Path integral method for DNA denaturation
NASA Astrophysics Data System (ADS)
Zoli, Marco
2009-04-01
The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillment of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature Tc∗ , whereas the fraction of unbound base pairs grows continuously around and above Tc∗ . The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appears as a highly cooperative phenomenon displaying a smooth crossover versus T . The thermodynamical properties have been computed in a large temperature range by varying the size of the path ensemble at the lower bound of the range. No significant physical dependence on the system size has been envisaged. The entropy grows continuously versus T while the specific heat displays a remarkable peak at Tc∗ . The location of the peak versus T varies with the stiffness of the anharmonic stacking interaction along the strand. The presented results suggest that denaturation in homogeneous DNA has the features of a second-order phase transition. The method accounts for the cooperative behavior of a very large number of degrees of freedom while the computation time is kept within a reasonable limit.
Path Integral Monte Carlo Methods for Fermions
NASA Astrophysics Data System (ADS)
Ethan, Ethan; Dubois, Jonathan; Ceperley, David
2014-03-01
In general, Quantum Monte Carlo methods suffer from a sign problem when simulating fermionic systems. This causes the efficiency of a simulation to decrease exponentially with the number of particles and inverse temperature. To circumvent this issue, a nodal constraint is often implemented, restricting the Monte Carlo procedure from sampling paths that cause the many-body density matrix to change sign. Unfortunately, this high-dimensional nodal surface is not a priori known unless the system is exactly solvable, resulting in uncontrolled errors. We will discuss two possible routes to extend the applicability of finite-temperatue path integral Monte Carlo. First we extend the regime where signful simulations are possible through a novel permutation sampling scheme. Afterwards, we discuss a method to variationally improve the nodal surface by minimizing a free energy during simulation. Applications of these methods will include both free and interacting electron gases, concluding with discussion concerning extension to inhomogeneous systems. Support from DOE DE-FG52-09NA29456, DE-AC52-07NA27344, LLNL LDRD 10- ERD-058, and the Lawrence Scholar program.
Path Integrals and Exotic Options:. Methods and Numerical Results
NASA Astrophysics Data System (ADS)
Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.
2005-09-01
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.
NASA Astrophysics Data System (ADS)
Lloyd, Seth; Dreyer, Olaf
2016-02-01
Path integrals calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration. This paper defines a universal path integral, which sums over all computable structures. This path integral contains as sub-integrals all possible computable path integrals, including those of field theory, the standard model of elementary particles, discrete models of quantum gravity, string theory, etc. The universal path integral possesses a well-defined measure that guarantees its finiteness. The probabilities for events corresponding to sub-integrals can be calculated using the method of decoherent histories. The universal path integral supports a quantum theory of the universe in which the world that we see around us arises out of the interference between all computable structures.
Nearest neighbor interaction in the Path Integral Renormalization Group method
NASA Astrophysics Data System (ADS)
de Silva, Wasanthi; Clay, R. Torsten
2014-03-01
The Path Integral Renormalization Group (PIRG) method is an efficient numerical algorithm for studying ground state properties of strongly correlated electron systems. The many-body ground state wave function is approximated by an optimized linear combination of Slater determinants which satisfies the variational principle. A major advantage of PIRG is that is does not suffer the Fermion sign problem of quantum Monte Carlo. Results are exact in the noninteracting limit and can be enhanced using space and spin symmetries. Many observables can be calculated using Wick's theorem. PIRG has been used predominantly for the Hubbard model with a single on-site Coulomb interaction U. We describe an extension of PIRG to the extended Hubbard model (EHM) including U and a nearest-neighbor interaction V. The EHM is particularly important in models of charge-transfer solids (organic superconductors) and at 1/4-filling drives a charge-ordered state. The presence of lattice frustration also makes studying these systems difficult. We test the method with comparisons to small clusters and long one dimensional chains, and show preliminary results for a coupled-chain model for the (TMTTF)2X materials. This work was supported by DOE grant DE-FG02-06ER46315.
