Data Exchange (ETDEWEB)
Grosche, C [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
1991-11-01
Quantum mechanics on the hyperbolic spaces of rank one is discussed by path integration technique. Hyperbolic spaces are multi-dimensional generalisation of the hyperbolic plane, i.e. the Poincare upper half-plane endowed with a hyperbolic geometry. We evalute the path integral on S{sub 1} {approx equal} SO (n,1)/SO(n) and S{sub 2} {approx equal} SU(n,1)/S(U(1) x U(n)) in a particular coordinate system, yielding explicitly the wave-functions and the energy spectrum. Futhermore we can exploit a general property of all these spaces, namely that they can be parametrized by a pseudopolar coordinate system. This allows a separation in path integration over spheres and an additional path integration over the remaining hyperbolic coordinate, yielding effectively a path integral for a modified Poeschl-Teller potential. Only continuous spectra can exist in all the cases. For all the hyperbolic spaces of rank one we find a general formula for the largest lower bound (zero-point energy) of the spectrum which is given by E{sub O} = h{sup 2} /8m(m{sub {alpha}} +2m{sub 2} {alpha}){sup 2} (m {alpha} and m{sub 2}{alpha} denote the dimension of the root subspace corresponding to the roots {alpha} and 2{alpha}, respectively). I also discuss the case, where a constant magnetic field on H{sup n} is incorporated. (orig.).
Path integration on hyperbolic spaces
International Nuclear Information System (INIS)
Grosche, C.
1991-11-01
Quantum mechanics on the hyperbolic spaces of rank one is discussed by path integration technique. Hyperbolic spaces are multi-dimensional generalisation of the hyperbolic plane, i.e. the Poincare upper half-plane endowed with a hyperbolic geometry. We evalute the path integral on S 1 ≅ SO (n,1)/SO(n) and S 2 ≅ SU(n,1)/S[U(1) x U(n)] in a particular coordinate system, yielding explicitly the wave-functions and the energy spectrum. Futhermore we can exploit a general property of all these spaces, namely that they can be parametrized by a pseudopolar coordinate system. This allows a separation in path integration over spheres and an additional path integration over the remaining hyperbolic coordinate, yielding effectively a path integral for a modified Poeschl-Teller potential. Only continuous spectra can exist in all the cases. For all the hyperbolic spaces of rank one we find a general formula for the largest lower bound (zero-point energy) of the spectrum which is given by E O = h 2 /8m(m α +2m 2 α) 2 (m α and m 2 α denote the dimension of the root subspace corresponding to the roots α and 2α, respectively). I also discuss the case, where a constant magnetic field on H n is incorporated. (orig.)
Refined algebraic quantisation in a system with nonconstant gauge invariant structure functions
International Nuclear Information System (INIS)
Martínez-Pascual, Eric
2013-01-01
In a previous work [J. Louko and E. Martínez-Pascual, “Constraint rescaling in refined algebraic quantisation: Momentum constraint,” J. Math. Phys. 52, 123504 (2011)], refined algebraic quantisation (RAQ) within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling one momentum-type constraint was investigated. In the present work, the first steps to generalise this analysis to cases where more constraints occur are developed. The system under consideration contains two momentum-type constraints, originally abelian, where rescalings of these constraints by a non-vanishing function of the coordinates are allowed. These rescalings induce structure functions at the level of the gauge algebra. Providing a specific parametrised family of real-valued scaling functions, the implementation of the corresponding rescaled quantum momentum-type constraints is performed using RAQ when the gauge algebra: (i) remains abelian and (ii) undergoes into an algebra of a nonunimodular group with nonconstant gauge invariant structure functions. Case (ii) becomes the first example known to the author where an open algebra is handled in refined algebraic quantisation. Challenging issues that arise in the presence of non-gauge invariant structure functions are also addressed
Path Integration on the Upper Half-Plane
Reijiro, KUBO; Research Institute for Theoretical Physics Hiroshima University
1987-01-01
Feynman's path integral is considered on the Poincare upper half-plane. It is shown that the fundamental solution to the heat equation ∂f/∂t=Δ_Hf can be expressed in terms of a path integral. A simple relation between the path integral and the Selberg trace formula is discussed briefly.
Path integral for relativistic particle theory
International Nuclear Information System (INIS)
Fradkin, E.S.; Gitman, D.M.; Shvartsman, Sh.M.
1990-06-01
An action for a relativistic spinning particle interacting with external electromagnetic field is considered in reparametrization and local supergauge invariant form. It is shown that various path integral representations derived for the causal Green function correspond to the different forms of the relativistic particle action. The analogy of the path integral derived with the Lagrangian path integral of the field theory is discussed. It is shown that to obtain the causal propagator, the integration over the null mode of the Lagrangian multiplier corresponding to the reparametrization invariance, has to be performed in the (0,+infinity) limits. (author). 23 refs
Path integration on the upper half-plane
International Nuclear Information System (INIS)
Kubo, Reijiro.
1987-06-01
Feynman's path integral is considered on the Poincare upper half-plane. It is shown that the fundamental solution to the heat equation δf/δt = Δ H f can be expressed in terms of a path integral. A simple relation between the path integral and the Selberg trace formula is discussed briefly. (author)
Purely geometric path integral for spin-foams
International Nuclear Information System (INIS)
Shirazi, Atousa Chaharsough; Engle, Jonathan
2014-01-01
Spin-foams are a proposal for defining the dynamics of loop quantum gravity via path integral. In order for a path integral to be at least formally equivalent to the corresponding canonical quantization, at each point in the space of histories it is important that the integrand have not only the correct phase—a topic of recent focus in spin-foams—but also the correct modulus, usually referred to as the measure factor. The correct measure factor descends from the Liouville measure on the reduced phase space, and its calculation is a task of canonical analysis. The covariant formulation of gravity from which spin-foams are derived is the Plebanski–Holst formulation, in which the basic variables are a Lorentz connection and a Lorentz-algebra valued 2-form, called the Plebanski 2-form. However, in the final spin-foam sum, one usually sums over only spins and intertwiners, which label eigenstates of the Plebanski 2-form alone. The spin-foam sum is therefore a discretized version of a Plebanski–Holst path integral in which only the Plebanski 2-form appears, and in which the connection degrees of freedom have been integrated out. We call this a purely geometric Plebanski–Holst path integral. In prior work in which one of the authors was involved, the measure factor for the Plebanski–Holst path integral with both connection and 2-form variables was calculated. Before one discretizes this measure and incorporates it into a spin-foam sum, however, one must integrate out the connection in order to obtain the purely geometric version of the path integral. To calculate this purely geometric path integral is the principal task of the present paper, and it is done in two independent ways. Background independence of the resulting path integral is discussed in the final section, and gauge-fixing is discussed in appendix B. (paper)
Path Integrals in Quantum Mechanics
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Louko, J
2005-01-01
Jean Zinn-Justin's textbook Path Integrals in Quantum Mechanics aims to familiarize the reader with the path integral as a calculational tool in quantum mechanics and field theory. The emphasis is on quantum statistical mechanics, starting with the partition function Tr exp(-β H) and proceeding through the diffusion equation to barrier penetration problems and their semiclassical limit. The 'real time' path integral is defined via analytic continuation and used for the path-integral representation of the nonrelativistic S-matrix and its perturbative expansion. Holomorphic and Grassmannian path integrals are introduced and applied to nonrelativistic quantum field theory. There is also a brief discussion of path integrals in phase space. The introduction includes a brief historical review of path integrals, supported by a bibliography with some 40 entries. As emphasized in the introduction, mathematical rigour is not a central issue in the book. This allows the text to present the calculational techniques in a very readable manner: much of the text consists of worked-out examples, such as the quartic anharmonic oscillator in the barrier penetration chapter. At the end of each chapter there are exercises, some of which are of elementary coursework type, but the majority are more in the style of extended examples. Most of the exercises indeed include the solution or a sketch thereof. The book assumes minimal previous knowledge of quantum mechanics, and some basic quantum mechanical notation is collected in an appendix. The material has a large overlap with selected chapters in the author's thousand-page textbook Quantum Field Theory and Critical Phenomena (2002 Oxford: Clarendon). The stand-alone scope of the present work has, however, allowed a more focussed organization of this material, especially in the chapters on, respectively, holomorphic and Grassmannian path integrals. In my view the book accomplishes its aim admirably and is eminently usable as a textbook
New framework for the Feynman path integral
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Shaharir, M.Z.
1986-01-01
The well-known Fourier integral solution of the free diffusion equation in an arbitrary Euclidean space is reduced to Feynmannian integrals using the method partly contained in the formulation of the Fresnelian integral. By replacing the standard Hilbert space underlying the present mathematical formulation of the Feynman path integral by a new Hilbert space, the space of classical paths on the tangent bundle to the Euclidean space (and more general to an arbitrary Riemannian manifold) equipped with a natural inner product, we show that our Feynmannian integral is in better agreement with the qualitative features of the original Feynman path integral than the previous formulations of the integral
Distribution definition of path integrals
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Kerler, W.
1979-01-01
By starting from quantum mechanics it turns out that a rather general definition of quantum functional integrals can be given which is based on distribution theory. It applies also to curved space and provides clear rules for non-linear transformations. The refinements necessary in usual definitions of path integrals are pointed out. Since the quantum nature requires special care with time sequences, it is not the classical phase space which occurs in the phase-space form of the path integral. Feynman's configuration-space form only applies to a highly specialized situation, and therefore is not a very advantageous starting point for general investigations. It is shown that the commonly used substitutions of variables do not properly account for quantum effects. The relation to the traditional ordering problem is clarified. The distribution formulation has allowed to treat constrained systems directly at the quantum level, to complete the path integral formulation of the equivalence theorem, and to define functional integrals also for space translation after the transition to fields. (orig.)
Perfect discretization of reparametrization invariant path integrals
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Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian
2011-01-01
To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.
Perfect discretization of reparametrization invariant path integrals
Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian
2011-05-01
To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.
Perfect discretization of path integrals
Steinhaus, Sebastian
2011-01-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discu...
Generalized measures and the Feynman path integral
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Maslov, V.P.; Chebotarev, A.M.
1976-01-01
Generalizations are obtained for the earlier results by the authors concerning the inclusion of the Feynmann path integral in the momentum representation into the general integration theory. Feynmann path integrals are considered which do not represent T-products. Generalized Feynmann measure in the configuration representation is introduced
Path Integral Formulation of Anomalous Diffusion Processes
Friedrich, Rudolf; Eule, Stephan
2011-01-01
We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint probability distributions for the class of processes under consideration. We show that Continuous Time Random Walks (CTRWs) are included in our framework. A closed expression for the path probability distribution of CTRWs is found in terms of their waiting time distribution as the solution of a Dyson ...
Differential neural network configuration during human path integration
Arnold, Aiden E. G. F; Burles, Ford; Bray, Signe; Levy, Richard M.; Iaria, Giuseppe
2014-01-01
Path integration is a fundamental skill for navigation in both humans and animals. Despite recent advances in unraveling the neural basis of path integration in animal models, relatively little is known about how path integration operates at a neural level in humans. Previous attempts to characterize the neural mechanisms used by humans to visually path integrate have suggested a central role of the hippocampus in allowing accurate performance, broadly resembling results from animal data. However, in recent years both the central role of the hippocampus and the perspective that animals and humans share similar neural mechanisms for path integration has come into question. The present study uses a data driven analysis to investigate the neural systems engaged during visual path integration in humans, allowing for an unbiased estimate of neural activity across the entire brain. Our results suggest that humans employ common task control, attention and spatial working memory systems across a frontoparietal network during path integration. However, individuals differed in how these systems are configured into functional networks. High performing individuals were found to more broadly express spatial working memory systems in prefrontal cortex, while low performing individuals engaged an allocentric memory system based primarily in the medial occipito-temporal region. These findings suggest that visual path integration in humans over short distances can operate through a spatial working memory system engaging primarily the prefrontal cortex and that the differential configuration of memory systems recruited by task control networks may help explain individual biases in spatial learning strategies. PMID:24808849
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Problems related to consideration of operator nonpermutability in Hamiltonian path integral (HPI) are considered in the review. Integrals are investigated using trajectories in configuration space (nonrelativistic quantum mechanics). Problems related to trajectory integrals in HPI phase space are discussed: the problem of operator nonpermutability consideration (extra terms problem) and corresponding equivalence rules; ambiguity of HPI usual recording; transition to curvilinear coordinates. Problem of quantization of dynamical systems with couplings has been studied. As in the case of canonical transformations, quantization of the systems with couplings of the first kind requires the consideration of extra terms
Bosonic path integral for spin-1/2 particles
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Jacobson, T.
1989-01-01
The 3D Dirac propagator is expressed as a path integral over curves of commuting two-component spinors. This is related to the path integral recently employed by Polyakov to demonstrate Fermi-Bose transmutation for solitons in the gauged CP 1 model with Chern-Simons term. Several difficulties concerning the latter path integral are identified and corrected from our point of view. (orig.)
Path integral representations on the complex sphere
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Grosche, C.
2007-08-01
In this paper we discuss the path integral representations for the coordinate systems on the complex sphere S 3C . The Schroedinger equation, respectively the path integral, separates in exactly 21 orthogonal coordinate systems. We enumerate these coordinate systems and we are able to present the path integral representations explicitly in the majority of the cases. In each solution the expansion into the wave-functions is stated. Also, the kernel and the corresponding Green function can be stated in closed form in terms of the invariant distance on the sphere, respectively on the hyperboloid. (orig.)
Path-integral approach to resonant electron-molecule scattering
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Winterstetter, M.; Domcke, W.
1993-01-01
A path-integral formulation of resonant electron-molecule scattering is developed within the framework of the projection-operator formalism of scattering theory. The formation and decay of resonances is treated in real time as a quantum-mechanical electronic-tunneling process, modified by the coupling of the electronic motion with the nuclear degrees of freedom. It is shown that the electronic continuum can be summed over in the path-integral formulation, resulting formally in the path integral for an effective two-state system with coupling to vibrations. The harmonic-oscillator approximation is adopted for the vibrational motion in the present work. Approximation methods are introduced which render the numerical evaluation of the sum over paths feasible for up to ∼10 3 elementary time slices. The theory is numerically realized for simple but nontrivial models representing the 2 Π g d-wave shape resonance in e - +N 2 collisions and the 2 Σ u + p-wave shape resonance in e - +H 2 collisions, respectively. The accuracy of the path-integral results is assessed by comparison with exact numerical reference data for these models. The essential virtue of the path-integral approach is the fact that the computational effort scales at most linearly with the number of vibrational degrees of freedom. The path-integral method is thus well suited to treat electron collisions with polyatomic molecules and molecular aggregates
Path integral measure for first-order and metric gravities
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Aros, Rodrigo; Contreras, Mauricio; Zanelli, Jorge
2003-01-01
The equivalence between the path integrals for first-order gravity and the standard torsion-free, metric gravity in 3 + 1 dimensions is analysed. Starting with the path integral for first-order gravity, the correct measure for the path integral of the metric theory is obtained
Path integral solution of the Dirichlet problem
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LaChapelle, J.
1997-01-01
A scheme for functional integration developed by Cartier/DeWitt-Morette is first reviewed and then employed to construct the path integral representation for the solution of the Dirichlet problem in terms of first exit time. The path integral solution is then applied to calculate the fixed-energy point-to-point transition amplitude both in configuration and phase space. The path integral solution can also be derived using physical principles based on Feynman close-quote s original reasoning. We check that the Fourier transform in energy of the fixed-energy point-to-point transition amplitude gives the well known time-dependent transition amplitude, and calculate the WKB approximation. copyright 1997 Academic Press, Inc
Polymer quantum mechanics some examples using path integrals
International Nuclear Information System (INIS)
Parra, Lorena; Vergara, J. David
2014-01-01
In this work we analyze several physical systems in the context of polymer quantum mechanics using path integrals. First we introduce the group averaging method to quantize constrained systems with path integrals and later we use this procedure to compute the effective actions for the polymer non-relativistic particle and the polymer harmonic oscillator. We analyze the measure of the path integral and we describe the semiclassical dynamics of the systems
Path integral representations on the complex sphere
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Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2007-08-15
In this paper we discuss the path integral representations for the coordinate systems on the complex sphere S{sub 3C}. The Schroedinger equation, respectively the path integral, separates in exactly 21 orthogonal coordinate systems. We enumerate these coordinate systems and we are able to present the path integral representations explicitly in the majority of the cases. In each solution the expansion into the wave-functions is stated. Also, the kernel and the corresponding Green function can be stated in closed form in terms of the invariant distance on the sphere, respectively on the hyperboloid. (orig.)
Two-path plasmonic interferometer with integrated detector
Dyer, Gregory Conrad; Shaner, Eric A.; Aizin, Gregory
2016-03-29
An electrically tunable terahertz two-path plasmonic interferometer with an integrated detection element can down convert a terahertz field to a rectified DC signal. The integrated detector utilizes a resonant plasmonic homodyne mixing mechanism that measures the component of the plasma waves in-phase with an excitation field that functions as the local oscillator in the mixer. The plasmonic interferometer comprises two independently tuned electrical paths. The plasmonic interferometer enables a spectrometer-on-a-chip where the tuning of electrical path length plays an analogous role to that of physical path length in macroscopic Fourier transform interferometers.
Path Integrals in Quantum Mechanics
International Nuclear Information System (INIS)
Chetouani, L
2005-01-01
By treating path integrals the author, in this book, places at the disposal of the reader a modern tool for the comprehension of standard quantum mechanics. Thus the most important applications, such as the tunnel effect, the diffusion matrix, etc, are presented from an original point of view on the action S of classical mechanics while having it play a central role in quantum mechanics. What also emerges is that the path integral describes these applications more richly than are described traditionally by differential equations, and consequently explains them more fully. The book is certainly of high quality in all aspects: original in presentation, rigorous in the demonstrations, judicious in the choice of exercises and, finally, modern, for example in the treatment of the tunnel effect by the method of instantons. Moreover, the correspondence that exists between classical and quantum mechanics is well underlined. I thus highly recommend this book (the French version being already available) to those who wish to familiarize themselves with formulation by path integrals. They will find, in addition, interesting topics suitable for exploring further. (book review)
Rules for integrals over products of distributions from coordinate independence of path integrals
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Kleinert, H.; Chervyakov, A.
2001-01-01
In perturbative calculations of quantum-mechanical path integrals in curvilinear coordinates, one encounters Feynman diagrams involving multiple temporal integrals over products of distributions which are mathematically undefined. In addition, there are terms proportional to powers of Dirac δ-functions at the origin coming from the measure of path integration. We derive simple rules for dealing with such singular terms from the natural requirement of coordinate independence of the path integrals. (orig.)
Path integral discussion for Smorodinsky-Winternitz potentials. Pt. 1
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Grosche, C.; Pogosyan, G.S.; Sissakian, A.N.
1994-02-01
Path integral formulations for the Smorodinsky-Winternitz potentials in two- and three-dimensional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky-Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integralformulation is not possible, we list in all soluble cases the path integral evaluations explicity in terms of the propagators and the spectral expansions into the wave-functions. (orig.)
Formal Series of Generalised Functions and Their Application to Deformation Quantisation
Tosiek, Jaromir
2016-01-01
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of positivity in formal series calculus is proposed. Problems with defining quantum states over the set of formal series are analysed.
Medial temporal lobe roles in human path integration.
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Naohide Yamamoto
Full Text Available Path integration is a process in which observers derive their location by integrating self-motion signals along their locomotion trajectory. Although the medial temporal lobe (MTL is thought to take part in path integration, the scope of its role for path integration remains unclear. To address this issue, we administered a variety of tasks involving path integration and other related processes to a group of neurosurgical patients whose MTL was unilaterally resected as therapy for epilepsy. These patients were unimpaired relative to neurologically intact controls in many tasks that required integration of various kinds of sensory self-motion information. However, the same patients (especially those who had lesions in the right hemisphere walked farther than the controls when attempting to walk without vision to a previewed target. Importantly, this task was unique in our test battery in that it allowed participants to form a mental representation of the target location and anticipate their upcoming walking trajectory before they began moving. Thus, these results put forth a new idea that the role of MTL structures for human path integration may stem from their participation in predicting the consequences of one's locomotor actions. The strengths of this new theoretical viewpoint are discussed.
Phase-space path-integral calculation of the Wigner function
International Nuclear Information System (INIS)
Samson, J H
2003-01-01
The Wigner function W(q, p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid method in the configuration-space path integral. Paths can be classified by the midpoint of their ends; short paths where the midpoint is close to (q, p) and which lie in regions of low energy (low P function of the Hamiltonian) will dominate, and the enclosed area will determine the sign of the Wigner function. As a demonstration, the method is applied to a sequence of density matrices interpolating between a Poissonian number distribution and a number state, each member of which can be represented exactly by a discretized path integral with a finite number of vertices. Saddle-point evaluation of these integrals recovers (up to a constant factor) the WKB approximation to the Wigner function of a number state
The transformation techniques in path integration
International Nuclear Information System (INIS)
Inomata, A.
1989-01-01
In this paper general remarks are made concerning the time transformation techniques in path integration and their implementations. Time transformations may be divided into two classes: global (integrable) time transformations and local (nonintegrable) time transformations. Although a brief account of global time transformations is given, attention is focused on local transformations. First, time transformations in the classical Kepler problem are reviewed. Then, problems encountered in implementing a local time transformation in quantum mechanics are analyzed. A several propositions pertinent to the implementation of local time transformations, particularly basic to the local time rescaling trick in a discretized path integral, are presented
The formal path integral and quantum mechanics
International Nuclear Information System (INIS)
Johnson-Freyd, Theo
2010-01-01
Given an arbitrary Lagrangian function on R d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.
Which coordinate system for modelling path integration?
Vickerstaff, Robert J; Cheung, Allen
2010-03-21
Path integration is a navigation strategy widely observed in nature where an animal maintains a running estimate, called the home vector, of its location during an excursion. Evidence suggests it is both ancient and ubiquitous in nature, and has been studied for over a century. In that time, canonical and neural network models have flourished, based on a wide range of assumptions, justifications and supporting data. Despite the importance of the phenomenon, consensus and unifying principles appear lacking. A fundamental issue is the neural representation of space needed for biological path integration. This paper presents a scheme to classify path integration systems on the basis of the way the home vector records and updates the spatial relationship between the animal and its home location. Four extended classes of coordinate systems are used to unify and review both canonical and neural network models of path integration, from the arthropod and mammalian literature. This scheme demonstrates analytical equivalence between models which may otherwise appear unrelated, and distinguishes between models which may superficially appear similar. A thorough analysis is carried out of the equational forms of important facets of path integration including updating, steering, searching and systematic errors, using each of the four coordinate systems. The type of available directional cue, namely allothetic or idiothetic, is also considered. It is shown that on balance, the class of home vectors which includes the geocentric Cartesian coordinate system, appears to be the most robust for biological systems. A key conclusion is that deducing computational structure from behavioural data alone will be difficult or impossible, at least in the absence of an analysis of random errors. Consequently it is likely that further theoretical insights into path integration will require an in-depth study of the effect of noise on the four classes of home vectors. Copyright 2009 Elsevier Ltd
Nonperturbative path integral expansion II
International Nuclear Information System (INIS)
Kaiser, H.J.
1976-05-01
The Feynman path integral representation of the 2-point function for a self-interacting Bose field is investigated using an expansion ('Path Integral Expansion', PIE) of the exponential of the kinetic term of the Lagrangian. This leads to a series - illustrated by a graph scheme - involving successively a coupling of more and more points of the lattice space commonly employed in the evaluation of path integrals. The values of the individual PIE graphs depend of course on the lattice constant. Two methods - Pade approximation and Borel-type extrapolation - are proposed to extract information about the continuum limit from a finite-order PIE. A more flexible PIE is possible by expanding besides the kinetic term a suitably chosen part of the interaction term too. In particular, if the co-expanded part is a mass term the calculation becomes only slightly more complicated than in the original formulation and the appearance of the graph scheme is unchanged. A significant reduction of the number of graphs and an improvement of the convergence of the PIE can be achieved by performing certain sums over an infinity of graph elements. (author)
Space-time transformations in radial path integrals
International Nuclear Information System (INIS)
Steiner, F.
1984-09-01
Nonlinear space-time transformations in the radial path integral are discussed. A transformation formula is derived, which relates the original path integral to the Green's function of a new quantum system with an effective potential containing an observable quantum correction proportional(h/2π) 2 . As an example the formula is applied to spherical Brownian motion. (orig.)
Covariant path integrals on hyperbolic surfaces
Schaefer, Joe
1997-11-01
DeWitt's covariant formulation of path integration [B. De Witt, "Dynamical theory in curved spaces. I. A review of the classical and quantum action principles," Rev. Mod. Phys. 29, 377-397 (1957)] has two practical advantages over the traditional methods of "lattice approximations;" there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature -1. The Pauli-DeWitt curvature correction term arises, as in DeWitt's work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman-Kac formula for the automorphic Schrödinger equation on the Riemann surface ΓH. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47-90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, "The path integral on the Poincare upper half plane and for Liouville quantum mechanics," Phys. Lett. A 123, 319-328 (1987).
Quantum mechanics on the half-line using path integrals
International Nuclear Information System (INIS)
Clark, T.E.; Menikoff, R.; Sharp, D.H.
1980-01-01
We study the Feynman path-integral formalism for the constrained problem of a free particle moving on the half-line. It is shown that the effect of the boundary condition at the origin can be incorporated into the path integral by a simple modification of the action. The small-time behavior of the Green's function can be obtained from the stationary-phase evaluation of our expression for the path integral, which in this case includes contributions from both the direct and reflected classical paths
Defect-vectors and path integrals in fracture mechanics
International Nuclear Information System (INIS)
Roche, R.L.
1979-01-01
It seems necessary to introduce the J integral without hypothesis on material behavior. The aim of this paper is this introduction and its consequences. Successively are presented: introduction to defect-vectors and defect-momentum, definition of J(K) and J(L) integrals, equilibrium and energy momentum tensor, energetic signification of the path J and L integrals, and local aspects of the criteria based on path integrals [fr
Canonical transformations and hamiltonian path integrals
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms
Regularizing Feynman path integrals using the generalized Kontsevich-Vishik trace
Hartung, Tobias
2017-12-01
A fully regulated definition of Feynman's path integral is presented here. The proposed re-formulation of the path integral coincides with the familiar formulation whenever the path integral is well defined. In particular, it is consistent with respect to lattice formulations and Wick rotations, i.e., it can be used in Euclidean and Minkowski space-time. The path integral regularization is introduced through the generalized Kontsevich-Vishik trace, that is, the extension of the classical trace to Fourier integral operators. Physically, we are replacing the time-evolution semi-group by a holomorphic family of operators such that the corresponding path integrals are well defined in some half space of C . The regularized path integral is, thus, defined through analytic continuation. This regularization can be performed by means of stationary phase approximation or computed analytically depending only on the Hamiltonian and the observable (i.e., known a priori). In either case, the computational effort to evaluate path integrals or expectations of observables reduces to the evaluation of integrals over spheres. Furthermore, computations can be performed directly in the continuum and applications (analytic computations and their implementations) to a number of models including the non-trivial cases of the massive Schwinger model and a φ4 theory.
Sp(2) covariant quantisation of general gauge theories
Energy Technology Data Exchange (ETDEWEB)
Vazquez-Bello, J L
1994-11-01
The Sp(2) covariant quantization of gauge theories is studied. The geometrical interpretation of gauge theories in terms of quasi principal fibre bundles Q(M{sub s}, G{sub s}) is reviewed. It is then described the Sp(2) algebra of ordinary Yang-Mills theory. A consistent formulation of covariant Lagrangian quantisation for general gauge theories based on Sp(2) BRST symmetry is established. The original N = 1, ten dimensional superparticle is considered as an example of infinitely reducible gauge algebras, and given explicitly its Sp(2) BRST invariant action. (author). 18 refs.
Sp(2) covariant quantisation of general gauge theories
International Nuclear Information System (INIS)
Vazquez-Bello, J.L.
1994-11-01
The Sp(2) covariant quantization of gauge theories is studied. The geometrical interpretation of gauge theories in terms of quasi principal fibre bundles Q(M s , G s ) is reviewed. It is then described the Sp(2) algebra of ordinary Yang-Mills theory. A consistent formulation of covariant Lagrangian quantisation for general gauge theories based on Sp(2) BRST symmetry is established. The original N = 1, ten dimensional superparticle is considered as an example of infinitely reducible gauge algebras, and given explicitly its Sp(2) BRST invariant action. (author). 18 refs
Path integral solution for some time-dependent potential
International Nuclear Information System (INIS)
Storchak, S.N.
1989-12-01
The quantum-mechanical problem with a time-dependent potential is solved by the path integral method. The solution is obtained by the application of the previously derived general formula for rheonomic homogeneous point transformation and reparametrization in the path integral. (author). 4 refs
Time-space noncommutativity: quantised evolutions
International Nuclear Information System (INIS)
Balachandran, Aiyalam P.; Govindarajan, Thupil R.; Teotonio-Sobrinho, Paulo; Martins, Andrey Gomes
2004-01-01
In previous work, we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al. Here we extend it to certain noncommutative versions of the cylinder, R 3 and Rx S 3 . In all these models, only discrete time translations are possible, a result known before in the first two cases. One striking consequence of quantised time translations is that even though a time independent hamiltonian is an observable, in scattering processes, it is conserved only modulo 2π/θ, where θ is the noncommutative parameter. (In contrast, on a one-dimensional periodic lattice of lattice spacing a and length L = Na, only momentum mod 2π/L is observable (and can be conserved).) Suggestions for further study of this effect are made. Scattering theory is formulated and an approach to quantum field theory is outlined. (author)
Master equations and the theory of stochastic path integrals
Weber, Markus F.; Frey, Erwin
2017-04-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from
Master equations and the theory of stochastic path integrals.
Weber, Markus F; Frey, Erwin
2017-04-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon
Covariant path integrals on hyperbolic surfaces
International Nuclear Information System (INIS)
Schaefer, J.
1997-01-01
DeWitt close-quote s covariant formulation of path integration [B. De Witt, open-quotes Dynamical theory in curved spaces. I. A review of the classical and quantum action principles,close quotes Rev. Mod. Phys. 29, 377 endash 397 (1957)] has two practical advantages over the traditional methods of open-quotes lattice approximations;close quotes there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature -1. The Pauli endash DeWitt curvature correction term arises, as in DeWitt close-quote s work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman endash Kac formula for the automorphic Schroedinger equation on the Riemann surface Γ backslash H. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47 endash 90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, open-quotes The path integral on the Poincare upper half plane and for Liouville quantum mechanics,close quotes Phys. Lett. A 123, 319 endash 328 (1987). copyright 1997 American Institute of Physics
A new type of phase-space path integral
International Nuclear Information System (INIS)
Marinov, M.S.
1991-01-01
Evolution of Wigner's quasi-distribution of a quantum system is represented by means of a path integral in phase space. Instead of the Hamiltonian action, a new functional is present in the integral, and its extrema in the functional space are also given by the classical trajectories. The phase-space paths appear in the integral with real weights, so complex integrals are not necessary. The semiclassical approximation and some applications are discussed briefly. (orig.)
Field theory a path integral approach
Das, Ashok
2006-01-01
This unique book describes quantum field theory completely within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas.Adding new material keenly requested by readers, this second edition is an important expansion of the popular first edition. Two extra chapters cover path integral quantization of gauge theories and anomalies, and a new section extends the supersymmetry chapter, where singular potentials in supersymmetric systems are described.
Remembered landmarks enhance the precision of path integration
Directory of Open Access Journals (Sweden)
Shannon O´Leary
2005-01-01
Full Text Available When navigating by path integration, knowledge of ones position becomes increasingly uncertain as one walks from a known location. This uncertainty decreases if one perceives a known landmark location nearby. We hypothesized that remembering landmarks might serve a similar purpose for path integration as directly perceiving them. If this is true, walking near a remembered landmark location should enhance response consistency in path integration tasks. To test this, we asked participants to view a target and then attempt to walk to it without vision. Some participants saw the target plus a landmark during the preview. Compared with no-landmark trials, response consistency nearly doubled when participants passed near the remembered landmark location. Similar results were obtained when participants could audibly perceive the landmark while walking. A control experiment ruled out perceptual context effects during the preview. We conclude that remembered landmarks can enhance path integration even though they are not directly perceived.
Path integration on space times with symmetry
International Nuclear Information System (INIS)
Low, S.G.
1985-01-01
Path integration on space times with symmetry is investigated using a definition of path integration of Gaussian integrators. Gaussian integrators, systematically developed using the theory of projective distributions, may be defined in terms of a Jacobi operator Green function. This definition of the path integral yields a semiclassical expansion of the propagator which is valid on caustics. The semiclassical approximation to the free particle propagator on symmetric and reductive homogeneous spaces is computed in terms of the complete solution of the Jacobi equation. The results are used to test the validity of using the Schwinger-DeWitt transform to compute an approximation to the coincidence limit of a field theory Green function from a WKB propagator. The method is found not to be valid except for certain special cases. These cases include manifolds constructed from the direct product of flat space and group manifolds, on which the free particle WKB approximation is exact and two sphere. The multiple geodesic contribution to 2 > on Schwarzschild in the neighborhood of rho = 3M is computed using the transform
Path integral quantization of parametrized field theory
International Nuclear Information System (INIS)
Varadarajan, Madhavan
2004-01-01
Free scalar field theory on a flat spacetime can be cast into a generally covariant form known as parametrized field theory in which the action is a functional of the scalar field as well as the embedding variables which describe arbitrary, in general curved, foliations of the flat spacetime. We construct the path integral quantization of parametrized field theory in order to analyze issues at the interface of quantum field theory and general covariance in a path integral context. We show that the measure in the Lorentzian path integral is nontrivial and is the analog of the Fradkin-Vilkovisky measure for quantum gravity. We construct Euclidean functional integrals in the generally covariant setting of parametrized field theory using key ideas of Schleich and show that our constructions imply the existence of nonstandard 'Wick rotations' of the standard free scalar field two-point function. We develop a framework to study the problem of time through computations of scalar field two-point functions. We illustrate our ideas through explicit computation for a time independent (1+1)-dimensional foliation. Although the problem of time seems to be absent in this simple example, the general case is still open. We discuss our results in the contexts of the path integral formulation of quantum gravity and the canonical quantization of parametrized field theory
Low level constraints on dynamic contour path integration.
Directory of Open Access Journals (Sweden)
Sophie Hall
Full Text Available Contour integration is a fundamental visual process. The constraints on integrating discrete contour elements and the associated neural mechanisms have typically been investigated using static contour paths. However, in our dynamic natural environment objects and scenes vary over space and time. With the aim of investigating the parameters affecting spatiotemporal contour path integration, we measured human contrast detection performance of a briefly presented foveal target embedded in dynamic collinear stimulus sequences (comprising five short 'predictor' bars appearing consecutively towards the fovea, followed by the 'target' bar in four experiments. The data showed that participants' target detection performance was relatively unchanged when individual contour elements were separated by up to 2° spatial gap or 200 ms temporal gap. Randomising the luminance contrast or colour of the predictors, on the other hand, had similar detrimental effect on grouping dynamic contour path and subsequent target detection performance. Randomising the orientation of the predictors reduced target detection performance greater than introducing misalignment relative to the contour path. The results suggest that the visual system integrates dynamic path elements to bias target detection even when the continuity of path is disrupted in terms of spatial (2°, temporal (200 ms, colour (over 10 colours and luminance (-25% to 25% information. We discuss how the findings can be largely reconciled within the functioning of V1 horizontal connections.
Path Integrals and Anomalies in Curved Space
International Nuclear Information System (INIS)
Louko, Jorma
2007-01-01
Bastianelli and van Nieuwenhuizen's monograph 'Path Integrals and Anomalies in Curved Space' collects in one volume the results of the authors' 15-year research programme on anomalies that arise in Feynman diagrams of quantum field theories on curved manifolds. The programme was spurred by the path-integral techniques introduced in Alvarez-Gaume and Witten's renowned 1983 paper on gravitational anomalies which, together with the anomaly cancellation paper by Green and Schwarz, led to the string theory explosion of the 1980s. The authors have produced a tour de force, giving a comprehensive and pedagogical exposition of material that is central to current research. The first part of the book develops from scratch a formalism for defining and evaluating quantum mechanical path integrals in nonlinear sigma models, using time slicing regularization, mode regularization and dimensional regularization. The second part applies this formalism to quantum fields of spin 0, 1/2, 1 and 3/2 and to self-dual antisymmetric tensor fields. The book concludes with a discussion of gravitational anomalies in 10-dimensional supergravities, for both classical and exceptional gauge groups. The target audience is researchers and graduate students in curved spacetime quantum field theory and string theory, and the aims, style and pedagogical level have been chosen with this audience in mind. Path integrals are treated as calculational tools, and the notation and terminology are throughout tailored to calculational convenience, rather than to mathematical rigour. The style is closer to that of an exceedingly thorough and self-contained review article than to that of a textbook. As the authors mention, the first part of the book can be used as an introduction to path integrals in quantum mechanics, although in a classroom setting perhaps more likely as supplementary reading than a primary class text. Readers outside the core audience, including this reviewer, will gain from the book a
Path integrals in curvilinear coordinates
International Nuclear Information System (INIS)
Prokhorov, L.V.
1984-01-01
Integration limits are studied for presenting the path integral curvilinear coordinates. For spherical (and topoloqically equivalent) coordinates it is shown that in formulas involving classical action in the exponent integration over all variables should be carried out within infinite limits. Another peculiarity is associated with appearance of the operator q which provides a complete definition of the wave functions out of the physical region. arguments are given upporting the validity of the cited statament in the general case
A path-integral approach to inclusive processes
International Nuclear Information System (INIS)
Sukumar, C.V.
1995-01-01
The cross section for an inclusive scattering process may be expressed in terms of a double path integral. Evaluation of the double path integral by the stationary-phase approximation yields classical equations of motion for the stationary trajectories and a classical cross section for the inclusive process which depends on the polarization of the initial state. Polarization analyzing powers are calculated from this theory and the results are compared with those obtained in an earlier paper. ((orig.))
Defect vectors and path integrals in fracture mechanics
International Nuclear Information System (INIS)
Roche, R.L.
1979-01-01
Several criteria have been proposed in Elastic Plastic Fracture Mechanics. One of the most interesting ones is the J 1 criterion where J 1 is a path integral surrounding the crack tip. Other path integrals (or surface integrals in 3D problems) can be used. But all these integrals are introduced on an elastic basis, though they are applied in plasticity. This paper shows that it is possible to introduce these integrals without any reference to the elastic behavior of the material. The method is based on the 'defect vector theory' which is an extension of the energy-momentum tensor theory. (orig.)
International Nuclear Information System (INIS)
Kleinert, H.; Chervyakov, A.
2003-01-01
In perturbative calculations of quantum-statistical zero-temperature path integrals in curvilinear coordinates one encounters Feynman diagrams involving multiple temporal integrals over products of distributions, which are mathematically undefined. In addition, there are terms proportional to powers of Dirac δ-functions at the origin coming from the measure of path integration. We give simple rules for integrating products of distributions in such a way that the results ensure coordinate independence of the path integrals. The rules are derived by using equations of motion and partial integration, while keeping track of certain minimal features originating in the unique definition of all singular integrals in 1-ε dimensions. Our rules yield the same results as the much more cumbersome calculations in 1-ε dimensions where the limit ε→0 is taken at the end. They also agree with the rules found in an independent treatment on a finite time interval
δ'-function perturbations and Neumann boundary-conditions by path integration
International Nuclear Information System (INIS)
Grosche, C.
1994-02-01
δ'-function perturbations and Neumann boundary conditions are incorporated into the path integral formalism. The starting point is the consideration of the path integral representation for the one dimensional Dirac particle together with a relativistic point interaction. The non-relativistic limit yields either a usual δ-function or a δ'-function perturbation; making their strengths infinitely repulsive one obtains Dirichlet, respectively Neumann boundary conditions in the path integral. (orig.)
Quantisation of the holographic Ricci dark energy model
Energy Technology Data Exchange (ETDEWEB)
Albarran, Imanol; Bouhmadi-López, Mariam, E-mail: imanol@ubi.pt, E-mail: mbl@ubi.pt [Departamento de Física, Universidade da Beira Interior, 6200 Covilhã (Portugal)
2015-08-01
While general relativity is an extremely robust theory to describe the gravitational interaction in our Universe, it is expected to fail close to singularities like the cosmological ones. On the other hand, it is well known that some dark energy models might induce future singularities; this can be the case for example within the setup of the Holographic Ricci Dark Energy model (HRDE). On this work, we perform a cosmological quantisation of the HRDE model and obtain under which conditions a cosmic doomsday can be avoided within the quantum realm. We show as well that this quantum model not only avoid future singularities but also the past Big Bang.
International Nuclear Information System (INIS)
Canright, G.S.
1992-01-01
I offer a pedagogical review of the homotopy arguments for fractional statistics in two dimensions. These arguments arise naturally in path-integral language since they necessarily consider the properties of paths rather than simply permutations. The braid group replaces the permutation group as the basic structure for quantum statistics; hence properties of the braid group on several surfaces are briefly discussed. Finally, the question of multiple (real-space) occupancy is addressed; I suggest that the ''traditional'' treatment of this question (ie, an assumption that many-anyon wavefunctions necessarily vanish for multiple occupancy) needs reexamination
A Key Event Path Analysis Approach for Integrated Systems
Directory of Open Access Journals (Sweden)
Jingjing Liao
2012-01-01
Full Text Available By studying the key event paths of probabilistic event structure graphs (PESGs, a key event path analysis approach for integrated system models is proposed. According to translation rules concluded from integrated system architecture descriptions, the corresponding PESGs are constructed from the colored Petri Net (CPN models. Then the definitions of cycle event paths, sequence event paths, and key event paths are given. Whereafter based on the statistic results after the simulation of CPN models, key event paths are found out by the sensitive analysis approach. This approach focuses on the logic structures of CPN models, which is reliable and could be the basis of structured analysis for discrete event systems. An example of radar model is given to characterize the application of this approach, and the results are worthy of trust.