Path-integral method for the source apportionment of photochemical pollutants
NASA Astrophysics Data System (ADS)
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
Path Integral Simulations of Graphene
NASA Astrophysics Data System (ADS)
Yousif, Hosam
2007-10-01
Some properties of graphene are explored using a path integral approach. The path integral method allows us to simulate relatively large systems using monte carlo techniques and extract thermodynamic quantities. We simulate the effects of screening a large external charge potential, as well as conductivity and charge distributions in graphene sheets.
Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method
ERIC Educational Resources Information Center
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.)
Path Integrals and Supersolids
NASA Astrophysics Data System (ADS)
Ceperley, D. M.
2008-11-01
Recent experiments by Kim and Chan on solid 4He have been interpreted as discovery of a supersolid phase of matter. Arguments based on wavefunctions have shown that such a phase exists, but do not necessarily apply to solid 4He. Imaginary time path integrals, implemented using Monte Carlo methods, provide a definitive answer; a clean system of solid 4He should be a normal quantum solid, not one with superfluid properties. The Kim-Chan phenomena must be due to defects introduced when the solid is formed.
Accelerated path integral methods for atomistic simulations at ultra-low temperatures
NASA Astrophysics Data System (ADS)
Uhl, Felix; Marx, Dominik; Ceriotti, Michele
2016-08-01
Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat (PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH5+. We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH4 to illustrate the limits of using such colored noise thermostats close to the many body quantum ground state.
Accelerated path integral methods for atomistic simulations at ultra-low temperatures.
Uhl, Felix; Marx, Dominik; Ceriotti, Michele
2016-08-01
Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat (PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH5 (+). We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH4 to illustrate the limits of using such colored noise thermostats close to the many body quantum ground state. PMID:27497533
Computing energy spectra for quantum systems using the Feynman-Kac path integral method
NASA Astrophysics Data System (ADS)
Rejcek, J. M.; Fazleev, N. G.
2009-10-01
We use group theory considerations and properties of a continuous path to define a failure tree numerical procedure for calculating the lowest energy eigenvalues for quantum systems using the Feynman-Kac path integral method. Within this method the solution of the imaginary time Schr"odinger equation is approximated by random walk simulations on a discrete grid constrained only by symmetry considerations of the Hamiltonian. The required symmetry constraints on random walk simulations are associated with a given irreducible representation and are found by identifying the eigenvalues for the irreducible representations corresponding to the symmetric or antisymmetric eigenfunctions for each group operator. The numerical method is applied to compute the eigenvalues of the ground and excited states of the hydrogen and helium atoms.
Error Reduction Methods for Integrated-path Differential-absorption Lidar Measurements
NASA Technical Reports Server (NTRS)
Chen, Jeffrey R.; Numata, Kenji; Wu, Stewart T.
2012-01-01
We report new modeling and error reduction methods for differential-absorption optical-depth (DAOD) measurements of atmospheric constituents using direct-detection integrated-path differential-absorption lidars. Errors from laser frequency noise are quantified in terms of the line center fluctuation and spectral line shape of the laser pulses, revealing relationships verified experimentally. A significant DAOD bias is removed by introducing a correction factor. Errors from surface height and reflectance variations can be reduced to tolerable levels by incorporating altimetry knowledge and "log after averaging", or by pointing the laser and receiver to a fixed surface spot during each wavelength cycle to shorten the time of "averaging before log".
Calculating splittings between energy levels of different symmetry using path-integral methods.
Mátyus, Edit; Althorpe, Stuart C
2016-03-21
It is well known that path-integral methods can be used to calculate the energy splitting between the ground and the first excited state. Here we show that this approach can be generalized to give the splitting patterns between all the lowest energy levels from different symmetry blocks that lie below the first-excited totally symmetric state. We demonstrate this property numerically for some two-dimensional models. The approach is likely to be useful for computing rovibrational energy levels and tunnelling splittings in floppy molecules and gas-phase clusters. PMID:27004864
Error reduction methods for integrated-path differential-absorption lidar measurements.
Chen, Jeffrey R; Numata, Kenji; Wu, Stewart T
2012-07-01
We report new modeling and error reduction methods for differential-absorption optical-depth (DAOD) measurements of atmospheric constituents using direct-detection integrated-path differential-absorption lidars. Errors from laser frequency noise are quantified in terms of the line center fluctuation and spectral line shape of the laser pulses, revealing relationships verified experimentally. A significant DAOD bias is removed by introducing a correction factor. Errors from surface height and reflectance variations can be reduced to tolerable levels by incorporating altimetry knowledge and "log after averaging", or by pointing the laser and receiver to a fixed surface spot during each wavelength cycle to shorten the time of "averaging before log". PMID:22772254
Thermoalgebras and path integral
NASA Astrophysics Data System (ADS)
Khanna, F. C.; Malbouisson, A. P. C.; Malbouisson, J. M. C.; Santana, A. E.
2009-09-01
Using a representation for Lie groups closely associated with thermal problems, we derive the algebraic rules of the real-time formalism for thermal quantum field theories, the so-called thermo-field dynamics (TFD), including the tilde conjugation rules for interacting fields. These thermo-group representations provide a unified view of different approaches for finite-temperature quantum fields in terms of a symmetry group. On these grounds, a path integral formalism is constructed, using Bogoliubov transformations, for bosons, fermions and non-abelian gauge fields. The generalization of the results for quantum fields in (S1)d×R topology is addressed.
Squeezed states and path integrals
NASA Technical Reports Server (NTRS)
Daubechies, Ingrid; Klauder, John R.
1992-01-01
The continuous-time regularization scheme for defining phase-space path integrals is briefly reviewed as a method to define a quantization procedure that is completely covariant under all smooth canonical coordinate transformations. As an illustration of this method, a limited set of transformations is discussed that have an image in the set of the usual squeezed states. It is noteworthy that even this limited set of transformations offers new possibilities for stationary phase approximations to quantum mechanical propagators.
NASA Astrophysics Data System (ADS)
Imada, Masatoshi; Kashima, Tsuyoshi
2000-09-01
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after a numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from the optimized linear combination of retained states in the truncated Hilbert space with a numerically chosen basis. This algorithm does not suffer from the negative sign problem and can be applied to any type of Hamiltonian in any dimension. The efficiency is tested in examples of the Hubbard model where the basis of Slater determinants is numerically optimized. We show results on fast convergence and accuracy achieved with a small number of retained states.
Scattering theory with path integrals
Rosenfelder, R.
2014-03-15
Starting from well-known expressions for the T-matrix and its derivative in standard nonrelativistic potential scattering, I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow immediately.
Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas
2014-06-21
We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψ{sub T}, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 − 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.
NASA Astrophysics Data System (ADS)
Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas
2014-06-01
We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψT, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 - 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.
Torsional path integral Monte Carlo method for the quantum simulation of large molecules
NASA Astrophysics Data System (ADS)
Miller, Thomas F.; Clary, David C.
2002-05-01
A molecular application is introduced for calculating quantum statistical mechanical expectation values of large molecules at nonzero temperatures. The Torsional Path Integral Monte Carlo (TPIMC) technique applies an uncoupled winding number formalism to the torsional degrees of freedom in molecular systems. The internal energy of the molecules ethane, n-butane, n-octane, and enkephalin are calculated at standard temperature using the TPIMC technique and compared to the expectation values obtained using the harmonic oscillator approximation and a variational technique. All studied molecules exhibited significant quantum mechanical contributions to their internal energy expectation values according to the TPIMC technique. The harmonic oscillator approximation approach to calculating the internal energy performs well for the molecules presented in this study but is limited by its neglect of both anharmonicity effects and the potential coupling of intramolecular torsions.
Path Integrals on Ultrametric Spaces.
NASA Astrophysics Data System (ADS)
Blair, Alan
A framework for the study of path integrals on adelic spaces is developed, and it is shown that a family of path space measures on the localizations of an algebraic number field may, under certain conditions, be combined to form a global path space measure on its adele ring. An operator on the field of p-adic numbers analogous to the harmonic oscillator operator is then analyzed, and used to construct an Ornstein-Uhlenbeck type process on the adele ring of the rationals. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617 -253-5668; Fax 617-253-1690.).