Rigorous time slicing approach to Feynman path integrals
Fujiwara, Daisuke
2017-01-01
This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved. The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schrödinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent. But equivalence is not fully proved mathematically, because, compared with Schrödinger's method, there is still much to be done concerning rigorous mathematical treatment of Feynman's method. Feynman himself defined a path integral as the limit of a sequence of integrals over finite-dimensional spaces which is obtained by...
Flexible integration of path-planning capabilities
Stobie, Iain C.; Tambe, Milind; Rosenbloom, Paul S.
1993-05-01
Robots pursuing complex goals must plan paths according to several criteria of quality, including shortness, safety, speed and planning time. Many sources and kinds of knowledge, such as maps, procedures and perception, may be available or required. Both the quality criteria and sources of knowledge may vary widely over time, and in general they will interact. One approach to address this problem is to express all criteria and goals numerically in a single weighted graph, and then to search this graph to determine a path. Since this is problematic with symbolic or uncertain data and interacting criteria, we propose that what is needed instead is an integration of many kinds of planning capabilities. We describe a hybrid approach to integration, based on experiments with building simulated mobile robots using Soar, an integrated problem-solving and learning system. For flexibility, we have implemented a combination of internal planning, reactive capabilities and specialized tools. We illustrate how these components can complement each other's limitations and produce plans which integrate geometric and task knowledge.
Path-integral computation of superfluid densities
International Nuclear Information System (INIS)
Pollock, E.L.; Ceperley, D.M.
1987-01-01
The normal and superfluid densities are defined by the response of a liquid to sample boundary motion. The free-energy change due to uniform boundary motion can be calculated by path-integral methods from the distribution of the winding number of the paths around a periodic cell. This provides a conceptually and computationally simple way of calculating the superfluid density for any Bose system. The linear-response formulation relates the superfluid density to the momentum-density correlation function, which has a short-ranged part related to the normal density and, in the case of a superfluid, a long-ranged part whose strength is proportional to the superfluid density. These facts are discussed in the context of path-integral computations and demonstrated for liquid 4 He along the saturated vapor-pressure curve. Below the experimental superfluid transition temperature the computed superfluid fractions agree with the experimental values to within the statistical uncertainties of a few percent in the computations. The computed transition is broadened by finite-sample-size effects
Comment on 'Path integral solution for a Mie-type potential'
International Nuclear Information System (INIS)
Steiner, F.
1985-01-01
We comment on several incorrect results given in a recent paper by Erkoc and Sever (ES). In particular, it is pointed out that their path integral formula for the one-dimensional Mie-Lennard-Jones potential is wrong, since a quantum correction proportional to (h/2π) 2 - which is a consequence of the stochastic nature of the Feynman paths - has been overlooked. The correct expression can be obtained from a general path integral formula, which we have derived in a previous paper. For the particular potential discussed in detail by ES, we give a complete path integral treatment, which allows us to derive the energies and normalized wave functions of the discrete spectrum. (orig.)
Some instructive examples of Mayer's interference in path integral
International Nuclear Information System (INIS)
Fiziev, P.P.
1984-01-01
A new technique of path integral evaluation by a discretization procedure is proposed. It is based on the requirement, found previously, to single out the set of classical trajectories over which the summation is performed. The notion of Mayer's interference is introduced and illustrated by a number of simple examples. The choice of the set of paths is shown to induce a corresponding quantization procedure and this line is followed to demonstrate its connection with the symmetries of the problem. The possibility of extracting information on the space of quantum states from path integrals has been reviewed. A class of paths has been found; the summation over these paths within the framework of the suggested approach produces the well known results for the motion in a homogeneous field and for the harmonic oscillator
PathSys: integrating molecular interaction graphs for systems biology
Directory of Open Access Journals (Sweden)
Raval Alpan
2006-02-01
Full Text Available Abstract Background The goal of information integration in systems biology is to combine information from a number of databases and data sets, which are obtained from both high and low throughput experiments, under one data management scheme such that the cumulative information provides greater biological insight than is possible with individual information sources considered separately. Results Here we present PathSys, a graph-based system for creating a combined database of networks of interaction for generating integrated view of biological mechanisms. We used PathSys to integrate over 14 curated and publicly contributed data sources for the budding yeast (S. cerevisiae and Gene Ontology. A number of exploratory questions were formulated as a combination of relational and graph-based queries to the integrated database. Thus, PathSys is a general-purpose, scalable, graph-data warehouse of biological information, complete with a graph manipulation and a query language, a storage mechanism and a generic data-importing mechanism through schema-mapping. Conclusion Results from several test studies demonstrate the effectiveness of the approach in retrieving biologically interesting relations between genes and proteins, the networks connecting them, and of the utility of PathSys as a scalable graph-based warehouse for interaction-network integration and a hypothesis generator system. The PathSys's client software, named BiologicalNetworks, developed for navigation and analyses of molecular networks, is available as a Java Web Start application at http://brak.sdsc.edu/pub/BiologicalNetworks.
Semi-classical approximation to path integrals - phases and catastrophes
International Nuclear Information System (INIS)
Levit, S.
1977-01-01
Problems of phases and catastrophes were encountered when trying to apply the classical S-matrix theory to the scattering phenomena in nuclear physics. The path integral formulation provided a suitable basis for the treatment of these and related problems. Within conventional mathematical language it was possible to give practical prescriptions and discuss their limitations. Since the semi-classical (stationary phase) approximation is commonly used in any application of the path integral method, the results are not restricted to the scattering problems and may be of general interest. The derivation of the uniform approximations in the energy representation should use the exact path integral expression as the starting point, rather than performing Fourier transforms on the expressions derived in the present lecture. (B.G.)
An alternative path integral for quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Krishnan, Chethan; Kumar, K.V. Pavan; Raju, Avinash [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India)
2016-10-10
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This “Neumann ensemble” perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
Path integral approach to eikonal and next-to-eikonal exponentiation
Laenen, E.; Stavenga, G.; White, C.D.
2009-01-01
We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting
Integrated robust controller for vehicle path following
Energy Technology Data Exchange (ETDEWEB)
Mashadi, Behrooz; Ahmadizadeh, Pouyan, E-mail: p-ahmadizadeh@iust.ac.ir; Majidi, Majid, E-mail: m-majidi@iust.ac.ir [Iran University of Science and Technology, School of Automotive Engineering (Iran, Islamic Republic of); Mahmoodi-Kaleybar, Mehdi, E-mail: m-mahmoodi-k@iust.ac.ir [Iran University of Science and Technology, School of Mechanical Engineering (Iran, Islamic Republic of)
2015-02-15
The design of an integrated 4WS+DYC control system to guide a vehicle on a desired path is presented. The lateral dynamics of the path follower vehicle is formulated by considering important parameters. To reduce the effect of uncertainties in vehicle parameters, a robust controller is designed based on a μ-synthesis approach. Numerical simulations are performed using a nonlinear vehicle model in MATLAB environment in order to investigate the effectiveness of the designed controller. Results of simulations show that the controller has a profound ability to making the vehicle track the desired path in the presence of uncertainties.
Integrated robust controller for vehicle path following
International Nuclear Information System (INIS)
Mashadi, Behrooz; Ahmadizadeh, Pouyan; Majidi, Majid; Mahmoodi-Kaleybar, Mehdi
2015-01-01
The design of an integrated 4WS+DYC control system to guide a vehicle on a desired path is presented. The lateral dynamics of the path follower vehicle is formulated by considering important parameters. To reduce the effect of uncertainties in vehicle parameters, a robust controller is designed based on a μ-synthesis approach. Numerical simulations are performed using a nonlinear vehicle model in MATLAB environment in order to investigate the effectiveness of the designed controller. Results of simulations show that the controller has a profound ability to making the vehicle track the desired path in the presence of uncertainties
Geometry, Heat Equation and Path Integrals on the Poincare Upper Half-Plane
Reijiro, KUBO; Research Institute for Theoretical Physics Hiroshima University
1988-01-01
Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation ∂f/∂t=Δ_Hf is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrodinger equation is also valid for our case.
Factorization-algebraization-path integration
International Nuclear Information System (INIS)
Inomata, A.; Wilson, R.
1986-01-01
The authors review the method of factorization proposed by Schroedinger of a quantum mechanical second-order linear differential equation into a product of two first-order differential operators, often referred to as ladder operators, as well as the modifications made to Schroedinger's method by Infeld and Hull. They then review the group theoretical treatments proposed by Miller of the Schroedinger-Infeld-Hull factorizations and go on to demonstrate the application of dynamical symmetry to path integral calculations. 30 references
Rapidly converging path integral formalism. Pt. 1
International Nuclear Information System (INIS)
Bender, I.; Gromes, D.; Marquard, U.
1990-01-01
The action to be used in the path integral formalism is expanded in a systematic way in powers of the time spacing ε in order to optimize the convergence to the continuum limit. This modifies and extends the usual formalism in a transparent way. The path integral approximation to the Green function obtained by this method approaches the continuum Green function with a higher power of ε than the usual one. The general theoretical derivations are exemplified analytically for the harmonic oscillator and by Monte Carlo methods for the anharmonic oscillator. We also show how curvilinear coordinates and curved spaces can naturally be treated within this formalism. Work on field theory is in progress. (orig.)
Power Series Expansion of Propagator for Path Integral and Its Applications
International Nuclear Information System (INIS)
Ou Yuanjin; Liang Xianting
2007-01-01
In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exact than the previous one obtained with other approximation methods. By using the same method, we obtain a propagator of path integral for the driven harmonic oscillator, which does not have any exact expansion. The more exact propagators may improve the path integral results for these systems.
Geometry, heat equation and path integrals on the Poincare upper half-plane
International Nuclear Information System (INIS)
Kubo, Reijiro.
1987-08-01
Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation δf/δt = Δ H f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's proof that Feynman's path integral satisfies the Schroedinger equation is also valid for our case. (author)
Path integral for gauge theories with fermions
International Nuclear Information System (INIS)
Fujikawa, K.
1980-01-01
The Atiyah-Singer index theorem indicates that a naive unitary transformation of basis vectors for fermions interacting with gauge fields is not allowed in general. On the basis of this observation, it was previously shown that the path-integral measure of a gauge-invariant fermion theory is transformed nontrivially under the chiral transformation, and thus leads to a simple derivation of ''anomalous'' chiral Ward-Takahashi identities. We here clarify some of the technical aspects associated with the discussion. It is shown that the Jacobian factor in the path-integral measure, which corresponds to the Adler-Bell-Jackiw anomaly, is independent of any smooth regularization procedure of large eigenvalues of D in Euclidean theory; this property holds in any even-dimensional space-time and also for the gravitational anomaly. The appearance of the anomaly and its connection with the index theorem are thus related to the fact that the primary importance is attached to the Lorentz-covariant ''energy'' operator D and that D and γ 5 do not commute. The abnormal behavior of the path-integral measure at the zero-frequency sector in the presence of instantons and its connection with spontaneous symmetry breaking is also clarified. We comment on several other problems associated with the anomaly and on the Pauli-Villars regularization method
An alternative derivation of the Faddeev-Popov path integral
International Nuclear Information System (INIS)
Cabo, A.; Martinez, D.L.; Chaichian, M.; Presnajder, P.
1991-01-01
A new derivation of the Faddeev-Popov path integral is presented. The use of gauge invariant transformations and gauge fixing conditions in the phase space allows to introduce straightforwardly Lorentz invariant gauge conditions into the path integral, thus avoiding the necessity of going first through a Coulomb-like gauge as it is usually done. The case of systems with finite degrees of freedom and the abelian (QED) one are also presented for illustration. (orig.)
An Anatomically Constrained Model for Path Integration in the Bee Brain.
Stone, Thomas; Webb, Barbara; Adden, Andrea; Weddig, Nicolai Ben; Honkanen, Anna; Templin, Rachel; Wcislo, William; Scimeca, Luca; Warrant, Eric; Heinze, Stanley
2017-10-23
Path integration is a widespread navigational strategy in which directional changes and distance covered are continuously integrated on an outward journey, enabling a straight-line return to home. Bees use vision for this task-a celestial-cue-based visual compass and an optic-flow-based visual odometer-but the underlying neural integration mechanisms are unknown. Using intracellular electrophysiology, we show that polarized-light-based compass neurons and optic-flow-based speed-encoding neurons converge in the central complex of the bee brain, and through block-face electron microscopy, we identify potential integrator cells. Based on plausible output targets for these cells, we propose a complete circuit for path integration and steering in the central complex, with anatomically identified neurons suggested for each processing step. The resulting model circuit is thus fully constrained biologically and provides a functional interpretation for many previously unexplained architectural features of the central complex. Moreover, we show that the receptive fields of the newly discovered speed neurons can support path integration for the holonomic motion (i.e., a ground velocity that is not precisely aligned with body orientation) typical of bee flight, a feature not captured in any previously proposed model of path integration. In a broader context, the model circuit presented provides a general mechanism for producing steering signals by comparing current and desired headings-suggesting a more basic function for central complex connectivity, from which path integration may have evolved. Copyright © 2017 Elsevier Ltd. All rights reserved.
Spatial Updating Strategy Affects the Reference Frame in Path Integration.
He, Qiliang; McNamara, Timothy P
2018-06-01
This study investigated how spatial updating strategies affected the selection of reference frames in path integration. Participants walked an outbound path consisting of three successive waypoints in a featureless environment and then pointed to the first waypoint. We manipulated the alignment of participants' final heading at the end of the outbound path with their initial heading to examine the adopted reference frame. We assumed that the initial heading defined the principal reference direction in an allocentric reference frame. In Experiment 1, participants were instructed to use a configural updating strategy and to monitor the shape of the outbound path while they walked it. Pointing performance was best when the final heading was aligned with the initial heading, indicating the use of an allocentric reference frame. In Experiment 2, participants were instructed to use a continuous updating strategy and to keep track of the location of the first waypoint while walking the outbound path. Pointing performance was equivalent regardless of the alignment between the final and the initial headings, indicating the use of an egocentric reference frame. These results confirmed that people could employ different spatial updating strategies in path integration (Wiener, Berthoz, & Wolbers Experimental Brain Research 208(1) 61-71, 2011), and suggested that these strategies could affect the selection of the reference frame for path integration.
Definition of path integrals and rules for non-linear transformations
International Nuclear Information System (INIS)
Kerler, W.
1978-01-01
Functional integrals are defined as the limit of multidimensional integrals based on fundamental generating distributions. The 'lattice choice' is put into a suitable functional form. The independence of the particular choice and the necessity of this fact are shown. Various forms of the path integrals are derived and discussed. The relation to the traditional ordering problem is pointed out. The mechanism of non-linear transformations of variables is investigated and rules are given. In the case of fields it turns out that the path integrals can also be considered for space translations. (Auth.)
Stringer, Simon M; Rolls, Edmund T
2006-12-01
A key issue is how networks in the brain learn to perform path integration, that is update a represented position using a velocity signal. Using head direction cells as an example, we show that a competitive network could self-organize to learn to respond to combinations of head direction and angular head rotation velocity. These combination cells can then be used to drive a continuous attractor network to the next head direction based on the incoming rotation signal. An associative synaptic modification rule with a short term memory trace enables preceding combination cell activity during training to be associated with the next position in the continuous attractor network. The network accounts for the presence of neurons found in the brain that respond to combinations of head direction and angular head rotation velocity. Analogous networks in the hippocampal system could self-organize to perform path integration of place and spatial view representations.
Rotational error in path integration: encoding and execution errors in angle reproduction.
Chrastil, Elizabeth R; Warren, William H
2017-06-01
Path integration is fundamental to human navigation. When a navigator leaves home on a complex outbound path, they are able to keep track of their approximate position and orientation and return to their starting location on a direct homebound path. However, there are several sources of error during path integration. Previous research has focused almost exclusively on encoding error-the error in registering the outbound path in memory. Here, we also consider execution error-the error in the response, such as turning and walking a homebound trajectory. In two experiments conducted in ambulatory virtual environments, we examined the contribution of execution error to the rotational component of path integration using angle reproduction tasks. In the reproduction tasks, participants rotated once and then rotated again to face the original direction, either reproducing the initial turn or turning through the supplementary angle. One outstanding difficulty in disentangling encoding and execution error during a typical angle reproduction task is that as the encoding angle increases, so does the required response angle. In Experiment 1, we dissociated these two variables by asking participants to report each encoding angle using two different responses: by turning to walk on a path parallel to the initial facing direction in the same (reproduction) or opposite (supplementary angle) direction. In Experiment 2, participants reported the encoding angle by turning both rightward and leftward onto a path parallel to the initial facing direction, over a larger range of angles. The results suggest that execution error, not encoding error, is the predominant source of error in angular path integration. These findings also imply that the path integrator uses an intrinsic (action-scaled) rather than an extrinsic (objective) metric.
Path integral for a relativistic-particle theory
International Nuclear Information System (INIS)
Fradkin, E.S.; Gitman, D.M.; Shvartsman, S.M.
1991-01-01
An action of a relativistic spinning particle written in reparametrization and local super-invariant form is consistently determined by using the path integral representation for the Green's function of the spinor field. It is shown that, to obtain the causal propagator, the integration over the null mode of the onebein variable must be performed in the (0, + ∞ limits
Variational nature, integration, and properties of Newton reaction path.
Bofill, Josep Maria; Quapp, Wolfgang
2011-02-21
The distinguished coordinate path and the reduced gradient following path or its equivalent formulation, the Newton trajectory, are analyzed and unified using the theory of calculus of variations. It is shown that their minimum character is related to the fact that the curve is located in a valley region. In this case, we say that the Newton trajectory is a reaction path with the category of minimum energy path. In addition to these findings a Runge-Kutta-Fehlberg algorithm to integrate these curves is also proposed.
Variational nature, integration, and properties of Newton reaction path
Bofill, Josep Maria; Quapp, Wolfgang
2011-02-01
The distinguished coordinate path and the reduced gradient following path or its equivalent formulation, the Newton trajectory, are analyzed and unified using the theory of calculus of variations. It is shown that their minimum character is related to the fact that the curve is located in a valley region. In this case, we say that the Newton trajectory is a reaction path with the category of minimum energy path. In addition to these findings a Runge-Kutta-Fehlberg algorithm to integrate these curves is also proposed.
Path integrals in quantum mechanics, statistics, polymer physics, and financial markets
Kleinert, Hagen
2009-01-01
This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying p
Double path-integral migration velocity analysis: a real data example
International Nuclear Information System (INIS)
Costa, Jessé C; Schleicher, Jörg
2011-01-01
Path-integral imaging forms an image with no knowledge of the velocity model by summing over the migrated images obtained for a set of migration velocity models. Double path-integral imaging migration extracts the stationary velocities, i.e. those velocities at which common-image gathers align horizontally, as a byproduct. An application of the technique to a real data set demonstrates that quantitative information about the time migration velocity model can be determined by double path-integral migration velocity analysis. Migrated images using interpolations with different regularizations of the extracted velocities prove the high quality of the resulting time-migration velocity information. The so-obtained velocity model can then be used as a starting model for subsequent velocity analysis tools like migration tomography or other tomographic methods
An analysis of 3D particle path integration algorithms
International Nuclear Information System (INIS)
Darmofal, D.L.; Haimes, R.
1996-01-01
Several techniques for the numerical integration of particle paths in steady and unsteady vector (velocity) fields are analyzed. Most of the analysis applies to unsteady vector fields, however, some results apply to steady vector field integration. Multistep, multistage, and some hybrid schemes are considered. It is shown that due to initialization errors, many unsteady particle path integration schemes are limited to third-order accuracy in time. Multistage schemes require at least three times more internal data storage than multistep schemes of equal order. However, for timesteps within the stability bounds, multistage schemes are generally more accurate. A linearized analysis shows that the stability of these integration algorithms are determined by the eigenvalues of the local velocity tensor. Thus, the accuracy and stability of the methods are interpreted with concepts typically used in critical point theory. This paper shows how integration schemes can lead to erroneous classification of critical points when the timestep is finite and fixed. For steady velocity fields, we demonstrate that timesteps outside of the relative stability region can lead to similar integration errors. From this analysis, guidelines for accurate timestep sizing are suggested for both steady and unsteady flows. In particular, using simulation data for the unsteady flow around a tapered cylinder, we show that accurate particle path integration requires timesteps which are at most on the order of the physical timescale of the flow
A taxonomy of integral reaction path analysis
Energy Technology Data Exchange (ETDEWEB)
Grcar, Joseph F.; Day, Marcus S.; Bell, John B.
2004-12-23
W. C. Gardiner observed that achieving understanding through combustion modeling is limited by the ability to recognize the implications of what has been computed and to draw conclusions about the elementary steps underlying the reaction mechanism. This difficulty can be overcome in part by making better use of reaction path analysis in the context of multidimensional flame simulations. Following a survey of current practice, an integral reaction flux is formulated in terms of conserved scalars that can be calculated in a fully automated way. Conditional analyses are then introduced, and a taxonomy for bidirectional path analysis is explored. Many examples illustrate the resulting path analysis and uncover some new results about nonpremixed methane-air laminar jets.
Path-integral invariants in abelian Chern–Simons theory
International Nuclear Information System (INIS)
Guadagnini, E.; Thuillier, F.
2014-01-01
We consider the U(1) Chern–Simons gauge theory defined in a general closed oriented 3-manifold M; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The non-perturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent U(1) principal bundles over M; the different sectors of configuration space are labelled by the elements of the first homology group of M and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the non-perturbative contributions to the mean values. The functional integration is carried out in any 3-manifold M, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin–Turaev surgery invariants
Some illustrative examples of Mayer's interference in the path integral
International Nuclear Information System (INIS)
Fizichev, P.P.
1983-01-01
A new technique is proposed for evaluation of path integrals by means of a discretization procedure. It is based on the previously established necessity to single out the set of classical trajectories along which the summation is performed. The notion of Mayer interference is introduced and is illustrated on a number of simple examples. It is shown that the choice of the set of paths induced a corresponding quantization prosymmetries of the problem. The possibility is shown of extracting information about the space of quantum states from the path integral. A class of paths is established the summation over which in the framework of the suggested approach leads to the well-known results for the motion is a homogeneous field and for the harmonic oscillator
Path Integration Applied to Structural Systems with Uncertain Properties
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Köylüoglu, H. Ugur
Path integration (cell-to-cell mapping) method is applied to evaluate the joint probability density function (jpdf) of the response of the structural systems, with uncertain properties, subject to white noise excitation. A general methodology to deal with uncertainties is outlined and applied...... to the friction controlled slip of a structure on a foundation where the friction coefficient is modelled as a random variable. Exact results derived using the total probability theorem are compared to the ones obtained via path integration....
Path integral for a relativistic-particle theory
Energy Technology Data Exchange (ETDEWEB)
Fradkin, E.S. (AN SSSR, Moscow (SU)); Gitman, D.M. (Moskovskij Inst. Radiotekhniki, Ehlektroniki i Automatiki, Moscow (SU)); Shvartsman, S.M. (Tomskij Pedagogicheskij Inst., Tomsk (SU))
1991-06-01
An action of a relativistic spinning particle written in reparametrization and local super-invariant form is consistently determined by using the path integral representation for the Green's function of the spinor field. It is shown that, to obtain the causal propagator, the integration over the null mode of the onebein variable must be performed in the (0, + {infinity}) limits.
Path integral representation of the symmetric Rosen-Morse potential
International Nuclear Information System (INIS)
Duru, I.H.
1983-09-01
An integral formula for the Green's function of symmetric Rosen-Morse potential is obtained by solving path integrals. The correctly normalized wave functions and bound state energy spectrum are derived. (author)
Recent developments in the path integral approach to anomalies
International Nuclear Information System (INIS)
Fujikawa, Kazuo.
1986-08-01
After a brief summary of the path integral approach to anomalous identities, some of the recent developments in this approach are discussed. The topics discussed include (i) Construction of the effective action by means of the covariant current, (ii) Gauss law constraint in anomalous gauge theories, (iii) Path integral approach to anomalies in superconformal transformations, (iv) Conformal and ghost number anomalies in string theory in analogy with the instanton calculation, (v) Covariant local Lorentz anomaly and its connection with the mathematical construction of the consistent anomaly. (author)
Path integral theory and deep inelastic scattering of nuclei
International Nuclear Information System (INIS)
Neto, J.L.
1981-10-01
A formalism, based on Feynman's path integral, is developed and used in the theory of deep inelastic collisions of nuclei. Having shown how to express the propagator of the Wigner function of an isolated system as a (double) path integral in phase space, random processes are considered and the influence functional in interacting systems is discussed. A semi-classical description for the reduced Wigner and a generalized Langevin equation are given. Finally, the formalism is used in a random matrix model for deep inelastic collisions. (U.K.)
Conditionally solvable path integral problems
International Nuclear Information System (INIS)
Grosche, C.
1995-05-01
Some specific conditionally exactly solvable potentials are discussed within the path integral formalism. They generalize the usually known potentials by the incorporation of a fractional power behaviour and strongly anharmonic terms. We find four different kinds of such potentials, the first is related to the Coulomb potential, the second is an anharmonic confinement potential, and the third and the fourth are related to the Manning-Rosen potential. (orig.)
International Nuclear Information System (INIS)
Wehner, M.F.
1983-01-01
A path-integral solution is derived for processes described by nonlinear Fokker-Plank equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a surface integral which incorporates the boundary conditions. A previously developed numerical method, based on a histogram representation of the probability distribution, is extended to a trapezoidal representation. This improved numerical approach is combined with the present path-integral formalism for restricted processes and is show t give accurate results. 35 refs., 5 figs
Age differences in virtual environment and real world path integration
Directory of Open Access Journals (Sweden)
Diane E Adamo
2012-09-01
Full Text Available Accurate path integration requires the integration of visual, proprioceptive, and vestibular self-motion cues and age effects associated with alterations in processing information from these systems may contribute to declines in path integration abilities. The present study investigated age-related differences in path integration in conditions that varied as a function of available sources of sensory information. Twenty-two healthy, young (23.8 ± 3.0 yrs. and 16 older (70.1 ± 6.4 yrs. adults participated in distance reproduction and triangle completion tasks performed in a virtual environment and two real world conditions: guided walking and wheelchair propulsion. For walking and wheelchair propulsion conditions, participants wore a blindfold and wore noise-blocking headphones and were guided through the workspace by the experimenter. For the virtual environment (VE condition, participants viewed self-motion information on a computer monitor and used a joystick to navigate through the environment. For triangle completion tasks, older compared to younger individuals showed greater errors in rotation estimations performed in the wheelchair condition; and for rotation and distance estimations in the VE condition. Distance reproduction tasks, in contrast, did not show any age effects. These findings demonstrate that age differences in path integration vary as a function of the available sources of information and by the complexity of outbound pathway.
Canonical quantisation via conditional symmetries of the closed FLRW model coupled to a scalar field
International Nuclear Information System (INIS)
Zampeli, Adamantia
2015-01-01
We study the classical, quantum and semiclassical solutions of a Robertson-Walker spacetime coupled to a massless scalar field. The Lagrangian of these minisuperspace models is singular and the application of the theory of Noether symmetries is modified to include the conditional symmetries of the corresponding (weakly vanishing) Hamiltonian. These are found to be the simultaneous symmetries of the supermetric and the superpotential. The quantisation is performed adopting the Dirac proposal for constrained systems. The innovation in the approach we use is that the integrals of motion related to the conditional symmetries are promoted to operators together with the Hamiltonian and momentum constraints. These additional conditions imposed on the wave function render the system integrable and it is possible to obtain solutions of the Wheeler-DeWitt equation. Finally, we use the wave function to perform a semiclassical analysis following Bohm and make contact with the classical solution. The analysis starts with a modified Hamilton-Jacobi equation from which the semiclassical momenta are defined. The solutions of the semiclassical equations are then studied and compared to the classical ones in order to understand the nature and behaviour of the classical singularities. (paper)
A Dynamic Bayesian Observer Model Reveals Origins of Bias in Visual Path Integration.
Lakshminarasimhan, Kaushik J; Petsalis, Marina; Park, Hyeshin; DeAngelis, Gregory C; Pitkow, Xaq; Angelaki, Dora E
2018-06-20
Path integration is a strategy by which animals track their position by integrating their self-motion velocity. To identify the computational origins of bias in visual path integration, we asked human subjects to navigate in a virtual environment using optic flow and found that they generally traveled beyond the goal location. Such a behavior could stem from leaky integration of unbiased self-motion velocity estimates or from a prior expectation favoring slower speeds that causes velocity underestimation. Testing both alternatives using a probabilistic framework that maximizes expected reward, we found that subjects' biases were better explained by a slow-speed prior than imperfect integration. When subjects integrate paths over long periods, this framework intriguingly predicts a distance-dependent bias reversal due to buildup of uncertainty, which we also confirmed experimentally. These results suggest that visual path integration in noisy environments is limited largely by biases in processing optic flow rather than by leaky integration. Copyright © 2018 Elsevier Inc. All rights reserved.
Note on path integral quantization of hydrogen atom
International Nuclear Information System (INIS)
Storchak, S.N.
1988-01-01
For path integrals whose integration measures are generated by stochastic processes of a definite form (Stratonovich-type equations are a local form for stochastic differential equations of these processes) it has been shown that under quantization of hydrogen atom the reparametrization and reduction Jacobians are mutually cancelled. 12 refs
Path integrals and coherent states of SU(2) and SU(1,1)
Inomata, Akira; Kuratsuji, Hiroshi
1992-01-01
The authors examine several topical subjects, commencing with a general introduction to path integrals in quantum mechanics and the group theoretical backgrounds for path integrals. Applications of harmonic analysis, polar coordinate formulation, various techniques and path integrals on SU(2) and SU(1, 1) are discussed. Soluble examples presented include particle-flux system, a pulsed oscillator, magnetic monopole, the Coulomb problem in curved space and others.The second part deals with the SU(2) coherent states and their applications. Construction and generalization of the SU(2) coherent sta
Path integrals over phase space, their definition and simple properties
International Nuclear Information System (INIS)
Tarski, J.; Technische Univ. Clausthal, Clausthal-Zellerfeld
1981-10-01
Path integrals over phase space are defined in two ways. Some properties of these integrals are established. These properties concern the technique of integration and the quantization rule isup(-I)deltasub(q) p. (author)
Path-integral method for the source apportionment of photochemical pollutants
Dunker, A. M.
2015-06-01
A new, path-integral method is presented for apportioning the concentrations of pollutants predicted by a photochemical model to emissions from different sources. A novel feature of the method is that it can apportion the difference in a species concentration between two simulations. For example, the anthropogenic ozone increment, which is the difference between a simulation with all emissions present and another simulation with only the background (e.g., biogenic) emissions included, can be allocated to the anthropogenic emission sources. The method is based on an existing, exact mathematical equation. This equation is applied to relate the concentration difference between simulations to line or path integrals of first-order sensitivity coefficients. The sensitivities describe the effects of changing the emissions and are accurately calculated by the decoupled direct method. The path represents a continuous variation of emissions between the two simulations, and each path can be viewed as a separate emission-control strategy. The method does not require auxiliary assumptions, e.g., whether ozone formation is limited by the availability of volatile organic compounds (VOCs) or nitrogen oxides (NOx), and can be used for all the species predicted by the model. A simplified configuration of the Comprehensive Air Quality Model with Extensions (CAMx) is used to evaluate the accuracy of different numerical integration procedures and the dependence of the source contributions on the path. A Gauss-Legendre formula using three or four points along the path gives good accuracy for apportioning the anthropogenic increments of ozone, nitrogen dioxide, formaldehyde, and nitric acid. Source contributions to these increments were obtained for paths representing proportional control of all anthropogenic emissions together, control of NOx emissions before VOC emissions, and control of VOC emissions before NOx emissions. There are similarities in the source contributions from the
User's guide to Monte Carlo methods for evaluating path integrals
Westbroek, Marise J. E.; King, Peter R.; Vvedensky, Dimitri D.; Dürr, Stephan
2018-04-01
We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular attention to the existence of autocorrelations and the calculation of reliable errors. The over-relaxation technique is presented as a way to counter strong autocorrelations. The simulation methods can be extended to compute observables for path integrals in other settings.
Efficient stochastic thermostatting of path integral molecular dynamics.
Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E; Manolopoulos, David E
2010-09-28
The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.
3D Model Retrieval Based on Vector Quantisation Index Histograms
International Nuclear Information System (INIS)
Lu, Z M; Luo, H; Pan, J S
2006-01-01
This paper proposes a novel technique to retrieval 3D mesh models using vector quantisation index histograms. Firstly, points are sampled uniformly on mesh surface. Secondly, to a point five features representing global and local properties are extracted. Thus feature vectors of points are obtained. Third, we select several models from each class, and employ their feature vectors as a training set. After training using LBG algorithm, a public codebook is constructed. Next, codeword index histograms of the query model and those in database are computed. The last step is to compute the distance between histograms of the query and those of the models in database. Experimental results show the effectiveness of our method
International Nuclear Information System (INIS)
Bodendorfer, N; Zipfel, A
2016-01-01
Building on a recent proposal for a quantum reduction to spherical symmetry from full loop quantum gravity, we investigate the relation between a quantisation of spherically symmetric general relativity and a reduction at the quantum level. To this end, we generalise the previously proposed quantum reduction by dropping the gauge fixing condition on the radial diffeomorphisms, thus allowing us to make direct contact with previous work on reduced quantisation. A dictionary between spherically symmetric variables and observables with respect to the reduction constraints in the full theory is discussed, as well as an embedding of reduced quantum states to a subsector of the quantum symmetry reduced full theory states. On this full theory subsector, the quantum algebra of the mentioned observables is computed and shown to qualitatively reproduce the quantum algebra of the reduced variables in the large quantum number limit for a specific choice of regularisation. Insufficiencies in recovering the reduced algebra quantitatively from the full theory are attributed to the oversimplified full theory quantum states we use. (paper)
Non-Gaussian path integration in self-interacting scalar field theories
International Nuclear Information System (INIS)
Kaya, Ali
2004-01-01
In self-interacting scalar field theories kinetic expansion is an alternative way of calculating the generating functional for Green's functions where the zeroth order non-Gaussian path integral becomes diagonal in x-space and reduces to the product of an ordinary integral at each point which can be evaluated exactly. We discuss how to deal with such functional integrals and propose a new perturbative expansion scheme which combines the elements of the kinetic expansion with the usual perturbation theory techniques. It is then shown that, when the cutoff dependences of the bare parameters in the potential are chosen to have a well defined non-Gaussian path integral without the kinetic term, the theory becomes trivial in the continuum limit
Path integral quantization in the temporal gauge
International Nuclear Information System (INIS)
Scholz, B.; Steiner, F.
1983-06-01
The quantization of non-Abelian gauge theories in the temporal gauge is studied within Feynman's path integral approach. The standard asymptotic boundary conditions are only imposed on the transverse gauge fields. The fictituous longitudinal gauge quanta are eliminated asymptotically by modified boundary conditions. This abolishes the residual time-independent gauge transformations and leads to a unique fixing of the temporal gauge. The resulting path integral for the generating functional respects automatically Gauss's law. The correct gauge field propagator is derived. It does not suffer from gauge singularities at n x k = 0 present in the usual treatment of axial gauges. The standard principal value prescription does not work. As a check, the Wilson loop in temporal gauge is calculated with the new propagator. To second order (and to all orders in the Abelian case) the result agrees with the one obtained in the Feynman and Coulomb gauge. (orig.)
A new path-integral representation of the T-matrix in potential scattering
International Nuclear Information System (INIS)
Carron, J.; Rosenfelder, R.
2011-01-01
We employ the method used by Barbashov and collaborators in Quantum Field Theory to derive a path-integral representation of the T-matrix in nonrelativistic potential scattering which is free of functional integration over fictitious variables as was necessary before. The resulting expression serves as a starting point for a variational approximation applied to high-energy scattering from a Gaussian potential. Good agreement with exact partial-wave calculations is found even at large scattering angles. A novel path-integral representation of the scattering length is obtained in the low-energy limit. -- Highlights: → We derive a new path-integral representation for the T-matrix in quantum scattering from a potential. → The method is based on a technique used by Barbashov and collaborators in Quantum Field Theory. → Unlike previous approaches no unphysical degrees of freedom in the path integral are needed. → The new representation is used for a variational approximation of the T-matrix at high energies. → A new expression for the scattering length at low energy is derived.
Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies
Bastianelli, Fiorenzo; Corradini, Olindo; Iacconi, Laura
2018-05-01
Particles in a curved space are classically described by a nonlinear sigma model action that can be quantized through path integrals. The latter require a precise regularization to deal with the derivative interactions arising from the nonlinear kinetic term. Recently, for maximally symmetric spaces, simplified path integrals have been developed: they allow to trade the nonlinear kinetic term with a purely quadratic kinetic term (linear sigma model). This happens at the expense of introducing a suitable effective scalar potential, which contains the information on the curvature of the space. The simplified path integral provides a sensible gain in the efficiency of perturbative calculations. Here we extend the construction to models with N = 1 supersymmetry on the worldline, which are applicable to the first quantized description of a Dirac fermion. As an application we use the simplified worldline path integral to compute the type-A trace anomaly of a Dirac fermion in d dimensions up to d = 16.
Chiral symmetry in the path-integral approach
International Nuclear Information System (INIS)
Schaposnik, F.A.
1987-01-01
The derivation of anomalous Ward-Takahashi identities related to chiral symmetries in the path-integral framework is presented. Some two-dimensional models in both abelian and non-abelian cases are discussed. The quantization of such theories using Weyl fermions is also presented. (L.C.) [pt
Lecture notes in topics in path integrals and string representations
Botelho, Luiz C L
2017-01-01
Functional Integrals is a well-established method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and string theory. This book presents a unique, original and modern treatment of strings representations on Bosonic Quantum Chromodynamics and Bosonization theory on 2d Gauge Field Models, besides of rigorous mathematical studies on the analytical regularization scheme on Euclidean quantum field path integrals and stochastic quantum field theory. It follows an analytic approach based on Loop space techniques, functional determinant exact evaluations and exactly solubility of four dimensional QCD loop wave equations through Elfin Botelho fermionic extrinsic self avoiding string path integrals.
On the path integral representation of the Wigner function and the Barker–Murray ansatz
International Nuclear Information System (INIS)
Sels, Dries; Brosens, Fons; Magnus, Wim
2012-01-01
The propagator of the Wigner function is constructed from the Wigner–Liouville equation as a phase space path integral over a new effective Lagrangian. In contrast to a paper by Barker and Murray (1983) , we show that the path integral can in general not be written as a linear superposition of classical phase space trajectories over a family of non-local forces. Instead, we adopt a saddle point expansion to show that the semiclassical Wigner function is a linear superposition of classical solutions for a different set of non-local time dependent forces. As shown by a simple example the specific form of the path integral makes the formulation ideal for Monte Carlo simulation. -- Highlights: ► We derive the quantum mechanical propagator of the Wigner function in the path integral representation. ► We show that the Barker–Murray ansatz is incomplete, explain the error and provide an alternative. ► An example of a Monte Carlo simulation of the semiclassical path integral is included.
Reparametrization in the path integral over finite dimensional manifold with a time-dependent metric
International Nuclear Information System (INIS)
Storchak, S.N.
1988-01-01
The path reparametrization procedure in the path integral is considered using the methods of stochastic processes for diffusion on finite dimensional manifold with a time-dependent metric. the reparametrization Jacobian has been obtained. The formulas of reparametrization for a symbolic presentation of the path integral have been derived
Entropic sampling in the path integral Monte Carlo method
International Nuclear Information System (INIS)
Vorontsov-Velyaminov, P N; Lyubartsev, A P
2003-01-01
We have extended the entropic sampling Monte Carlo method to the case of path integral representation of a quantum system. A two-dimensional density of states is introduced into path integral form of the quantum canonical partition function. Entropic sampling technique within the algorithm suggested recently by Wang and Landau (Wang F and Landau D P 2001 Phys. Rev. Lett. 86 2050) is then applied to calculate the corresponding entropy distribution. A three-dimensional quantum oscillator is considered as an example. Canonical distributions for a wide range of temperatures are obtained in a single simulation run, and exact data for the energy are reproduced
Path integral measure for gravitational interactions
Directory of Open Access Journals (Sweden)
Kazuo Fujikawa
1983-10-01
Full Text Available It is pointed out that the path-integral variables as well as the local measure for gravitational interactions are uniquely specified if one imposes the anomaly-free condition on the Becchi-Rouet-Stora supersymmetry associated with general coordinate transformations. This prescription is briefly illustrated for the Einstein gravity and supergravity in four space-time dimensions and the relativistic string theory in two dimensions.
Anomaly extraction from the path integral
International Nuclear Information System (INIS)
Christos, G.A.
1983-01-01
Fujikawa's recently proposed derivation of the anomaly from the path integral is examined. It is attempted to give a better understanding of his work. In particular, evasions of his result are discussed; for example it is shown how chiral U(1) axial invariance can be maintained by employing a gauge variant regularization prescription. A brief connection with the point-splitting method is also made. (orig.)