Nasif, Hesham R.; Neyama, Atsushi
2002-07-01
This work represents a WIRS code developed using wavelet Galerkin method to solve radionuclide transport model in near field and far field of a repository for high-level radioactive waste. After overpack failure, radionuclides diffuse through the bentonite buffer material to the water bearing fracture around the repository transport horizontally through this geosphere then transport vertically through the major water conducting fault (MWCF) reach the biosphere. The radionuclides transport barriers considered in this model are engineered barrier system (EBS), geosphere, and MWCF. Hydraulic conductivity of the bentonite is more than three orders of magnitude smaller than that of the surrounding host rock, so the only transport mechanism through EBS is diffusion. In the host rock, the problem is of advection-diffusion type with highly varying parameters from one medium to other due to the variability in length, transmissivity and other transport-relevant properties of the transport paths. Daubechies' wavelet is used as a basis function to solve the nonlinear partial differential equations arising from the model formulation of the radionuclides transport. Since the scaling functions are compactly supported, only a finite number of the connection coefficients are nonzero. The resultant matrix has a block diagonal structure, which can be inverted easily. We tested our WGM algorithm with several problems to verify the model. The solutions are very accurate with a proper selection of Daubechies' order and dilation order. The solution is very accurate at the interfaces where the radionuclide concentration exhibits very steep gradients. (authors)
Integrated assignment and path planning
NASA Astrophysics Data System (ADS)
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
Numerical evaluation of Feynman path integrals
NASA Astrophysics Data System (ADS)
Baird, William Hugh
1999-11-01
The notion of path integration developed by Feynman, while an incredibly successful method of solving quantum mechanical problems, leads to frequently intractable integrations over an infinite number of paths. Two methods now exist which sidestep this difficulty by defining "densities" of actions which give the relative number of paths found at different values of the action. These densities are sampled by computer generation of paths and the propagators are found to a high degree of accuracy for the case of a particle on the infinite half line and in a finite square well in one dimension. The problem of propagation within a two dimensional radial well is also addressed as the precursor to the problem of a particle in a stadium (quantum billiard).
Optical tomography with discretized path integral.
Yuan, Bingzhi; Tamaki, Toru; Kushida, Takahiro; Mukaigawa, Yasuhiro; Kubo, Hiroyuki; Raytchev, Bisser; Kaneda, Kazufumi
2015-07-01
We present a framework for optical tomography based on a path integral. Instead of directly solving the radiative transport equations, which have been widely used in optical tomography, we use a path integral that has been developed for rendering participating media based on the volume rendering equation in computer graphics. For a discretized two-dimensional layered grid, we develop an algorithm to estimate the extinction coefficients of each voxel with an interior point method. Numerical simulation results are shown to demonstrate that the proposed method works well. PMID:26839903
NASA Astrophysics Data System (ADS)
Ling, Hong; Schäfer, Klaus; Xin, Jinyuan; Qin, Min; Suppan, Peter; Wang, Yuesi
2014-08-01
Traffic emissions are a very important factor in Beijing's urban air quality. To investigate small-scale spatial variations in air pollutants, a campaign was carried out from April 2009 through March 2011 in Beijing. DOAS (differential optical absorption spectroscopy) systems and in situ instruments were used. Atmospheric NO, NO2, O3 and SO2 mixing ratios were monitored. Meanwhile, HCHO mixing ratios were measured by two different DOAS systems. Diurnal variations of these mixing ratios were analysed. Differences between the path-integrated and in situ measurements were investigated based on the results from the campaign. The influences of different weather situations, dilution conditions and light-path locations were investigated as well. The results show that the differences between path-integrated and in situ mixing ratios were affected by combinations of emission source strengths, weather conditions, chemical transformations and local convection. Path-integrated measurements satisfy the requirements of traffic emission investigations better than in situ measurements.
Path integral for inflationary perturbations
NASA Astrophysics Data System (ADS)
Prokopec, Tomislav; Rigopoulos, Gerasimos
2010-07-01
The quantum theory of cosmological perturbations in single-field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well-known gauge-invariant quadratic action for scalar and tensor perturbations, and determine the interactions to arbitrary order. This approach does not require the explicit solution of the energy and momentum constraints, a novel feature which simplifies the determination of the interaction vertices. The constraints and the necessary imposition of gauge conditions is reflected in the appearance of various commuting and anticommuting auxiliary fields in the action. These auxiliary fields are not propagating physical degrees of freedom but need to be included in internal lines and loops in a diagrammatic expansion. To illustrate the formalism we discuss the tree-level three-point and four-point functions of the inflaton perturbations, reproducing the results already obtained by the methods used in the current literature. Loop calculations are left for future work.
Özarslan, Evren; Westin, Carl-Fredrik; Mareci, Thomas H.
2016-01-01
The influence of Gaussian diffusion on the magnetic resonance signal is determined by the apparent diffusion coefficient (ADC) and tensor (ADT) of the diffusing fluid as well as the gradient waveform applied to sensitize the signal to diffusion. Estimations of ADC and ADT from diffusion-weighted acquisitions necessitate computations of, respectively, the b-value and b-matrix associated with the employed pulse sequence. We establish the relationship between these quantities and the gradient waveform by expressing the problem as a path integral and explicitly evaluating it. Further, we show that these important quantities can be conveniently computed for any gradient waveform using a simple algorithm that requires a few lines of code. With this representation, our technique complements the multiple correlation function (MCF) method commonly used to compute the effects of restricted diffusion, and provides a consistent and convenient framework for studies that aim to infer the microstructural features of the specimen. PMID:27182208
NASA Technical Reports Server (NTRS)
Taylor, B.
1990-01-01
The design of Integrated Circuits has evolved past the black art practiced by a few semiconductor companies to a world wide community of users. This was basically accomplished by the development of computer aided design tools which were made available to this community. As the tools matured into different components of the design task they were accepted into the community at large. However, the next step in this evolution is being ignored by the large tool vendors hindering the continuation of this process. With system level definition and simulation through the logic specification well understood, why is the physical generation so blatantly ignored. This portion of the development is still treated as an isolated task with information being passed from the designer to the layout function. Some form of result given back but it severely lacks full definition of what has transpired. The level of integration in I.C.'s for tomorrow, whether through new processes or applications will require higher speeds, increased transistor density, and non-digital performance which can only be achieved through attention to the physical implementation.
Quantitative Molecular Thermochemistry Based on Path Integrals
Glaesemann, K R; Fried, L E
2005-03-14
The calculation of thermochemical data requires accurate molecular energies and heat capacities. Traditional methods rely upon the standard harmonic normal mode analysis to calculate the vibrational and rotational contributions. We utilize path integral Monte Carlo (PIMC) for going beyond the harmonic analysis, to calculate the vibrational and rotational contributions to ab initio energies. This is an application and extension of a method previously developed in our group.
Path integral learning of multidimensional movement trajectories
NASA Astrophysics Data System (ADS)
André, João; Santos, Cristina; Costa, Lino
2013-10-01
This paper explores the use of Path Integral Methods, particularly several variants of the recent Path Integral Policy Improvement (PI2) algorithm in multidimensional movement parametrized policy learning. We rely on Dynamic Movement Primitives (DMPs) to codify discrete and rhythmic trajectories, and apply the PI2-CMA and PIBB methods in the learning of optimal policy parameters, according to different cost functions that inherently encode movement objectives. Additionally we merge both of these variants and propose the PIBB-CMA algorithm, comparing all of them with the vanilla version of PI2. From the obtained results we conclude that PIBB-CMA surpasses all other methods in terms of convergence speed and iterative final cost, which leads to an increased interest in its application to more complex robotic problems.
Nagashima, H; Tsuda, S; Tsuboi, N; Koshi, M; Hayashi, K A; Tokumasu, T
2014-04-01
In this paper, we describe the analysis of the thermodynamic properties of cryogenic hydrogen using classical molecular dynamics (MD) and path integral MD (PIMD) method to understand the effects of the quantum nature of hydrogen molecules. We performed constant NVE MD simulations across a wide density-temperature region to establish an equation of state (EOS). Moreover, the quantum effect on the difference of molecular mechanism of pressure-volume-temperature relationship was addressed. The EOS was derived based on the classical mechanism idea only using the MD simulation results. Simulation results were compared with each MD method and experimental data. As a result, it was confirmed that although the EOS on the basis of classical MD cannot reproduce the experimental data of saturation property of hydrogen in the high-density region, the EOS on the basis of PIMD well reproduces those thermodynamic properties of hydrogen. Moreover, it was clarified that taking quantum effects into account makes the repulsion force larger and the potential well shallower. Because of this mechanism, the intermolecular interaction of hydrogen molecules diminishes and the virial pressure increases. PMID:24712800
Nagashima, H.; Tsuda, S.; Tsuboi, N.; Koshi, M.; Hayashi, K. A.; Tokumasu, T.