Functional approach without path integrals to finite temperature free fermions
International Nuclear Information System (INIS)
Souza, S.M. de; Santos, O. Rojas; Thomaz, M.T.
1999-01-01
Charret et al applied the properties of Grassmann generators to develop a new method to calculate the coefficients of the high temperature expansion of the grand canonical partition function of self-interacting fermionic models on d-dimensions (d ≥1). The methodology explores the anti-commuting nature of fermionic fields and avoids the calculation of the fermionic path integral. we apply this new method to the relativistic free Dirac fermions and recover the known results in the literature without the β-independent and μindependent infinities that plague the continuum path integral formulation. (author)
Calculation of quantum-mechanical system energy spectra using path integrals
International Nuclear Information System (INIS)
Evseev, A.M.; Dmitriev, V.P.
1977-01-01
A solution of the Feynman quantum-mechanical integral connecting a wave function (psi (x, t)) at a moment t+tau (tau → 0) with the wave function at the moment t is provided by complex variable substitution and subsequent path integration. Time dependence of the wave function is calculated by the Monte Carlo method. The Fourier inverse transformation of the wave function by path integration calculated has been applied to determine the energy spectra. Energy spectra are presented of a hydrogen atom derived from wave function psi (x, t) at different x, as well as boson energy spectra of He, Li, and Be atoms obtained from psi (x, t) at X = O
The 1+1 SU(2) Yang-Mills path integral
International Nuclear Information System (INIS)
Swanson, Mark S
2004-01-01
The path integral for SU(2) invariant two-dimensional Yang-Mills theory is recast in terms of the chromoelectric field strength by integrating the gauge fields from the theory. Implementing Gauss's law as a constraint in this process induces a topological term in the action that is no longer invariant under large gauge transformations. For the case that the partition function is considered over a circular spatial degree of freedom, it is shown that the effective action of the path integral is quantum mechanically WKB exact and localizes onto a set of chromoelectric zero modes satisfying antiperiodic boundary conditions. Summing over the zero modes yields a partition function that can be reexpressed using the Poisson resummation technique, allowing an easy determination of the energy spectrum, which is found to be identical to that given by other approaches
Integrated assignment and path planning
Murphey, Robert A.
2005-11-01
A surge of interest in unmanned systems has exposed many new and challenging research problems across many fields of engineering and mathematics. These systems have the potential of transforming our society by replacing dangerous and dirty jobs with networks of moving machines. This vision is fundamentally separate from the modern view of robotics in that sophisticated behavior is realizable not by increasing individual vehicle complexity, but instead through collaborative teaming that relies on collective perception, abstraction, decision making, and manipulation. Obvious examples where collective robotics will make an impact include planetary exploration, space structure assembly, remote and undersea mining, hazardous material handling and clean-up, and search and rescue. Nonetheless, the phenomenon driving this technology trend is the increasing reliance of the US military on unmanned vehicles, specifically, aircraft. Only a few years ago, following years of resistance to the use of unmanned systems, the military and civilian leadership in the United States reversed itself and have recently demonstrated surprisingly broad acceptance of increasingly pervasive use of unmanned platforms in defense surveillance, and even attack. However, as rapidly as unmanned systems have gained acceptance, the defense research community has discovered the technical pitfalls that lie ahead, especially for operating collective groups of unmanned platforms. A great deal of talent and energy has been devoted to solving these technical problems, which tend to fall into two categories: resource allocation of vehicles to objectives, and path planning of vehicle trajectories. An extensive amount of research has been conducted in each direction, yet, surprisingly, very little work has considered the integrated problem of assignment and path planning. This dissertation presents a framework for studying integrated assignment and path planning and then moves on to suggest an exact
Path integral quantization of the Symplectic Leaves of the SU(2)*Poisson-Lie Group
International Nuclear Information System (INIS)
Morariu, B.
1997-01-01
The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of Uq(su(2)). This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parameterizations and also compare the results with the path integral quantization of spin
On the path integral in imaginary Lobachevsky space
International Nuclear Information System (INIS)
Grosche, C.
1993-10-01
The path integral on the single-sheeted hyperboloid, i.e. in D-dimensional imaginary Lobachevsky space, is evaluated. A potential problem which we call 'Kepler-problem', and the case of a constant magnetic field are also discussed. (orig.)
An operator expansion technique for path integral analysis
International Nuclear Information System (INIS)
Tsvetkov, I.V.
1995-01-01
A new method of path integral analysis in the framework of a power series technique is presented. The method is based on the operator expansion of an exponential. A regular procedure to calculate the correction terms is found. (orig.)
A Neural Path Integration Mechanism for Adaptive Vector Navigation in Autonomous Agents
DEFF Research Database (Denmark)
Goldschmidt, Dennis; Dasgupta, Sakyasingha; Wörgötter, Florentin
2015-01-01
Animals show remarkable capabilities in navigating their habitat in a fully autonomous and energy-efficient way. In many species, these capabilities rely on a process called path integration, which enables them to estimate their current location and to find their way back home after long-distance...... of autonomous agent navigation, but it also reproduces various aspects of animal navigation. Finally, we discuss how the proposed path integration mechanism may be used as a scaffold for spatial learning in terms of vector navigation.......Animals show remarkable capabilities in navigating their habitat in a fully autonomous and energy-efficient way. In many species, these capabilities rely on a process called path integration, which enables them to estimate their current location and to find their way back home after long...
Classical and quantum dynamics from classical paths to path integrals
Dittrich, Walter
2016-01-01
Graduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name a few. Well-chosen and detailed examples illustrate the perturbation theory, canonical transformations, the action principle and demonstrate the usage of path integrals. This new edition has been revised and enlarged with chapters on quantum electrodynamics, high energy physics, Green’s functions and strong interaction.
Feynman path integrals - from the prodistribution definition to the calculation of glory scattering
International Nuclear Information System (INIS)
DeWitt-Morette, C.
1984-01-01
In these lectures I present a path integral calculation, starting from a global definition of Feynman path integrals and ending at a scattering cross section formula. Along the way I discuss some basic issues which had to be resolved to exploit the computational power of the proposed definition of Feynman integrals. I propose to compute the glory scattering of gravitational waves by black holes. (orig./HSI)
Feynman path integral formulation of quantum mechanics
International Nuclear Information System (INIS)
Mizrahi, M.M.
1975-01-01
The subject of this investigation is Feynman's path integral quantization scheme, which is a powerful global formalism with great intuitive appeal. It stems from the simple idea that a probability amplitude for a system to make a transition between two states is the ''sum'' of the amplitudes for all the possible ways the transition can take place
Fourier path-integral Monte Carlo methods: Partial averaging
International Nuclear Information System (INIS)
Doll, J.D.; Coalson, R.D.; Freeman, D.L.
1985-01-01
Monte Carlo Fourier path-integral techniques are explored. It is shown that fluctuation renormalization techniques provide an effective means for treating the effects of high-order Fourier contributions. The resulting formalism is rapidly convergent, is computationally convenient, and has potentially useful variational aspects
Trouvé, Hélène; Couturier, Yves; Etheridge, Francis; Saint-Jean, Olivier; Somme, Dominique
2010-06-30
The literature on integration indicates the need for an enhanced theorization of institutional integration. This article proposes path dependence as an analytical framework to study the systems in which integration takes place. PRISMA proposes a model for integrating health and social care services for older adults. This model was initially tested in Quebec. The PRISMA France study gave us an opportunity to analyze institutional integration in France. A qualitative approach was used. Analyses were based on semi-structured interviews with actors of all levels of decision-making, observations of advisory board meetings, and administrative documents. Our analyses revealed the complexity and fragmentation of institutional integration. The path dependency theory, which analyzes the change capacity of institutions by taking into account their historic structures, allows analysis of this situation. The path dependency to the Bismarckian system and the incomplete reforms of gerontological policies generate the coexistence and juxtaposition of institutional systems. In such a context, no institution has sufficient ability to determine gerontology policy and build institutional integration by itself. Using path dependence as an analytical framework helps to understand the reasons why institutional integration is critical to organizational and clinical integration, and the complex construction of institutional integration in France.
High-density amorphous ice: A path-integral simulation
Herrero, Carlos P.; Ramírez, Rafael
2012-09-01
Structural and thermodynamic properties of high-density amorphous (HDA) ice have been studied by path-integral molecular dynamics simulations in the isothermal-isobaric ensemble. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. Quantum nuclear motion is found to affect several observable properties of the amorphous solid. At low temperature (T = 50 K) the molar volume of HDA ice is found to increase by 6%, and the intramolecular O-H distance rises by 1.4% due to quantum motion. Peaks in the radial distribution function of HDA ice are broadened with respect to their classical expectancy. The bulk modulus, B, is found to rise linearly with the pressure, with a slope ∂B/∂P = 7.1. Our results are compared with those derived earlier from classical and path-integral simulations of HDA ice. We discuss similarities and discrepancies with those earlier simulations.
Propagators and path integrals
Energy Technology Data Exchange (ETDEWEB)
Holten, J.W. van
1995-08-22
Path-integral expressions for one-particle propagators in scalar and fermionic field theories are derived, for arbitrary mass. This establishes a direct connection between field theory and specific classical point-particle models. The role of world-line reparametrization invariance of the classical action and the implementation of the corresponding BRST-symmetry in the quantum theory are discussed. The presence of classical world-line supersymmetry is shown to lead to an unwanted doubling of states for massive spin-1/2 particles. The origin of this phenomenon is traced to a `hidden` topological fermionic excitation. A different formulation of the pseudo-classical mechanics using a bosonic representation of {gamma}{sub 5} is shown to remove these extra states at the expense of losing manifest supersymmetry. (orig.).
General new time formalism in the path integral
International Nuclear Information System (INIS)
Pak, N.K.; Sokmen, I.
1983-08-01
We describe a general method of applying point canonical transformations to the path integral followed by the corresponding new time transformations aimed at reducing an arbitrary one-dimensional problem into an exactly solvable form. Our result is independent of operator ordering ambiguities by construction. (author)
A discrete history of the Lorentzian path integral
Loll, R.
2003-01-01
In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main features. At the regularized, discrete level this approach
International Nuclear Information System (INIS)
Zaytsev, S A
2010-01-01
The possibility of using straight-line paths of integration in computing the integral representation of the three-body Coulomb Green's function is discussed. In our numerical examples two different kinds of integration contours in the complex energy planes are considered. It is demonstrated that straight-line paths, which cross the positive real axis, are suitable for numerical computation.
PathJam: a new service for integrating biological pathway information
Directory of Open Access Journals (Sweden)
Glez-Peña Daniel
2010-03-01
Full Text Available Biological pathways are crucial to much of the scientific research today including the study of specific biological processes related with human diseases. PathJam is a new comprehensive and freely accessible web-server application integrating scattered human pathway annotation from several public sources. The tool has been designed for both (i being intuitive for wet-lab users providing statistical enrichment analysis of pathway annotations and (ii giving support to the development of new integrative pathway applications. PathJam’s unique features and advantages include interactive graphs linking pathways and genes of interest, downloadable results in fully compatible formats, GSEA compatible output files and a standardized RESTful API.
The Role of Spatial Memory and Frames of Reference in the Precision of Angular Path Integration
Arthur, Joeanna C.; Philbeck, John W.; Kleene, Nicholas J.; Chichka, David
2012-01-01
Angular path integration refers to the ability to maintain an estimate of self-location after a rotational displacement by integrating internally-generated (idiothetic) self-motion signals over time. Previous work has found that non-sensory inputs, namely spatial memory, can play a powerful role in angular path integration (Arthur et al., 2007, 2009). Here we investigated the conditions under which spatial memory facilitates angular path integration. We hypothesized that the benefit of spatia...
Integrated flight path planning system and flight control system for unmanned helicopters.
Jan, Shau Shiun; Lin, Yu Hsiang
2011-01-01
This paper focuses on the design of an integrated navigation and guidance system for unmanned helicopters. The integrated navigation system comprises two systems: the Flight Path Planning System (FPPS) and the Flight Control System (FCS). The FPPS finds the shortest flight path by the A-Star (A*) algorithm in an adaptive manner for different flight conditions, and the FPPS can add a forbidden zone to stop the unmanned helicopter from crossing over into dangerous areas. In this paper, the FPPS computation time is reduced by the multi-resolution scheme, and the flight path quality is improved by the path smoothing methods. Meanwhile, the FCS includes the fuzzy inference systems (FISs) based on the fuzzy logic. By using expert knowledge and experience to train the FIS, the controller can operate the unmanned helicopter without dynamic models. The integrated system of the FPPS and the FCS is aimed at providing navigation and guidance to the mission destination and it is implemented by coupling the flight simulation software, X-Plane, and the computing software, MATLAB. Simulations are performed and shown in real time three-dimensional animations. Finally, the integrated system is demonstrated to work successfully in controlling the unmanned helicopter to operate in various terrains of a digital elevation model (DEM).
Integrated Flight Path Planning System and Flight Control System for Unmanned Helicopters
Jan, Shau Shiun; Lin, Yu Hsiang
2011-01-01
This paper focuses on the design of an integrated navigation and guidance system for unmanned helicopters. The integrated navigation system comprises two systems: the Flight Path Planning System (FPPS) and the Flight Control System (FCS). The FPPS finds the shortest flight path by the A-Star (A*) algorithm in an adaptive manner for different flight conditions, and the FPPS can add a forbidden zone to stop the unmanned helicopter from crossing over into dangerous areas. In this paper, the FPPS computation time is reduced by the multi-resolution scheme, and the flight path quality is improved by the path smoothing methods. Meanwhile, the FCS includes the fuzzy inference systems (FISs) based on the fuzzy logic. By using expert knowledge and experience to train the FIS, the controller can operate the unmanned helicopter without dynamic models. The integrated system of the FPPS and the FCS is aimed at providing navigation and guidance to the mission destination and it is implemented by coupling the flight simulation software, X-Plane, and the computing software, MATLAB. Simulations are performed and shown in real time three-dimensional animations. Finally, the integrated system is demonstrated to work successfully in controlling the unmanned helicopter to operate in various terrains of a digital elevation model (DEM). PMID:22164029
Mathematical theory of Feynman path integrals an introduction
Albeverio, Sergio A; Mazzucchi, Sonia
2008-01-01
Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory. The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
Relation between the Polyakov and the Fradkin-Vilkoviski path integrals for the bosonic string
Energy Technology Data Exchange (ETDEWEB)
Jaskolski, Z.; Rytel, L.; Klimek, M.
1988-07-21
The relation between Polyakov's path integral and the Fradkin-Vilkoviski integral in extended phase space is analyzed on an example of a free closed bosonic string. It is shown in D=26 that locally, in every Teichmueller sector, both methods provide the same result. Beyond D=26 the Fradkin-Vilkoviski path integral appears to be depending on the gauge fixing.
Polymer density functional approach to efficient evaluation of path integrals
DEFF Research Database (Denmark)
Brukhno, Andrey; Vorontsov-Velyaminov, Pavel N.; Bohr, Henrik
2005-01-01
A polymer density functional theory (P-DFT) has been extended to the case of quantum statistics within the framework of Feynman path integrals. We start with the exact P-DFT formalism for an ideal open chain and adapt its efficient numerical solution to the case of a ring. We show that, similarly......, the path integral problem can, in principle, be solved exactly by making use of the two-particle pair correlation function (2p-PCF) for the ends of an open polymer, half of the original. This way the exact data for one-dimensional quantum harmonic oscillator are reproduced in a wide range of temperatures....... The exact solution is not, though, reachable in three dimensions (3D) because of a vast amount of storage required for 2p-PCF. In order to treat closed paths in 3D, we introduce a so-called "open ring" approximation which proves to be rather accurate in the limit of long chains. We also employ a simple self...
International Nuclear Information System (INIS)
Utama, Briandhika; Purqon, Acep
2016-01-01
Path Integral is a method to transform a function from its initial condition to final condition through multiplying its initial condition with the transition probability function, known as propagator. At the early development, several studies focused to apply this method for solving problems only in Quantum Mechanics. Nevertheless, Path Integral could also apply to other subjects with some modifications in the propagator function. In this study, we investigate the application of Path Integral method in financial derivatives, stock options. Black-Scholes Model (Nobel 1997) was a beginning anchor in Option Pricing study. Though this model did not successfully predict option price perfectly, especially because its sensitivity for the major changing on market, Black-Scholes Model still is a legitimate equation in pricing an option. The derivation of Black-Scholes has a high difficulty level because it is a stochastic partial differential equation. Black-Scholes equation has a similar principle with Path Integral, where in Black-Scholes the share's initial price is transformed to its final price. The Black-Scholes propagator function then derived by introducing a modified Lagrange based on Black-Scholes equation. Furthermore, we study the correlation between path integral analytical solution and Monte-Carlo numeric solution to find the similarity between this two methods. (paper)
Numerical calculations in elementary quantum mechanics using Feynman path integrals
International Nuclear Information System (INIS)
Scher, G.; Smith, M.; Baranger, M.
1980-01-01
We show that it is possible to do numerical calculations in elementary quantum mechanics using Feynman path integrals. Our method involves discretizing both time and space, and summing paths through matrix multiplication. We give numerical results for various one-dimensional potentials. The calculations of energy levels and wavefunctions take approximately 100 times longer than with standard methods, but there are other problems for which such an approach should be more efficient
International Nuclear Information System (INIS)
Lin, T.L.; Wang, R.; Bi, W.P.; El Kaabouchi, A.; Pujos, C.; Calvayrac, F.; Wang, Q.A.
2013-01-01
We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model of simulation is a one-dimensional particle subject to conservative force and Gaussian random displacement. The probability that a sample path between two fixed points is taken is computed from the number of particles moving along this path, an output of the simulation, divided by the total number of particles arriving at the final point. It is found that the path probability decays exponentially with increasing action of the sample paths. The decay rate increases with decreasing randomness. This result supports the existence of a classical analog of the Feynman factor in the path integral formulation of quantum mechanics for Hamiltonian systems
Integrating out the standard Higgs field in the path integral
International Nuclear Information System (INIS)
Dittmaier, S.
1996-01-01
We integrate out the Higgs boson in the electroweak standard model at one loop and construct a low-energy effective Lagrangian assuming that the Higgs mass is much larger than the gauge-boson masses. Instead of applying diagrammatical techniques, we integrate out the Higgs boson directly in the path integral, which turns out to be much simpler. By using the background-field method and the Stueckelberg formalism, we directly find a manifestly gauge-invariant result. The heavy-Higgs effects on fermionic couplings are derived, too. At one loop the log M H terms of the heavy-Higgs limit of the electroweak standard model coincide with the UV-divergent terms in the gauged non-linear σ-model, but vertex functions differ in addition by finite constant terms. Finally, the leading Higgs effects to some physical processes are calculated from the effective Lagrangian. (orig.)
A path integral approach to the Hodgkin-Huxley model
Baravalle, Roman; Rosso, Osvaldo A.; Montani, Fernando
2017-11-01
To understand how single neurons process sensory information, it is necessary to develop suitable stochastic models to describe the response variability of the recorded spike trains. Spikes in a given neuron are produced by the synergistic action of sodium and potassium of the voltage-dependent channels that open or close the gates. Hodgkin and Huxley (HH) equations describe the ionic mechanisms underlying the initiation and propagation of action potentials, through a set of nonlinear ordinary differential equations that approximate the electrical characteristics of the excitable cell. Path integral provides an adequate approach to compute quantities such as transition probabilities, and any stochastic system can be expressed in terms of this methodology. We use the technique of path integrals to determine the analytical solution driven by a non-Gaussian colored noise when considering the HH equations as a stochastic system. The different neuronal dynamics are investigated by estimating the path integral solutions driven by a non-Gaussian colored noise q. More specifically we take into account the correlational structures of the complex neuronal signals not just by estimating the transition probability associated to the Gaussian approach of the stochastic HH equations, but instead considering much more subtle processes accounting for the non-Gaussian noise that could be induced by the surrounding neural network and by feedforward correlations. This allows us to investigate the underlying dynamics of the neural system when different scenarios of noise correlations are considered.
Quantum mechanical path integrals in curved spaces and the type-A trace anomaly
Energy Technology Data Exchange (ETDEWEB)
Bastianelli, Fiorenzo [Dipartimento di Fisica ed Astronomia, Università di Bologna,via Irnerio 46, I-40126 Bologna (Italy); INFN, Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Corradini, Olindo [Dipartimento di Scienze Fisiche, Informatiche e Matematiche,Università di Modena e Reggio Emilia,Via Campi 213/A, I-41125 Modena (Italy); INFN, Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Vassura, Edoardo [Dipartimento di Fisica ed Astronomia, Università di Bologna,via Irnerio 46, I-40126 Bologna (Italy); INFN, Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy)
2017-04-10
Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in arbitrary coordinates is well understood, and known to require the use of a regularization scheme, in this article we take up an old proposal of constructing the path integral by using Riemann normal coordinates. The method assumes that curvature effects are taken care of by a scalar effective potential, so that the particle lagrangian is reduced to that of a linear sigma model interacting with the effective potential. After fixing the correct effective potential, we test the construction on spaces of maximal symmetry and use it to compute heat kernel coefficients and type-A trace anomalies for a scalar field in arbitrary dimensions up to d=12. The results agree with expected ones, which are reproduced with great efficiency and extended to higher orders. We prove explicitly the validity of the simplified path integral on maximally symmetric spaces. This simplified path integral might be of further use in worldline applications, though its application on spaces of arbitrary geometry remains unclear.
Bennett, Ilana J; Stark, Craig E L
2016-03-01
Pattern separation describes the orthogonalization of similar inputs into unique, non-overlapping representations. This computational process is thought to serve memory by reducing interference and to be mediated by the dentate gyrus of the hippocampus. Using ultra-high in-plane resolution diffusion tensor imaging (hrDTI) in older adults, we previously demonstrated that integrity of the perforant path, which provides input to the dentate gyrus from entorhinal cortex, was associated with mnemonic discrimination, a behavioral outcome designed to load on pattern separation. The current hrDTI study assessed the specificity of this perforant path integrity-mnemonic discrimination relationship relative to other cognitive constructs (identified using a factor analysis) and white matter tracts (hippocampal cingulum, fornix, corpus callosum) in 112 healthy adults (20-87 years). Results revealed age-related declines in integrity of the perforant path and other medial temporal lobe (MTL) tracts (hippocampal cingulum, fornix). Controlling for global effects of brain aging, perforant path integrity related only to the factor that captured mnemonic discrimination performance. Comparable integrity-mnemonic discrimination relationships were also observed for the hippocampal cingulum and fornix. Thus, whereas perforant path integrity specifically relates to mnemonic discrimination, mnemonic discrimination may be mediated by a broader MTL network. Copyright © 2015 Elsevier Inc. All rights reserved.
The relation between Polyakov's and Fradkin's path integrals for bosonic string
International Nuclear Information System (INIS)
Jaskolski, Z.; Rytel, L.; Klimek, M.
1987-04-01
The relation between Polyakov's path integral and Fradkin's integral in extended phase space is analyzed on an example of a free closed bosonic string. It is shown in D=26 that locally, in every Teichmueller sector, both methods provide the same result. Beyond D=26 Fradkin's integral appears to be depending on the gauge fixing. (author). 12 refs
Energy Technology Data Exchange (ETDEWEB)
Belgiorno, Francesco [Politecnico di Milano, Dipartimento di Matematica, Milano (Italy); INdAM-GNFM, Milano (Italy); Cacciatori, Sergio L. [Universita dell' Insubria, Department of Science and High Technology, Como (Italy); INFN sezione di Milano, Milano (Italy); Dalla Piazza, Francesco [Universita ' ' La Sapienza' ' , Dipartimento di Matematica, Roma (Italy); Doronzo, Michele [Universita dell' Insubria, Department of Science and High Technology, Como (Italy)
2016-06-15
We investigate the quantisation in the Heisenberg representation of a model which represents a simplification of the Hopfield model for dielectric media, where the electromagnetic field is replaced by a scalar field φ and the role of the polarisation field is played by a further scalar field ψ. The model, which is quadratic in the fields, is still characterised by a non-trivial physical content, as the physical particles correspond to the polaritons of the standard Hopfield model of condensed matter physics. Causality is also taken into account and a discussion of the standard interaction representation is also considered. (orig.)
The use of a path independent integral in non-linear fracture mechanics
International Nuclear Information System (INIS)
Hellen, T.K.
1977-01-01
The use of the Rice J-intergral to assess conditions at a crack tip in an elastic or non-linear elastic body is well known. The integral equals the energy release rate and is path independent for any contour surrounding the crack tip provided no other singularities are encompassed. The path independence propertiy breaks down, however, in more general situations such as in three dimensional stress systems, plasticity unloading, thermal or creep states. Hence the required crack tip characteristics represented by the value of the integral round a contour whose radius about the tip tends to zero, is not reproduced along contours away from the tip. Consequently, an alternative integral, designated J*, has been proposed which equals J for elastic cases and in the other cases cited above remains path independent. A computer program for calculating the J and J* integrals has been developed as an extension to the BERSAFE finite element system. A full analysis of the cracked structure including plasticity, creep and thermal strains is conducted and the results are stored on a permanent data set. The integral values may then be calculated using the post-processor program for any number of contours and load or time steps, without recourse to further expensive computations. (Auth. )
Feynman path integral related to stochastic schroedinger equation
International Nuclear Information System (INIS)
Belavkin, V.P.; Smolyanov, O.G.
1998-01-01
The derivation of the Schroedinger equation describing the continuous measurement process is presented. The representation of the solution of the stochastic Schroedinger equation for continuous measurements is obtained by means of the Feynman path integral. The connection with the heuristic approach to the description of continuous measurements is considered. The connection with the Senon paradox is established [ru
Walters, Daniel; Stringer, Simon; Rolls, Edmund
2013-01-01
The head direction cell system is capable of accurately updating its current representation of head direction in the absence of visual input. This is known as the path integration of head direction. An important question is how the head direction cell system learns to perform accurate path integration of head direction. In this paper we propose a model of velocity path integration of head direction in which the natural time delay of axonal transmission between a linked continuous attractor network and competitive network acts as a timing mechanism to facilitate the correct speed of path integration. The model effectively learns a "look-up" table for the correct speed of path integration. In simulation, we show that the model is able to successfully learn two different speeds of path integration across two different axonal conduction delays, and without the need to alter any other model parameters. An implication of this model is that, by learning look-up tables for each speed of path integration, the model should exhibit a degree of robustness to damage. In simulations, we show that the speed of path integration is not significantly affected by degrading the network through removing a proportion of the cells that signal rotational velocity.
International Nuclear Information System (INIS)
LaChapelle, J.
2004-01-01
A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schroedinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette
The product form for path integrals on curved manifolds
Grosche, C.
1988-03-01
A general and simple framework for treating path integrals on curved manifolds is presented. The crucial point will be a product ansatz for the metric tensor and the quantum hamiltonian, i.e. we shall write g αβ = h αγh βγ and H = (1/2m)h αγp αp βh βγ + V + ΔV , respectively, a prescription which we shall call “product form” definition. The p α are hermitian momenta and Δ V is a well-defined quantum correction. We shall show that this ansatz, which looks quite special, is in fact - under reasonable assumptions in quantum mechanics - a very general one. We shall derive the lagrangian path integral in the “product form” definition and shall also prove that the Schro¨dinger equation can be derived from the corresponding short-time kernel. We shall discuss briefly an application of this prescription to the problem of free quantum motion on the Poincare´upper half-plane.
Worldline path integrals for fermions with general couplings
International Nuclear Information System (INIS)
D'Hoker, E.; Gagne, D.G.
1996-01-01
We derive a worldline path integral representation for the effective action of a multiplet of Dirac fermions coupled to the most general set of matrix-valued scalar, pseudoscalar, vector, axial vector and antisymmetric tensor background fields. By representing internal degrees of freedom in terms of worldline fermions as well, we obtain a formulation which manifestly exhibits chiral gauge invariance. (orig.)
Cendagorta, Joseph R.; Bačić, Zlatko; Tuckerman, Mark E.
2018-03-01
We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.
Cendagorta, Joseph R; Bačić, Zlatko; Tuckerman, Mark E
2018-03-14
We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.
Canonical path integral measures for Holst and Plebanski gravity: I. Reduced phase space derivation
International Nuclear Information System (INIS)
Engle, Jonathan; Han Muxin; Thiemann, Thomas
2010-01-01
An important aspect in defining a path integral quantum theory is the determination of the correct measure. For interacting theories and theories with constraints, this is non-trivial, and is normally not the heuristic 'Lebesgue measure' usually used. There have been many determinations of a measure for gravity in the literature, but none for the Palatini or Holst formulations of gravity. Furthermore, the relations between different resulting measures for different formulations of gravity are usually not discussed. In this paper we use the reduced phase technique in order to derive the path-integral measure for the Palatini and Holst formulation of gravity, which is different from the Lebesgue measure up to local measure factors which depend on the spacetime volume element and spatial volume element. From this path integral for the Holst formulation of general relativity we can also give a new derivation of the Plebanski path integral and discover a discrepancy with the result due to Buffenoir, Henneaux, Noui and Roche whose origin we resolve. This paper is the first in a series that aims at better understanding the relation between canonical loop quantum gravity and the spin-foam approach.
Data assimilation using a GPU accelerated path integral Monte Carlo approach
Quinn, John C.; Abarbanel, Henry D. I.
2011-09-01
The answers to data assimilation questions can be expressed as path integrals over all possible state and parameter histories. We show how these path integrals can be evaluated numerically using a Markov Chain Monte Carlo method designed to run in parallel on a graphics processing unit (GPU). We demonstrate the application of the method to an example with a transmembrane voltage time series of a simulated neuron as an input, and using a Hodgkin-Huxley neuron model. By taking advantage of GPU computing, we gain a parallel speedup factor of up to about 300, compared to an equivalent serial computation on a CPU, with performance increasing as the length of the observation time used for data assimilation increases.
Quantum gravitation. The Feynman path integral approach
International Nuclear Information System (INIS)
Hamber, Herbert W.
2009-01-01
The book covers the theory of Quantum Gravitation from the point of view of Feynman path integrals. These provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. The path integral method is suitable for both perturbative as well as non-perturbative studies, and is known to already provide a framework of choice for the theoretical investigation of non-abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman's formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. Later the lattice formulation of gravity is presented as an essential tool towards an understanding of key features of the non-perturbative vacuum. The book ends with a discussion of contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe. (orig.)
Ray optics for diffraction: a useful paradox in a path integral context
International Nuclear Information System (INIS)
Schulman, L.S.
1984-01-01
Geometrical diffraction theory uses ray tracing techniques to calculate diffraction and other properties of the electromagnetic field generally considered characteristically wave like. The author studies this dualism of the classical electromagnetic field so as to distinguish those aspects of quantum dualism that arise simply as properties of oscillatory integrals and those that may have deeper origins. By a series of transformations the solutions of certain optics problems are reduced to the evaluation of a Feynman path integral and the known semiclassical approximations for the path integral provide a justification for the geometrical diffraction theory. Particular attention is paid to the problem of edge diffraction and for a half plane barrier a closed form solution is obtained. A classical variational principle for barrier penetration is also presented. (Auth.)
Feynman path integral and the interaction picture
International Nuclear Information System (INIS)
Pugh, R.E.
1986-01-01
The role of interaction-picture fields in the construction of coherent states and in the derivation of the Feynman path integral for interacting scalar quantum fields is examined. Special attention is paid to the dependence of the integrand on the intermediate times and it is shown that the Feynman rules are valid prior to taking the limit wherein the number of intermediate times goes to infinity; thus, this number does not act as a cutoff in divergent amplitudes. Specific normalization factors are determined
Path integral analysis of Jarzynski's equality: Analytical results
Minh, David D. L.; Adib, Artur B.
2009-02-01
We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time-dependent natural frequency, we find such trajectories, evaluate the work-weighted propagators, and validate Jarzynski’s equality.
Tunnel splitting in biaxial spin models investigated with spin-coherent-state path integrals
International Nuclear Information System (INIS)
Chen Zhide; Liang, J.-Q.; Pu, F.-C.
2003-01-01
Tunnel splitting in biaxial spin models is investigated with a full evaluation of the fluctuation functional integrals of the Euclidean kernel in the framework of spin-coherent-state path integrals which leads to a magnitude of tunnel splitting quantitatively comparable with the numerical results in terms of diagonalization of the Hamilton operator. An additional factor resulted from a global time transformation converting the position-dependent mass to a constant one seems to be equivalent to the semiclassical correction of the Lagrangian proposed by Enz and Schilling. A long standing question whether the spin-coherent-state representation of path integrals can result in an accurate tunnel splitting is therefore resolved
Path integral for multi-field inflation
Energy Technology Data Exchange (ETDEWEB)
Gong, Jinn-Ouk [Asia Pacific Center for Theoretical Physics, Pohang 37673 (Korea, Republic of); Department of Physics, Postech, Pohang 37673 (Korea, Republic of); Seo, Min-Seok [Center for Theoretical Physics of the Universe, Institute for Basic Science, 34051 Daejeon (Korea, Republic of); Shiu, Gary [Department of Physics, University of Wisconsin-Madison, Madison, WI 53706 (United States); Department of Physics & Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay (Hong Kong)
2016-07-20
We develop the path integral formalism for studying cosmological perturbations in multi-field inflation, which is particularly well suited to study quantum theories with gauge symmetries such as diffeomorphism invariance. We formulate the gauge fixing conditions based on the Poisson brackets of the constraints, from which we derive two convenient gauges that are appropriate for multi-field inflation. We then adopt the in-in formalism to derive the most general expression for the power spectrum of the curvature perturbation including the corrections from the interactions of the curvature mode with other light degrees of freedom. We also discuss the contributions of the interactions to the bispectrum.
Preregularization and the path integral approach to the chiral anomaly
International Nuclear Information System (INIS)
Elias, V.; McKeon, G.; Steele, T.; Mann, R.B.; Treml, T.F.; Sherry, T.N.
1987-01-01
We explore the connection between perturbative and non-perturbative (path-integral) approaches to the axial anomaly. In particular, we show how the Jacobian associated with the fermionic measure corresponding to local axial transformations may be calculated directly from shift-of-integration-variable surface terms in four Euclidean dimensions. No regularization (explicit parametrization of UV infinities) is required in this approach, but invariance of the Jacobian under vector gauge transformations (i.e. preregularization) is required to remove a variable-of-integration ambiguity within the expression for the Jacobian of the fermionic measure. (orig.)
Path integral for coherent states of the dynamical U2 group and U2/1 supergroup
International Nuclear Information System (INIS)
Kochetov, E.A.
1992-01-01
A part-integral formulation in the representation of coherent states for the unitary U 2 group and U 2/1 supergroup is introduced. U 2 and U 2/1 path integrals are shown to be defined on the coset spaces U 2 /U 1 xU 1 and U 2/1 /U 1/1 xU 1 , respectively. These coset appears as curved classical phase spaces. Partition functions are expressed as path integrals over these spaces. In the case when U 2 and U 2/1 are the dynamical groups, the corresponding path integrals are evaluated with the help of linear fractional transformations that appear as the group (supergroup) action in the coset space (superspace). Possible applications for quantum models are discussed. 9 refs
The path integral formulation of fractional Brownian motion for the general Hurst exponent
International Nuclear Information System (INIS)
Calvo, I; Sanchez, R
2008-01-01
In 1995, Sebastian (1995 J. Phys. A: Math. Gen. 28 4305) gave a path integral computation of the propagator of subdiffusive fractional Brownian motion (fBm), i.e. fBm with a Hurst or self-similarity exponent H element of (0, 1/2). The extension of Sebastian's calculation to superdiffusion, H element of (1/2, 1], becomes however quite involved due to the appearance of additional boundary conditions on fractional derivatives of the path. In this communication, we address the construction of the path integral representation in a different fashion, which allows us to treat both subdiffusion and superdiffusion on an equal footing. The derivation of the propagator of fBm for the general Hurst exponent is then performed in a neat and unified way. (fast track communication)
Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping
Lu, Jianfeng; Zhou, Zhennan
2018-02-01
To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limit, the ring polymer evolves according to an averaged Hamiltonian with respect to all possible surface index configurations of the ring polymer and thus connects the surface hopping approach to the mean-field path-integral molecular dynamics. A multiscale integrator for the infinite swapping limit is also proposed to enable efficient sampling based on the limiting dynamics. Numerical results demonstrate the huge improvement of sampling efficiency of the infinite swapping compared with the direct simulation of path-integral molecular dynamics with surface hopping.
On some mathematical problems in the definition of Feynman path integral
International Nuclear Information System (INIS)
Combe, P.; Rodriguez, R.; Sirugue-Collin, M.
1976-07-01
It is shown how integration on a Hilbert space of paths can be performed to get exact evolution of non relativistic quantum systems for a rather large class of potentials including polynomial interaction
Noncommutative quantum electrodynamics in path integral framework
International Nuclear Information System (INIS)
Bourouaine, S; Benslama, A
2005-01-01
In this paper, the dynamics of a relativistic particle of spin 1/2, interacting with an external electromagnetic field in noncommutative space, is studied in the path integral framework. By adopting the Fradkin-Gitman formulation, the exact Green's function in noncommutative space (NCGF) for the quadratic case of a constant electromagnetic field is computed, and it is shown that its form is similar to its counterpart given in commutative space. In addition, it is deduced that the effect of noncommutativity has the same effect as an additional constant field depending on a noncommutative θ matrix
Dynamics on the group manifolds and path integral
International Nuclear Information System (INIS)
Marinov, M.S.; Terentyev, M.V.
1979-01-01
Classical and quantum dynamics onn the compact simple Lie group and on the sphere of arbitrary dimensionality are considered. The accuracy of the semiclassical approximation for Green functions is discussed. Various path integral representations of the Green functions are presented. The special features of these representations due to the compactness and curvature are analysed. Basic results of the theory of Lie algebras and Lie groups used in the main text are presented
Path integral methods for the dynamics of stochastic and disordered systems
International Nuclear Information System (INIS)
Hertz, John A; Roudi, Yasser; Sollich, Peter
2017-01-01
We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models. (topical review)
International Nuclear Information System (INIS)
Nissimov, E.; Pacheva, S.; Solomon, S.
1989-02-01
By further study of the geometry of the harmonic superspace constraints, we make explicit the relation between the operator and path integral approaches to the manifestly covariant harmonic superstring. In particular we find the correct complete set of functionally independent gauge symmetries for the auxiliary variables and identify the ones corresponding to the harmonic superfield postulate in the operator formalism. Then, we deduce in a systematic way the lagrangian path integral from the well defined covariant hamiltonian formulation of the GS superstring. (authors)
Introduction to functional and path integral methods in quantum field theory
International Nuclear Information System (INIS)
Strathdee, J.
1991-11-01
The following aspects concerning the use of functional and path integral methods in quantum field theory are discussed: generating functionals and the effective action, perturbation series, Yang-Mills theory and BRST symmetry. 10 refs, 3 figs
Classical and quantum dynamics from classical paths to path integrals
Dittrich, Walter
2017-01-01
Graduate students who wish to become familiar with advanced computational strategies in classical and quantum dynamics will find in this book both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name just a few topics. Well-chosen and detailed examples illustrate perturbation theory, canonical transformations and the action principle, and demonstrate the usage of path integrals. The fifth edition has been revised and enlarged to include chapters on quantum electrodynamics, in particular, Schwinger’s proper time method and the treatment of classical and quantum mechanics with Lie brackets and pseudocanonical transformations. It is shown that operator quantum electrodynamics can be equivalently described with c-numbers, as demonstrated by calculating the propagation function for an electron in a prescribed classical electromagnetic field.
Path integral methods via the use of the central limit theorem and application
International Nuclear Information System (INIS)
Thrapsaniotis, E G
2008-01-01
We consider a path integral in the phase space possibly with an influence functional in it and we use a method based on the use of the central limit theorem on the phase of the path integral representation to extract an equivalent expression which can be used in numerical calculations. Moreover we give conditions under which we can extract closed analytical results. As a specific application we consider a general system of two coupled and forced harmonic oscillators with coupling of the form x 1 x α 2 and we derive the relevant sign solved propagator
Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration
Energy Technology Data Exchange (ETDEWEB)
Balakrishna, Jayashree [Department of Mathematics and Natural Sciences, College of Arts and Sciences, Harris-Stowe State University, St. Louis, MO (United States); Bondarescu, Ruxandra [Department of Physics, University of Zurich, Zurich (Switzerland); Moran, Christine C., E-mail: corbett@tapir.caltech.edu [TAPIR, Department of Theoretical Astrophysics, California Institute of Technology, Pasadena, CA (United States)
2016-11-25
We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.
Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration
International Nuclear Information System (INIS)
Balakrishna, Jayashree; Bondarescu, Ruxandra; Moran, Christine C.
2016-01-01
We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.
Integrating cell on chip—Novel waveguide platform employing ultra-long optical paths
Directory of Open Access Journals (Sweden)
Lena Simone Fohrmann
2017-09-01
Full Text Available Optical waveguides are the most fundamental building blocks of integrated optical circuits. They are extremely well understood, yet there is still room for surprises. Here, we introduce a novel 2D waveguide platform which affords a strong interaction of the evanescent tail of a guided optical wave with an external medium while only employing a very small geometrical footprint. The key feature of the platform is its ability to integrate the ultra-long path lengths by combining low propagation losses in a silicon slab with multiple reflections of the guided wave from photonic crystal (PhC mirrors. With a reflectivity of 99.1% of our tailored PhC-mirrors, we achieve interaction paths of 25 cm within an area of less than 10 mm2. This corresponds to 0.17 dB/cm effective propagation which is much lower than the state-of-the-art loss of approximately 1 dB/cm of single mode silicon channel waveguides. In contrast to conventional waveguides, our 2D-approach leads to a decay of the guided wave power only inversely proportional to the optical path length. This entirely different characteristic is the major advantage of the 2D integrating cell waveguide platform over the conventional channel waveguide concepts that obey the Beer-Lambert law.
Integrating cell on chip—Novel waveguide platform employing ultra-long optical paths
Fohrmann, Lena Simone; Sommer, Gerrit; Pitruzzello, Giampaolo; Krauss, Thomas F.; Petrov, Alexander Yu.; Eich, Manfred
2017-09-01
Optical waveguides are the most fundamental building blocks of integrated optical circuits. They are extremely well understood, yet there is still room for surprises. Here, we introduce a novel 2D waveguide platform which affords a strong interaction of the evanescent tail of a guided optical wave with an external medium while only employing a very small geometrical footprint. The key feature of the platform is its ability to integrate the ultra-long path lengths by combining low propagation losses in a silicon slab with multiple reflections of the guided wave from photonic crystal (PhC) mirrors. With a reflectivity of 99.1% of our tailored PhC-mirrors, we achieve interaction paths of 25 cm within an area of less than 10 mm2. This corresponds to 0.17 dB/cm effective propagation which is much lower than the state-of-the-art loss of approximately 1 dB/cm of single mode silicon channel waveguides. In contrast to conventional waveguides, our 2D-approach leads to a decay of the guided wave power only inversely proportional to the optical path length. This entirely different characteristic is the major advantage of the 2D integrating cell waveguide platform over the conventional channel waveguide concepts that obey the Beer-Lambert law.
On the coordinate (in)dependence of the formal path integral
DEFF Research Database (Denmark)
Johnson-Freyd, Theo
. In this short note, aimed primarily at mathematicians, we first briefly recall the notions of Lagrangian classical and quantum field theory and the standard coordinate-full definition of the “formal” or “Feynman-diagrammatic” path integral construction. We then outline a proof of the following claim: the formal...
Potential theory, path integrals and the Laplacian of the indicator
R.-J. Lange (Rutger-Jan)
2012-01-01
markdownabstractThis paper links the field of potential theory — i.e. the Dirichlet and Neumann problems for the heat and Laplace equation — to that of the Feynman path integral, by postulating the some seemingly ill-defined potential. The Laplacian of the indicator can be interpreted using the
The path integral model of D-pairing for HTSC, heavy fermion superconductors, and superfluids
International Nuclear Information System (INIS)
Brusov, P.N.; Brusova, N.P.
1996-01-01
A model of d-pairing for superconducting and superfluid Fermi-systems has been formulated within the path integration technique. By path integration over open-quote fastclose quotes and open-quotes slowclose quotes Fermi-fields, the action functional (which determines all properties of model system) has been obtained. This functional could be used for the determination of different superconducting (superfluid) states, for calculation of the transition temperatures for these states, and for the calculation of the collective mode spectrum for HTSC, as well as for heavy fermion superconductors
On the simplified path integral on spheres
Energy Technology Data Exchange (ETDEWEB)
Bastianelli, Fiorenzo [Universita di Bologna, Dipartimento di Fisica ed Astronomia, Bologna (Italy); INFN, Sezione di Bologna, Bologna (Italy); Albert-Einstein-Institut, Max-Planck-Institut fuer Gravitationsphysik, Golm (Germany); Corradini, Olindo [Universita degli Studi di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Modena (Italy); INFN, Sezione di Bologna, Bologna (Italy); Albert-Einstein-Institut, Max-Planck-Institut fuer Gravitationsphysik, Golm (Germany)
2017-11-15
We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the particle action. The emerging linear sigma model contains a scalar effective potential that reproduces the effects of the curvature. We present here further details of the construction, and extend its perturbative evaluation to orders high enough to read off the type-A trace anomalies of a conformal scalar in dimensions d = 14 and d = 16. (orig.)
Noncommutative quantum electrodynamics in path integral framework
Energy Technology Data Exchange (ETDEWEB)
Bourouaine, S; Benslama, A [Departement de Physique, Faculte des Sciences, Universite Mentouri, Constantine (Algeria)
2005-08-19
In this paper, the dynamics of a relativistic particle of spin 1/2, interacting with an external electromagnetic field in noncommutative space, is studied in the path integral framework. By adopting the Fradkin-Gitman formulation, the exact Green's function in noncommutative space (NCGF) for the quadratic case of a constant electromagnetic field is computed, and it is shown that its form is similar to its counterpart given in commutative space. In addition, it is deduced that the effect of noncommutativity has the same effect as an additional constant field depending on a noncommutative {theta} matrix.
Diffusion in periodic potentials with path integral hyperdynamics.
Ikonen, T; Khandkar, M D; Chen, L Y; Ying, S C; Ala-Nissila, T
2011-08-01
We consider the diffusion of brownian particles in one-dimensional periodic potentials as a test bench for the recently proposed stochastic path integral hyperdynamics (PIHD) scheme [Chen and Horing, J. Chem. Phys. 126, 224103 (2007)]. First, we consider the case where PIHD is used to enhance the transition rate of activated rare events. To this end, we study the diffusion of a single brownian particle moving in a spatially periodic potential in the high-friction limit at low temperature. We demonstrate that the boost factor as compared to straight molecular dynamics (MD) has nontrivial behavior as a function of the bias force. Instead of growing monotonically with the bias, the boost attains an optimal maximum value due to increased error in the finite path sampling induced by the bias. We also observe that the PIHD method can be sensitive to the choice of numerical integration algorithm. As the second case, we consider parallel resampling of multiple bias force values in the case of a brownian particle in a periodic potential subject to an external ac driving force. We confirm that there is no stochastic resonance in this system. However, while the PIHD method allows one to obtain data for multiple values of the ac bias, the boost with respect to MD remains modest due to the simplicity of the equation of motion in this case.
Zhou, Hufeng; Jin, Jingjing; Zhang, Haojun; Yi, Bo; Wozniak, Michal; Wong, Limsoon
2012-01-01
Pathway data are important for understanding the relationship between genes, proteins and many other molecules in living organisms. Pathway gene relationships are crucial information for guidance, prediction, reference and assessment in biochemistry, computational biology, and medicine. Many well-established databases--e.g., KEGG, WikiPathways, and BioCyc--are dedicated to collecting pathway data for public access. However, the effectiveness of these databases is hindered by issues such as incompatible data formats, inconsistent molecular representations, inconsistent molecular relationship representations, inconsistent referrals to pathway names, and incomprehensive data from different databases. In this paper, we overcome these issues through extraction, normalization and integration of pathway data from several major public databases (KEGG, WikiPathways, BioCyc, etc). We build a database that not only hosts our integrated pathway gene relationship data for public access but also maintains the necessary updates in the long run. This public repository is named IntPath (Integrated Pathway gene relationship database for model organisms and important pathogens). Four organisms--S. cerevisiae, M. tuberculosis H37Rv, H. Sapiens and M. musculus--are included in this version (V2.0) of IntPath. IntPath uses the "full unification" approach to ensure no deletion and no introduced noise in this process. Therefore, IntPath contains much richer pathway-gene and pathway-gene pair relationships and much larger number of non-redundant genes and gene pairs than any of the single-source databases. The gene relationships of each gene (measured by average node degree) per pathway are significantly richer. The gene relationships in each pathway (measured by average number of gene pairs per pathway) are also considerably richer in the integrated pathways. Moderate manual curation are involved to get rid of errors and noises from source data (e.g., the gene ID errors in WikiPathways and
Expressing Solutions of the Dirac Equation in Terms of Feynman Path Integral
Hose, R D
2006-01-01
Using the separation of the variables technique, the free particle solutions of the Dirac equation in the momentum space are shown to be actually providing the definition of Delta function for the Schr dinger picture. Further, the said solution is shown to be derivable on the sole strength of geometrical argument that the Dirac equation for free particle is an equation of a plane in momentum space. During the evolution of time in the Schr dinger picture, the normal to the said Dirac equation plane is shown to be constantly changing in direction due to the uncertainty principle and thereby, leading to a zigzag path for the Dirac particle in the momentum space. Further, the time evolution of the said Delta function solutions of the Dirac equation is shown to provide Feynman integral of all such zigzag paths in the momentum space. Towards the end of the paper, Feynman path integral between two fixed spatial points in the co-ordinate space during a certain time interv! al is shown to be composed, in time sequence...
The use of a path independent integral in non-linear fracture mechanics
International Nuclear Information System (INIS)
Hellen, T.K.
1977-01-01
A computer program for calculating the J and J* integrals has been developed as an extension to the BERSAFE finite element system. A full analysis of the cracked structure including plasticity, creep and thermal strains is conducted and the results are stored on a permanent data set. The integral values may then be calculated using the post-processor program for any number of contours and load or time steps, without recourse to further expensive computations. Numerical examples are presented comparing the J and J* integrals for a number of cracked plates under thermal, plastic and creep environments. To demonstrate the accuracy for a simple thermo-elastic case, a centre cracked plate subject to a symmetric quadratic gradient is included. Here, the J integral is shown to be path dependent whereas good independence is seen for the J* integral. The case of an elastic-plastic plate is invetigated to demonstrate path independence for both integrals in non-linear elasticity, and the effects of unloading are discussed. An alternative method for obtaining the change of potential energy over a small crack extension is briefly mentioned and compared to the J and J* results in this case. An axisymmetric bar with an internal penny-shaped crack subjected to tension is discussed under elastic-plastic materials behavior
Putz, Mihai V
2009-11-10
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.
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.
Introduction to quantum mechanics Schrödinger equation and path integral
Müller-Kirsten, H J W
2012-01-01
This text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrodinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions. In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introdu...
A path integral for heavy-quarks in a hot plasma
Beraudo, A.; Faccioli, P.; Garberoglio, G.; 10.1016/j.nuclphysa.2010.06.007
2010-01-01
We propose a model for the propagation of a heavy-quark in a hot plasma, to be viewed as a first step towards a full description of the dynamics of heavy quark systems in a quark-gluon plasma, including bound state formation. The heavy quark is treated as a non relativistic particle interacting with a fluctuating field, whose correlator is determined by a hard thermal loop approximation. This approximation, which concerns only the medium in which the heavy quark propagates, is the only one that is made, and it can be improved. The dynamics of the heavy quark is given exactly by a quantum mechanical path integral that is calculated in this paper in the Euclidean space-time using numerical Monte Carlo techniques. The spectral function of the heavy quark in the medium is then reconstructed using a Maximum Entropy Method. The path integral is also evaluated exactly in the case where the mass of the heavy quark is infinite; one then recovers known results concerning the complex optical potential that controls the ...
International Nuclear Information System (INIS)
Jaskolski, Z.
1991-05-01
The geometrical approach to the functional integral over Faddeev-Popov ghost fields is developed and applied to construct the BRST extension of the off-shell closed string amplitudes in the constant curvature gauge. In this gauge the overlap path integral for off-shell amplitudes is evaluated. It leads to the nonlocal sewing procedure generating all off-shell amplitudes from the cubic interaction vertex. The general scheme of the reconstruction of a covariant closed string field theory from the off-shell amplitudes is discussed within the path integral framework. (author). 30 refs
Path integral methods for the dynamics of stochastic and disordered systems
DEFF Research Database (Denmark)
Hertz, John A.; Roudi, Yasser; Sollich, Peter
2017-01-01
We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey...
Monte Carlo evaluation of path integral for the nuclear shell model
International Nuclear Information System (INIS)
Lang, G.H.
1993-01-01
The authors present a path-integral formulation of the nuclear shell model using auxillary fields; the path-integral is evaluated by Monte Carlo methods. The method scales favorably with valence-nucleon number and shell-model basis: full-basis calculations are demonstrated up to the rare-earth region, which cannot be treated by other methods. Observables are calculated for the ground state and in a thermal ensemble. Dynamical correlations are obtained, from which strength functions are extracted through the Maximum Entropy method. Examples in the s-d shell, where exact diagonalization can be carried out, compared well with exact results. The open-quotes sign problemclose quotes generic to quantum Monte Carlo calculations is found to be absent in the attractive pairing-plus-multipole interactions. The formulation is general for interacting fermion systems and is well suited for parallel computation. The authors have implemented it on the Intel Touchstone Delta System, achieving better than 99% parallelization
Functional integration of vertical flight path and speed control using energy principles
Lambregts, A. A.
1984-01-01
A generalized automatic flight control system was developed which integrates all longitudinal flight path and speed control functions previously provided by a pitch autopilot and autothrottle. In this design, a net thrust command is computed based on total energy demand arising from both flight path and speed targets. The elevator command is computed based on the energy distribution error between flight path and speed. The engine control is configured to produce the commanded net thrust. The design incorporates control strategies and hierarchy to deal systematically and effectively with all aircraft operational requirements, control nonlinearities, and performance limits. Consistent decoupled maneuver control is achieved for all modes and flight conditions without outer loop gain schedules, control law submodes, or control function duplication.
International Nuclear Information System (INIS)
Grosche, C.
1993-10-01
In this paper path integration in two- and three-dimensional spaces of constant curvature is discussed: i.e. the flat spaces R 2 and R 3 , the two- and three-dimensional sphere and the two- and three dimensional pseudosphere. The Laplace operator in these spaces admits separation of variables in various coordinate systems. In all these coordinate systems the path integral formulation will be stated, however in most of them an explicit solution in terms of the spectral expansion can be given only on a formal level. What can be stated in all cases, are the propagator and the corresponding Green function, respectively, depending on the invariant distance which is a coordinate independent quantity. This property gives rise to numerous identities connecting the corresponding path integral representations and propagators in various coordinate systems with each other. (orig.)
Dynamic response characteristics of dual flow-path integrally bladed rotors
Beck, Joseph A.; Brown, Jeffrey M.; Scott-Emuakpor, Onome E.; Cross, Charles J.; Slater, Joseph C.
2015-02-01
New turbine engine designs requiring secondary flow compression often look to dual flow-path integrally bladed rotors (DFIBRs) since these stages have the ability to perform work on the secondary, or bypassed, flow-field. While analogous to traditional integrally bladed rotor stages, DFIBR designs have many differences that result in unique dynamic response characteristics that must be understood to avoid fatigue. This work investigates these characteristics using reduced-order models (ROMs) that incorporate mistuning through perturbations to blade frequencies. This work provides an alternative to computationally intensive geometric-mistuning approaches for DFIBRs by utilizing tuned blade mode reductions and substructure coupling in cyclic coordinates. Free and forced response results are compared to full finite element model (FEM) solutions to determine if any errors are related to the reduced-order model formulation reduction methods. It is shown that DFIBRs have many more frequency veering regions than their single flow-path integrally blade rotor (IBR) counterparts. Modal families are shown to transition between system, inner-blade, and outer-blade motion. Furthermore, findings illustrate that while mode localization of traditional IBRs is limited to a single or small subset of blades, DFIBRs can have modal energy localized to either an inner- or outer-blade set resulting in many blades responding above tuned levels. Lastly, ROM forced response predictions compare well to full FEM predictions for the two test cases shown.
Energy Optimal Path Planning: Integrating Coastal Ocean Modelling with Optimal Control
Subramani, D. N.; Haley, P. J., Jr.; Lermusiaux, P. F. J.
2016-02-01
A stochastic optimization methodology is formulated for computing energy-optimal paths from among time-optimal paths of autonomous vehicles navigating in a dynamic flow field. To set up the energy optimization, the relative vehicle speed and headings are considered to be stochastic, and new stochastic Dynamically Orthogonal (DO) level-set equations that govern their stochastic time-optimal reachability fronts are derived. Their solution provides the distribution of time-optimal reachability fronts and corresponding distribution of time-optimal paths. An optimization is then performed on the vehicle's energy-time joint distribution to select the energy-optimal paths for each arrival time, among all stochastic time-optimal paths for that arrival time. The accuracy and efficiency of the DO level-set equations for solving the governing stochastic level-set reachability fronts are quantitatively assessed, including comparisons with independent semi-analytical solutions. Energy-optimal missions are studied in wind-driven barotropic quasi-geostrophic double-gyre circulations, and in realistic data-assimilative re-analyses of multiscale coastal ocean flows. The latter re-analyses are obtained from multi-resolution 2-way nested primitive-equation simulations of tidal-to-mesoscale dynamics in the Middle Atlantic Bight and Shelbreak Front region. The effects of tidal currents, strong wind events, coastal jets, and shelfbreak fronts on the energy-optimal paths are illustrated and quantified. Results showcase the opportunities for longer-duration missions that intelligently utilize the ocean environment to save energy, rigorously integrating ocean forecasting with optimal control of autonomous vehicles.
Accurate path integration in continuous attractor network models of grid cells.
Burak, Yoram; Fiete, Ila R
2009-02-01
Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of approximately 10-100 meters and approximately 1-10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.
Introduction to gauge field theory
International Nuclear Information System (INIS)
Bailin, D.; Love, A.
1986-01-01
This book provides a postgraduate level introduction to gauge field theory entirely from a path integral standpoint without any reliance on the more traditional method of canonical quantisation. The ideas are developed by quantising the self-interacting scalar field theory, and are then used to deal with all the gauge field theories relevant to particle physics, quantum electrodynamics, quantum chromodynamics, electroweak theory, grand unified theories, and field theories at non-zero temperature. The use of these theories to make precise experimental predictions requires the development of the renormalised theories. This book provides a knowledge of relativistic quantum mechanics, but not of quantum field theory. The topics covered form a foundation for a knowledge of modern relativistic quantum field theory, providing a comprehensive coverage with emphasis on the details of actual calculations rather than the phenomenology of the applications
Jang, Seogjoo; Voth, Gregory A
2017-05-07
Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.
The mapping approach in the path integral formalism applied to curve-crossing systems
International Nuclear Information System (INIS)
Novikov, Alexey; Kleinekathoefer, Ulrich; Schreiber, Michael
2004-01-01
The path integral formalism in a combined phase-space and coherent-state representation is applied to the problem of curve-crossing dynamics. The system of interest is described by two coupled one-dimensional harmonic potential energy surfaces interacting with a heat bath consisting of harmonic oscillators. The mapping approach is used to rewrite the Lagrangian function of the electronic part of the system. Using the Feynman-Vernon influence-functional method the bath is eliminated whereas the non-Gaussian part of the path integral is treated using the generating functional for the electronic trajectories. The dynamics of a Gaussian wave packet is analyzed along a one-dimensional reaction coordinate within a perturbative treatment for a small coordinate shift between the potential energy surfaces
International Nuclear Information System (INIS)
Dasgupta, I.
1998-01-01
We discuss new bounce-like (but non-time-reversal-invariant) solutions to Euclidean equations of motion, which we dub boomerons. In the Euclidean path integral approach to quantum theories, boomerons make an imaginary contribution to the vacuum energy. The fake vacuum instability can be removed by cancelling boomeron contributions against contributions from time reversed boomerons (anti-boomerons). The cancellation rests on a sign choice whose significance is not completely understood in the path integral method. (orig.)
Walters, D M; Stringer, S M
2010-07-01
A key question in understanding the neural basis of path integration is how individual, spatially responsive, neurons may self-organize into networks that can, through learning, integrate velocity signals to update a continuous representation of location within an environment. It is of vital importance that this internal representation of position is updated at the correct speed, and in real time, to accurately reflect the motion of the animal. In this article, we present a biologically plausible model of velocity path integration of head direction that can solve this problem using neuronal time constants to effect natural time delays, over which associations can be learned through associative Hebbian learning rules. The model comprises a linked continuous attractor network and competitive network. In simulation, we show that the same model is able to learn two different speeds of rotation when implemented with two different values for the time constant, and without the need to alter any other model parameters. The proposed model could be extended to path integration of place in the environment, and path integration of spatial view.
Mixed time slicing in path integral simulations
International Nuclear Information System (INIS)
Steele, Ryan P.; Zwickl, Jill; Shushkov, Philip; Tully, John C.
2011-01-01
A simple and efficient scheme is presented for using different time slices for different degrees of freedom in path integral calculations. This method bridges the gap between full quantization and the standard mixed quantum-classical (MQC) scheme and, therefore, still provides quantum mechanical effects in the less-quantized variables. Underlying the algorithm is the notion that time slices (beads) may be 'collapsed' in a manner that preserves quantization in the less quantum mechanical degrees of freedom. The method is shown to be analogous to multiple-time step integration techniques in classical molecular dynamics. The algorithm and its associated error are demonstrated on model systems containing coupled high- and low-frequency modes; results indicate that convergence of quantum mechanical observables can be achieved with disparate bead numbers in the different modes. Cost estimates indicate that this procedure, much like the MQC method, is most efficient for only a relatively few quantum mechanical degrees of freedom, such as proton transfer. In this regime, however, the cost of a fully quantum mechanical simulation is determined by the quantization of the least quantum mechanical degrees of freedom.
Path Integral Treatment of Proton Transport Processes in BaZrO3
DEFF Research Database (Denmark)
Zhang, Qianfan; Wahnstrom, Goran; Björketun, Mårten
2008-01-01
Nuclear quantum effects on proton transfer and reorientation in BaZrO3 is investigated theoretically using the ab initio path-integral molecular-dynamics simulation technique. The result demonstrates that adding quantum fluctuations has a large effect on, in particular, the transfer barrier...
A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates
International Nuclear Information System (INIS)
Shiga, Motoyuki; Fujisaki, Hiroshi
2012-01-01
We propose a generalization of the intrinsic reaction coordinate (IRC) for quantum many-body systems described in terms of the mass-weighted ring polymer centroids in the imaginary-time path integral theory. This novel kind of reaction coordinate, which may be called the ''centroid IRC,'' corresponds to the minimum free energy path connecting reactant and product states with a least amount of reversible work applied to the center of masses of the quantum nuclei, i.e., the centroids. We provide a numerical procedure to obtain the centroid IRC based on first principles by combining ab initio path integral simulation with the string method. This approach is applied to NH 3 molecule and N 2 H 5 - ion as well as their deuterated isotopomers to study the importance of nuclear quantum effects in the intramolecular and intermolecular proton transfer reactions. We find that, in the intramolecular proton transfer (inversion) of NH 3 , the free energy barrier for the centroid variables decreases with an amount of about 20% compared to the classical one at the room temperature. In the intermolecular proton transfer of N 2 H 5 - , the centroid IRC is largely deviated from the ''classical'' IRC, and the free energy barrier is reduced by the quantum effects even more drastically.
Path integrals and pseudoclassical description for spinning particles in arbitrary dimensions
Energy Technology Data Exchange (ETDEWEB)
Gitman, D.M. [Sao Paulo Univ. (Brazil). Inst. de Fisica
1997-03-17
The propagator of a spinning particle in an external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has distinct solutions in even and odd dimensions. In even dimensions the representation is just a generalization of the one in four dimensions (which is already known). In this case the gauge invariant part of the effective action in the path integral has the form of the standard (Berezin-Marinov) pseudoclassical action. In odd dimensions the solution is presented for the first time and, in particular, it turns out that the gauge invariant part of the effective action differs from the standard one. We propose this new action as a candidate to describe spinning particles in odd dimensions. Studying the Hamiltonization of the pseudoclassical theory with the new action we show that the operator quantization leads to an adequate minimal quantum theory of spinning particles in odd dimensions. Finally the consideration is generalized for the case of a particle with an anomalous magnetic moment. (orig.).
Path integral approach for electron transport in disturbed magnetic field lines
Energy Technology Data Exchange (ETDEWEB)
Kanno, Ryutaro; Nakajima, Noriyoshi; Takamaru, Hisanori
2002-05-01
A path integral method is developed to investigate statistical property of an electron transport described as a Langevin equation in a statically disturbed magnetic field line structure; especially a transition probability of electrons strongly tied to field lines is considered. The path integral method has advantages that 1) it does not include intrinsically a growing numerical error of an orbit, which is caused by evolution of the Langevin equation under a finite calculation accuracy in a chaotic field line structure, and 2) it gives a method of understanding the qualitative content of the Langevin equation and assists to expect statistical property of the transport. Monte Carlo calculations of the electron distributions under both effects of chaotic field lines and collisions are demonstrated to comprehend above advantages through some examples. The mathematical techniques are useful to study statistical properties of various phenomena described as Langevin equations in general. By using parallel generators of random numbers, the Monte Carlo scheme to calculate a transition probability can be suitable for a parallel computation. (author)
Constant external fields in gauge theory and the spin 0, 1/2, 1 path integrals
International Nuclear Information System (INIS)
Reuter, M.; Schmidt, M.G.
1996-10-01
We investigate the usefulness of the ''string-inspired technique'' for gauge theory calculations in a constant external field background. Our approach is based on Strassler's worldline path integral approach to the Bern-Kosower formalism, and on the construction of worldline (super-) Green's functions incorporating external fields as well as internal propagators. The worldline path integral representation of the gluon loop is reexamined in detail. We calculate the two-loop effective actions induced for a constant external field by a scalar and spinor loop, and the corresponding one-loop effective action in the gluon loop case. (orig.)
High-order Path Integral Monte Carlo methods for solving strongly correlated fermion problems
Chin, Siu A.
2015-03-01
In solving for the ground state of a strongly correlated many-fermion system, the conventional second-order Path Integral Monte Carlo method is plagued with the sign problem. This is due to the large number of anti-symmetric free fermion propagators that are needed to extract the square of the ground state wave function at large imaginary time. In this work, I show that optimized fourth-order Path Integral Monte Carlo methods, which uses no more than 5 free-fermion propagators, in conjunction with the use of the Hamiltonian energy estimator, can yield accurate ground state energies for quantum dots with up to 20 polarized electrons. The correlations are directly built-in and no explicit wave functions are needed. This work is supported by the Qatar National Research Fund NPRP GRANT #5-674-1-114.
Path integral measure and the fermion-boson equivalence in the Schwinger model
International Nuclear Information System (INIS)
Maiella, G.
1980-02-01
I perform a change of field variables in the Schwinger model using the non-invariance of path integral measure under γ 5 transformations. The known equivalence of the model with a bosonic field theory and the Kogut-Susskind dipole mechanism is then derived. (author)
Path-integral and Ornstein-Zernike study of quantum fluid structures on the crystallization line
International Nuclear Information System (INIS)
Sesé, Luis M.
2016-01-01
Liquid neon, liquid para-hydrogen, and the quantum hard-sphere fluid are studied with path integral Monte Carlo simulations and the Ornstein-Zernike pair equation on their respective crystallization lines. The results cover the whole sets of structures in the r-space and the k-space and, for completeness, the internal energies, pressures and isothermal compressibilities. Comparison with experiment is made wherever possible, and the possibilities of establishing k-space criteria for quantum crystallization based on the path-integral centroids are discussed. In this regard, the results show that the centroid structure factor contains two significant parameters related to its main peak features (amplitude and shape) that can be useful to characterize freezing.
Path-integral and Ornstein-Zernike study of quantum fluid structures on the crystallization line
Energy Technology Data Exchange (ETDEWEB)
Sesé, Luis M., E-mail: msese@ccia.uned.es [Departamento de Ciencias y Técnicas Fisicoquímicas, Universidad Nacional de Educación a Distancia, Paseo Senda del Rey 9, 28040 Madrid (Spain)
2016-03-07
Liquid neon, liquid para-hydrogen, and the quantum hard-sphere fluid are studied with path integral Monte Carlo simulations and the Ornstein-Zernike pair equation on their respective crystallization lines. The results cover the whole sets of structures in the r-space and the k-space and, for completeness, the internal energies, pressures and isothermal compressibilities. Comparison with experiment is made wherever possible, and the possibilities of establishing k-space criteria for quantum crystallization based on the path-integral centroids are discussed. In this regard, the results show that the centroid structure factor contains two significant parameters related to its main peak features (amplitude and shape) that can be useful to characterize freezing.
Electrical crosstalk in integrated Mach-Zehnder modulators caused by a shared ground path
Yao, W.; Gilardi, G.; Smit, M.K.; Wale, M.J.
2015-01-01
We show that the majority of electrical crosstalk between integrated Mach-Zehnder modulators can be caused by a shared ground path and demonstrate that in its absence crosstalk and related transmission penalty is greatly reduced.
Energy Technology Data Exchange (ETDEWEB)
Butko, Yana A., E-mail: yanabutko@yandex.ru, E-mail: kinderknecht@math.uni-sb.de [Bauman Moscow State Technical University, 2nd Baumanskaya street, 5, Moscow 105005, Russia and University of Saarland, Postfach 151150, D-66041 Saarbrücken (Germany); Grothaus, Martin, E-mail: grothaus@mathematik.uni-kl.de [University of Kaiserslautern, 67653 Kaiserslautern (Germany); Smolyanov, Oleg G., E-mail: Smolyanov@yandex.ru [Lomonosov Moscow State University, Vorob’evy gory 1, Moscow 119992 (Russian Federation)
2016-02-15
Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.
International Nuclear Information System (INIS)
Butko, Yana A.; Grothaus, Martin; Smolyanov, Oleg G.
2016-01-01
Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures
Quantum gravity in three dimensions, Witten spinors and the quantisation of length
Wieland, Wolfgang
2018-05-01
In this paper, I investigate the quantisation of length in euclidean quantum gravity in three dimensions. The starting point is the classical hamiltonian formalism in a cylinder of finite radius. At this finite boundary, a counter term is introduced that couples the gravitational field in the interior to a two-dimensional conformal field theory for an SU (2) boundary spinor, whose norm determines the conformal factor between the fiducial boundary metric and the physical metric in the bulk. The equations of motion for this boundary spinor are derived from the boundary action and turn out to be the two-dimensional analogue of the Witten equations appearing in Witten's proof of the positive mass theorem. The paper concludes with some comments on the resulting quantum theory. It is shown, in particular, that the length of a one-dimensional cross section of the boundary turns into a number operator on the Fock space of the theory. The spectrum of this operator is discrete and matches the results from loop quantum gravity in the spin network representation.
Transport coefficients for deeply inelastic scattering from the Feynman path integral method
International Nuclear Information System (INIS)
Brink, D.M.; Neto, J.; Weidenmueller, H.A.
1979-01-01
Friction and diffusion coefficients can be derived simply by combining statistical arguments with the Feynman path integral method. A transport equation for Feynman's influence functional is obtained, and transport coefficients are deduced from it. The expressions are discussed in the limits of weak, and of strong coupling. (Auth.)
Raymond, Neil; Iouchtchenko, Dmitri; Roy, Pierre-Nicholas; Nooijen, Marcel
2018-05-01
We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition function in a product basis of continuous nuclear and discrete electronic degrees of freedom without the use of any mapping schemes. We separate our Hamiltonian into a harmonic portion and a coupling portion; the partition function can then be calculated as the product of a Monte Carlo estimator (of the coupling contribution to the partition function) and a normalization factor (that is evaluated analytically). A Gaussian mixture model is used to evaluate the Monte Carlo estimator in a computationally efficient manner. Using two model systems, we demonstrate our approach to reduce the stochastic error associated with the Monte Carlo estimator. We show that the selection of the harmonic oscillators comprising the sampling distribution directly affects the efficiency of the method. Our results demonstrate that our path integral Monte Carlo method's deviation from exact Trotter calculations is dominated by the choice of the sampling distribution. By improving the sampling distribution, we can drastically reduce the stochastic error leading to lower computational cost.
From classical to quantum fields
Baulieu, Laurent; Sénéor, Roland
2017-01-01
Quantum Field Theory has become the universal language of most modern theoretical physics. This introductory textbook shows how this beautiful theory offers the correct mathematical framework to describe and understand the fundamental interactions of elementary particles. The book begins with a brief reminder of basic classical field theories, electrodynamics and general relativity, as well as their symmetry properties, and proceeds with the principles of quantisation following Feynman's path integral approach. Special care is used at every step to illustrate the correct mathematical formulation of the underlying assumptions. Gauge theories and the problems encountered in their quantisation are discussed in detail. The last chapters contain a full description of the Standard Model of particle physics and the attempts to go beyond it, such as grand unified theories and supersymmetry. Written for advanced undergraduate and beginning graduate students in physics and mathematics, the book could also serve as a re...
Quantum mechanical path integrals with Wiener measures for all polynomial Hamiltonians
International Nuclear Information System (INIS)
Klauder, J.R.; Daubechies, I.
We construct arbitrary matrix elements of the quantum evolution operator for a wide class of self-adjoint canonical Hamiltonians, including those which are polynomial in the Heisenberg operators, as the limit of well-defined path integrals involving Wiener measure on phase space, as a diffusion constant diverges. A related construction achieves a similar result for an arbitrary spin Hamiltonian. (orig.)
Path integral for Dirac particle in plane wave field
International Nuclear Information System (INIS)
Zeggari, S.; Boudjedaa, T.; Chetouani, L.
2001-01-01
The problem of a relativistic spinning particle in interaction with an electromagnetic plane wave field is treated via path integrals. The dynamics of the spin of the particle is described using the supersymmetric action proposed by Fradkin and Gitman. The problem has been solved by using two identities, one bosonic and the other fermionic, which are related directly to the classical equations of motion. The exact expression of the relative Green's function is given and the result agrees with those of the literature. Further, the suitably normalized wave functions are also extracted. (orig.)
Path integral for Dirac particle in plane wave field
Energy Technology Data Exchange (ETDEWEB)
Zeggari, S.; Boudjedaa, T.; Chetouani, L. [Mentouri Univ., Constantine (Algeria). Dept. of Physique
2001-10-01
The problem of a relativistic spinning particle in interaction with an electromagnetic plane wave field is treated via path integrals. The dynamics of the spin of the particle is described using the supersymmetric action proposed by Fradkin and Gitman. The problem has been solved by using two identities, one bosonic and the other fermionic, which are related directly to the classical equations of motion. The exact expression of the relative Green's function is given and the result agrees with those of the literature. Further, the suitably normalized wave functions are also extracted. (orig.)
Connection between Fourier coefficient and Discretized Cartesian path integration
International Nuclear Information System (INIS)
Coalson, R.D.
1986-01-01
The relationship between so-called Discretized and Fourier coefficient formulations of Cartesian path integration is examined. In particular, an intimate connection between the two is established by rewriting the Discretized formulation in a manifestly Fourier-like way. This leads to improved understanding of both the limit behavior and the convergence properties of computational prescriptions based on the two formalisms. The performance of various prescriptions is compared with regard to calculation of on-diagonal statistical density matrix elements for a number of prototypical 1-d potentials. A consistent convergence order among these prescriptions is established
Path integral approach to multidimensional quantum tunnelling
International Nuclear Information System (INIS)
Balantekin, A.B.; Takigawa, N.
1985-01-01
Path integral formulation of the coupled channel problem in the case of multidimensional quantum tunneling is presented and two-time influence functionals are introduced. The two-time influence functionals are calculated explicitly for the three simplest cases: Harmonic oscillators linearly or quadratically coupled to the translational motion and a system with finite number of equidistant energy levels linearly coupled to the translational motion. The effects of these couplings on the transmission probability are studied for two limiting cases, adiabatic case and when the internal system has a degenerate energy spectrum. The condition for the transmission probability to show a resonant structure is discussed and exemplified. Finally, the properties of the dissipation factor in the adiabatic limit and its correlation with the friction coefficient in the classically accessible region are studied
International Nuclear Information System (INIS)
Bowes, J.P.; Foot, R.; Volkas, R.R.
1997-01-01
In gauge theories like the standard model, the electric charges of the fermions can be heavily constrained from the classical structure of the theory and from the cancellation of anomalies. There is however mounting evidence suggesting that these anomaly constraints are not as well motivated as the classical constraints. In light of this, possible modifications of the minimal standard model are discussed which will give a complete electric charge quantisation from classical constraints alone. Because these modifications to the Standard Model involve the consideration of baryon number violating scalar interactions, a complete catalogue of the simplest ways to modify the Standard Model is presented so as to introduce explicit baryon number violation. 9 refs., 7 figs
International Nuclear Information System (INIS)
Govorkov, A.B.
1980-01-01
The density matrix, rather than the wavefunction describing the system of a fixed number of non-relativistic identical particles, is subject to the second quantisation. Here the bilinear operators which move a particle from a given state to another appear and satisfy the Lie algebraic relations of the unitary group SU(rho) when the dimension rho→infinity. The drawing into consideration of the system with a variable number of particles implies the extension of this algebra into one of the simple Lie algebras of classical (orthogonal, symplectic or unitary) groups in the even-dimensional spaces. These Lie algebras correspond to the para-Fermi-, para-Bose- and para-uniquantisation of fields, respectively. (author)
Energy Technology Data Exchange (ETDEWEB)
Bowes, J.P.; Foot, R.; Volkas, R.R.
1997-06-01
In gauge theories like the standard model, the electric charges of the fermions can be heavily constrained from the classical structure of the theory and from the cancellation of anomalies. There is however mounting evidence suggesting that these anomaly constraints are not as well motivated as the classical constraints. In light of this, possible modifications of the minimal standard model are discussed which will give a complete electric charge quantisation from classical constraints alone. Because these modifications to the Standard Model involve the consideration of baryon number violating scalar interactions, a complete catalogue of the simplest ways to modify the Standard Model is presented so as to introduce explicit baryon number violation. 9 refs., 7 figs.
Jing, Xiaoli; Cheng, Haobo; Wen, Yongfu
2018-04-01
A new local integration algorithm called quality map path integration (QMPI) is reported for shape reconstruction in the fringe reflection technique. A quality map is proposed to evaluate the quality of gradient data locally, and functions as a guideline for the integrated path. The presented method can be employed in wavefront estimation from its slopes over the general shaped surface with slope noise equivalent to that in practical measurements. Moreover, QMPI is much better at handling the slope data with local noise, which may be caused by the irregular shapes of the surface under test. The performance of QMPI is discussed by simulations and experiment. It is shown that QMPI not only improves the accuracy of local integration, but can also be easily implemented with no iteration compared to Southwell zonal reconstruction (SZR). From an engineering point-of-view, the proposed method may also provide an efficient and stable approach for different shapes with high-precise demand.
Makri, Nancy
2014-10-07
The real-time path integral representation of the reduced density matrix for a discrete system in contact with a dissipative medium is rewritten in terms of the number of blips, i.e., elementary time intervals over which the forward and backward paths are not identical. For a given set of blips, it is shown that the path sum with respect to the coordinates of all remaining time points is isomorphic to that for the wavefunction of a system subject to an external driving term and thus can be summed by an inexpensive iterative procedure. This exact decomposition reduces the number of terms by a factor that increases exponentially with propagation time. Further, under conditions (moderately high temperature and/or dissipation strength) that lead primarily to incoherent dynamics, the "fully incoherent limit" zero-blip term of the series provides a reasonable approximation to the dynamics, and the blip series converges rapidly to the exact result. Retention of only the blips required for satisfactory convergence leads to speedup of full-memory path integral calculations by many orders of magnitude.
Path integral representation of Lorentzian spinfoam model, asymptotics and simplicial geometries
International Nuclear Information System (INIS)
Han, Muxin; Krajewski, Thomas
2014-01-01
A new path integral representation of Lorentzian Engle–Pereira–Rovelli–Livine spinfoam model is derived by employing the theory of unitary representation of SL(2,C). The path integral representation is taken as a starting point of semiclassical analysis. The relation between the spinfoam model and classical simplicial geometry is studied via the large-spin asymptotic expansion of the spinfoam amplitude with all spins uniformly large. More precisely, in the large-spin regime, there is an equivalence between the spinfoam critical configuration (with certain nondegeneracy assumption) and a classical Lorentzian simplicial geometry. Such an equivalence relation allows us to classify the spinfoam critical configurations by their geometrical interpretations, via two types of solution-generating maps. The equivalence between spinfoam critical configuration and simplical geometry also allows us to define the notion of globally oriented and time-oriented spinfoam critical configuration. It is shown that only at the globally oriented and time-oriented spinfoam critical configuration, the leading-order contribution of spinfoam large-spin asymptotics gives precisely an exponential of Lorentzian Regge action of General Relativity. At all other (unphysical) critical configurations, spinfoam large-spin asymptotics modifies the Regge action at the leading-order approximation. (paper)
Unified path integral approach to theories of diffusion-influenced reactions
Prüstel, Thorsten; Meier-Schellersheim, Martin
2017-08-01
Building on mathematical similarities between quantum mechanics and theories of diffusion-influenced reactions, we develop a general approach for computational modeling of diffusion-influenced reactions that is capable of capturing not only the classical Smoluchowski picture but also alternative theories, as is here exemplified by a volume reactivity model. In particular, we prove the path decomposition expansion of various Green's functions describing the irreversible and reversible reaction of an isolated pair of molecules. To this end, we exploit a connection between boundary value and interaction potential problems with δ - and δ'-function perturbation. We employ a known path-integral-based summation of a perturbation series to derive a number of exact identities relating propagators and survival probabilities satisfying different boundary conditions in a unified and systematic manner. Furthermore, we show how the path decomposition expansion represents the propagator as a product of three factors in the Laplace domain that correspond to quantities figuring prominently in stochastic spatially resolved simulation algorithms. This analysis will thus be useful for the interpretation of current and the design of future algorithms. Finally, we discuss the relation between the general approach and the theory of Brownian functionals and calculate the mean residence time for the case of irreversible and reversible reactions.
Explaining Technology Integration in K-12 Classrooms: A Multilevel Path Analysis Model
Liu, Feng; Ritzhaupt, Albert D.; Dawson, Kara; Barron, Ann E.