2014-04-07
In this paper, we describe the analysis of the thermodynamic properties of cryogenic hydrogen using classical molecular dynamics (MD) and path integral MD (PIMD) method to understand the effects of the quantum nature of hydrogen molecules. We performed constant NVE MD simulations across a wide density–temperature region to establish an equation of state (EOS). Moreover, the quantum effect on the difference of molecular mechanism of pressure–volume–temperature relationship was addressed. The EOS was derived based on the classical mechanism idea only using the MD simulation results. Simulation results were compared with each MD method and experimental data. As a result, it was confirmed that although the EOS on the basis of classical MD cannot reproduce the experimental data of saturation property of hydrogen in the high-density region, the EOS on the basis of PIMD well reproduces those thermodynamic properties of hydrogen. Moreover, it was clarified that taking quantum effects into account makes the repulsion force larger and the potential well shallower. Because of this mechanism, the intermolecular interaction of hydrogen molecules diminishes and the virial pressure increases.
NASA Astrophysics Data System (ADS)
Yolcu, Cem; Memiç, Muhammet; Şimşek, Kadir; Westin, Carl-Fredrik; Özarslan, Evren
2016-05-01
We study the influence of diffusion on NMR experiments when the molecules undergo random motion under the influence of a force field and place special emphasis on parabolic (Hookean) potentials. To this end, the problem is studied using path integral methods. Explicit relationships are derived for commonly employed gradient waveforms involving pulsed and oscillating gradients. The Bloch-Torrey equation, describing the temporal evolution of magnetization, is modified by incorporating potentials. A general solution to this equation is obtained for the case of parabolic potential by adopting the multiple correlation function (MCF) formalism, which has been used in the past to quantify the effects of restricted diffusion. Both analytical and MCF results were found to be in agreement with random walk simulations. A multidimensional formulation of the problem is introduced that leads to a new characterization of diffusion anisotropy. Unlike the case of traditional methods that employ a diffusion tensor, anisotropy originates from the tensorial force constant, and bulk diffusivity is retained in the formulation. Our findings suggest that some features of the NMR signal that have traditionally been attributed to restricted diffusion are accommodated by the Hookean model. Under certain conditions, the formalism can be envisioned to provide a viable approximation to the mathematically more challenging restricted diffusion problems.
NASA Astrophysics Data System (ADS)
Wong, Kin-Yiu
We have simulated two enzymatic reactions with molecular dynamics (MD) and combined quantum mechanical/molecular mechanical (QM/MM) techniques. One reaction is the hydrolysis of the insecticide paraoxon catalyzed by phosphotriesterase (PTE). PTE is a bioremediation candidate for environments contaminated by toxic nerve gases (e.g., sarin) or pesticides. Based on the potential of mean force (PMF) and the structural changes of the active site during the catalysis, we propose a revised reaction mechanism for PTE. Another reaction is the hydrolysis of the second-messenger cyclic adenosine 3'-5'-monophosphate (cAMP) catalyzed by phosphodiesterase (PDE). Cyclicnucleotide PDE is a vital protein in signal-transduction pathways and thus a popular target for inhibition by drugs (e.g., ViagraRTM). A two-dimensional (2-D) free-energy profile has been generated showing that the catalysis by PDE proceeds in a two-step SN2-type mechanism. Furthermore, to characterize a chemical reaction mechanism in experiment, a direct probe is measuring kinetic isotope effects (KIEs). KIEs primarily arise from internuclear quantum-statistical effects, e.g., quantum tunneling and quantization of vibration. To systematically incorporate the quantum-statistical effects during MD simulations, we have developed an automated integration-free path-integral (AIF-PI) method based on Kleinert's variational perturbation theory for the centroid density of Feynman's path integral. Using this analytic method, we have performed ab initio pathintegral calculations to study the origin of KIEs on several series of proton-transfer reactions from carboxylic acids to aryl substituted alpha-methoxystyrenes in water. In addition, we also demonstrate that the AIF-PI method can be used to systematically compute the exact value of zero-point energy (beyond the harmonic approximation) by simply minimizing the centroid effective potential.