2017-01-01
The purpose of this research was to design and test a model of classroom technology integration in the context of K-12 schools. The proposed multilevel path analysis model includes teacher, contextual, and school related variables on a teacher's use of technology and confidence and comfort using technology as mediators of classroom technology…
Some comments on rigorous quantum field path integrals in the analytical regularization scheme
Energy Technology Data Exchange (ETDEWEB)
Botelho, Luiz C.L. [Universidade Federal Fluminense (UFF), Niteroi, RJ (Brazil). Dept. de Matematica Aplicada]. E-mail: botelho.luiz@superig.com.br
2008-07-01
Through the systematic use of the Minlos theorem on the support of cylindrical measures on R{sup {infinity}}, we produce several mathematically rigorous path integrals in interacting euclidean quantum fields with Gaussian free measures defined by generalized powers of the Laplacian operator. (author)
Some comments on rigorous quantum field path integrals in the analytical regularization scheme
International Nuclear Information System (INIS)
Botelho, Luiz C.L.
2008-01-01
Through the systematic use of the Minlos theorem on the support of cylindrical measures on R ∞ , we produce several mathematically rigorous path integrals in interacting euclidean quantum fields with Gaussian free measures defined by generalized powers of the Laplacian operator. (author)
The role of spatial memory and frames of reference in the precision of angular path integration.
Arthur, Joeanna C; Philbeck, John W; Kleene, Nicholas J; Chichka, David
2012-09-01
Angular path integration refers to the ability to maintain an estimate of self-location after a rotational displacement by integrating internally-generated (idiothetic) self-motion signals over time. Previous work has found that non-sensory inputs, namely spatial memory, can play a powerful role in angular path integration (Arthur et al., 2007, 2009). Here we investigated the conditions under which spatial memory facilitates angular path integration. We hypothesized that the benefit of spatial memory is particularly likely in spatial updating tasks in which one's self-location estimate is referenced to external space. To test this idea, we administered passive, non-visual body rotations (ranging 40°-140°) about the yaw axis and asked participants to use verbal reports or open-loop manual pointing to indicate the magnitude of the rotation. Prior to some trials, previews of the surrounding environment were given. We found that when participants adopted an egocentric frame of reference, the previously-observed benefit of previews on within-subject response precision was not manifested, regardless of whether remembered spatial frameworks were derived from vision or spatial language. We conclude that the powerful effect of spatial memory is dependent on one's frame of reference during self-motion updating. Copyright © 2012 Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Rosenfelder, R. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1997-12-01
This lectures aim at giving graduate students an introduction to a working knowledge of path integral methods in a wide variety of fields in physics. Consequently, the the lecture notes are organized in three main parts dealing with non-relativistic quantum mechanics, many-body physics and field theory. In the first part the basic concepts of path integrals are developed in the usual heuristic, non-mathematical way followed by the standard examples of quadratic Lagrangians for which the path integrals can be solved exactly. Applications include semi-classical expansions, scattering problems and the representation of Green functions as path integrals. In the last chapter of this part it is shown how (euclidean) path integrals can be treated numerically by Monte-Carlo methods with a program for the anharmonic oscillator as an explicit example. The second part deals with the application of path integrals in statistical mechanics and many-body problems. Various chapters treat the partition functions, the polaron problem as a non-relativistic field theory and path integrals over ordinary and Grassmannian coherent states. Perturbation theory and the diagrammatic rules are derived in an unified way for both bosons and fermions and illustrated by simple examples. Finally, in the third part path integrals in relativistic quantum field theory are discussed. Standard topics like the generating functional for Green functions, perturbative expansions, effective actions and quantization of gauge theories are treated. Some special applications (the wordline formalism and spin in relativistic path integrals, the derivation of anomalies by path integral methods) are contained in additional chapters. The last section tries to give a simple introduction into lattice (gauge) field theory including a numerical example which can be run on a PC. The set of problems which accompanied the lectures is also included in the present notes. (author) 15 figs., refs.
Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.
Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F
2018-02-13
Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.
Real-space path integration is impaired in Alzheimer’s disease and mild cognitive impairment
Czech Academy of Sciences Publication Activity Database
Mokrišová, I.; Laczó, J.; Andel, R.; Gažová, I.; Vyhnálek, M.; Nedělská, Z.; Levčík, David; Cerman, J.; Vlček, Kamil; Hort, J.
2016-01-01
Roč. 307, Jul 1 (2016), s. 150-158 ISSN 0166-4328 Institutional support: RVO:67985823 Keywords : Alzheimer disease * mild cognitive impairment * spatial navigation * hippocampus * path integration Subject RIV: FH - Neurology Impact factor: 3.002, year: 2016
Two-scale large deviations for chemical reaction kinetics through second quantization path integral
International Nuclear Information System (INIS)
Li, Tiejun; Lin, Feng
2016-01-01
Motivated by the study of rare events for a typical genetic switching model in systems biology, in this paper we aim to establish the general two-scale large deviations for chemical reaction systems. We build a formal approach to explicitly obtain the large deviation rate functionals for the considered two-scale processes based upon the second quantization path integral technique. We get three important types of large deviation results when the underlying two timescales are in three different regimes. This is realized by singular perturbation analysis to the rate functionals obtained by the path integral. We find that the three regimes possess the same deterministic mean-field limit but completely different chemical Langevin approximations. The obtained results are natural extensions of the classical large volume limit for chemical reactions. We also discuss its implication on the single-molecule Michaelis–Menten kinetics. Our framework and results can be applied to understand general multi-scale systems including diffusion processes. (paper)
International Nuclear Information System (INIS)
Zhang Zhongcan; Hu Chenguo; Fang Zhenyun
1998-01-01
The authors study the method which directly adopts the azimuthal angles and the rotation angle of the axis to describe the evolving process of the angular momentum eigenstates under the space rotation transformation. The authors obtain the angular momentum rotation and multi-rotation matrix elements' path integral which evolves with the parameter λ(0→θ,θ the rotation angle), and establish the general method of treating the functional (path) integral as a normal multi-integrals
Path integrals for inertialess classical particles under-going rapid stochastic trembling. I
International Nuclear Information System (INIS)
Bezak, V.
1978-01-01
Feynman path integrals are studied in reference to the Fokker-Planck (Smoluchowski) equation. Examples are presented including the motion of an inertialess classical charged particle between electrodes in plate and cylindrical capacitors with charges fluctuating rapidly as Gaussian white-noise stochastic processes. Another example concerns magnetodiffusion of a charged particle in an non-polarized electromagnetic beam characterized by a white-noise spectrum. (author)
Application of path integral method to heavy ion reactions, 1. General formalism
Energy Technology Data Exchange (ETDEWEB)
Fujita, J; Negishi, T [Tokyo Univ. of Education (Japan). Dept. of Physics
1976-03-01
The semiclassical approach for heavy ion reactions has become more and more important in analyzing rapidly accumulating data. The purpose of this paper is to lay a quantum-mechanical foundation of the conventional semiclassical treatments in heavy ion physics by using Feynman's path integral method on the basis of the second paper of Pechukas, and discuss simple consequences of the formalism.
Investigation of the spinfoam path integral with quantum cuboid intertwiners
Bahr, Benjamin; Steinhaus, Sebastian
2016-05-01
In this work, we investigate the 4d path integral for Euclidean quantum gravity on a hypercubic lattice, as given by the spinfoam model by Engle, Pereira, Rovelli, Livine, Freidel and Krasnov. To tackle the problem, we restrict to a set of quantum geometries that reflects the large amount of lattice symmetries. In particular, the sum over intertwiners is restricted to quantum cuboids, i.e. coherent intertwiners which describe a cuboidal geometry in the large-j limit. Using asymptotic expressions for the vertex amplitude, we find several interesting properties of the state sum. First of all, the value of coupling constants in the amplitude functions determines whether geometric or nongeometric configurations dominate the path integral. Secondly, there is a critical value of the coupling constant α , which separates two phases. In both phases, the diffeomorphism symmetry appears to be broken. In one, the dominant contribution comes from highly irregular, in the other from highly regular configurations, both describing flat Euclidean space with small quantum fluctuations around them, viewed in different coordinate systems. On the critical point diffeomorphism symmetry is nearly restored, however. Thirdly, we use the state sum to compute the physical norm of kinematical states, i.e. their norm in the physical Hilbert space. We find that states which describe boundary geometry with high torsion have an exponentially suppressed physical norm. We argue that this allows one to exclude them from the state sum in calculations.
Path integral formulation of the Hodge duality on the brane
International Nuclear Information System (INIS)
Hahn, Sang-Ok; Kiem, Youngjai; Kim, Yoonbai; Oh, Phillial
2001-01-01
In the warped compactification with a single Randall-Sundrum brane, a puzzling claim has been made that scalar fields can be bound to the brane but their Hodge dual higher-rank antisymmetric tensors cannot. By explicitly requiring the Hodge duality, a prescription to resolve this puzzle was recently proposed by Duff and Liu. In this Brief Report, we implement the Hodge duality via the path integral formulation in the presence of the background gravity fields of warped compactifications. It is shown that the prescription of Duff and Liu can be naturally understood within this framework
Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method
Fanaro, Maria de los Angeles; Otero, Maria Rita; Arlego, Marcelo
2012-01-01
This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. (Contains 3 figures.)
International Nuclear Information System (INIS)
Rezende, J.
1983-01-01
We give a simple proof of Feynman's formula for the Green's function of the n-dimensional harmonic oscillator valid for every time t with Im t<=0. As a consequence the Schroedinger equation for the anharmonic oscillator is integrated and expressed by the Feynman path integral on Hilbert space. (orig.)
Defect forces, defect couples and path integrals in fracture mechanics
International Nuclear Information System (INIS)
Roche, R.L.
1979-07-01
In this work, it is shown that the path integrals can be introduced without any reference to the material behavior. The method is based on the definition in a continuous medium of a set of vectors and couples having the dimension of a force or a moment. More precisely, definitions are given of volume defect forces, surface defect forces, volume defect couples, and surface defect couples. This is done with the help of the stress working variation of a particule moving through the solid. The most important result is: the resultant of all the defect forces included in a volume V is the J integral on the surface surrounding V and the moment resultant is the L integral. So these integrals are defined without any assumption on the material constitutive equation. Another result is the material form of the virtual work principle - defect forces are acting like conventional forces in the conventional principles of virtual work. This lead to the introduction of the energy momentum tensor and of the associated couple stress. Application of this method is made to fracture mechanics in studying the defect forces distribution around a crack [fr
Path integral for spinning particle in the plane wave field: Global and local projections
International Nuclear Information System (INIS)
Boudiaf, N.; Boudjedaa, T.; Chetouani, L.
2001-01-01
The Green function related to the problem of a Dirac particle interacting with a plane wave is calculated via the path integral formalism proposed recently by Alexandrou et al. according to the two so-called global and local projections. With the help of the incorporation of two simple identities, it is shown that the contribution to the calculation of the integrals comes essentially from classical solutions projected along the direction of wave propagation. (orig.)
Quantum density fluctuations in liquid neon from linearized path-integral calculations
International Nuclear Information System (INIS)
Poulsen, Jens Aage; Scheers, Johan; Nyman, Gunnar; Rossky, Peter J.
2007-01-01
The Feynman-Kleinert linearized path-integral [J. A. Poulsen et al., J. Chem. Phys. 119, 12179 (2003)] representation of quantum correlation functions is applied to compute the spectrum of density fluctuations for liquid neon at T=27.6 K, p=1.4 bar, and Q vector 1.55 Aa -1 . The calculated spectrum as well as the kinetic energy of the liquid are in excellent agreement with the experiment of Cunsolo et al. [Phys. Rev. B 67, 024507 (2003)
Effects of Quantum Nuclear Delocalisation on NMR Parameters from Path Integral Molecular Dynamics
Czech Academy of Sciences Publication Activity Database
Dračínský, Martin; Hodgkinson, P.
2014-01-01
Roč. 20, č. 8 (2014), s. 2201-2207 ISSN 0947-6539 Grant - others:Seventh Framework Programme of the European Union(XE) FP7-299242 People Institutional support: RVO:61388963 Keywords : density functional calculations * isotope effects * NMR spectroscopy * nuclear delocalisation * path integral molecular dynamics Subject RIV: CC - Organic Chemistry Impact factor: 5.731, year: 2014
Worldline path integrals for a Dirac particle in a weak gravitational plane wave
International Nuclear Information System (INIS)
Haouat, S.; Chetouani, L.
2008-01-01
The problem of a relativistic spinning particle interacting with a weak gravitational plane wave in (3+1) dimensions is formulated in the frame work of covariant supersymmetric path integrals. The relative Green function is expressed through a functional integral over bosonic trajectories that describe the external motion and fermionic variables that describe the spin degrees of freedom. The (3+1) dimensional problem is reduced to the (1+1) dimensional one by using an identity. Next, the relative propagator is exactly calculated and the wave functions are extracted. (orig.)
Ordering, symbols and finite-dimensional approximations of path integrals
International Nuclear Information System (INIS)
Kashiwa, Taro; Sakoda, Seiji; Zenkin, S.V.
1994-01-01
We derive general form of finite-dimensional approximations of path integrals for both bosonic and fermionic canonical systems in terms of symbols of operators determined by operator ordering. We argue that for a system with a given quantum Hamiltonian such approximations are independent of the type of symbols up to terms of O(ε), where ε of is infinitesimal time interval determining the accuracy of the approximations. A new class of such approximations is found for both c-number and Grassmannian dynamical variables. The actions determined by the approximations are non-local and have no classical continuum limit except the cases of pq- and qp-ordering. As an explicit example the fermionic oscillator is considered in detail. (author)
PRELIMINARY PROJECT PLAN FOR LANSCE INTEGRATED FLIGHT PATHS 11A, 11B, 12, and 13
International Nuclear Information System (INIS)
Bultman, D. H.; Weinacht, D.
2000-01-01
This Preliminary Project Plan Summarizes the Technical, Cost, and Schedule baselines for an integrated approach to developing several flight paths at the Manual Lujan Jr. Neutron Scattering Center at the Los Alamos Neutron Science Center. For example, the cost estimate is intended to serve only as a rough order of magnitude assessment of the cost that might be incurred as the flight paths are developed. Further refinement of the requirements and interfaces for each beamline will permit additional refinement and confidence in the accuracy of all three baselines (Technical, Cost, Schedule)
Path space measures for Dirac and Schroedinger equations: Nonstandard analytical approach
International Nuclear Information System (INIS)
Nakamura, T.
1997-01-01
A nonstandard path space *-measure is constructed to justify the path integral formula for the Dirac equation in two-dimensional space endash time. A standard measure as well as a standard path integral is obtained from it. We also show that, even for the Schroedinger equation, for which there is no standard measure appropriate for a path integral, there exists a nonstandard measure to define a *-path integral whose standard part agrees with the ordinary path integral as defined by a limit from time-slice approximant. copyright 1997 American Institute of Physics
Energy Technology Data Exchange (ETDEWEB)
Agarwal, Animesh, E-mail: animesh@zedat.fu-berlin.de; Delle Site, Luigi, E-mail: dellesite@fu-berlin.de [Institute for Mathematics, Freie Universität Berlin, Berlin (Germany)
2015-09-07
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement.
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.
Sinitskiy, Anton V; Voth, Gregory A
2015-09-07
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals
International Nuclear Information System (INIS)
Sinitskiy, Anton V.; Voth, Gregory A.
2015-01-01
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments
Optical propagators in vector and spinor theories by path integral formalism
International Nuclear Information System (INIS)
Linares, J.
1993-01-01
The construction of an extended parabolic (wide-angle) vector and spinor wave theory is presented. For that, optical propagators in monochromatic vector light optics and monoenergetic spinor electron optics are evaluated by the path integral formalism. The auxiliary parameter method introduced by Fock and the Feynman-Dyson perturbative series are used. The proposed theory supplies, by a generalized Fermat's principle, the Mukunda-Simon-Sudarshan transformation for the passage from scalar to vector light (or spinor electron) optics in an asymptotic approximation. (author). 19 refs
Energy Technology Data Exchange (ETDEWEB)
Etim, E; Basili, C [Rome Univ. (Italy). Ist. di Matematica
1978-08-21
The lagrangian in the path integral solution of the master equation of a stationary Markov process is derived by application of the Ehrenfest-type theorem of quantum mechanics and the Cauchy method of finding inverse functions. Applied to the non-linear Fokker-Planck equation the authors reproduce the result obtained by integrating over Fourier series coefficients and by other methods.
Covariant and consistent anomalies in two dimensions in path-integral formulation
International Nuclear Information System (INIS)
Joglekar, S.D.; Saini, G.
1993-01-01
We give a definition of a one-parameter family of regularized chiral currents in a chiral non-Abelian gauge theory in two dimensions in path-integral formulation. We show that covariant and consistent currents are obtained from this family by selecting two specific values of the free parameter, and thus our regularization interpolates between these two. Our procedure uses chiral bases constructed from eigenfunctions of the same operator for ψ L and anti ψ L . Definition of integration measure and regularization is done in terms of the same Hermitian operator D α =∂+iαA. Covariant and consistent currents (and indeed the entire family) are classically conserved. Difference with previous works are explained, in particular, that an anomaly in the general basis does differ from the Jacobian contribution. (orig.)
Heading-vector navigation based on head-direction cells and path integration.
Kubie, John L; Fenton, André A
2009-05-01
Insect navigation is guided by heading vectors that are computed by path integration. Mammalian navigation models, on the other hand, are typically based on map-like place representations provided by hippocampal place cells. Such models compute optimal routes as a continuous series of locations that connect the current location to a goal. We propose a "heading-vector" model in which head-direction cells or their derivatives serve both as key elements in constructing the optimal route and as the straight-line guidance during route execution. The model is based on a memory structure termed the "shortcut matrix," which is constructed during the initial exploration of an environment when a set of shortcut vectors between sequential pairs of visited waypoint locations is stored. A mechanism is proposed for calculating and storing these vectors that relies on a hypothesized cell type termed an "accumulating head-direction cell." Following exploration, shortcut vectors connecting all pairs of waypoint locations are computed by vector arithmetic and stored in the shortcut matrix. On re-entry, when local view or place representations query the shortcut matrix with a current waypoint and goal, a shortcut trajectory is retrieved. Since the trajectory direction is in head-direction compass coordinates, navigation is accomplished by tracking the firing of head-direction cells that are tuned to the heading angle. Section 1 of the manuscript describes the properties of accumulating head-direction cells. It then shows how accumulating head-direction cells can store local vectors and perform vector arithmetic to perform path-integration-based homing. Section 2 describes the construction and use of the shortcut matrix for computing direct paths between any pair of locations that have been registered in the shortcut matrix. In the discussion, we analyze the advantages of heading-based navigation over map-based navigation. Finally, we survey behavioral evidence that nonhippocampal
Quantum Mechanics, Path Integrals and Option Pricing: Reducing the Complexity of Finance
Baaquie, Belal E.; Coriano, Claudio; Srikant, Marakani
2002-01-01
Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of options. The ideas are sketched out for simple models, such as the Black-Scholes model, where analytical and numerical results are compared. Application of the method to nonlinear sy...
Moran, B.; Kulkarni, S.S.; Reeves, H.W.
2007-01-01
A path-independent (conservation) integral is developed for the characterization of solute concentration and flux in a biofilm in the vicinity of a detachment or other flux limiting boundary condition. Steady state conditions of solute diffusion are considered and biofilm kinetics are described by an uptake term which can be expressed in terms of a potential (Michaelis-Menten kinetics). An asymptotic solution for solute concentration at the tip of the detachment is obtained and shown to be analogous to that of antiplane crack problems in linear elasticity. It is shown that the amplitude of the asymptotic solution can be calculated by evaluating a path-independent integral. The special case of a semi-infinite detachment in an infinite strip is considered and the amplitude of the asymptotic field is related to the boundary conditions and problem parameters in closed form for zeroth and first order kinetics and numerically for Michaelis-Menten kinetics. ?? Springer Science+Business Media, Inc. 2007.
Fractional path planning and path tracking
International Nuclear Information System (INIS)
Melchior, P.; Jallouli-Khlif, R.; Metoui, B.
2011-01-01
This paper presents the main results of the application of fractional approach in path planning and path tracking. A new robust path planning design for mobile robot was studied in dynamic environment. The normalized attractive force applied to the robot is based on a fictitious fractional attractive potential. This method allows to obtain robust path planning despite robot mass variation. The danger level of each obstacles is characterized by the fractional order of the repulsive potential of the obstacles. Under these conditions, the robot dynamic behavior was studied by analyzing its X - Y path planning with dynamic target or dynamic obstacles. The case of simultaneously mobile obstacles and target is also considered. The influence of the robot mass variation is studied and the robustness analysis of the obtained path shows the robustness improvement due to the non integer order properties. Pre shaping approach is used to reduce system vibration in motion control. Desired systems inputs are altered so that the system finishes the requested move without residual vibration. This technique, developed by N.C. Singer and W.P.Seering, is used for flexible structure control, particularly in the aerospace field. In a previous work, this method was extended for explicit fractional derivative systems and applied to second generation CRONE control, the robustness was also studied. CRONE (the French acronym of C ommande Robuste d'Ordre Non Entier ) control system design is a frequency-domain based methodology using complex fractional integration.
International Nuclear Information System (INIS)
Dekker, H.
1978-01-01
The lagrangian for the action occurring in the path integral solution of the nonlinear Fokker-Planck equation with constant diffusion function is derived by means of a straightforward Fourier series analysis. In this manner the path between the prepoint and the postpoint in the short time propagator is not restricted a priori to the usually considered straight line. Earlier results by Graham, Stratonovich, Horsthemke and Back, and the author's are recovered and thus put on much safer ground. (Auth.)
Maximally-localized position, Euclidean path-integral, and thermodynamics in GUP quantum mechanics
Bernardo, Reginald Christian S.; Esguerra, Jose Perico H.
2018-04-01
In dealing with quantum mechanics at very high energies, it is essential to adapt to a quasiposition representation using the maximally-localized states because of the generalized uncertainty principle. In this paper, we look at maximally-localized states as eigenstates of the operator ξ = X + iβP that we refer to as the maximally-localized position. We calculate the overlap between maximally-localized states and show that the identity operator can be expressed in terms of the maximally-localized states. Furthermore, we show that the maximally-localized position is diagonal in momentum-space and that the maximally-localized position and its adjoint satisfy commutation and anti-commutation relations reminiscent of the harmonic oscillator commutation and anti-commutation relations. As application, we use the maximally-localized position in developing the Euclidean path-integral and introduce the compact form of the propagator for maximal localization. The free particle momentum-space propagator and the propagator for maximal localization are analytically evaluated up to quadratic-order in β. Finally, we obtain a path-integral expression for the partition function of a thermodynamic system using the maximally-localized states. The partition function of a gas of noninteracting particles is evaluated. At temperatures exceeding the Planck energy, we obtain the gas' maximum internal energy N / 2 β and recover the zero heat capacity of an ideal gas.
International Nuclear Information System (INIS)
Lobanov, Yu.Yu.; Shidkov, E.P.
1987-01-01
The method for numerical evaluation of path integrals in Eucledean quantum mechanics without lattice discretization is elaborated. The method is based on the representation of these integrals in the form of functional integrals with respect to the conditional Wiener measure and on the use of the derived approximate exact on a class of polynomial functionals of a given degree. By the computations of non-perturbative characteristics, concerned the topological structure of vacuum, the advantages of this method versus lattice Monte-Carlo calculations are demonstrated
Hippocampal “Time Cells”: Time versus Path Integration
Kraus, Benjamin J.; Robinson, Robert J.; White, John A.; Eichenbaum, Howard; Hasselmo, Michael E.
2014-01-01
SUMMARY Recent studies have reported the existence of hippocampal “time cells,” neurons that fire at particular moments during periods when behavior and location are relatively constant. However, an alternative explanation of apparent time coding is that hippocampal neurons “path integrate” to encode the distance an animal has traveled. Here, we examined hippocampal neuronal firing patterns as rats ran in place on a treadmill, thus “clamping” behavior and location, while we varied the treadmill speed to distinguish time elapsed from distance traveled. Hippocampal neurons were strongly influenced by time and distance, and less so by minor variations in location. Furthermore, the activity of different neurons reflected integration over time and distance to varying extents, with most neurons strongly influenced by both factors and some significantly influenced by only time or distance. Thus, hippocampal neuronal networks captured both the organization of time and distance in a situation where these dimensions dominated an ongoing experience. PMID:23707613
Kleinert, H.; Zatloukal, V.
2013-11-01
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.
Path integral approach to electron scattering in classical electromagnetic potential
International Nuclear Information System (INIS)
Xu Chuang; Feng Feng; Li Ying-Jun
2016-01-01
As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential. (paper)
Nonperturbative time-convolutionless quantum master equation from the path integral approach
International Nuclear Information System (INIS)
Nan Guangjun; Shi Qiang; Shuai Zhigang
2009-01-01
The time-convolutionless quantum master equation is widely used to simulate reduced dynamics of a quantum system coupled to a bath. However, except for several special cases, applications of this equation are based on perturbative calculation of the dissipative tensor, and are limited to the weak system-bath coupling regime. In this paper, we derive an exact time-convolutionless quantum master equation from the path integral approach, which provides a new way to calculate the dissipative tensor nonperturbatively. Application of the new method is demonstrated in the case of an asymmetrical two-level system linearly coupled to a harmonic bath.
International Nuclear Information System (INIS)
Khrapko, R.I.
1985-01-01
A uniform description of various path-dependent functions is presented with the help of expansion of the type of the Taylor series. So called ''path-integrals'' and ''path-tensor'' are introduced which are systems of many-component quantities whose values are defined for arbitrary paths in coordinated region of space in such a way that they contain a complete information on the path. These constructions are considered as elementary path-dependent functions and are used instead of power monomials in the usual Taylor series. Coefficients of such an expansion are interpreted as partial derivatives dependent on the order of the differentiations or else as nonstandard cavariant derivatives called two-point derivatives. Some examples of pathdependent functions are presented.Space curvature tensor is considered whose geometrica properties are determined by the (non-transitive) translator of parallel transport of a general type. Covariant operation leading to the ''extension'' of tensor fiels is pointed out
Path optimization method for the sign problem
Directory of Open Access Journals (Sweden)
Ohnishi Akira
2018-01-01
Full Text Available We propose a path optimization method (POM to evade the sign problem in the Monte-Carlo calculations for complex actions. Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method are promising and extensively discussed. In these methods, real field variables are complexified and the integration manifold is determined by the flow equations or stochastically sampled. When we have singular points of the action or multiple critical points near the original integral surface, however, we have a risk to encounter the residual and global sign problems or the singular drift term problem. One of the ways to avoid the singular points is to optimize the integration path which is designed not to hit the singular points of the Boltzmann weight. By specifying the one-dimensional integration-path as z = t +if(t(f ϵ R and by optimizing f(t to enhance the average phase factor, we demonstrate that we can avoid the sign problem in a one-variable toy model for which the complex Langevin method is found to fail. In this proceedings, we propose POM and discuss how we can avoid the sign problem in a toy model. We also discuss the possibility to utilize the neural network to optimize the path.
International Nuclear Information System (INIS)
Song, Linze; Shi, Qiang
2015-01-01
We present a new non-perturbative method to calculate the charge carrier mobility using the imaginary time path integral approach, which is based on the Kubo formula for the conductivity, and a saddle point approximation to perform the analytic continuation. The new method is first tested using a benchmark calculation from the numerical exact hierarchical equations of motion method. Imaginary time path integral Monte Carlo simulations are then performed to explore the temperature dependence of charge carrier delocalization and mobility in organic molecular crystals (OMCs) within the Holstein and Holstein-Peierls models. The effects of nonlocal electron-phonon interaction on mobility in different charge transport regimes are also investigated
Energy Technology Data Exchange (ETDEWEB)
Gitman, D.M. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Kupriyanov, V.G. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Tomsk State University, Physics Department, Tomsk (Russian Federation)
2008-03-15
It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them {theta}-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing {theta}-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract {theta}-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as {theta}-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The {theta}-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case. (orig.)
International Nuclear Information System (INIS)
Exner, P.; Kolerov, G.I.
1980-01-01
A Hilbert space of paths, the elements of which are determined by trigonometric series, was proposed and used recently by Truman. This space is shown to consist precisely of all absolutely continuous paths ending in the origin with square-integrable derivatives
International Nuclear Information System (INIS)
Botelho, Luiz C.L.
1998-02-01
We study four dimensional Effective Bosonic Field Theories for massive fermion field in the infrared region and massive fermion in ultraviolet region by using an appropriate Fermion Path Integral Chiral variable change and the Polyakov's Fermi-Bose transmutation in the 3D-Abelian Thrirring model. (author)
Path integral quantization of the Aharonov-Bohm-Coulomb system in momentum space
International Nuclear Information System (INIS)
Lin, De-Hone
2001-01-01
The Coulomb system with a charge moving in the fields of Ahanorov and Bohm is quantized via path integral in momentum space. Due to the dynamics of the system in momentum space being in curve space, our result not only gives the Green function of this interesting system in momentum space but provides the second example to answer an open problem of quantum dynamics in curved spaces posed by DeWitt in 1957: We find that the physical Hamiltonian in curved spaces does not contain the Riemannian scalar curvature R
International Nuclear Information System (INIS)
Mak, C. H.
2009-01-01
A practical method to tackle the sign problem in real-time path integral simulations is proposed based on the multilevel blocking idea. The formulation is made possible by using a cumulant expansion of the action, which in addition to addressing the sign problem, provides an unbiased estimator for the action from a statistically noisy sample of real-time paths. The cumulant formulation also allows the analytical gradients of the action to be computed with little extra computational effort, and it can easily be implemented in a massively parallel environment.
Path-integral quantization of solitons using the zero-mode Feynman rule
International Nuclear Information System (INIS)
Sung Sheng Chang
1978-01-01
We propose a direct expansion treatment to quantize solitons without collective coordinates. Feynman's path integral for a free particle subject to an external force is directly used as the generating functional for the zero-frequency mode. The generating functional has no infrared singularity and defines a zero-mode Feynman rule which also gives a correct perturbative expansion for the harmonic-oscillator Green's function by treating the quadratic potential as a perturbation. We use the zero-mode Feynman rule to calculate the energy shift due to the second-order quantum corrections for solitons. Our result agrees with previous predictions using the collective-coordinate method or the method of Goldstone and Jackiw
Response of Non-Linear Systems to Renewal Impulses by Path Integration
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Iwankiewicz, R.
The cell-to-cell mapping (path integration) technique has been devised for MDOF non-linear and non-hysteretic systems subjected to random trains of impulses driven by an ordinary renewal point process with gamma-distributed integer parameter interarrival times (an Erlang process). Since the renewal...... point process has not independent increments the state vector of the system, consisting of the generalized displacements and velocities, is not a Markov process. Initially it is shown how the indicated systems can be converted to an equivalent Poisson driven system at the expense of introducing...... additional discrete-valued state variables for which the stochastic equations are also formulated....
Richter, Martin; Fingerhut, Benjamin P.
2017-06-01
The description of non-Markovian effects imposed by low frequency bath modes poses a persistent challenge for path integral based approaches like the iterative quasi-adiabatic propagator path integral (iQUAPI) method. We present a novel approximate method, termed mask assisted coarse graining of influence coefficients (MACGIC)-iQUAPI, that offers appealing computational savings due to substantial reduction of considered path segments for propagation. The method relies on an efficient path segment merging procedure via an intermediate coarse grained representation of Feynman-Vernon influence coefficients that exploits physical properties of system decoherence. The MACGIC-iQUAPI method allows us to access the regime of biological significant long-time bath memory on the order of hundred propagation time steps while retaining convergence to iQUAPI results. Numerical performance is demonstrated for a set of benchmark problems that cover bath assisted long range electron transfer, the transition from coherent to incoherent dynamics in a prototypical molecular dimer and excitation energy transfer in a 24-state model of the Fenna-Matthews-Olson trimer complex where in all cases excellent agreement with numerically exact reference data is obtained.
Koh, Yang Wei
2018-03-01
In current studies of mean-field quantum spin systems, much attention is placed on the calculation of the ground-state energy and the excitation gap, especially the latter, which plays an important role in quantum annealing. In pure systems, the finite gap can be obtained by various existing methods such as the Holstein-Primakoff transform, while the tunneling splitting at first-order phase transitions has also been studied in detail using instantons in many previous works. In disordered systems, however, it remains challenging to compute the gap of large-size systems with specific realization of disorder. Hitherto, only quantum Monte Carlo techniques are practical for such studies. Recently, Knysh [Nature Comm. 7, 12370 (2016), 10.1038/ncomms12370] proposed a method where the exponentially large dimensionality of such systems is condensed onto a random potential of much lower dimension, enabling efficient study of such systems. Here we propose a slightly different approach, building upon the method of static approximation of the partition function widely used for analyzing mean-field models. Quantum effects giving rise to the excitation gap and nonextensive corrections to the free energy are accounted for by incorporating dynamical paths into the path integral. The time-dependence of the trace of the time-ordered exponential of the effective Hamiltonian is calculated by solving a differential equation perturbatively, yielding a finite-size series expansion of the path integral. Formulae for the first excited-state energy are proposed to aid in computing the gap. We illustrate our approach using the infinite-range ferromagnetic Ising model and the Hopfield model, both in the presence of a transverse field.
Directory of Open Access Journals (Sweden)
Aristeidis Antonakis
2017-04-01
Full Text Available In this article, a new multi-objective approach to the aircraft climb path optimization problem, based on the Particle Swarm Optimization algorithm, is introduced to be used for aircraft–engine integration studies. This considers a combination of a simulation with a traditional Energy approach, which incorporates, among others, the use of a proposed path-tracking scheme for guidance in the Altitude–Mach plane. The adoption of population-based solver serves to simplify case setup, allowing for direct interfaces between the optimizer and aircraft/engine performance codes. A two-level optimization scheme is employed and is shown to improve search performance compared to the basic PSO algorithm. The effectiveness of the proposed methodology is demonstrated in a hypothetic engine upgrade scenario for the F-4 aircraft considering the replacement of the aircraft’s J79 engine with the EJ200; a clear advantage of the EJ200-equipped configuration is unveiled, resulting, on average, in 15% faster climbs with 20% less fuel.
International Nuclear Information System (INIS)
Mimura, Kazushi; Kawamura, Masaki; Okada, Masato
2004-01-01
An exact solution of the transient dynamics of an associative memory model storing an infinite number of limit cycles with l finite steps is shown by means of the path-integral analysis. Assuming the Maxwell construction ansatz, we have succeeded in deriving the stationary state equations of the order parameters from the macroscopic recursive equations with respect to the finite-step sequence processing model which has retarded self-interactions. We have also derived the stationary state equations by means of the signal-to-noise analysis (SCSNA). The signal-to-noise analysis must assume that crosstalk noise of an input to spins obeys a Gaussian distribution. On the other hand, the path-integral method does not require such a Gaussian approximation of crosstalk noise. We have found that both the signal-to-noise analysis and the path-integral analysis give completely the same result with respect to the stationary state in the case where the dynamics is deterministic, when we assume the Maxwell construction ansatz. We have shown the dependence of the storage capacity (α c ) on the number of patterns per one limit cycle (l). At l = 1, the storage capacity is α c = 0.138 as in the Hopfield model. The storage capacity monotonically increases with the number of steps, and converges to α c = 0.269 at l ≅ 10. The original properties of the finite-step sequence processing model appear as long as the number of steps of the limit cycle has order l = O(1)
Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?
Penney, Mark D.; Enshan Koh, Dax; Spekkens, Robert W.
2017-07-01
It is straightforward to compute the transition amplitudes of a quantum circuit using the sum-over-paths methodology when the gates in the circuit are balanced, where a balanced gate is one for which all non-zero transition amplitudes are of equal magnitude. Here we consider the question of whether, for such circuits, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action, as they are for continuous-time paths. We show how to do so for certain kinds of quantum circuits, namely, Clifford circuits where the elementary systems are continuous-variable systems or discrete systems of odd-prime dimension. These types of circuit are distinguished by having phase-space representations that serve to define their classical counterparts. For discrete systems, the phase-space coordinates are also discrete variables. We show that for each gate in the generating set, one can associate a symplectomorphism on the phase-space and to each of these one can associate a generating function, defined on two copies of the configuration space. For discrete systems, the latter association is achieved using tools from algebraic geometry. Finally, we show that if the action functional for a discrete-time path through a sequence of gates is defined using the sum of the corresponding generating functions, then it yields the correct relative phases for the path-sum expression. These results are likely to be relevant for quantizing physical theories where time is fundamentally discrete, characterizing the classical limit of discrete-time quantum dynamics, and proving complexity results for quantum circuits.
Mei-Zhi, Yuan; Jing-Ru, Sun; Tao, Chen; Xiao-Yu, Zhang; Liang-Cai, He; Jia-Song, Wang
2016-05-12
To evaluate the effect of the clinical nursing path integrated with the holistic nursing on advanced schistosomiasis patients with ascites. A total of 226 advanced schistosomiasis patients with ascites were randomly divided into a control group and an experimental group (113 cases each group). The subjects in the experimental group were nursed by the clinical nursing path integrated with the holistic nursing, while those in the control group were nursed only by the holistic nursing. Then the clinical relevant indexes of the two groups were observed, and the quality of life of the patients before and after hospital discharge was assessed. The improvement rate, satisfaction degree, and awareness rate of health knowledge of the patients in the experiment group were 93.8%, 100% and 97.4%, respectively, which were significantly higher than those of the control group (all P holistic nursing can effectively improve the improvement rate and decrease the mortality of the advanced schistosomiasis patients with ascites; meanwhile, it can shorten the hospitalization time and save the hospitalization cost. Therefore, this nursing model is suitable for popularization and application in the treatment and nursing work of the advanced schistosomiasis assistance.
Toward solving the sign problem with path optimization method
Mori, Yuto; Kashiwa, Kouji; Ohnishi, Akira
2017-12-01
We propose a new approach to circumvent the sign problem in which the integration path is optimized to control the sign problem. We give a trial function specifying the integration path in the complex plane and tune it to optimize the cost function which represents the seriousness of the sign problem. We call it the path optimization method. In this method, we do not need to solve the gradient flow required in the Lefschetz-thimble method and then the construction of the integration-path contour arrives at the optimization problem where several efficient methods can be applied. In a simple model with a serious sign problem, the path optimization method is demonstrated to work well; the residual sign problem is resolved and precise results can be obtained even in the region where the global sign problem is serious.
2012-06-06
...Notice is hereby given that the U.S. International Trade Commission has received a complaint entitled Certain Integrated Circuit Packages Provided With Multiple Heat-Conducting Paths and Products Containing Same, DN 2899; the Commission is soliciting comments on any public interest issues raised by the complaint or complainant's filing under section 210.8(b) of the Commission's Rules of Practice and Procedure (19 CFR 210.8(b)).
Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?
International Nuclear Information System (INIS)
Penney, Mark D; Koh, Dax Enshan; Spekkens, Robert W
2017-01-01
It is straightforward to compute the transition amplitudes of a quantum circuit using the sum-over-paths methodology when the gates in the circuit are balanced, where a balanced gate is one for which all non-zero transition amplitudes are of equal magnitude. Here we consider the question of whether, for such circuits, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action, as they are for continuous-time paths. We show how to do so for certain kinds of quantum circuits, namely, Clifford circuits where the elementary systems are continuous-variable systems or discrete systems of odd-prime dimension. These types of circuit are distinguished by having phase-space representations that serve to define their classical counterparts. For discrete systems, the phase-space coordinates are also discrete variables. We show that for each gate in the generating set, one can associate a symplectomorphism on the phase-space and to each of these one can associate a generating function, defined on two copies of the configuration space. For discrete systems, the latter association is achieved using tools from algebraic geometry. Finally, we show that if the action functional for a discrete-time path through a sequence of gates is defined using the sum of the corresponding generating functions, then it yields the correct relative phases for the path-sum expression. These results are likely to be relevant for quantizing physical theories where time is fundamentally discrete, characterizing the classical limit of discrete-time quantum dynamics, and proving complexity results for quantum circuits. (paper)
Path-integral Monte Carlo study of phonons in the bcc phase of Helium-3
Sorkin, V.; Polturak, E.; Adler, Joan
2006-01-01
Using Path Integral Monte Carlo and the Maximum Entropy method, we calculate the dynamic structure factor of solid He-3 in the bcc phase at a finite temperature of T = 1.6 K and a molar volume of 21.5 cm^3. From the single phonon dynamic structure factor, we obtain both the longitudinal and transverse phonon branches along the main crystalline directions, [001], [011] and [111]. Our results are compared with other theoretical predictions and available experimental data.
Thermal properties of graphene from path-integral simulations
Herrero, Carlos P.; Ramírez, Rafael
2018-03-01
Thermal properties of graphene monolayers are studied by path-integral molecular dynamics simulations, which take into account the quantization of vibrational modes in the crystalline membrane and allow one to consider anharmonic effects in these properties. This system was studied at temperatures in the range from 12 to 2000 K and zero external stress, by describing the interatomic interactions through the LCBOPII effective potential. We analyze the internal energy and specific heat and compare the results derived from the simulations with those yielded by a harmonic approximation for the vibrational modes. This approximation turns out to be rather precise up to temperatures of about 400 K. At higher temperatures, we observe an influence of the elastic energy due to the thermal expansion of the graphene sheet. Zero-point and thermal effects on the in-plane and "real" surface of graphene are discussed. The thermal expansion coefficient α of the real area is found to be positive at all temperatures, in contrast to the expansion coefficient αp of the in-plane area, which is negative at low temperatures and becomes positive for T ≳ 1000 K.
Miller, Melvin E., Ed.; Cook-Greuter, Susanne R., Ed.