Polymer quantum mechanics some examples using path integrals
Parra, Lorena; Vergara, J. David
2014-01-14
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.
Fractional Levy motion through path integrals
Calvo, Ivan; Sanchez, Raul; Carreras, Benjamin A
2009-01-01
Fractional Levy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the propagator of fLm by using path integral methods. The propagators of Brownian motion and fractional Brownian motion are recovered as particular cases. The fractional diffusion equation corresponding to fLm is also obtained.
Dunker, Alan M; Koo, Bonyoung; Yarwood, Greg
2015-06-01
The anthropogenic increment of a species is the difference in concentration between a base-case simulation with all emissions included and a background simulation without the anthropogenic emissions. The Path-Integral Method (PIM) is a new technique that can determine the contributions of individual anthropogenic sources to this increment. The PIM was applied to a simulation of O3 formation in July 2030 in the U.S., using the Comprehensive Air Quality Model with Extensions and assuming advanced controls on light-duty vehicles (LDVs) and other sources. The PIM determines the source contributions by integrating first-order sensitivity coefficients over a range of emissions, a path, from the background case to the base case. There are many potential paths, with each representing a specific emission-control strategy leading to zero anthropogenic emissions, i.e., controlling all sources together versus controlling some source(s) preferentially are different paths. Three paths were considered, and the O3, formaldehyde, and NO2 anthropogenic increments were apportioned to five source categories. At rural and urban sites in the eastern U.S. and for all three paths, point sources typically have the largest contribution to the O3 and NO2 anthropogenic increments, and either LDVs or area sources, the smallest. Results for formaldehyde are more complex. PMID:25938820
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. PMID:26701710
NASA Astrophysics Data System (ADS)
Mielke, Steven L.; Truhlar, Donald G.
2015-01-01
We present an improved version of our "path-by-path" enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P-6) to O(P-12), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational-rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan-Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ˜1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300-3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.
Local-time representation of path integrals
NASA Astrophysics Data System (ADS)
Jizba, Petr; Zatloukal, Václav
2015-12-01
We derive a local-time path-integral representation for a generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over x -dependent local-time profiles. The latter quantify the time that the sample paths x (t ) in the Feynman path integral spend in the vicinity of an arbitrary point x . Generalization of the local-time representation that includes arbitrary functionals of the local time is also provided. We argue that the results obtained represent a powerful alternative to the traditional Feynman-Kac formula, particularly in the high- and low-temperature regimes. To illustrate this point, we apply our local-time representation to analyze the asymptotic behavior of the Bloch density matrix at low temperatures. Further salient issues, such as connections with the Sturm-Liouville theory and the Rayleigh-Ritz variational principle, are also discussed.
Path-integral derivation of the complex ABCD Huygens integral
Wright, E.M.; Garrison, J.C.
1987-09-01
The Huygens integral, or Green's function, for paraxial beam propagation in a generalized lenslike medium is derived as a Feynman path integral involving a summation over real rays. This formulation provides a physically intuitive understanding of the structure of the Green's function. The path integral is evaluated by introducing in a consistent manner the notion of complex rays, and the familiar result for the Huygens integral in terms of the complex ABCD matrix of the medium is obtained.
Mielke, Steven L; Truhlar, Donald G
2016-01-21
Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function. PMID:26801023
NASA Astrophysics Data System (ADS)
Mielke, Steven L.; Truhlar, Donald G.
2016-01-01
Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.
Mielke, Steven L. E-mail: truhlar@umn.edu; Truhlar, Donald G. E-mail: truhlar@umn.edu
2015-01-28
We present an improved version of our “path-by-path” enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P{sup −6}) to O(P{sup −12}), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational–rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan–Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ∼1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300–3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.