This book contains 11 papers on creativity, spirituality, and transcendence as paths to integrity and wisdom in the mature self. The book begins with the paper "Introduction--Creativity in Adulthood: Personal Maturity and Openness to Extraordinary Sources of Inspiration" (Susanne R. Cook-Greuter, Melvin E. Miller). The next four papers,…
Improving the variational path integral approach to the quantum double-well potential
International Nuclear Information System (INIS)
Bao Jingdong; Wang Hongyu
2002-01-01
An improved variational path integral approach is developed and applied to the quantum double-well potential, in which part of the quartic term of the potential is included in the trial action. The expression of the effective classical potential (ECP) under a non-Gaussian expectation is obtained. Here the frequency and fourth-order derivative of the potential are treated as two variational parameters, determined by the minimization of the ECP at each point. We calculate the ECP, the free energy and the level splitting of a symmetrical double-well potential. It is shown that the present results are better than those of the Feynman-Kleinert Gaussian variational method. (author)
PathText: a text mining integrator for biological pathway visualizations
Kemper, Brian; Matsuzaki, Takuya; Matsuoka, Yukiko; Tsuruoka, Yoshimasa; Kitano, Hiroaki; Ananiadou, Sophia; Tsujii, Jun'ichi
2010-01-01
Motivation: Metabolic and signaling pathways are an increasingly important part of organizing knowledge in systems biology. They serve to integrate collective interpretations of facts scattered throughout literature. Biologists construct a pathway by reading a large number of articles and interpreting them as a consistent network, but most of the models constructed currently lack direct links to those articles. Biologists who want to check the original articles have to spend substantial amounts of time to collect relevant articles and identify the sections relevant to the pathway. Furthermore, with the scientific literature expanding by several thousand papers per week, keeping a model relevant requires a continuous curation effort. In this article, we present a system designed to integrate a pathway visualizer, text mining systems and annotation tools into a seamless environment. This will enable biologists to freely move between parts of a pathway and relevant sections of articles, as well as identify relevant papers from large text bases. The system, PathText, is developed by Systems Biology Institute, Okinawa Institute of Science and Technology, National Centre for Text Mining (University of Manchester) and the University of Tokyo, and is being used by groups of biologists from these locations. Contact: brian@monrovian.com. PMID:20529930
Ab initio path-integral molecular dynamics and the quantum nature of hydrogen bonds
International Nuclear Information System (INIS)
Feng Yexin; Chen Ji; Wang Enge; Li Xin-Zheng
2016-01-01
The hydrogen bond (HB) is an important type of intermolecular interaction, which is generally weak, ubiquitous, and essential to life on earth. The small mass of hydrogen means that many properties of HBs are quantum mechanical in nature. In recent years, because of the development of computer simulation methods and computational power, the influence of nuclear quantum effects (NQEs) on the structural and energetic properties of some hydrogen bonded systems has been intensively studied. Here, we present a review of these studies by focussing on the explanation of the principles underlying the simulation methods, i.e., the ab initio path-integral molecular dynamics. Its extension in combination with the thermodynamic integration method for the calculation of free energies will also be introduced. We use two examples to show how this influence of NQEs in realistic systems is simulated in practice. (topical review)
Singh, Upendra N.; Refaat, Tamer F.; Petros, Mulugeta
2017-01-01
The societal benefits of understanding climate change through identification of global carbon dioxide sources and sinks led to the desired NASA's active sensing of carbon dioxide emissions over nights, days, and seasons (ASCENDS) space-based missions of global carbon dioxide measurements. For more than 15 years, NASA Langley Research Center (LaRC) have developed several carbon dioxide active remote sensors using the differential absorption lidar (DIAL) technique operating at the two-micron wavelength. Currently, an airborne two-micron triple-pulse integrated path differential absorption (IPDA) lidar is under development. This IPDA lidar measures carbon dioxide as well as water vapor, the dominant interfering molecule on carbon dioxide remote sensing. Advancement of this triple-pulse IPDA lidar development is presented.
Diagrammatical methods within the path integral representation for quantum systems
International Nuclear Information System (INIS)
Alastuey, A
2014-01-01
The path integral representation has been successfully applied to the study of equilibrium properties of quantum systems for a long time. In particular, such a representation allowed Ginibre to prove the convergence of the low-fugacity expansions for systems with short-range interactions. First, I will show that the crucial trick underlying Ginibre's proof is the introduction of an equivalent classical system made with loops. Within the Feynman-Kac formula for the density matrix, such loops naturally emerge by collecting together the paths followed by particles exchanged in a given cyclic permutation. Two loops interact via an average of two- body genuine interactions between particles belonging to different loops, while the interactions between particles inside a given loop are accounted for in a loop fugacity. It turns out that the grand-partition function of the genuine quantum system exactly reduces to its classical counterpart for the gas of loops. The corresponding so-called magic formula can be combined with standard Mayer diagrammatics for the classical gas of loops. This provides low-density representations for the quantum correlations or thermodynamical functions, which are quite useful when collective effects must be taken into account properly. Indeed, resummations and or reorganizations of Mayer graphs can be performed by exploiting their remarkable topological and combinatorial properties, while statistical weights and bonds are purely c-numbers. The interest of that method will be illustrated through a brief description of its application to two long-standing problems, namely recombination in Coulomb systems and condensation in the interacting Bose gas.
Path-integral in collective variables and its application to nuclear and hadron physics
International Nuclear Information System (INIS)
Pervushin, V.N.; Rajnkhardt, Kh.; Ehbert, D.
1979-01-01
The application of functional integrals to describe collective degrees of freedom in different fields of physics is reviewed for the period since 1965. The application of path integrals to the schematic model of nuclear multiparticle systems with pairing and particle-hole forces permits to lay strict foundations under the so called theory of nuclear field, which hitherto was proved euristically. The Abel gauge theory of interacting massless quarks and vector gluons is described. In this model radiative corrections cause spontaneous dynamic breaking of the chiral γ 5 -invariance. The application of functional integration to two-dimensional quantum chromodynamics is also analyzed. It is shown that the local quark-gluon theory can be transformed in an infinite-component nonpolynomial field theory in terms of colourless bound states - mesons. A modified perturbation theory appears in the form of 1/Nsub(c)-expansion (Nsub(c) - number of quarks), that is formally is very akin to the 1/Ω-expansion (Ωdegeneracy of single-particle states) in the theory of nuclear field
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
Ivancevic, Vladimir G
2008-01-01
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...
A transformed path integral approach for solution of the Fokker-Planck equation
Subramaniam, Gnana M.; Vedula, Prakash
2017-10-01
A novel path integral (PI) based method for solution of the Fokker-Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.
International Nuclear Information System (INIS)
Liu, Jian; Zhang, Zhijun
2016-01-01
Path integral Liouville dynamics (PILD) is applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane). The dipole-derivative autocorrelation function is employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems
DiversePathsJ: diverse shortest paths for bioimage analysis.
Uhlmann, Virginie; Haubold, Carsten; Hamprecht, Fred A; Unser, Michael
2018-02-01
We introduce a formulation for the general task of finding diverse shortest paths between two end-points. Our approach is not linked to a specific biological problem and can be applied to a large variety of images thanks to its generic implementation as a user-friendly ImageJ/Fiji plugin. It relies on the introduction of additional layers in a Viterbi path graph, which requires slight modifications to the standard Viterbi algorithm rules. This layered graph construction allows for the specification of various constraints imposing diversity between solutions. The software allows obtaining a collection of diverse shortest paths under some user-defined constraints through a convenient and user-friendly interface. It can be used alone or be integrated into larger image analysis pipelines. http://bigwww.epfl.ch/algorithms/diversepathsj. michael.unser@epfl.ch or fred.hamprecht@iwr.uni-heidelberg.de. Supplementary data are available at Bioinformatics online. © The Author(s) 2017. Published by Oxford University Press.
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.
Polygonal-path approximation on the path spaces of quantum mechanical systems: extended Feynman maps
International Nuclear Information System (INIS)
Exner, R.; Kolerov, G.I.
1981-01-01
Various types of polygonal-path approximations appearing in the functional-integration theory are discussed. The uniform approximation is applied to extend the definition of the Feynman maps from our previous paper and to prove consistency of this extension. Relations of the extended Fsub(-i)-map to the Wiener integral are given. In particular, the basic theorem about the sequential Wiener integral by Cameron is improved [ru
Generation of a quantum integrable class of discrete-time or relativistic periodic Toda chains
International Nuclear Information System (INIS)
Kundu, Anjan
1994-01-01
A new integrable class of quantum models representing a family of different discrete-time or relativistic generalisations of the periodic Toda chain (TC), including that of a recently proposed classical model close to TC [Lett. Math. Phys. 29 (1993) 165] is presented. All such models are shown to be obtainable from a single ancestor model at different realisations of the underlying quantised algebra. As a consequence the 2x2 Lax operators and the associated quantum R-matrices for these models are easily derived ensuring their quantum integrability. It is shown that the functional Bethe ansatz developed for the quantum TC is trivially generalised to achieve separation of variables also for the present models. ((orig.))
Artoun, Ojenie; David-Rus, Diana; Emmett, Matthew; Fishman, Lou; Fital, Sandra; Hogan, Chad; Lim, Jisun; Lushi, Enkeleida; Marinov, Vesselin
2006-05-01
In this report we summarize an extension of Fourier analysis for the solution of the wave equation with a non-constant coefficient corresponding to an inhomogeneous medium. The underlying physics of the problem is exploited to link pseudodifferential operators and phase space path integrals to obtain a marching algorithm that incorporates the backward scattering into the evolution of the wave. This allows us to successfully apply single-sweep, one-way marching methods in inherently two-way environments, which was not achieved before through other methods for this problem.
Path-integral simulation of ice Ih: The effect of pressure
Herrero, Carlos P.; Ramírez, Rafael
2011-12-01
The effect of pressure on structural and thermodynamic properties of ice Ih has been studied by means of path-integral molecular dynamics simulations at temperatures between 50 and 300 K. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. Positive (compression) and negative (tension) pressures have been considered, which allowed us to approach the limits for the mechanical stability of this solid water phase. We have studied the pressure dependence of the crystal volume, bulk modulus, interatomic distances, atomic delocalization, and kinetic energy. The spinodal point at both negative and positive pressures is derived from the vanishing of the bulk modulus. For P300 K. At positive pressure the spinodal is associated with ice amorphization, and at low temperatures it is found to be between 1.1 and 1.3 GPa. Quantum nuclear effects cause a reduction of the metastability region of ice Ih.
Iterative quantum-classical path integral with dynamically consistent state hopping
Energy Technology Data Exchange (ETDEWEB)
Walters, Peter L.; Makri, Nancy [Department of Chemistry, University of Illinois, Urbana, Illinois 61801 (United States)
2016-01-28
We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort.
Directory of Open Access Journals (Sweden)
P.O. Judt
2015-10-01
Full Text Available In many engineering applications special requirements are directed to a material's fracture behavior and the prediction of crack paths. Especially if the material exhibits anisotropic elastic properties or fracture toughnesses, e.g. in textured or composite materials, the simulation of crack paths is challenging. Here, the application of path independent interaction integrals (I-integrals, J-, L- and M-integrals is beneficial for an accurate crack tip loading analysis. Numerical tools for the calculation of loading quantities using these path-invariant integrals are implemented into the commercial finite element (FE-code ABAQUS. Global approaches of the integrals are convenient considering crack tips approaching other crack faces, internal boundaries or material interfaces. Curved crack faces require special treatment with respect to integration contours. Numerical crack paths are predicted based on FE calculations of the boundary value problem in connection with an intelligent adaptive re-meshing algorithm. Considering fracture toughness anisotropy and accounting for inelastic effects due to small plastic zones in the crack tip region, the numerically predicted crack paths of different types of specimens with material interfaces and internal boundaries are compared to subcritically grown paths obtained from experiments.
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
Multi-rate path-following control for unmanned air vehicles
Guerreiro Tome Antunes, D.J.; Silvestre, C.J.; Cunha, R.
2008-01-01
A methodology is provided to tackle the path-following integrated guidance and control problem for unmanned air vehicles with measured outputs available at different rates. The path-following problem is addressed by defining a suitable non-linear path dependent error space to express the vehicle’s
Channel Capacity Calculation at Large SNR and Small Dispersion within Path-Integral Approach
Reznichenko, A. V.; Terekhov, I. S.
2018-04-01
We consider the optical fiber channel modelled by the nonlinear Shrödinger equation with additive white Gaussian noise. Using Feynman path-integral approach for the model with small dispersion we find the first nonzero corrections to the conditional probability density function and the channel capacity estimations at large signal-to-noise ratio. We demonstrate that the correction to the channel capacity in small dimensionless dispersion parameter is quadratic and positive therefore increasing the earlier calculated capacity for a nondispersive nonlinear optical fiber channel in the intermediate power region. Also for small dispersion case we find the analytical expressions for simple correlators of the output signals in our noisy channel.
Du, Juan; Liu, Jiqiao; Bi, Decang; Ma, Xiuhua; Hou, Xia; Zhu, Xiaolei; Chen, Weibiao
2018-04-01
A ground-based double-pulse 1572 nm integrated path differential absorption (IPDA) lidar was developed for carbon dioxide (CO2) column concentrations measurement. The lidar measured the CO2 concentrations continuously by receiving the scattered echo signal from a building about 1300 m away. The other two instruments of TDLAS and in-situ CO2 analyzer measured the CO2 concentrations on the same time. A CO2 concentration measurement of 430 ppm with 1.637 ppm standard error was achieved.
Energy Technology Data Exchange (ETDEWEB)
Geng, Yijia; Xu, Shuping; Xu, Weiqing, E-mail: xuwq@jlu.edu.cn [State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130012 (China); Chen, Lei [State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130012 (China); College of Physics, Jilin University, Changchun 130012 (China); Chen, Gang [State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130012 (China); College of Chemistry, Jilin University, Changchun 130012 (China); Bi, Wenbin [State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130012 (China); School of Chemistry and Environmental Engineering, Changchun University of Science and Technology, Changchun 130022 (China); Cui, Haining [College of Physics, Jilin University, Changchun 130012 (China)
2015-05-15
An integrated and portable Raman analyzer featuring an inverted probe fixed on a motor-driving adjustable optical module was designed for the combination of a microfluidic system. It possesses a micro-imaging function. The inverted configuration is advantageous to locate and focus microfluidic channels. Different from commercial micro-imaging Raman spectrometers using manual switchable light path, this analyzer adopts a dichroic beam splitter for both imaging and signal collection light paths, which avoids movable parts and improves the integration and stability of optics. Combined with surface-enhanced Raman scattering technique, this portable Raman micro-analyzer is promising as a powerful tool for microfluidic analytics.
Accelerating the convergence of path integral dynamics with a generalized Langevin equation
Ceriotti, Michele; Manolopoulos, David E.; Parrinello, Michele
2011-02-01
The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.
Accelerating the convergence of path integral dynamics with a generalized Langevin equation.
Ceriotti, Michele; Manolopoulos, David E; Parrinello, Michele
2011-02-28
The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.
Fragmentation function in non-equilibrium QCD using closed-time path integral formalism
International Nuclear Information System (INIS)
Nayak, Gouranga C.
2009-01-01
In this paper we implement the Schwinger-Keldysh closed-time path integral formalism in non-equilibrium QCD in accordance to the definition of the Collins-Soper fragmentation function. We consider a high-p T parton in QCD medium at initial time τ 0 with an arbitrary non-equilibrium (non-isotropic) distribution function f(vector (p)) fragmenting to a hadron. We formulate the parton-to-hadron fragmentation function in non-equilibrium QCD in the light-cone quantization formalism. It may be possible to include final-state interactions with the medium via a modification of the Wilson lines in this definition of the non-equilibrium fragmentation function. This may be relevant to the study of hadron production from a quark-gluon plasma at RHIC and LHC. (orig.)
A Path Space Extension for Robust Light Transport Simulation
DEFF Research Database (Denmark)
Hachisuka, Toshiya; Pantaleoni, Jacopo; Jensen, Henrik Wann
2012-01-01
We present a new sampling space for light transport paths that makes it possible to describe Monte Carlo path integration and photon density estimation in the same framework. A key contribution of our paper is the introduction of vertex perturbations, which extends the space of paths with loosely...
Parton degrees of freedom from the path-integral formalism
International Nuclear Information System (INIS)
Liu, Keh-Fei
2000-01-01
We formulate the hadronic tensor W μν of deep inelastic scattering in the path-integral formalism. It is shown that there are 3 gauge invariant and topologically distinct contributions. In addition to the valence contribution, there are two sources for the sea--one in the connected insertion and the other in the disconnected insertion. The operator product expansion is carried out in this formalism. The operator rescaling and mixing reveal that the connected sea partons evolve the same way as the valence; i.e., their evolution is decoupled from the disconnected sea and the gluon distribution functions. We explore the phenomenological consequences of this classification in terms of the small x behavior, Gottfried sum rule violation, and flavor dependence. In particular, we point out that in the nucleon u(bar sign) and d(bar sign) partons have both connected and disconnected sea contributions, whereas the s(bar sign) parton has only the disconnected sea contribution. This difference between u(bar sign)+d(bar sign) and s(bar sign), as far as we know, has not been taken into account in the fitting of parton distribution functions to experiments. (c) 2000 The American Physical Society
Path integral formulation and Feynman rules for phylogenetic branching models
Energy Technology Data Exchange (ETDEWEB)
Jarvis, P D; Bashford, J D; Sumner, J G [School of Mathematics and Physics, University of Tasmania, GPO Box 252C, 7001 Hobart, TAS (Australia)
2005-11-04
A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the number of taxa under consideration, and hence the rank of the underlying joint probability state tensor. We point out the combinatorial necessity for a second-quantized, or Fock space setting, incorporating discrete counting labels for taxa and character types, to allow for a description in the number basis. Rate operators describing both time evolution without branching, and also phylogenetic branching events, are identified. A detailed development of these ideas is given, using standard transcriptions from the microscopic formulation of non-equilibrium reaction-diffusion or birth-death processes. These give the relations between stochastic rate matrices, the matrix elements of the corresponding evolution operators representing them, and the integral kernels needed to implement these as path integrals. The 'free' theory (without branching) is solved, and the correct trilinear 'interaction' terms (representing branching events) are presented. The full model is developed in perturbation theory via the derivation of explicit Feynman rules which establish that the probabilities (pattern frequencies of leaf colourations) arising as matrix elements of the time evolution operator are identical with those computed via the standard analysis. Simple examples (phylogenetic trees with two or three leaves), are discussed in detail. Further implications for the work are briefly considered including the role of time reparametrization covariance.
Path integral formulation and Feynman rules for phylogenetic branching models
International Nuclear Information System (INIS)
Jarvis, P D; Bashford, J D; Sumner, J G
2005-01-01
A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the number of taxa under consideration, and hence the rank of the underlying joint probability state tensor. We point out the combinatorial necessity for a second-quantized, or Fock space setting, incorporating discrete counting labels for taxa and character types, to allow for a description in the number basis. Rate operators describing both time evolution without branching, and also phylogenetic branching events, are identified. A detailed development of these ideas is given, using standard transcriptions from the microscopic formulation of non-equilibrium reaction-diffusion or birth-death processes. These give the relations between stochastic rate matrices, the matrix elements of the corresponding evolution operators representing them, and the integral kernels needed to implement these as path integrals. The 'free' theory (without branching) is solved, and the correct trilinear 'interaction' terms (representing branching events) are presented. The full model is developed in perturbation theory via the derivation of explicit Feynman rules which establish that the probabilities (pattern frequencies of leaf colourations) arising as matrix elements of the time evolution operator are identical with those computed via the standard analysis. Simple examples (phylogenetic trees with two or three leaves), are discussed in detail. Further implications for the work are briefly considered including the role of time reparametrization covariance
International Nuclear Information System (INIS)
Bertschinger, E.
1987-01-01
Path integrals may be used to describe the statistical properties of a random field such as the primordial density perturbation field. In this framework the probability distribution is given for a Gaussian random field subjected to constraints such as the presence of a protovoid or supercluster at a specific location in the initial conditions. An algorithm has been constructed for generating samples of a constrained Gaussian random field on a lattice using Monte Carlo techniques. The method makes possible a systematic study of the density field around peaks or other constrained regions in the biased galaxy formation scenario, and it is effective for generating initial conditions for N-body simulations with rare objects in the computational volume. 21 references
Moments of inertia and the shapes of Brownian paths
International Nuclear Information System (INIS)
Fougere, F.; Desbois, J.
1993-01-01
The joint probability law of the principal moments of inertia of Brownian paths (open or closed) is computed, using constrained path integrals and Random Matrix Theory. The case of two-dimensional paths is discussed in detail. In particular, it is shown that the ratio of the average values of the largest and smallest moments is equal to 4.99 (open paths) and 3.07 (closed paths). Results of numerical simulations are also presented, which include investigation of the relationships between the moments of inertia and the arithmetic area enclosed by a path. (authors) 28 refs., 2 figs
Probabilistic simulation of fermion paths
International Nuclear Information System (INIS)
Zhirov, O.V.
1989-01-01
Permutation symmetry of fermion path integral allows (while spin degrees of freedom are ignored) to use in its simulation any probabilistic algorithm, like Metropolis one, heat bath, etc. 6 refs., 2 tabs
A fast spectrum dual path flow cermet reactor
International Nuclear Information System (INIS)
Anghaie, S.; Feller, G.J.; Peery, S.D.; Parsley, R.C.
1993-01-01
A cermet fueled, dual path fast reactor for space nuclear propulsion applications is conceptually designed. The reactor utilizes an outer annulus core and an inner cylindrical core with radial and axial reflector. The dual path flow minimizes the impact of power peaking near the radial reflector. Basic neutronics and core design aspects of the reactor are discussed. The dual path reactor is integrated into a 25000 lbf thrust nuclear rocket
Relations between the EU and Republic of Kosovo - The path of Kosovo integration towards the EU
Directory of Open Access Journals (Sweden)
Arif Riza
2016-07-01
Full Text Available Almost all the European Union member states have surpassed various challenges toward their integration into the European family. Although all these challenges are special cases on their own, Kosovo’s journey differs from the above mentioned cases, because Kosovo has not been recognized as an independent state by some members of the European family. The other key element that differs Kosovo’s journey from other cases is the presence of international institutions such as: EULEX, ICO, UNMIK, KFOR etc. in Kosovo’s territory. These organizations were not present in other member states of the European Union and other countries which aim for European integration. This manuscript aims to analyze the Kosovo challenges in its path towards the European family, which is only possible if Kosovo can create sustainable politics and cause fundamental changes in all fields, whether in public or private institutions, in order to build the rule of law. In general, this article will discuss the presence of international institutions in Kosovo such as: EULEX, ICO, UNMIK, KFOR and other international organizations, their effects on the rule of law, economic development and the sustainability of institutions. Moreover, this paper will particularly analyze the influence of the above mentioned factors to ease Kosovo’s path, as an observed country, compared to other countries in the region.
Bats Use Path Integration Rather Than Acoustic Flow to Assess Flight Distance along Flyways.
Aharon, Gal; Sadot, Meshi; Yovel, Yossi
2017-12-04
Navigation can be achieved using different strategies from simple beaconing to complex map-based movement [1-4]. Bats display remarkable navigation capabilities, ranging from nightly commutes of several kilometers and up to seasonal migrations over thousands of kilometers [5]. Many bats have been suggested to fly along fixed routes termed "flyways," when flying from their roost to their foraging sites [6]. Flyways commonly stretch along linear landscape elements such as tree lines, hedges, or rivers [7]. When flying along a flyway, bats must estimate the distance they have traveled in order to determine when to turn. This can be especially challenging when moving along a repetitive landscape. Some bats, like Kuhl's pipistrelles, which we studied here, have limited vision [8] and were suggested to rely on bio-sonar for navigation. These bats could therefore estimate distance using three main sensory-navigation strategies, all of which we have examined: acoustic flow, acoustic landmarks, or path integration. We trained bats to fly along a linear flyway and land on a platform. We then tested their behavior when the platform was removed under different manipulations, including changing the acoustic flow, moving the start point, and adding wind. We found that bats do not require acoustic flow, which was hypothesized to be important for their navigation [9-15], and that they can perform the task without landmarks. Our results suggest that Kuhl's pipistrelles use internal self-motion cues-also known as path integration-rather than external information to estimate flight distance for at least dozens of meters when navigating along linear flyways. Copyright © 2017 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Loredana Teresa Pedata
2012-12-01
Full Text Available The path and the pilot study presented here come from a synergy between a pharmaceutical, universities and institutions in the area. The intervention evaluation wants to establish itself as a means of "re-thinking" youth intervention benefited: the assumption that the integration of knowledge can constitute an enrichment of the whole person, we believe that such enrichment is more likely to occur in group in comparison with others and the development of social skills and human resources.
Path probabilities of continuous time random walks
International Nuclear Information System (INIS)
Eule, Stephan; Friedrich, Rudolf
2014-01-01
Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman–Kac formulae. (paper)
Optimal multigrid algorithms for the massive Gaussian model and path integrals
International Nuclear Information System (INIS)
Brandt, A.; Galun, M.
1996-01-01
Multigrid algorithms are presented which, in addition to eliminating the critical slowing down, can also eliminate the open-quotes volume factorclose quotes. The elimination of the volume factor removes the need to produce many independent fine-grid configurations for averaging out their statistical deviations, by averaging over the many samples produced on coarse grids during the multigrid cycle. Thermodynamic limits of observables can be calculated to relative accuracy var-epsilon r in just O(var-epsilon r -2 ) computer operations, where var-epsilon r is the error relative to the standard deviation of the observable. In this paper, we describe in detail the calculation of the susceptibility in the one-dimensional massive Gaussian model, which is also a simple example of path integrals. Numerical experiments show that the susceptibility can be calculated to relative accuracy var-epsilon r in about 8 var-epsilon r -2 random number generations, independent of the mass size
Path integral measure and triangulation independence in discrete gravity
Dittrich, Bianca; Steinhaus, Sebastian
2012-02-01
A path integral measure for gravity should also preserve the fundamental symmetry of general relativity, which is diffeomorphism symmetry. In previous work, we argued that a successful implementation of this symmetry into discrete quantum gravity models would imply discretization independence. We therefore consider the requirement of triangulation independence for the measure in (linearized) Regge calculus, which is a discrete model for quantum gravity, appearing in the semi-classical limit of spin foam models. To this end we develop a technique to evaluate the linearized Regge action associated to Pachner moves in 3D and 4D and show that it has a simple, factorized structure. We succeed in finding a local measure for 3D (linearized) Regge calculus that leads to triangulation independence. This measure factor coincides with the asymptotics of the Ponzano Regge Model, a 3D spin foam model for gravity. We furthermore discuss to which extent one can find a triangulation independent measure for 4D Regge calculus and how such a measure would be related to a quantum model for 4D flat space. To this end, we also determine the dependence of classical Regge calculus on the choice of triangulation in 3D and 4D.
Propagation Effects in Space/Earth Paths.
1980-08-01
0 h In both integrals ds is a differential of curved ray path and includes refractive bending. In either integral, the factor aTar is, by the Rayleigh...interference. Ionospheric modification may also result from the emission of exhaust effluents from HLLV’s. The associated changes in ionospherio chemistry can
Energy Technology Data Exchange (ETDEWEB)
Yearsley, James M [Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom)
2008-07-18
We present a derivation of the propagator for a particle in the presence of the step and delta function potentials. These propagators are known, but we present a direct path integral derivation, based on the path decomposition expansion and the Brownian motion definition of the path integral. The derivation exploits properties of the Catalan numbers, which enumerate certain classes of lattice paths.
Lerner, Vladimir S.
2012-01-01
The impulses, cutting entropy functional (EF) measure on trajectories Markov diffusion process, integrate information path functional (IPF) composing discrete information Bits extracted from observing random process. Each cut brings memory of the cutting entropy, which provides both reduction of the process entropy and discrete unit of the cutting entropy a Bit. Consequently, information is memorized entropy cutting in random observations which process interactions. The origin of information ...
Fishman, Louis
2000-11-01
The role of mathematical modeling in the physical sciences will be briefly addressed. Examples will focus on computational acoustics, with applications to underwater sound propagation, electromagnetic modeling, optics, and seismic inversion. Direct and inverse wave propagation problems in both the time and frequency domains will be considered. Focusing on fixed-frequency (elliptic) wave propagation problems, the usual, two-way, partial differential equation formulation will be exactly reformulated, in a well-posed manner, as a one-way (marching) problem. This is advantageous for both direct and inverse considerations, as well as stochastic modeling problems. The reformulation will require the introduction of pseudodifferential operators and their accompanying phase space analysis (calculus), in addition to path integral representations for the fundamental solutions and their subsequent computational algorithms. Unlike the more traditional, purely numerical applications of, for example, finite-difference and finite-element methods, this approach, in effect, writes the exact, or, more generally, the asymptotically correct, answer as a functional integral and, subsequently, computes it directly. The overall computational philosophy is to combine analysis, asymptotics, and numerical methods to attack complicated, real-world problems. Exact and asymptotic analysis will stress the complementary nature of the direct and inverse formulations, as well as indicating the explicit structural connections between the time- and frequency-domain solutions.
Piloting and Path Integration within and across Boundaries
Mou, Weimin; Wang, Lin
2015-01-01
Three experiments investigated whether navigation is less efficient across boundaries than within boundaries. In an immersive virtual environment, participants learned objects' locations in a large room or a small room. Participants then pointed to the objects' original locations after physically walking a circuitous path without vision.…
An UML Statechart Diagram-Based MM-Path Generation Approach for Object-Oriented Integration Testing
Ruilian Zhao; Ling Lin
2008-01-01
MM-Path, an acronym for Method/Message Path, describes the dynamic interactions between methods in object-oriented systems. This paper discusses the classifications of MM-Path, based on the characteristics of object-oriented software. We categorize it according to the generation reasons, the effect scope and the composition of MM-Path. A formalized representation of MM-Path is also proposed, which has considered the influence of state on response method sequences of messages. .Moreover, an au...
Energy Technology Data Exchange (ETDEWEB)
Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Pogosyan, G.S. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics]|[Guadalajara Univ., Jalisco (Mexico). Dept. de Matematicas CUCEI; Sissakian, A.N. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics
2006-08-15
This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze in the spaces D{sub III} and D{sub IV} five respectively four superintegrable potentials, which were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is determined by a higher order polynomial equation. We show that also the free motion in Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We state the energy spectrum and the wave-functions, respectively. (orig.)
A path-following driver/vehicle model with optimized lateral dynamic controller
Directory of Open Access Journals (Sweden)
Behrooz Mashadi
Full Text Available Reduction in traffic congestion and overall number of accidents, especially within the last decade, can be attributed to the enormous progress in active safety. Vehicle path following control with the presence of driver commands can be regarded as one of the important issues in vehicle active safety systems development and more realistic explanation of vehicle path tracking problem. In this paper, an integrated driver/DYC control system is presented that regulates the steering angle and yaw moment, considering driver previewed path. Thus, the driver previewed distance, the heading error and the lateral deviation between the vehicle and desired path are used as inputs. Then, the controller determines and applies a corrective steering angle and a direct yaw moment to make the vehicle follow the desired path. A PID controller with optimized gains is used for the control of integrated driver/DYC system. Genetic Algorithm as an intelligent optimization method is utilized to adapt PID controller gains for various working situations. Proposed integrated driver/DYC controller is examined on lane change manuvers andthe sensitivity of the control system is investigated through the changes in the driver model and vehicle parameters. Simulation results show the pronounced effectiveness of the controller in vehicle path following and stability.
Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics
International Nuclear Information System (INIS)
Everett, Allen
2004-01-01
We consider two approaches to evading paradoxes in quantum mechanics with closed timelike curves. In a model similar to Politzer's, assuming pure states and using path integrals, we show that the problems of paradoxes and of unitarity violation are related; preserving unitarity avoids paradoxes by modifying the time evolution so that improbable events become certain. Deutsch has argued, using the density matrix, that paradoxes do not occur in the 'many worlds interpretation'. We find that in this approach account must be taken of the resolution time of the device that detects objects emerging from a wormhole or other time machine. When this is done one finds that this approach is viable only if macroscopic objects traversing a wormhole interact with it so strongly that they are broken into microscopic fragments
International Nuclear Information System (INIS)
Mieck, B.
2007-01-01
We consider bosonic atoms with a repulsive contact interaction in a trap potential for a Bose-Einstein condensation (BEC) and additionally include a random potential. The ensemble averages for two models of static (I) and dynamic (II) disorder are performed and investigated in parallel. The bosonic many body systems of the two disorder models are represented by coherent state path integrals on the Keldysh time contour which allow exact ensemble averages for zero and finite temperatures. These ensemble averages of coherent state path integrals therefore present alternatives to replica field theories or super-symmetric averaging techniques. Hubbard-Stratonovich transformations (HST) lead to two corresponding self-energies for the hermitian repulsive interaction and for the non-hermitian disorder-interaction. The self-energy of the repulsive interaction is absorbed by a shift into the disorder-self-energy which comprises as an element of a larger symplectic Lie algebra sp(4M) the self-energy of the repulsive interaction as a subalgebra (which is equivalent to the direct product of M x sp(2); 'M' is the number of discrete time intervals of the disorder-self-energy in the generating function). After removal of the remaining Gaussian integral for the self-energy of the repulsive interaction, the first order variations of the coherent state path integrals result in the exact mean field or saddle point equations, solely depending on the disorder-self-energy matrix. These equations can be solved by continued fractions and are reminiscent to the 'Nambu-Gorkov' Green function formalism in superconductivity because anomalous terms or pair condensates of the bosonic atoms are also included into the selfenergies. The derived mean field equations of the models with static (I) and dynamic (II) disorder are particularly applicable for BEC in d=3 spatial dimensions because of the singularity of the density of states at vanishing wavevector. However, one usually starts out from
Poltavsky, Igor; DiStasio, Robert A.; Tkatchenko, Alexandre
2018-03-01
Nuclear quantum effects (NQE), which include both zero-point motion and tunneling, exhibit quite an impressive range of influence over the equilibrium and dynamical properties of molecules and materials. In this work, we extend our recently proposed perturbed path-integral (PPI) approach for modeling NQE in molecular systems [I. Poltavsky and A. Tkatchenko, Chem. Sci. 7, 1368 (2016)], which successfully combines the advantages of thermodynamic perturbation theory with path-integral molecular dynamics (PIMD), in a number of important directions. First, we demonstrate the accuracy, performance, and general applicability of the PPI approach to both molecules and extended (condensed-phase) materials. Second, we derive a series of estimators within the PPI approach to enable calculations of structural properties such as radial distribution functions (RDFs) that exhibit rapid convergence with respect to the number of beads in the PIMD simulation. Finally, we introduce an effective nuclear temperature formalism within the framework of the PPI approach and demonstrate that such effective temperatures can be an extremely useful tool in quantitatively estimating the "quantumness" associated with different degrees of freedom in the system as well as providing a reliable quantitative assessment of the convergence of PIMD simulations. Since the PPI approach only requires the use of standard second-order imaginary-time PIMD simulations, these developments enable one to include a treatment of NQE in equilibrium thermodynamic properties (such as energies, heat capacities, and RDFs) with the accuracy of higher-order methods but at a fraction of the computational cost, thereby enabling first-principles modeling that simultaneously accounts for the quantum mechanical nature of both electrons and nuclei in large-scale molecules and materials.
A NEW APPROACH ON SHORTEST PATH IN FUZZY ENVIRONMENT
A. Nagoorgani; A. Mumtaj Begam
2010-01-01
This paper introduces a new type of fuzzy shortest path network problem using triangular fuzzy number. To find the smallest edge by the fuzzy distance using graded mean integration representation of generalized fuzzy number for every node. Thus the optimum shortest path for the given problem is obtained.
Eigenstates and dynamics of Hooke's atom: Exact results and path integral simulations
Gholizadehkalkhoran, Hossein; Ruokosenmäki, Ilkka; Rantala, Tapio T.
2018-05-01
The system of two interacting electrons in one-dimensional harmonic potential or Hooke's atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the "space splitting" arising from the one-dimensional Coulomb potential. Here, we complete the numerous previous studies of the ground state of Hooke's atom by including the excited states and dynamics, not considered earlier. With the perturbation theory, we reach essentially exact eigenstate energies and wave functions for the strong confinement regime as novel results. We also consider external perturbation induced quantum dynamics in a simple separable case. Finally, we test our novel numerical approach based on real-time path integrals (RTPIs) in reproducing the above. The RTPI turns out to be a straightforward approach with exact account of electronic correlations for solving the eigenstates and dynamics without the conventional restrictions of electronic structure methods.
Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems.
Liu, Xinzijian; Liu, Jian
2018-03-14
An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD), Liu et al. [J. Chem. Phys. 145, 024103 (2016)] and Zhang et al. [J. Chem. Phys. 147, 034109 (2017)], for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Its application to several representative one-dimensional and multi-dimensional models demonstrates that MES-PIMD in principle offers a practical tool in either of the diabatic and adiabatic representations for studying exact quantum statistics of complex/large MES systems when the Born-Oppenheimer approximation, Condon approximation, and harmonic bath approximation are broken.
Wilson, Robert H.; Vishwanath, Karthik; Mycek, Mary-Ann
2009-02-01
Monte Carlo (MC) simulations are considered the "gold standard" for mathematical description of photon transport in tissue, but they can require large computation times. Therefore, it is important to develop simple and efficient methods for accelerating MC simulations, especially when a large "library" of related simulations is needed. A semi-analytical method involving MC simulations and a path-integral (PI) based scaling technique generated time-resolved reflectance curves from layered tissue models. First, a zero-absorption MC simulation was run for a tissue model with fixed scattering properties in each layer. Then, a closed-form expression for the average classical path of a photon in tissue was used to determine the percentage of time that the photon spent in each layer, to create a weighted Beer-Lambert factor to scale the time-resolved reflectance of the simulated zero-absorption tissue model. This method is a unique alternative to other scaling techniques in that it does not require the path length or number of collisions of each photon to be stored during the initial simulation. Effects of various layer thicknesses and absorption and scattering coefficients on the accuracy of the method will be discussed.
Nonadiabatic transition path sampling
International Nuclear Information System (INIS)
Sherman, M. C.; Corcelli, S. A.
2016-01-01
Fewest-switches surface hopping (FSSH) is combined with transition path sampling (TPS) to produce a new method called nonadiabatic path sampling (NAPS). The NAPS method is validated on a model electron transfer system coupled to a Langevin bath. Numerically exact rate constants are computed using the reactive flux (RF) method over a broad range of solvent frictions that span from the energy diffusion (low friction) regime to the spatial diffusion (high friction) regime. The NAPS method is shown to quantitatively reproduce the RF benchmark rate constants over the full range of solvent friction. Integrating FSSH within the TPS framework expands the applicability of both approaches and creates a new method that will be helpful in determining detailed mechanisms for nonadiabatic reactions in the condensed-phase.
Directory of Open Access Journals (Sweden)
Wagner Gerd
2016-01-01
Full Text Available Integrated path concentrations of ambient levels of carbon dioxide and methane have been measured during nighttime periods at NIST, Boulder (CO, USA, using a ground-based, eyesafe laser system. In this contribution, we describe the transmitter and receiver system, demonstrate measurements of CO2 and CH4 in comparison with an in situ point sensor measurement using a commercial cavity ring-down instrument, and demonstrate a speckle noise reduction method.
Kinetic energy of solid and liquid para-hydrogen: a path integral Monte Carlo simulation
International Nuclear Information System (INIS)
Zoppi, M.; Neumann, M.
1992-01-01
The translational (center of mass) kinetic energy of solid and liquid para-hydrogen have been recently measured by means of Deep Inelastic Neutron Scattering. We have evaluated the same quantity, in similar thermodynamic conditions, by means of Path Integral Monte Carlo computer simulation, modelling the system as composed of a set of spherical molecules interacting through a pairwise additive Lennard-Jones potential. In spite of the crude approximations on the interaction potential, the agreement is excellent. The pressure was also computed by means of the same simulations. This quantity, compared with the equation of state for solid para-hydrogen given by Driessen and Silvera, gives an agreement of a lesser quality and a negative value for the liquid state. We attribute this discrepancy to the limitations of the Lennard-Jones potential. (orig.)
Polymer escape from a metastable Kramers potential: path integral hyperdynamics study.
Shin, Jaeoh; Ikonen, Timo; Khandkar, Mahendra D; Ala-Nissila, Tapio; Sung, Wokyung
2010-11-14
We study the dynamics of flexible, semiflexible, and self-avoiding polymer chains moving under a Kramers metastable potential. Due to thermal noise, the polymers, initially placed in the metastable well, can cross the potential barrier, but these events are extremely rare if the barrier is much larger than thermal energy. To speed up the slow rate processes in computer simulations, we extend the recently proposed path integral hyperdynamics method to the cases of polymers. We consider the cases where the polymers' radii of gyration are comparable to the distance between the well bottom and the barrier top. We find that, for a flexible polymers, the crossing rate (R) monotonically decreases with chain contour length (L), but with the magnitude much larger than the Kramers rate in the globular limit. For a semiflexible polymer, the crossing rate decreases with L but becomes nearly constant for large L. For a fixed L, the crossing rate becomes maximum at an intermediate bending stiffness. For the self-avoiding chain, the rate is a nonmonotonic function of L, first decreasing with L, and then, above a certain length, increasing with L. These findings can be instrumental for efficient separation of biopolymers.
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Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Pogosyan, G.S. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics]|[Guadalajara Univ., Jalisco (Mexico). Dept. de Matematicas CUCEI; Sissakian, A.N. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics
2006-07-15
In this paper the Feynman path integral technique is applied for superintegrable potentials on two-dimensional spaces of non-constant curvature: these spaces are Darboux spaces D{sub I} and D{sub II}, respectively. On D{sub I} there are three and on D{sub II} foru such potentials, respectively. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is either determined by a transcendental equation involving parabolic cylinder functions (Darboux space I), or by a higher order polynomial equation. The solutions on D{sub I} in particular show that superintegrable systems are not necessarily degenerate. We can also show how the limiting cases of flat space (Constant curvature zero) and the two-dimensional hyperboloid (constant negative curvature) emerge. (Orig.)
International Nuclear Information System (INIS)
Mieck, B.
2007-01-01
A super-symmetric coherent state path integral on the Keldysh time contour is considered for bosonic and fermionic atoms which interact among each other with a common short-ranged two-body potential. We investigate the symmetries of Bose-Einstein condensation for the equivalent bosonic and fermionic constituents with the same interaction potential so that a super-symmetry results between the bosonic and fermionic components of super-fields. Apart from the super-unitary invariance U(L vertical stroke S) of the density terms, we specialize on the examination of super-symmetries for pair condensate terms. Effective equations are derived for anomalous terms which are related to the molecular- and BCS- condensate pairs. A Hubbard-Stratonovich transformation from 'Nambu'-doubled super-fields leads to a generating function with super-matrices for the self-energy whose manifold is given by the orthosympletic super-group Osp(S,S vertical stroke 2L). A nonlinear sigma model follows from the spontaneous breaking of the ortho-symplectic super-group Osp(S,S vertical stroke 2L) to the coset decomposition Osp(S,S vertical stroke 2L) backslash U(L vertical stroke S) x U(L vertical stroke S). The invariant subgroup U(L vertical stroke S) for the vacuum or background fields is represented by the density terms in the self-energy whereas the super-matrices on the coset space Osp(S,S vertical stroke 2L) backslash U(L vertical stroke S) describe the anomalous molecular and BCS-pair condensate terms. A change of integration measure is performed for the coset decomposition Osp(S,S vertical stroke 2L) backslash U(L vertical stroke S) x U(L vertical stroke S), including a separation of density and anomalous parts of the self-energy with a gradient expansion for the Goldstone modes. The independent anomalous fields in the actions can be transformed by the inverse square root G Osp backslash U -1/2 of the metric tensor of Osp(S,S vertical stroke 2L) backslash U(L vertical stroke S) so that
Energy Technology Data Exchange (ETDEWEB)
Mieck, B. [Department of Physics in Duisburg, University Duisburg-Essen, Lotharstrasse 1, 47048 Duisburg (Germany)
2007-09-15
A super-symmetric coherent state path integral on the Keldysh time contour is considered for bosonic and fermionic atoms which interact among each other with a common short-ranged two-body potential. We investigate the symmetries of Bose-Einstein condensation for the equivalent bosonic and fermionic constituents with the same interaction potential so that a super-symmetry results between the bosonic and fermionic components of super-fields. Apart from the super-unitary invariance U(L vertical stroke S) of the density terms, we specialize on the examination of super-symmetries for pair condensate terms. Effective equations are derived for anomalous terms which are related to the molecular- and BCS- condensate pairs. A Hubbard-Stratonovich transformation from 'Nambu'-doubled super-fields leads to a generating function with super-matrices for the self-energy whose manifold is given by the orthosympletic super-group Osp(S,S vertical stroke 2L). A nonlinear sigma model follows from the spontaneous breaking of the ortho-symplectic super-group Osp(S,S vertical stroke 2L) to the coset decomposition Osp(S,S vertical stroke 2L) backslash U(L vertical stroke S) x U(L vertical stroke S). The invariant subgroup U(L vertical stroke S) for the vacuum or background fields is represented by the density terms in the self-energy whereas the super-matrices on the coset space Osp(S,S vertical stroke 2L) backslash U(L vertical stroke S) describe the anomalous molecular and BCS-pair condensate terms. A change of integration measure is performed for the coset decomposition Osp(S,S vertical stroke 2L) backslash U(L vertical stroke S) x U(L vertical stroke S), including a separation of density and anomalous parts of the self-energy with a gradient expansion for the Goldstone modes. The independent anomalous fields in the actions can be transformed by the inverse square root G{sub Osp} {sub backslash} {sub U}{sup -1/2} of the metric tensor of Osp(S,S vertical stroke 2L) backslash U
Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics
Tao, Xuecheng; Shushkov, Philip; Miller, Thomas F.
2018-03-01
We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.
International Nuclear Information System (INIS)
Huo, Pengfei; Miller, Thomas F. III; Coker, David F.
2013-01-01
A partial linearized path integral approach is used to calculate the condensed phase electron transfer (ET) rate by directly evaluating the flux-flux/flux-side quantum time correlation functions. We demonstrate for a simple ET model that this approach can reliably capture the transition between non-adiabatic and adiabatic regimes as the electronic coupling is varied, while other commonly used semi-classical methods are less accurate over the broad range of electronic couplings considered. Further, we show that the approach reliably recovers the Marcus turnover as a function of thermodynamic driving force, giving highly accurate rates over four orders of magnitude from the normal to the inverted regimes. We also demonstrate that the approach yields accurate rate estimates over five orders of magnitude of inverse temperature. Finally, the approach outlined here accurately captures the electronic coherence in the flux-flux correlation function that is responsible for the decreased rate in the inverted regime
Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer F.; Remus, Ruben G.; Fay, James J.; Reithmaier, Karl
2014-01-01
Double-pulse 2-micron lasers have been demonstrated with energy as high as 600 millijouls and up to 10 Hz repetition rate. The two laser pulses are separated by 200 microseconds and can be tuned and locked separately. Applying double-pulse laser in DIAL system enhances the CO2 measurement capability by increasing the overlap of the sampled volume between the on-line and off-line. To avoid detection complicity, integrated path differential absorption (IPDA) lidar provides higher signal-to-noise ratio measurement compared to conventional range-resolved DIAL. Rather than weak atmospheric scattering returns, IPDA rely on the much stronger hard target returns that is best suited for airborne platforms. In addition, the IPDA technique measures the total integrated column content from the instrument to the hard target but with weighting that can be tuned by the transmitter. Therefore, the transmitter could be tuned to weight the column measurement to the surface for optimum CO2 interaction studies or up to the free troposphere for optimum transport studies. Currently, NASA LaRC is developing and integrating a double-Pulsed 2-micron direct detection IPDA lidar for CO2 column measurement from an airborne platform. The presentation will describe the development of the 2-micron IPDA lidar system and present the airborne measurement of column CO2 and will compare to in-situ measurement for various ground target of different reflectivity.
Hard paths, soft paths or no paths? Cross-cultural perceptions of water solutions
Wutich, A.; White, A. C.; White, D. D.; Larson, K. L.; Brewis, A.; Roberts, C.
2014-01-01
In this study, we examine how development status and water scarcity shape people's perceptions of "hard path" and "soft path" water solutions. Based on ethnographic research conducted in four semi-rural/peri-urban sites (in Bolivia, Fiji, New Zealand, and the US), we use content analysis to conduct statistical and thematic comparisons of interview data. Our results indicate clear differences associated with development status and, to a lesser extent, water scarcity. People in the two less developed sites were more likely to suggest hard path solutions, less likely to suggest soft path solutions, and more likely to see no path to solutions than people in the more developed sites. Thematically, people in the two less developed sites envisioned solutions that involve small-scale water infrastructure and decentralized, community-based solutions, while people in the more developed sites envisioned solutions that involve large-scale infrastructure and centralized, regulatory water solutions. People in the two water-scarce sites were less likely to suggest soft path solutions and more likely to see no path to solutions (but no more likely to suggest hard path solutions) than people in the water-rich sites. Thematically, people in the two water-rich sites seemed to perceive a wider array of unrealized potential soft path solutions than those in the water-scarce sites. On balance, our findings are encouraging in that they indicate that people are receptive to soft path solutions in a range of sites, even those with limited financial or water resources. Our research points to the need for more studies that investigate the social feasibility of soft path water solutions, particularly in sites with significant financial and natural resource constraints.
International Nuclear Information System (INIS)
Hasselmann, K.; Hasselmann, S.; Giering, R.; Ocana, V.; Storch, H. von
1997-01-01
A structurally highly simplified, globally integrated coupled climate-economic costs model SIAM (Structural Integrated Assessment Model) is used to compute optimal paths of global CO 2 emissions that minimize the net sum of climate damage and mitigation costs. It studies the sensitivity of the computed optimal emission paths. The climate module is represented by a linearized impulse-response model calibrated against a coupled ocean-atmosphere general circulation climate model and a three-dimensional global carbon-cycle model. The cost terms are presented by expressions designed with respect to input assumptions. These include the discount rates for mitigation and damage costs, the inertia of the socio-economic system, and the dependence of climate damages on the changes in temperature and the rate of change of temperature. Different assumptions regarding these parameters are believed to cause the marked divergences of existing cost-benefit analyses. The long memory of the climate system implies that very long time horizons of several hundred years need to be considered to optimize CO 2 emissions on time scales relevant for a policy of sustainable development. Cost-benefit analyses over shorter time scales of a century or two can lead to dangerous underestimates of the long term climate impact of increasing greenhouse-gas emissions. To avert a major long term global warming, CO 2 emissions need to be reduced ultimately to very low levels. This may be done slowly but should not be interpreted as providing a time cushion for inaction: the transition becomes more costly the longer the necessary mitigation policies are delayed. However, the long time horizon provides adequate flexibility for later adjustments. Short term energy conservation alone is insufficient and can be viewed only as a useful measure in support of the necessary long term transition to carbon-free energy technologies. 46 refs., 9 figs., 2 tabs
Path coupling and aggregate path coupling
Kovchegov, Yevgeniy
2018-01-01
This book describes and characterizes an extension to the classical path coupling method applied to statistical mechanical models, referred to as aggregate path coupling. In conjunction with large deviations estimates, the aggregate path coupling method is used to prove rapid mixing of Glauber dynamics for a large class of statistical mechanical models, including models that exhibit discontinuous phase transitions which have traditionally been more difficult to analyze rigorously. The book shows how the parameter regions for rapid mixing for several classes of statistical mechanical models are derived using the aggregate path coupling method.
Path Creation, Path Dependence and Breaking Away from the Path
Wang, Jens; Hedman, Jonas; Tuunainen, Virpi Kristiina
2016-01-01
The explanation of how and why firms succeed or fail is a recurrent research challenge. This is particularly important in the context of technological innovations. We focus on the role of historical events and decisions in explaining such success and failure. Using a case study of Nokia, we develop and extend a multi-layer path dependence framework. We identify four layers of path dependence: technical, strategic and leadership, organizational, and external collaboration. We show how path dep...
Path-integral theory of the scattering of 4He atoms at the surface of liquid 4He
International Nuclear Information System (INIS)
Swanson, D.R.; Edwards, D.O.
1988-01-01
The path-integral theory of the scattering of a 4 He atom near the free surface of liquid 4 He, which was originally formulated by Echenique and Pendry, has been recalculated with use of a physically realistic static potential and atom-ripplon interaction outside the liquid. The static potential and atom-ripplon interaction are based on the variational calculation of Edwards and Fatouros. An important assumption in the path-integral theory is the ''impulse approximation'': that the motion of the scattered atom is very fast compared with the motion of the surface due to ripplons. This is found to be true only for ripplons with wave vectors smaller than q/sub m/∼0.2 A/sup -1/. If ripplons above q/sub m/ made an important contribution to the scattering of the atom there would be a substantial dependence of the elastic reflection coefficient on the angle of incidence of the atom. Since this is not observed experimentally, it is argued that ripplons above q/sub m/ give a negligible effect and should be excluded from the calculation. With this modification the theory gives a good fit to the experimental reflection coefficient as a function of the momentum and angle of incidence of the atom. The new version of the theory indicates that there is a substantial probability that an atom may reach the surface of the liquid without exciting any ripplons. The theory is not valid when the atom enters the liquid but analysis of the experiments shows that, once inside the liquid, the atom has a negligible chance of being scattered out again
Singh, U. N.; Petros, M.; Refaat, T. F.; Yu, J.; Ismail, S.
2017-09-01
The 2-micron wavelength region is suitable for atmospheric carbon dioxide (CO2) measurements due to the existence of distinct absorption features for the gas at this wavelength region [1]. For more than 20 years, researchers at NASA Langley Research Center (LaRC) have developed several high-energy and high repetition rate 2-micron pulsed lasers [2]. Currently, LaRC team is engaged in designing, developing and demonstrating a triple-pulsed 2-micron direct detection Integrated Path Differential Absorption (IPDA) lidar to measure the weighted-average column dry-air mixing ratios of carbon dioxide (XCO2) and water vapor (XH2O) from an airborne platform [1, 3-5]. This novel technique allows measurement of the two most dominant greenhouse gases, simultaneously and independently, using a single instrument. This paper will provide status and details of the development of this airborne 2-micron triple-pulse IPDA lidar. The presented work will focus on the advancement of critical IPDA lidar components. Updates on the state-of-the-art triple-pulse laser transmitter will be presented including the status of seed laser locking, wavelength control, receiver and detector upgrades, laser packaging and lidar integration. Future plans for IPDA lidar ground integration, testing and flight validation will also be discussed. This work enables new Earth observation measurements, while reducing risk, cost, size, volume, mass and development time of required instruments.
International Nuclear Information System (INIS)
Koinov, Z.G.; Yanchev, I.Y.
1981-09-01
The density of states in heavily doped strongly compansated semiconductors in a strong magnetic field is calculated by using the path-integral method. The case is considered when correlation exists in the impurity positions owing to the Coulomb interactions between the charged donors and acceptors during the high-temperature preparation of the samples. The semiclassical formula is rederived and corrections to it due to the long-range character of the potential and its short-range fluctuations are obtained. The density of states in the tail is studied and analytical results are given in the classical and quantum cases. (author)
International Nuclear Information System (INIS)
Wirtz, R; Taylor, R.P.; Newbury, R.; Nicholls, J.T.; Tribe, W.R.; Simmons, M.Y.
1999-01-01
Full text: The conductance of a quasi one-dimensional channel defined by a split-gate quantum point contact (QPC) on the surface of a AlGaAs/GaAs heterostructure shows quantised steps at n(2e 2 /h) where n is an integer. This experimental result is due to the reduction of the number of current carrying one-dimensional subbands caused by narrowing the QPC. The theoretical explanation however does not take electron-electron interactions into account. Recently Thomas et al. discovered a new feature at non-integral value of n ∼ 0.7 in very low-disorder samples (μ ∼ 450 m 2 V -1 s -1 ) which may originate from electron-electron interactions (e.g. spin polarisation at zero magnetic field). We are currently investigating the 0.7 feature as a function of applied hydrostatic pressure. Hydrostatic pressure affects the band structure and therefore the effective mass and the effective g-factor. In the case of bulk GaAs hydrostatic pressure reduces the magnitude of the effective g-factor, reaching a value of zero at approximately 1.7x10 9 Pa. Using a non-magnetic BeCu clamp-cell we achieve pressures up to 1 x 10 9 Pa, reducing the effective g-factor by more than 60%, in a temperature range 30mK to 300K and at magnetic fields up to 17T. We are therefore able to map the 0.7 feature as a function of p,T and B to assess the evidence for an electron-electron interaction driven origin of the 0.7 feature. We will present the preliminary results of our measurements
Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke's atom
Ruokosenmäki, Ilkka; Gholizade, Hossein; Kylänpää, Ilkka; Rantala, Tapio T.
2017-01-01
We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We also show usefulness of the perturbation theory for analytical approximates in case of strong confinements.
Roldán, Édgar; Gupta, Shamik
2017-08-01
We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location at a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows us to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset, (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster time scale than performing quenches of parameters of the harmonic potential.
Path-integral approach to the dynamics of a random chain with rigid constraints
International Nuclear Information System (INIS)
Ferrari, Franco; Paturej, Jaroslaw; Vilgis, Thomas A.
2008-01-01
In this work the dynamics of a chain consisting of a set of beads attached to the ends of segments of fixed lengths is investigated. The chain fluctuates at constant temperature in a viscous medium. For simplicity, all interactions among the beads have been switched off and the number of spatial dimensions has been limited to two. In the limit in which the chain becomes a continuous system, its behavior may be described by a path integral, in which the rigid constraints coming from the infinitesimally small segments are imposed by means of a functional δ function. In this way a model of the dynamics of the chain is obtained, which closely resembles a two-dimensional nonlinear σ model. The partition function of this generalized nonlinear σ model is computed explicitly for a ring-shaped chain in the semiclassical approximation. The behavior of the chain at both long and short scales of time and distances is investigated. The connection between the generalized nonlinear σ model presented here and the Rouse model is discussed
Singh, Upendra N.; Petros, Mulugeta; Refaat, Tamer F.; Yu, Jirong
2016-01-01
For more than 15 years, NASA Langley Research Center (LaRC) has contributed in developing several 2-micron carbon dioxide active remote sensors using the DIAL technique. Currently, an airborne 2-micron triple-pulse integrated path differential absorption (IPDA) lidar is under development at NASA LaRC. This paper focuses on the advancement of the 2-micron triple-pulse IPDA lidar development. Updates on the state-of-the-art triple-pulse laser transmitter will be presented including the status of wavelength control, packaging and lidar integration. In addition, receiver development updates will also be presented, including telescope integration, detection systems and data acquisition electronics. Future plan for IPDA lidar system for ground integration, testing and flight validation will be presented.
The paper describes preliminary results from a field experiment designed to evaluate a new approach to quantifying gaseous fugitive emissions from area air pollution sources. The new approach combines path-integrated concentration data acquired with any path-integrated optical re...
Energy Technology Data Exchange (ETDEWEB)
Kinugawa, Kenichi [Nara Women`s Univ., Nara (Japan). Dept. of Chemistry
1998-10-01
It has been unsuccessful to solve a set of time-dependent Schroedinger equations numerically for many-body quantum systems which involve, e.g., a number of hydrogen molecules, protons, and excess electrons at a low temperature, where quantum effect evidently appears. This undesirable situation is fatal for the investigation of real low-temperature chemical systems because they are essentially composed of many quantum degrees of freedom. However, if we use a new technique called `path integral centroid molecular dynamics (CMD) simulation` proposed by Cao and Voth in 1994, the real-time semi-classical dynamics of many degrees of freedom can be computed by utilizing the techniques already developed in the traditional classical molecular dynamics (MD) simulations. Therefore, the CMD simulation is expected to be very powerful tool for the quantum dynamics studies or real substances. (J.P.N.)
Mark Setterfield
2015-01-01
Path dependency is defined, and three different specific concepts of path dependency – cumulative causation, lock in, and hysteresis – are analyzed. The relationships between path dependency and equilibrium, and path dependency and fundamental uncertainty are also discussed. Finally, a typology of dynamical systems is developed to clarify these relationships.
Directory of Open Access Journals (Sweden)
Michael E. Hasselmo
2008-01-01
Full Text Available The entorhinal cortex plays an important role in spatial memory and episodic memory functions. These functions may result from cellular mechanisms for integration of the afferent input to entorhinal cortex. This article reviews physiological data on persistent spiking and membrane potential oscillations in entorhinal cortex then presents models showing how both these cellular mechanisms could contribute to properties observed during unit recording, including grid cell firing, and how they could underlie behavioural functions including path integration. The interaction of oscillations and persistent firing could contribute to encoding and retrieval of trajectories through space and time as a mechanism relevant to episodic memory.
International Nuclear Information System (INIS)
Grosche, C.
2007-08-01
In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short''Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional flat space and divides it by a three-dimensional superintegrable potential. Such superintegrable potentials will be the isotropic singular oscillator, the Holt-potential, the Coulomb potential, or two centrifugal potentials, respectively. In all cases a non-trivial space of non-constant curvature is generated. In order to obtain a proper quantum theory a curvature term has to be incorporated into the quantum Hamiltonian. For possible bound-state solutions we find equations up to twelfth order in the energy E. (orig.)
CERN. Geneva
2017-01-01
Join the path of code linting and discover how it can help you reach higher levels of programming enlightenment. Today we will cover how to embrace code linters to offload cognitive strain on preserving style standards in your code base as well as avoiding error-prone constructs. Additionally, I will show you the journey ahead for integrating several code linters in the programming tools your already use with very little effort.
Quad-rotor flight path energy optimization
Kemper, Edward
Quad-Rotor unmanned areal vehicles (UAVs) have been a popular area of research and development in the last decade, especially with the advent of affordable microcontrollers like the MSP 430 and the Raspberry Pi. Path-Energy Optimization is an area that is well developed for linear systems. In this thesis, this idea of path-energy optimization is extended to the nonlinear model of the Quad-rotor UAV. The classical optimization technique is adapted to the nonlinear model that is derived for the problem at hand, coming up with a set of partial differential equations and boundary value conditions to solve these equations. Then, different techniques to implement energy optimization algorithms are tested using simulations in Python. First, a purely nonlinear approach is used. This method is shown to be computationally intensive, with no practical solution available in a reasonable amount of time. Second, heuristic techniques to minimize the energy of the flight path are tested, using Ziegler-Nichols' proportional integral derivative (PID) controller tuning technique. Finally, a brute force look-up table based PID controller is used. Simulation results of the heuristic method show that both reliable control of the system and path-energy optimization are achieved in a reasonable amount of time.
Differential equations driven by rough paths with jumps
Friz, Peter K.; Zhang, Huilin
2018-05-01
We develop the rough path counterpart of Itô stochastic integration and differential equations driven by general semimartingales. This significantly enlarges the classes of (Itô/forward) stochastic differential equations treatable with pathwise methods. A number of applications are discussed.
Acquisition Path Analysis as a Collaborative Activity
International Nuclear Information System (INIS)
Nakao, A.; Grundule, R.; Gushchyn, K.; El Gebaly, A.; Higgy, R.; Tsvetkov, I.; Mandl, W.
2015-01-01
In the International Atomic Energy Agency, acquisition path analysis (APA) is indispensable to safeguards implementation. It is an integral part of both State evaluation process and the development of State level safeguards approaches, all performed through ongoing collaborative analysis of all available safeguards relevant information by State evaluation groups (SEG) with participation of other contributors, as required. To perform comprehensive State evaluation, to develop and revise State-level safeguards approaches, and to prepare annual implementation plans, the SEG in its collaborative analysis follows accepted safeguards methodology and guidance. In particular, the guide ''Performing Acquisition Path Analysis for the Development of a State-level Safeguards Approach for a State with a CSA'' is used. This guide identifies four major steps of the APA process: 1. Consolidating information about the State's past, present and planned nuclear fuel cycle-related capabilities and infrastructure; 2. Identifying and visually presenting technically plausible acquisition paths for the State; 3. Assessing acquisition path steps (State's technical capabilities and possible actions) along the identified acquisition paths; and 4. Assessing the time needed to accomplish each identified technically plausible acquisition path for the State. The paper reports on SEG members' and other contributors' experience with APA when following the above steps, including the identification of plausible acquisition pathways, estimation of time frames for all identified steps and determination of the time needed to accomplish each acquisition path. The difficulties that the SEG encountered during the process of performing the APA are also addressed. Feedback in the form of practical suggestions for improving the clarity of the acquisition path step assessment forms and a proposal for software support are also included. (author)
Quivers of Bound Path Algebras and Bound Path Coalgebras
Directory of Open Access Journals (Sweden)
Dr. Intan Muchtadi
2010-09-01
Full Text Available bras and coalgebras can be represented as quiver (directed graph, and from quiver we can construct algebras and coalgebras called path algebras and path coalgebras. In this paper we show that the quiver of a bound path coalgebra (resp. algebra is the dual quiver of its bound path algebra (resp. coalgebra.
The paper describes a new approach to quantify emissions from area air pollution sources. The approach combines path-integrated concentration data acquired with any path-integrated optical remote sensing (PI-ORS) technique and computed tomography (CT) technique. In this study, an...
2012-07-05
...Notice is hereby given that a complaint was filed with the U.S. International Trade Commission on May 31, 2012, under section 337 of the Tariff Act of 1930, as amended, on behalf of Industrial Technology Research Institute of Taiwan and ITRI International of San Jose, California. The complaint alleges violations of section 337 based upon the importation into the United States, the sale for importation, and the sale within the United States after importation of certain integrated circuit packages provided with multiple heat-conducting paths and products containing same by reason of infringement of certain claims of U.S. Patent No. 5,710,459 (``the `459 patent''). The complaint further alleges that an industry in the United States exists as required by subsection (a)(2) of section 337. The complainants request that the Commission institute an investigation and, after the investigation, issue an exclusion order and cease and desist order.
Colquitt, J A; LePine, J A; Noe, R A
2000-10-01
This article meta-analytically summarizes the literature on training motivation, its antecedents, and its relationships with training outcomes such as declarative knowledge, skill acquisition, and transfer. Significant predictors of training motivation and outcomes included individual characteristics (e.g., locus of control, conscientiousness, anxiety, age, cognitive ability, self-efficacy, valence, job involvement) and situational characteristics (e.g., climate). Moreover, training motivation explained incremental variance in training outcomes beyond the effects of cognitive ability. Meta-analytic path analyses further showed that the effects of personality, climate, and age on training outcomes were only partially mediated by self-efficacy, valence, and job involvement. These findings are discussed in terms of their practical significance and their implications for an integrative theory of training motivation.
Setting the right path and pace for integration.
Cwiek, Katherine A; Inniger, Meredith C; Zismer, Daniel K
2014-04-01
Far from being a monolithic trend, integration in health care today is progressing in various forms, and at different rates in different markets within and across the range of healthcare organizations. Each organization should develop a tailored strategy that delineates the level and type of integration it will pursue and at what pace to pursue it. This effort will require evaluation of external market conditions with respect to integration and competition and a candid assessment of intraorganizational integration. The compared results of the two analyses will provide the basis for formulating strategy.
Assessment of Hydrogen Sulfide Minimum Detection Limits of an Open Path Tunable Diode Laser
During June 2007, U.S. EPA conducted a feasibility study to determine whether the EPA OTM 10 measurement approach, also known as radial plume mapping (RPM), was feasible. A Boreal open-path tunable diode laser (OP-TDL) to collect path-integrated hydrogen sulfide measurements alon...
Path Searching Based Fault Automated Recovery Scheme for Distribution Grid with DG
Xia, Lin; Qun, Wang; Hui, Xue; Simeng, Zhu
2016-12-01
Applying the method of path searching based on distribution network topology in setting software has a good effect, and the path searching method containing DG power source is also applicable to the automatic generation and division of planned islands after the fault. This paper applies path searching algorithm in the automatic division of planned islands after faults: starting from the switch of fault isolation, ending in each power source, and according to the line load that the searching path traverses and the load integrated by important optimized searching path, forming optimized division scheme of planned islands that uses each DG as power source and is balanced to local important load. Finally, COBASE software and distribution network automation software applied are used to illustrate the effectiveness of the realization of such automatic restoration program.
Hadronization of quark-diquark model for nucleon structure and nuclear force by path integral
International Nuclear Information System (INIS)
Nagata, Keitaro
2003-01-01
One of the central issues of the hadron physics is how to interpret the properties and the origin of nuclear force. Nuclear force is in principle the manifestation of dynamics of quarks and gluons but no trial has been successful yet in describing the nuclear force by using QCD, the fundamental theory of the strong interactions. Phenomenon related to the chiral symmetry and the spontaneous breaking of the chiral symmetry is one of the important phenomena for the understanding of hadron physics. Nambu-Jona-Lasinio (NJL) model is one of the quark system models to explain the phenomena concerning the chiral symmetry. Although the method to deduce the Lagrangian describing mesons by applying the path integral to NJL model has been well known as the bosonization, it has been difficult to extend it to baryons because baryons are three-body system. In this paper, a method is reported to deduce Lagrangian which describes baryon-meson from quark-diquark Lagrangian by assuming that baryons are the bound states of quark and diquark. (S. Funahashi)
Theory of hot and rotating nuclei within the static path approximation
International Nuclear Information System (INIS)
Ansari, A.
1995-01-01
For the description of hot and rotating nuclei the static path approximation to the path integral representation of the partition function is at present the best practicable approach incorporating rigorously the statistical fluctuations in nuclear shape degrees of freedom. The paper briefly discusses the method and present a few of the recent results on level densities and GDR (giant dipole resonance) γ-absorption cross sections. (author). 22 refs., 2 figs
Integrated magnetic transformer assembly
DEFF Research Database (Denmark)
2014-01-01
The present invention relates to an integrated magnetics transformer assembly comprising a first magnetically permeable core forming a first substantially closed magnetic flux path and a second magnetically permeable core forming a second substantially closed magnetic flux path. A first input...... inductor winding is wound around a first predetermined segment of the first magnetically permeable core and a second input inductor winding is wound around a first predetermined segment of the second magnetically permeable core. The integrated magnetics transformer assembly further comprises a first output......-winding of the first output inductor winding and the first half-winding of the second output inductor winding are configured to produce aligned, i.e. in the same direction, magnetic fluxes through the first substantially closed magnetic flux path. The integrated magnetics transformer assembly is well- suited for use...
The Global Optimal Algorithm of Reliable Path Finding Problem Based on Backtracking Method
Directory of Open Access Journals (Sweden)
Liang Shen
2017-01-01
Full Text Available There is a growing interest in finding a global optimal path in transportation networks particularly when the network suffers from unexpected disturbance. This paper studies the problem of finding a global optimal path to guarantee a given probability of arriving on time in a network with uncertainty, in which the travel time is stochastic instead of deterministic. Traditional path finding methods based on least expected travel time cannot capture the network user’s risk-taking behaviors in path finding. To overcome such limitation, the reliable path finding algorithms have been proposed but the convergence of global optimum is seldom addressed in the literature. This paper integrates the K-shortest path algorithm into Backtracking method to propose a new path finding algorithm under uncertainty. The global optimum of the proposed method can be guaranteed. Numerical examples are conducted to demonstrate the correctness and efficiency of the proposed algorithm.
Multi-Dimensional Path Queries
DEFF Research Database (Denmark)
Bækgaard, Lars
1998-01-01
to create nested path structures. We present an SQL-like query language that is based on path expressions and we show how to use it to express multi-dimensional path queries that are suited for advanced data analysis in decision support environments like data warehousing environments......We present the path-relationship model that supports multi-dimensional data modeling and querying. A path-relationship database is composed of sets of paths and sets of relationships. A path is a sequence of related elements (atoms, paths, and sets of paths). A relationship is a binary path...
International Nuclear Information System (INIS)
Nakayama, Akira; Taketsugu, Tetsuya; Shiga, Motoyuki
2009-01-01
Efficiency of the ab initio hybrid Monte Carlo and ab initio path integral hybrid Monte Carlo methods is enhanced by employing an auxiliary potential energy surface that is used to update the system configuration via molecular dynamics scheme. As a simple illustration of this method, a dual-level approach is introduced where potential energy gradients are evaluated by computationally less expensive ab initio electronic structure methods. (author)
International Nuclear Information System (INIS)
Exner, P.; Kolerov, G.I.
1981-01-01
Properties of the subset of polygonal paths in the Hilbert space H of paths referring to a d-dimensional quantum-mechanical system are examined. Using the reproduction kernel technique we prove that each element of H is approximated by polygonal paths uniformly with respect to the ''norm'' of time-interval partitions. This result will be applied in the second part of the present paper to prove consistency of the uniform polygonal-path extension of the Feynman maps [ru
RSMDP-based Robust Q-learning for Optimal Path Planning in a Dynamic Environment
Directory of Open Access Journals (Sweden)
Yunfei Zhang
2014-07-01
Full Text Available This paper presents arobust Q-learning method for path planningin a dynamic environment. The method consists of three steps: first, a regime-switching Markov decision process (RSMDP is formed to present the dynamic environment; second a probabilistic roadmap (PRM is constructed, integrated with the RSMDP and stored as a graph whose nodes correspond to a collision-free world state for the robot; and third, an onlineQ-learning method with dynamic stepsize, which facilitates robust convergence of the Q-value iteration, is integrated with the PRM to determine an optimal path for reaching the goal. In this manner, the robot is able to use past experience for improving its performance in avoiding not only static obstacles but also moving obstacles, without knowing the nature of the obstacle motion. The use ofregime switching in the avoidance of obstacles with unknown motion is particularly innovative. The developed approach is applied to a homecare robot in computer simulation. The results show that the online path planner with Q-learning is able torapidly and successfully converge to the correct path.
Yoo-Kong, Sikarin; Liewrian, Watchara
2015-12-01
We report on a theoretical investigation concerning the polaronic effect on the transport properties of a charge carrier in a one-dimensional molecular chain. Our technique is based on the Feynman's path integral approach. Analytical expressions for the frequency-dependent mobility and effective mass of the carrier are obtained as functions of electron-phonon coupling. The result exhibits the crossover from a nearly free particle to a heavily trapped particle. We find that the mobility depends on temperature and decreases exponentially with increasing temperature at low temperature. It exhibits large polaronic-like behaviour in the case of weak electron-phonon coupling. These results agree with the phase transition (A.S. Mishchenko et al., Phys. Rev. Lett. 114, 146401 (2015)) of transport phenomena related to polaron motion in the molecular chain.
Mielke, Steven L; Dinpajooh, Mohammadhasan; Siepmann, J Ilja; Truhlar, Donald G
2013-01-07
We present a procedure to calculate ensemble averages, thermodynamic derivatives, and coordinate distributions by effective classical potential methods. In particular, we consider the displaced-points path integral (DPPI) method, which yields exact quantal partition functions and ensemble averages for a harmonic potential and approximate quantal ones for general potentials, and we discuss the implementation of the new procedure in two Monte Carlo simulation codes, one that uses uncorrelated samples to calculate absolute free energies, and another that employs Metropolis sampling to calculate relative free energies. The results of the new DPPI method are compared to those from accurate path integral calculations as well as to results of two other effective classical potential schemes for the case of an isolated water molecule. In addition to the partition function, we consider the heat capacity and expectation values of the energy, the potential energy, the bond angle, and the OH distance. We also consider coordinate distributions. The DPPI scheme performs best among the three effective potential schemes considered and achieves very good accuracy for all of the properties considered. A key advantage of the effective potential schemes is that they display much lower statistical sampling variances than those for accurate path integral calculations. The method presented here shows great promise for including quantum effects in calculations on large systems.
Generation of Path-Encoded Greenberger-Horne-Zeilinger States
Bergamasco, N.; Menotti, M.; Sipe, J. E.; Liscidini, M.
2017-11-01
We study the generation of Greenberger-Horne-Zeilinger (GHZ) states of three path-encoded photons. Inspired by the seminal work of Bouwmeester et al. [Phys. Rev. Lett. 82, 1345 (1999), 10.1103/PhysRevLett.82.1345] on polarization-entangled GHZ states, we find a corresponding path representation for the photon states of an optical circuit, identify the elements required for the state generation, and propose a possible implementation of our strategy. Besides the practical advantage of employing an integrated system that can be fabricated with proven lithographic techniques, our example suggests that it is possible to enhance the generation efficiency by using microring resonators.
Target Centroid Position Estimation of Phase-Path Volume Kalman Filtering
Directory of Open Access Journals (Sweden)
Fengjun Hu
2016-01-01
Full Text Available For the problem of easily losing track target when obstacles appear in intelligent robot target tracking, this paper proposes a target tracking algorithm integrating reduced dimension optimal Kalman filtering algorithm based on phase-path volume integral with Camshift algorithm. After analyzing the defects of Camshift algorithm, compare the performance with the SIFT algorithm and Mean Shift algorithm, and Kalman filtering algorithm is used for fusion optimization aiming at the defects. Then aiming at the increasing amount of calculation in integrated algorithm, reduce dimension with the phase-path volume integral instead of the Gaussian integral in Kalman algorithm and reduce the number of sampling points in the filtering process without influencing the operational precision of the original algorithm. Finally set the target centroid position from the Camshift algorithm iteration as the observation value of the improved Kalman filtering algorithm to fix predictive value; thus to make optimal estimation of target centroid position and keep the target tracking so that the robot can understand the environmental scene and react in time correctly according to the changes. The experiments show that the improved algorithm proposed in this paper shows good performance in target tracking with obstructions and reduces the computational complexity of the algorithm through the dimension reduction.
Integrated Schools: Finding a New Path
Orfield, Gary; Frankenberg, Erica; Siegel-Hawley, Genevieve
2010-01-01
Research shows that schools remain a powerful tool for shoring up individual opportunity and for attaining a thriving, multiracial democratic society. The authors point to social science evidence that demonstrates how segregated schooling limits the prospects of both minority and majority students and how integrated education can close the…
Accelerating cleanup. Paths to closure Hanford Site
International Nuclear Information System (INIS)
Edwards, C.
1998-01-01
This document was previously referred to as the Draft 2006 Plan. As part of the DOE's national strategy, the Richland Operations Office's Paths to Closure summarizes an integrated path forward for environmental cleanup at the Hanford Site. The Hanford Site underwent a concerted effort between 1994 and 1996 to accelerate the cleanup of the Site. These efforts are reflected in the current Site Baseline. This document describes the current Site Baseline and suggests strategies for further improvements in scope, schedule and cost. The Environmental Management program decided to change the name of the draft strategy and the document describing it in response to a series of stakeholder concerns, including the practicality of achieving widespread cleanup by 2006. Also, EM was concerned that calling the document a plan could be misconstrued to be a proposal by DOE or a decision-making document. The change in name, however, does not diminish the 2006 vision. To that end, Paths to Closure retains a focus on 2006, which serves as a point in time around which objectives and goals are established
Moerel, J.L.; Halswijk, W.
2010-01-01
These notes deal with the integration of a (sc)ramjet engine in either an axisymmetric or a waverider type of cruise missile configuration. The integration aspects relate to the integration of the external and internal flow paths in geometrical configurations that are being considered worldwide.
Molar excess volumes of liquid hydrogen and neon mixtures from path integral simulation
International Nuclear Information System (INIS)
Challa, S.R.; Johnson, J.K.
1999-01-01
Volumetric properties of liquid mixtures of neon and hydrogen have been calculated using path integral hybrid Monte Carlo simulations. Realistic potentials have been used for the three interactions involved. Molar volumes and excess volumes of these mixtures have been evaluated for various compositions at 29 and 31.14 K, and 30 atm. Significant quantum effects are observed in molar volumes. Quantum simulations agree well with experimental molar volumes. Calculated excess volumes agree qualitatively with experimental values. However, contrary to the existing understanding that large positive deviations from ideal mixtures are caused due to quantum effects in Ne - H 2 mixtures, both classical as well as quantum simulations predict the large positive deviations from ideal mixtures. Further investigations using two other Ne - H 2 potentials of Lennard - Jones (LJ) type show that excess volumes are very sensitive to the cross-interaction potential. We conclude that the cross-interaction potential employed in our simulations is accurate for volumetric properties. This potential is more repulsive compared to the two LJ potentials tested, which have been obtained by two different combining rules. This repulsion and a comparatively lower potential well depth can explain the positive deviations from ideal mixing. copyright 1999 American Institute of Physics
Cartier, Pierre; DeWitt-Morette, Cecile
2010-06-01
Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.
Vulnerabilities, Influences and Interaction Paths: Failure Data for Integrated System Risk Analysis
Malin, Jane T.; Fleming, Land
2006-01-01
We describe graph-based analysis methods for identifying and analyzing cross-subsystem interaction risks from subsystem connectivity information. By discovering external and remote influences that would be otherwise unexpected, these methods can support better communication among subsystem designers at points of potential conflict and to support design of more dependable and diagnosable systems. These methods identify hazard causes that can impact vulnerable functions or entities if propagated across interaction paths from the hazard source to the vulnerable target. The analysis can also assess combined impacts of And-Or trees of disabling influences. The analysis can use ratings of hazards and vulnerabilities to calculate cumulative measures of the severity and importance. Identification of cross-subsystem hazard-vulnerability pairs and propagation paths across subsystems will increase coverage of hazard and risk analysis and can indicate risk control and protection strategies.
International Nuclear Information System (INIS)
Janse van Rensburg, E J
2010-01-01
In this paper the models of pulled Dyck paths in Janse van Rensburg (2010 J. Phys. A: Math. Theor. 43 215001) are generalized to pulled Motzkin path models. The generating functions of pulled Motzkin paths are determined in terms of series over trinomial coefficients and the elastic response of a Motzkin path pulled at its endpoint (see Orlandini and Whittington (2004 J. Phys. A: Math. Gen. 37 5305-14)) is shown to be R(f) = 0 for forces pushing the endpoint toward the adsorbing line and R(f) = f(1 + 2cosh f))/(2sinh f) → f as f → ∞, for forces pulling the path away from the X-axis. In addition, the elastic response of a Motzkin path pulled at its midpoint is shown to be R(f) = 0 for forces pushing the midpoint toward the adsorbing line and R(f) = f(1 + 2cosh (f/2))/sinh (f/2) → 2f as f → ∞, for forces pulling the path away from the X-axis. Formal combinatorial identities arising from pulled Motzkin path models are also presented. These identities are the generalization of combinatorial identities obtained in directed paths models to their natural trinomial counterparts.
Energy Technology Data Exchange (ETDEWEB)
Janse van Rensburg, E J, E-mail: rensburg@yorku.c [Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3 (Canada)
2010-08-20
In this paper the models of pulled Dyck paths in Janse van Rensburg (2010 J. Phys. A: Math. Theor. 43 215001) are generalized to pulled Motzkin path models. The generating functions of pulled Motzkin paths are determined in terms of series over trinomial coefficients and the elastic response of a Motzkin path pulled at its endpoint (see Orlandini and Whittington (2004 J. Phys. A: Math. Gen. 37 5305-14)) is shown to be R(f) = 0 for forces pushing the endpoint toward the adsorbing line and R(f) = f(1 + 2cosh f))/(2sinh f) {yields} f as f {yields} {infinity}, for forces pulling the path away from the X-axis. In addition, the elastic response of a Motzkin path pulled at its midpoint is shown to be R(f) = 0 for forces pushing the midpoint toward the adsorbing line and R(f) = f(1 + 2cosh (f/2))/sinh (f/2) {yields} 2f as f {yields} {infinity}, for forces pulling the path away from the X-axis. Formal combinatorial identities arising from pulled Motzkin path models are also presented. These identities are the generalization of combinatorial identities obtained in directed paths models to their natural trinomial counterparts.
Janse van Rensburg, E. J.
2010-08-01
In this paper the models of pulled Dyck paths in Janse van Rensburg (2010 J. Phys. A: Math. Theor. 43 215001) are generalized to pulled Motzkin path models. The generating functions of pulled Motzkin paths are determined in terms of series over trinomial coefficients and the elastic response of a Motzkin path pulled at its endpoint (see Orlandini and Whittington (2004 J. Phys. A: Math. Gen. 37 5305-14)) is shown to be R(f) = 0 for forces pushing the endpoint toward the adsorbing line and R(f) = f(1 + 2cosh f))/(2sinh f) → f as f → ∞, for forces pulling the path away from the X-axis. In addition, the elastic response of a Motzkin path pulled at its midpoint is shown to be R(f) = 0 for forces pushing the midpoint toward the adsorbing line and R(f) = f(1 + 2cosh (f/2))/sinh (f/2) → 2f as f → ∞, for forces pulling the path away from the X-axis. Formal combinatorial identities arising from pulled Motzkin path models are also presented. These identities are the generalization of combinatorial identities obtained in directed paths models to their natural trinomial counterparts.
Machine Learning from Garden Path Sentences: The Application of Computational Linguistics
Directory of Open Access Journals (Sweden)
Jiali Du
2014-12-01
Full Text Available This paper discusses the application of computational linguistics in the machine learning (ML system for the processing of garden path sentences. ML is closely related to artificial intelligence and linguistic cognition. The rapid and efficient processing of the complex structures is an effective method to test the system. By means of parsing the garden path sentence, we draw a conclusion that the integration of theoretical and statistical methods is helpful for the development of ML system.
Topological quantum theories and integrable models
International Nuclear Information System (INIS)
Keski-Vakkuri, E.; Niemi, A.J.; Semenoff, G.; Tirkkonen, O.
1991-01-01
The path-integral generalization of the Duistermaat-Heckman integration formula is investigated for integrable models. It is shown that for models with periodic classical trajectories the path integral reduces to a form similar to the finite-dimensional Duistermaat-Heckman integration formula. This provides a relation between exactness of the stationary-phase approximation and Morse theory. It is also argued that certain integrable models can be related to topological quantum theories. Finally, it is found that in general the stationary-phase approximation presumes that the initial and final configurations are in different polarizations. This is exemplified by the quantization of the SU(2) coadjoint orbit
1975-06-01
Traditionally, synchronization of concurrent processes is coded in line by operations on semaphores or similar objects. Path expressions move the...discussion about a variety of synchronization primitives . An analysis of their relative power is found in [3]. Path expressions do not introduce yet...another synchronization primitive . A path expression relates to such primitives as a for- or while-statement of an ALGOL-like language relates to a JUMP
Milton, Kimball A
2015-01-01
Starting from the earlier notions of stationary action principles, these tutorial notes shows how Schwinger’s Quantum Action Principle descended from Dirac’s formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. Part I brings out in more detail the connection between the two formulations, and applications are discussed. Then, the Keldysh-Schwinger time-cycle method of extracting matrix elements is described. Part II will discuss the variational formulation of quantum electrodynamics and the development of source theory.
Hybrid waveguide-bulk multi-path interferometer with switchable amplitude and phase
Directory of Open Access Journals (Sweden)
Robert Keil
2016-11-01
Full Text Available We design and realise a hybrid interferometer consisting of three paths based on integrated as well as on bulk optical components. This hybrid construction offers a good compromise between stability and footprint on one side and means of intervention on the other. As experimentally verified by the absence of higher-order interferences, amplitude and phase can be manipulated in all paths independently. In conjunction with single photons, the setup can, therefore, be applied for fundamental investigations on quantum mechanics.
Energy Technology Data Exchange (ETDEWEB)
Heilmann, D.B.
2007-02-15
The two-plane HUBBARD model, which is a model for some electronic properties of undoped YBCO superconductors as well as displays a MOTT metal-to-insulator transition and a metal-to-band insulator transition, is studied within Dynamical Mean-Field Theory using HIRSCH-FYE Monte Carlo. In order to find the different transitions and distinguish the types of insulator, we calculate the single-particle spectral densities, the self-energies and the optical conductivities. We conclude that there is a continuous transition from MOTT to band insulator. In the second part, ground state properties of a diagonally disordered HUBBARD model is studied using a generalisation of Path Integral Renormalisation Group, a variational method which can also determine low-lying excitations. In particular, the distribution of antiferromagnetic properties is investigated. We conclude that antiferromagnetism breaks down in a percolation-type transition at a critical disorder, which is not changed appreciably by the inclusion of correlation effects, when compared to earlier studies. Electronic and excitation properties at the system sizes considered turn out to primarily depend on the geometry. (orig.)
International Nuclear Information System (INIS)
Heilmann, D.B.
2007-02-01
The two-plane HUBBARD model, which is a model for some electronic properties of undoped YBCO superconductors as well as displays a MOTT metal-to-insulator transition and a metal-to-band insulator transition, is studied within Dynamical Mean-Field Theory using HIRSCH-FYE Monte Carlo. In order to find the different transitions and distinguish the types of insulator, we calculate the single-particle spectral densities, the self-energies and the optical conductivities. We conclude that there is a continuous transition from MOTT to band insulator. In the second part, ground state properties of a diagonally disordered HUBBARD model is studied using a generalisation of Path Integral Renormalisation Group, a variational method which can also determine low-lying excitations. In particular, the distribution of antiferromagnetic properties is investigated. We conclude that antiferromagnetism breaks down in a percolation-type transition at a critical disorder, which is not changed appreciably by the inclusion of correlation effects, when compared to earlier studies. Electronic and excitation properties at the system sizes considered turn out to primarily depend on the geometry. (orig.)
Salam, Abdus; Wigner, E. P.
2010-03-01
Preface; List of contributors; Bibliography of P. A. M. Dirac; 1. Dirac in Cambridge R. J. Eden and J. C. Polkinghorne; 2. Travels with Dirac in the Rockies J. H. Van Vleck; 3. 'The golden age of theoretical physics': P. A. M. Dirac's scientific work from 1924 to 1933 Jagdish Mehra; 4. Foundation of quantum field theory Res Jost; 5. The early history of the theory of electron: 1897-1947 A. Pais; 6. The Dirac equation A. S. Wightman; 7. Fermi-Dirac statistics Rudolph Peierls; 8. Indefinite metric in state space W. Heisenberg; 9. On bras and kets J. M. Jauch; 10. The Poisson bracket C. Lanczos; 11. La 'fonction' et les noyaux L. Schwartz; 12. On the Dirac magnetic poles Edoardo Amadli and Nicola Cabibbo; 13. The fundamental constants and their time variation Freeman J. Dyson; 14. On the time-energy uncertainty relation Eugene P. Wigner; 15. The path-integral quantisation of gravity Abdus Salam and J. Strathdee; Index; Plates.
Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories arXiv
Alexandre, Jean; Millington, Peter; Seynaeve, Dries
We demonstrate the extension to PT-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimisation of the effective potential in a non-Hermitian model is accompanied by a massless scalar boson. Laying a basis for our analysis, we first show how the conventional quantisation of the path-integral formulation of quantum field theory can be extended consistently to a non-Hermitian model by considering PT conjugation instead of Hermitian conjugation. The extension of the Goldstone theorem to a PT-symmetric field theory is made possible by the existence of a conserved current that does not, however, correspond to a symmetry of the non-Hermitian Lagrangian. In addition to extending the proof of the Goldstone theorem to a PT-symmetric theory, we exhibit a specific example in which we verify the existence of a massless boson at the tree and one-loop levels.
Path Integral Monte Carlo Simulations of Warm Dense Matter and Plasmas
Energy Technology Data Exchange (ETDEWEB)
Militzer, Burkhard [Univ. of California, Berkeley, CA (United States)
2018-01-13
New path integral Monte Carlo simulation (PIMC) techniques will be developed and applied to derive the equation of state (EOS) for the regime of warm dense matter and dense plasmas where existing first-principles methods cannot be applied. While standard density functional theory has been used to accurately predict the structure of many solids and liquids up to temperatures on the order of 10,000 K, this method is not applicable at much higher temperature where electronic excitations become important because the number of partially occupied electronic orbitals reaches intractably large numbers and, more importantly, the use of zero-temperature exchange-correlation functionals introduces an uncontrolled approximation. Here we focus on PIMC methods that become more and more efficient with increasing temperatures and still include all electronic correlation effects. In this approach, electronic excitations increase the efficiency rather than reduce it. While it has commonly been assumed such methods can only be applied to elements without core electrons like hydrogen and helium, we recently showed how to extend PIMC to heavier elements by performing the first PIMC simulations of carbon and water plasmas [Driver, Militzer, Phys. Rev. Lett. 108 (2012) 115502]. Here we propose to continue this important development to extend the reach of PIMC simulations to yet heavier elements and also lower temperatures. The goal is to provide a robust first-principles simulation method that can accurately and efficiently study materials with excited electrons at solid-state densities in order to access parts of the phase diagram such the regime of warm dense matter and plasmas where so far only more approximate, semi-analytical methods could be applied.
Simons, Jacob V., Jr.
2017-01-01
The critical path method/program evaluation and review technique method of project scheduling is based on the importance of managing a project's critical path(s). Although a critical path is the longest path through a network, its location in large projects is facilitated by the computation of activity slack. However, logical fallacies in…
Forces in Motzkin paths in a wedge
International Nuclear Information System (INIS)
Janse van Rensburg, E J
2006-01-01
Entropic forces in models of Motzkin paths in a wedge geometry are considered as models of forces in polymers in confined geometries. A Motzkin path in the square lattice is a path from the origin to a point in the line Y = X while it never visits sites below this line, and it is constrained to give unit length steps only in the north and east directions and steps of length √2 in the north-east direction. Motzkin path models may be generalized to ensembles of NE-oriented paths above the line Y = rX, where r > 0 is an irrational number. These are paths giving east, north and north-east steps from the origin in the square lattice, and confined to the r-wedge formed by the Y-axis and the line Y = rX. The generating function g r of these paths is not known, but if r > 1, then I determine its radius of convergence to be t r = min (r-1)/r≤y≤r/(r+1) [y y (1-r(1-y)) 1-r(1-y) (r(1-y)-y) r(1-y)-y ] and if r is an element of (0, 1), then t r = 1/3. The entropic force the path exerts on the line Y rX may be computed from this. An asymptotic expression for the force for large values of r is given by F(r) = log(2r)/r 2 - (1+2log(2r))/2r 3 + O (log(2r)/r 4 ). In terms of the vertex angle α of the r-wedge, the moment of the force about the origin has leading terms F(α) log(2/α) - (α/2)(1+2log(2/α)) + O(α 2 log(2/α)) as α → 0 + and F(α) = 0 if α is element of [π/4, π/2]. Moreover, numerical integration of the force shows that the total work done by closing the wedge is 1.085 07... lattice units. An alternative ensemble of NE-oriented paths may be defined by slightly changing the generating function g r . In this model, it is possible to determine closed-form expressions for the limiting free energy and the force. The leading term in an asymptotic expansions for this force agrees with the leading term in the asymptotic expansion of the above model, and the subleading term only differs by a factor of 2
Capacity bounds for kth best path selection over generalized fading channels
Hanif, Muhammad Fainan; Yang, Hongchuan; Alouini, Mohamed-Slim
2014-01-01
Exact ergodic capacity calculation for fading wireless channels typically involves time-consuming numerical evaluation of infinite integrals. In this paper, lower and upper bounds on ergodic capacity for kth best path are presented. These bounds
International Nuclear Information System (INIS)
Grammatin, A.P.; Degen, A.B.; Katranova, N.A.
1995-01-01
A system of differential equations convenient for numerical computer integrating is proposed to calculate beam paths, elementary astigmatic beams, and the optical path in isotropic media with cylindrical distribution of the refractive index. A method for selecting the step of this integration is proposed. This technique is implemented in the program package for computers of the VAX series meant for the computer-aided design of optical systems. 4 refs
Integrated path towards geological storage
International Nuclear Information System (INIS)
Bouchard, R.; Delaytermoz, A.
2004-01-01
Among solutions to contribute to CO 2 emissions mitigation, sequestration is a promising path that presents the main advantage of being able to cope with the large volume at stake when considering the growing energy demand. Of particular importance, geological storage has widely been seen as an effective solution for large CO 2 sources like power plants or refineries. Many R and D projects have been initiated, whereby research institutes, government agencies and end-users achieve an effective collaboration. So far, progress has been made towards reinjection of CO 2 , in understanding and then predicting the phenomenon and fluid dynamics inside the geological target, while monitoring the expansion of the CO 2 bubble in the case of demonstration projects. A question arises however when talking about sequestration, namely the time scale to be taken into account. Time is indeed of the essence, and points out the need to understand leakage as well as trapping mechanisms. It is therefore of prime importance to be able to predict the fate of the injected fluids, in an accurate manner and over a relevant period of time. On the grounds of geology, four items are involved in geological storage reliability: the matrix itself, which is the recipient of the injected fluids; the seal, that is the mechanistic trap preventing the injected fluids to flow upward and escape; the lower part of the concerned structure, usually an aquifer, that can be a migration way for dissolved fluids; and the man- made injecting hole, the well, whose characteristics should be as good as the geological formation itself. These issues call for specific competencies such as reservoir engineering, geology and hydrodynamics, mineral chemistry, geomechanics, and well engineering. These competencies, even if put to use to a large extent in the oil industry, have never been connected with the reliability of geological storage as ultimate goal. This paper aims at providing an introduction to these
PATH: a lumped-element beam-transport simulation program with space charge
International Nuclear Information System (INIS)
Farrell, J.A.
1983-01-01
PATH is a group of computer programs for simulating charged-particle beam-transport systems. It was developed for evaluating the effects of some aberrations without a time-consuming integration of trajectories through the system. The beam-transport portion of PATH is derived from the well-known program, DECAY TURTLE. PATH contains all features available in DECAY TURTLE (including the input format) plus additional features such as a more flexible random-ray generator, longitudinal phase space, some additional beamline elements, and space-charge routines. One of the programs also provides a simulation of an Alvarez linear accelerator. The programs, originally written for a CDC 7600 computer system, also are available on a VAX-VMS system. All of the programs are interactive with input prompting for ease of use
Path Creation, Path Dependence and Breaking Away from the Path: Re-Examining the Case of Nokia
Wang, Jens; Hedman, Jonas; Tuunainen, Virpi Kristiina
2016-01-01
The explanation of how and why firms succeed or fail is a recurrent research challenge. This is particularly important in the context of technological innovations. We focus on the role of historical events and decisions in explaining such success and failure. Using a case study of Nokia, we develop and extend a multi-layer path dependence framework. We identify four layers of path dependence: technical, strategic and leadership, organizational, and external collaboration. We show how path dep...
Relationship between total quality management, critical paths, and outcomes management.
Lynn, P A
1996-09-01
Total quality management (TQM), clinical paths, and outcomes management are high-profile strategies in today's health care environment. Each strategy is distinct, yet there are interrelationships among them. TQM supports a customer-focused organizational culture, providing tools and techniques to identify and solve problems. Clinical paths are tools for enhancing patient care coordination and for identifying system-wide and patient population specific issues. Outcomes management is an integrated system for measuring the results in patient populations over time. There is a recent shift in outcomes measurement towards expanding both the nature of the outcomes examined and the timeframes in which they are studied.
Path integral Monte Carlo simulations of dense carbon-hydrogen plasmas
Zhang, Shuai; Militzer, Burkhard; Benedict, Lorin X.; Soubiran, François; Sterne, Philip A.; Driver, Kevin P.
2018-03-01
Carbon-hydrogen plasmas and hydrocarbon materials are of broad interest to laser shock experimentalists, high energy density physicists, and astrophysicists. Accurate equations of state (EOSs) of hydrocarbons are valuable for various studies from inertial confinement fusion to planetary science. By combining path integral Monte Carlo (PIMC) results at high temperatures and density functional theory molecular dynamics results at lower temperatures, we compute the EOSs for hydrocarbons from simulations performed at 1473 separate (ρ, T)-points distributed over a range of compositions. These methods accurately treat electronic excitation effects with neither adjustable parameter nor experimental input. PIMC is also an accurate simulation method that is capable of treating many-body interaction and nuclear quantum effects at finite temperatures. These methods therefore provide a benchmark-quality EOS that surpasses that of semi-empirical and Thomas-Fermi-based methods in the warm dense matter regime. By comparing our first-principles EOS to the LEOS 5112 model for CH, we validate the specific heat assumptions in this model but suggest that the Grüneisen parameter is too large at low temperatures. Based on our first-principles EOSs, we predict the principal Hugoniot curve of polystyrene to be 2%-5% softer at maximum shock compression than that predicted by orbital-free density functional theory and SESAME 7593. By investigating the atomic structure and chemical bonding of hydrocarbons, we show a drastic decrease in the lifetime of chemical bonds in the pressure interval from 0.4 to 4 megabar. We find the assumption of linear mixing to be valid for describing the EOS and the shock Hugoniot curve of hydrocarbons in the regime of partially ionized atomic liquids. We make predictions of the shock compression of glow-discharge polymers and investigate the effects of oxygen content and C:H ratio on its Hugoniot curve. Our full suite of first-principles simulation results may
Intercomparison of open-path trace gas measurements with two dual-frequency-comb spectrometers
Directory of Open Access Journals (Sweden)
E. M. Waxman
2017-09-01
Full Text Available We present the first quantitative intercomparison between two open-path dual-comb spectroscopy (DCS instruments which were operated across adjacent 2 km open-air paths over a 2-week period. We used DCS to measure the atmospheric absorption spectrum in the near infrared from 6023 to 6376 cm−1 (1568 to 1660 nm, corresponding to a 355 cm−1 bandwidth, at 0.0067 cm−1 sample spacing. The measured absorption spectra agree with each other to within 5 × 10−4 in absorbance without any external calibration of either instrument. The absorption spectra are fit to retrieve path-integrated concentrations for carbon dioxide (CO2, methane (CH4, water (H2O, and deuterated water (HDO. The retrieved dry mole fractions agree to 0.14 % (0.57 ppm for CO2, 0.35 % (7 ppb for CH4, and 0.40 % (36 ppm for H2O at ∼ 30 s integration time over the 2-week measurement campaign, which included 24 °C outdoor temperature variations and periods of strong atmospheric turbulence. This agreement is at least an order of magnitude better than conventional active-source open-path instrument intercomparisons and is particularly relevant to future regional flux measurements as it allows accurate comparisons of open-path DCS data across locations and time. We additionally compare the open-path DCS retrievals to a World Meteorological Organization (WMO-calibrated cavity ring-down point sensor located along the path with good agreement. Short-term and long-term differences between the open-path DCS and point sensor are attributed, respectively, to spatial sampling discrepancies and to inaccuracies in the current spectral database used to fit the DCS data. Finally, the 2-week measurement campaign yields diurnal cycles of CO2 and CH4 that are consistent with the presence of local sources of CO2 and absence of local sources of CH4.
Different strategies for spatial updating in yaw and pitch path integration
Directory of Open Access Journals (Sweden)
Caspar Mathias Goeke
2013-02-01
Full Text Available Research in spatial navigation revealed the existence of discrete strategies defined by the use of distinct reference frames during virtual path integration. The present study investigated the distribution of these navigation strategies as a function of gender, video gaming experience, and self-estimates of spatial navigation abilities in a population of 300 subjects. Participants watched videos of virtual passages through a star-field with one turn in either the horizontal (yaw or the vertical (pitch axis. At the end of a passage they selected one out of four homing arrows to indicate the initial starting location. To solve the task, participants could employ two discrete strategies, navigating within either an egocentric or an allocentric reference frame. The majority of valid subjects (232/260 consistently used the same strategy in more than 75% of all trials. With that approach 33.1% of all participants were classified as Turners (using an egocentric reference frame on both axes and 46.5% as Nonturners (using an allocentric reference frame on both axes. 9.2% of all participants consistently used an egocentric reference frame in the yaw plane but an allocentric reference frame in the pitch plane (Switcher. Investigating the influence of gender on navigation strategies revealed that females predominantly used the Nonturner strategy while males used both the Turner and the Nonturner strategy with comparable probabilities. Other than expected, video gaming experience did not influence strategy use. Based on a strong quantitative basis with the sample size about an order of magnitude larger than in typical psychophysical studies these results demonstrate that most people reliably use one out of three possible navigation strategies (Turners, Nonturners, Switchers for spatial updating and provides a sound estimate of how those strategies are distributed within the general population.
Simon, Donald L.
2010-01-01
Aircraft engine performance trend monitoring and gas path fault diagnostics are closely related technologies that assist operators in managing the health of their gas turbine engine assets. Trend monitoring is the process of monitoring the gradual performance change that an aircraft engine will naturally incur over time due to turbomachinery deterioration, while gas path diagnostics is the process of detecting and isolating the occurrence of any faults impacting engine flow-path performance. Today, performance trend monitoring and gas path fault diagnostic functions are performed by a combination of on-board and off-board strategies. On-board engine control computers contain logic that monitors for anomalous engine operation in real-time. Off-board ground stations are used to conduct fleet-wide engine trend monitoring and fault diagnostics based on data collected from each engine each flight. Continuing advances in avionics are enabling the migration of portions of the ground-based functionality on-board, giving rise to more sophisticated on-board engine health management capabilities. This paper reviews the conventional engine performance trend monitoring and gas path fault diagnostic architecture commonly applied today, and presents a proposed enhanced on-board architecture for future applications. The enhanced architecture gains real-time access to an expanded quantity of engine parameters, and provides advanced on-board model-based estimation capabilities. The benefits of the enhanced architecture include the real-time continuous monitoring of engine health, the early diagnosis of fault conditions, and the estimation of unmeasured engine performance parameters. A future vision to advance the enhanced architecture is also presented and discussed
MinePath: Mining for Phenotype Differential Sub-paths in Molecular Pathways
Koumakis, Lefteris; Kartsaki, Evgenia; Chatzimina, Maria; Zervakis, Michalis; Vassou, Despoina; Marias, Kostas; Moustakis, Vassilis; Potamias, George
2016-01-01
Pathway analysis methodologies couple traditional gene expression analysis with knowledge encoded in established molecular pathway networks, offering a promising approach towards the biological interpretation of phenotype differentiating genes. Early pathway analysis methodologies, named as gene set analysis (GSA), view pathways just as plain lists of genes without taking into account either the underlying pathway network topology or the involved gene regulatory relations. These approaches, even if they achieve computational efficiency and simplicity, consider pathways that involve the same genes as equivalent in terms of their gene enrichment characteristics. Most recent pathway analysis approaches take into account the underlying gene regulatory relations by examining their consistency with gene expression profiles and computing a score for each profile. Even with this approach, assessing and scoring single-relations limits the ability to reveal key gene regulation mechanisms hidden in longer pathway sub-paths. We introduce MinePath, a pathway analysis methodology that addresses and overcomes the aforementioned problems. MinePath facilitates the decomposition of pathways into their constituent sub-paths. Decomposition leads to the transformation of single-relations to complex regulation sub-paths. Regulation sub-paths are then matched with gene expression sample profiles in order to evaluate their functional status and to assess phenotype differential power. Assessment of differential power supports the identification of the most discriminant profiles. In addition, MinePath assess the significance of the pathways as a whole, ranking them by their p-values. Comparison results with state-of-the-art pathway analysis systems are indicative for the soundness and reliability of the MinePath approach. In contrast with many pathway analysis tools, MinePath is a web-based system (www.minepath.org) offering dynamic and rich pathway visualization functionality, with the
Aban, C. J. G.; Bacolod, R. O.; Confesor, M. N. P.
2015-06-01
A The White Noise Path Integral Approach is used in evaluating the B-cell density or the number of B-cell per unit volume for a basic type of immune system response based on the modeling done by Perelson and Wiegel. From the scaling principles of Perelson [1], the B- cell density is obtained where antigens and antibodies mutates and activation function f(|S-SA|) is defined describing the interaction between a specific antigen and a B-cell. If the activation function f(|S-SA|) is held constant, the major form of the B-cell density evaluated using white noise analysis is similar to the form of the B-cell density obtained by Perelson and Wiegel using a differential approach.A piecewise linear functionis also used to describe the activation f(|S-SA|). If f(|S-SA|) is zero, the density decreases exponentially. If f(|S-SA|) = S-SA-SB, the B- cell density increases exponentially until it reaches a certain maximum value. For f(|S-SA|) = 2SA-SB-S, the behavior of B-cell density is oscillating and remains to be in small values.
Gratton, Steven
2011-09-01
In this paper we present a path integral formulation of stochastic inflation. Volume weighting can be naturally implemented from this new perspective in a very straightforward way when compared to conventional Langevin approaches. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how inflation typically ends both with and without volume weighting. The calculation can be carried to times beyond those accessible to conventional Fokker-Planck approaches. Perhaps unexpectedly, complex histories sometimes emerge with volume weighting. The reward for this excursion into the complex plane is an insight into how volume-weighted inflation both loses memory of initial conditions and ends via slow roll. The slow-roll end of inflation mitigates certain “Youngness Paradox”-type criticisms of the volume-weighted paradigm. Thus it is perhaps time to rehabilitate proper-time volume weighting as a viable measure for answering at least some interesting cosmological questions.
International Nuclear Information System (INIS)
Gratton, Steven
2011-01-01
In this paper we present a path integral formulation of stochastic inflation. Volume weighting can be naturally implemented from this new perspective in a very straightforward way when compared to conventional Langevin approaches. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how inflation typically ends both with and without volume weighting. The calculation can be carried to times beyond those accessible to conventional Fokker-Planck approaches. Perhaps unexpectedly, complex histories sometimes emerge with volume weighting. The reward for this excursion into the complex plane is an insight into how volume-weighted inflation both loses memory of initial conditions and ends via slow roll. The slow-roll end of inflation mitigates certain ''Youngness Paradox''-type criticisms of the volume-weighted paradigm. Thus it is perhaps time to rehabilitate proper-time volume weighting as a viable measure for answering at least some interesting cosmological questions.
Wang, Fei; Chen, Hong; Guo, Konghui; Cao, Dongpu
2017-09-01
The path following and directional stability are two crucial problems when a road vehicle experiences a tire blow-out or sudden tire failure. Considering the requirement of rapid road vehicle motion control during a tire blow-out, this article proposes a novel linearized decoupling control procedure with three design steps for a class of second order multi-input-multi-output non-affine system. The evaluating indicators for controller performance are presented and a performance related control parameter distribution map is obtained based on the stochastic algorithm which is an innovation for non-blind parameter adjustment in engineering implementation. The analysis on the robustness of the proposed integrated controller is also performed. The simulation studies for a range of driving conditions are conducted, to demonstrate the effectiveness of the proposed controller.
Modern Canonical Quantum General Relativity
Thiemann, Thomas
2008-11-01
Preface; Notation and conventions; Introduction; Part I. Classical Foundations, Interpretation and the Canonical Quantisation Programme: 1. Classical Hamiltonian formulation of general relativity; 2. The problem of time, locality and the interpretation of quantum mechanics; 3. The programme of canonical quantisation; 4. The new canonical variables of Ashtekar for general relativity; Part II. Foundations of Modern Canonical Quantum General Relativity: 5. Introduction; 6. Step I: the holonomy-flux algebra [P]; 7. Step II: quantum-algebra; 8. Step III: representation theory of [A]; 9. Step IV: 1. Implementation and solution of the kinematical constraints; 10. Step V: 2. Implementation and solution of the Hamiltonian constraint; 11. Step VI: semiclassical analysis; Part III. Physical Applications: 12. Extension to standard matter; 13. Kinematical geometrical operators; 14. Spin foam models; 15. Quantum black hole physics; 16. Applications to particle physics and quantum cosmology; 17. Loop quantum gravity phenomenology; Part IV. Mathematical Tools and their Connection to Physics: 18. Tools from general topology; 19. Differential, Riemannian, symplectic and complex geometry; 20. Semianalytical category; 21. Elements of fibre bundle theory; 22. Holonomies on non-trivial fibre bundles; 23. Geometric quantisation; 24. The Dirac algorithm for field theories with constraints; 25. Tools from measure theory; 26. Elementary introduction to Gel'fand theory for Abelean C* algebras; 27. Bohr compactification of the real line; 28. Operatir -algebras and spectral theorem; 29. Refined algebraic quantisation (RAQ) and direct integral decomposition (DID); 30. Basics of harmonic analysis on compact Lie groups; 31. Spin network functions for SU(2); 32. + Functional analytical description of classical connection dynamics; Bibliography; Index.
Multi-AGV path planning with double-path constraints by using an improved genetic algorithm.
Directory of Open Access Journals (Sweden)
Zengliang Han
Full Text Available This paper investigates an improved genetic algorithm on multiple automated guided vehicle (multi-AGV path planning. The innovations embody in two aspects. First, three-exchange crossover heuristic operators are used to produce more optimal offsprings for getting more information than with the traditional two-exchange crossover heuristic operators in the improved genetic algorithm. Second, double-path constraints of both minimizing the total path distance of all AGVs and minimizing single path distances of each AGV are exerted, gaining the optimal shortest total path distance. The simulation results show that the total path distance of all AGVs and the longest single AGV path distance are shortened by using the improved genetic algorithm.
Analysis of Crack Propagation Path on the Anisotropic Bi-Material Rock
Directory of Open Access Journals (Sweden)
Chao-Shi Chen
2010-01-01
Full Text Available This paper presents a single-domain boundary element method (SDBEM for linear elastic fracture mechanics analysis in the 2D anisotropic bimaterial. In this formulation, the displacement integral equation is collocated on the uncracked boundary only, and the traction integral equation is collocated on one side of the crack surface only. The complete fundamental solution (Green's function for anisotropic bi-materials was also derived and implemented into the boundary integral formulation so the discretization along the interface can be avoided except for the interfacial crack part. A special crack-tip element was introduced to capture exactly the crack-tip behavior. A computer program with the FORTRAN code has been developed to effectively calculate the stress intensity factors, crack initiation angle, and propagation path of an anisotropic bi-material. This SDBEM program has been verified having a good accuracy with the previous researches. In addition, a rock of type (1/(2 disk specimen with a central crack was made to conduct the Brazilian test under diametrical loading. The result shows that the numerical analysis can predict relatively well the direction of crack initiation and the path of crack propagation.
An integrated magnetics component
DEFF Research Database (Denmark)
2013-01-01
The present invention relates to an integrated magnetics component comprising a magnetically permeable core comprising a base member extending in a horizontal plane and first, second, third and fourth legs protruding substantially perpendicularly from the base member. First, second, third...... and fourth output inductor windings are wound around the first, second, third and fourth legs, respectively. A first input conductor of the integrated magnetics component has a first conductor axis and extends in-between the first, second, third and fourth legs to induce a first magnetic flux through a first...... flux path of the magnetically permeable core. A second input conductor of the integrated magnetics component has a second coil axis extending substantially perpendicularly to the first conductor axis to induce a second magnetic flux through a second flux path of the magnetically permeable core...
Path-based Queries on Trajectory Data
DEFF Research Database (Denmark)
Krogh, Benjamin Bjerre; Pelekis, Nikos; Theodoridis, Yannis
2014-01-01
In traffic research, management, and planning a number of path-based analyses are heavily used, e.g., for computing turn-times, evaluating green waves, or studying traffic flow. These analyses require retrieving the trajectories that follow the full path being analyzed. Existing path queries cannot...... sufficiently support such path-based analyses because they retrieve all trajectories that touch any edge in the path. In this paper, we define and formalize the strict path query. This is a novel query type tailored to support path-based analysis, where trajectories must follow all edges in the path...... a specific path by only retrieving data from the first and last edge in the path. To correctly answer strict path queries existing network-constrained trajectory indexes must retrieve data from all edges in the path. An extensive performance study of NETTRA using a very large real-world trajectory data set...
Introduction to path integrals, matrix models and strings
International Nuclear Information System (INIS)
Jevicki, A.
1995-01-01
The major strength of the theory is then that it is integrable and exactly solvable. Its integrable nature leads to understanding of a w ∞ algebra as a space-time symmetry of string theory. This algebra acts in a nonlinear way on the basic collective field representing a massless tachyon. It is interpreted as a spectrum-generating algebra allowing to build an infinite sequence of discrete imaginary energy states which turn out to be remnants of higher string modes in two dimensions. The presence and interplay of discrete modes with the scalar tachyon are particularly interesting. The w ∞ symmetry is seen to serve as an organizational principle and is of much broader relevance. (orig.)
Singh, Upendra N.; Petros, Mulugeta; Refaat, Tamer F.; Yu, Jirong; Antill, Charles W.; Remus, Ruben
2016-01-01
This presentation will provide status and details of an airborne 2-micron triple-pulse integrated path differential absorption (IPDA) lidar being developed at NASA Langley Research Center with support from NASA ESTO Instrument Incubator Program. The development of this active optical remote sensing IPDA instrument is targeted for measuring both atmospheric carbon dioxide and water vapor in the atmosphere from an airborne platform. This presentation will focus on the advancement of the 2-micron triple-pulse IPDA lidar development. Updates on the state-of-the-art triple-pulse laser transmitter will be presented including the status of seed laser locking, wavelength control, receiver and detector upgrades, laser packaging and lidar integration. Future plan for IPDA lidar system for ground integration, testing and flight validation will also be presented.
Moix, Jeremy M; Ma, Jian; Cao, Jianshu
2015-03-07
A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly enabling the calculation of spectra of large excitonic systems across the complete range of system parameters and for arbitrary bath spectral densities. With the numerically exact absorption and emission operators, one can also immediately compute energy transfer rates using the multi-chromophoric Förster resonant energy transfer formalism. Benchmark calculations on the emission spectra of two level systems are presented demonstrating the efficacy of the stochastic approach. This is followed by calculations of the energy transfer rates between two weakly coupled dimer systems as a function of temperature and system-bath coupling strength. It is shown that the recently developed hybrid cumulant expansion (see Paper II) is the only perturbative method capable of generating uniformly reliable energy transfer rates and emission spectra across a broad range of system parameters.
UV laser long-path absorption spectroscopy
Dorn, Hans-Peter; Brauers, Theo; Neuroth, Rudolf
1994-01-01
Long path Differential Optical Absorption Spectroscopy (DOAS) using a picosecond UV laser as a light source was developed in our institute. Tropospheric OH radicals are measured by their rotational absorption lines around 308 nm. The spectra are obtained using a high resolution spectrograph. The detection system has been improved over the formerly used optomechanical scanning device by application of a photodiode array which increased the observed spectral range by a factor of 6 and which utilizes the light much more effectively leading to a considerable reduction of the measurement time. This technique provides direct measurements of OH because the signal is given by the product of the absorption coefficient and the OH concentration along the light path according to Lambert-Beers law. No calibration is needed. Since the integrated absorption coefficient is well known the accuracy of the measurement essentially depends on the extent to which the OH absorption pattern can be detected in the spectra. No interference by self generated OH radicals in the detection lightpath has been observed. The large bandwidth (greater than 0.15 nm) and the high spectral resolution (1.5 pm) allows absolute determination of interferences by other trace gas absorptions. The measurement error is directly accessible from the absorption-signal to baseline-noise ratio in the spectra. The applicability of the method strongly depends on visibility. Elevated concentrations of aerosols lead to considerable attenuation of the laser light which reduces the S/N-ratio. In the moderately polluted air of Julich, where we performed a number of OH measurement spectra. In addition absorption features of unidentified species were frequently detected. A quantitative deconvolution even of the known species is not easy to achieve and can leave residual structures in the spectra. Thus interferences usually increase the noise and deteriorate the OH detection sensitivity. Using diode arrays for sensitive
Detection of deregulated modules using deregulatory linked path.
Directory of Open Access Journals (Sweden)
Yuxuan Hu
Full Text Available The identification of deregulated modules (such as induced by oncogenes is a crucial step for exploring the pathogenic process of complex diseases. Most of the existing methods focus on deregulation of genes rather than the links of the path among them. In this study, we emphasize on the detection of deregulated links, and develop a novel and effective regulatory path-based approach in finding deregulated modules. Observing that a regulatory pathway between two genes might involve in multiple rather than a single path, we identify condition-specific core regulatory path (CCRP to detect the significant deregulation of regulatory links. Using time-series gene expression, we define the regulatory strength within each gene pair based on statistical dependence analysis. The CCRPs in regulatory networks can then be identified using the shortest path algorithm. Finally, we derive the deregulated modules by integrating the differential edges (as deregulated links of the CCRPs between the case and the control group. To demonstrate the effectiveness of our approach, we apply the method to expression data associated with different states of Human Epidermal Growth Factor Receptor 2 (HER2. The experimental results show that the genes as well as the links in the deregulated modules are significantly enriched in multiple KEGG pathways and GO biological processes, most of which can be validated to suffer from impact of this oncogene based on previous studies. Additionally, we find the regulatory mechanism associated with the crucial gene SNAI1 significantly deregulated resulting from the activation of HER2. Hence, our method provides not only a strategy for detecting the deregulated links in regulatory networks, but also a way to identify concerning deregulated modules, thus contributing to the target selection of edgetic drugs.
Energy Technology Data Exchange (ETDEWEB)
Arraut, Ivan [Institute of Theoretical Physics, Chinese Academy of Science, State Key Laboratory of Theoretical Physics, Beijing (China)
2017-08-15
If we apply the path-integral formulation in order to analyze the particle creation process of black holes inside the non-linear formulation of massive gravity, it is possible to demonstrate that the effect of the extra degrees of freedom is to deform the periodicity of the poles of the propagator in the complex t-plane. This might create the effect of extra particle creation process at scales where the extra degrees of freedom become relevant. For stationary solutions, depending on the values taken by the free parameters of the theory, the periodicity structure of the propagator reveal two effects. The first one is a shift on the positions of the pole of the propagator with respect to the GR case, affecting then the instant at which the particles are detected. The second one is the existence of branch points, affecting then the perception of particles. The branch point can be finite (including the zero order case) or infinite, depending on the free parameters of the theory. (orig.)
International Nuclear Information System (INIS)
Arraut, Ivan
2017-01-01
If we apply the path-integral formulation in order to analyze the particle creation process of black holes inside the non-linear formulation of massive gravity, it is possible to demonstrate that the effect of the extra degrees of freedom is to deform the periodicity of the poles of the propagator in the complex t-plane. This might create the effect of extra particle creation process at scales where the extra degrees of freedom become relevant. For stationary solutions, depending on the values taken by the free parameters of the theory, the periodicity structure of the propagator reveal two effects. The first one is a shift on the positions of the pole of the propagator with respect to the GR case, affecting then the instant at which the particles are detected. The second one is the existence of branch points, affecting then the perception of particles. The branch point can be finite (including the zero order case) or infinite, depending on the free parameters of the theory. (orig.)
Controlling low-rate signal path microdischarge for an ultra-low-background proportional counter
International Nuclear Information System (INIS)
Mace, E.K.; Aalseth, C.E.; Bonicalzi, R.M.; Day, A.R.; Hoppe, E.W.; Keillor, M.E.; Myers, A.W.; Overman, C.T.; Seifert, A.
2013-01-01
Pacific Northwest National Laboratory (PNNL) has developed an ultra-low-background proportional counter (ULBPC) made of high purity copper. These detectors are part of an ultra-low-background counting system (ULBCS) in the newly constructed shallow underground laboratory at PNNL (at a depth of ∼30 m water-equivalent). To control backgrounds, the current preamplifier electronics are located outside the ULBCS shielding. Thus the signal from the detector travels through ∼1 m of cable and is potentially susceptible to high voltage microdischarge and other sources of electronic noise. Based on initial successful tests, commercial cables and connectors were used for this critical signal path. Subsequent testing across different batches of commercial cables and connectors, however, showed unwanted (but still low) rates of microdischarge noise. To control this noise source, two approaches were pursued: first, to carefully validate cables, connectors, and other commercial components in this critical signal path, making modifications where necessary; second, to develop a custom low-noise, low-background preamplifier that can be integrated with the ULBPC and thus remove most commercial components from the critical signal path. This integrated preamplifier approach is based on the Amptek A250 low-noise charge-integrating preamplifier module. The initial microdischarge signals observed are presented and characterized according to the suspected source. Each of the approaches for mitigation is described, and the results from both are compared with each other and with the original performance seen with commercial cables and connectors. (author)
The DOZZ formula from the path integral
Kupiainen, Antti; Rhodes, Rémi; Vargas, Vincent
2018-05-01
We present a rigorous proof of the Dorn, Otto, Zamolodchikov, Zamolodchikov formula (the DOZZ formula) for the 3 point structure constants of Liouville Conformal Field Theory (LCFT) starting from a rigorous probabilistic construction of the functional integral defining LCFT given earlier by the authors and David. A crucial ingredient in our argument is a probabilistic derivation of the reflection relation in LCFT based on a refined tail analysis of Gaussian multiplicative chaos measures.