NASA Astrophysics Data System (ADS)
Blair, Alan D.
A framework for the study of path integrals on adèlic spaces is developed, and it is shown that a family of path space measures on the localizations of an algebraic number field may, under certain conditions, be combined to form a global path space measure on its adèle ring. An operator on the field of p-adic numbers analogous to the harmonic oscillator operator is then analyzed, and used to construct an Ornstein-Uhlenbeck type process on the adèle ring of the rationals.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Mielke, Steven L.; Dinpajooh, Mohammadhasan; Siepmann, J. Ilja; Truhlar, Donald G.
2013-01-01
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.
Quantum state of wormholes and path integral
Garay, L.J. )
1991-08-15
The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface {ital S} which divides the spacetime manifold into two disconnected parts. The ground-state wave function is picked out by requiring that there be no matter excitations in the asymptotic region. Once the path integrals over the lapse and shift functions are evaluated, the requirement that the spacetime be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is claimed that no wave function exists which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. The wormhole wave functions are worked out in minisuperspace models with massless minimal and conformal scalar fields.
Fermionic path integrals and local anomalies
NASA Astrophysics Data System (ADS)
Roepstorff, G.
2003-05-01
No doubt, the subject of path integrals proved to be an immensely fruitful human, i.e. Feynman's idea. No wonder it is more timely than ever. Some even claim that it is the most daring, innovative and revolutionary idea since the days of Heisenberg and Bohr. It is thus likely to generate enthusiasm, if not addiction among physicists who seek simplicity together with perfection. Professor Devreese's long-lasting interest in, if not passion on the subject stems from his firm conviction that, beyond being the tool of choice, path integration provides the key to all quantum phenomena, be it in solid state, atomic, molecular or particle physics as evidenced by the impressive list of publications at the address http://lib.ua.ac.be/AB/a867.html. In this note, I review a pitfall of fermionic path integrals and a way to get around it in situations relevant to the Standard Model of particle physics.
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. PMID:19962387
Local-time representation of path integrals.
Jizba, Petr; Zatloukal, Václav
2015-12-01
We derive a local-time path-integral representation for a generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over x-dependent local-time profiles. The latter quantify the time that the sample paths x(t) in the Feynman path integral spend in the vicinity of an arbitrary point x. Generalization of the local-time representation that includes arbitrary functionals of the local time is also provided. We argue that the results obtained represent a powerful alternative to the traditional Feynman-Kac formula, particularly in the high- and low-temperature regimes. To illustrate this point, we apply our local-time representation to analyze the asymptotic behavior of the Bloch density matrix at low temperatures. Further salient issues, such as connections with the Sturm-Liouville theory and the Rayleigh-Ritz variational principle, are also discussed. PMID:26764662
A taxonomy of integral reaction path analysis
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.
Mining Relational Paths in Integrated Biomedical Data
He, Bing; Tang, Jie; Ding, Ying; Wang, Huijun; Sun, Yuyin; Shin, Jae Hong; Chen, Bin; Moorthy, Ganesh; Qiu, Judy; Desai, Pankaj; Wild, David J.
2011-01-01
Much life science and biology research requires an understanding of complex relationships between biological entities (genes, compounds, pathways, diseases, and so on). There is a wealth of data on such relationships in publicly available datasets and publications, but these sources are overlapped and distributed so that finding pertinent relational data is increasingly difficult. Whilst most public datasets have associated tools for searching, there is a lack of searching methods that can cross data sources and that in particular search not only based on the biological entities themselves but also on the relationships between them. In this paper, we demonstrate how graph-theoretic algorithms for mining relational paths can be used together with a previous integrative data resource we developed called Chem2Bio2RDF to extract new biological insights about the relationships between such entities. In particular, we use these methods to investigate the genetic basis of side-effects of thiazolinedione drugs, and in particular make a hypothesis for the recently discovered cardiac side-effects of Rosiglitazone (Avandia) and a prediction for Pioglitazone which is backed up by recent clinical studies. PMID:22162991
How to (path-) integrate by differentiating
NASA Astrophysics Data System (ADS)
Kempf, Achim; Jackson, David M.; Morales, Alejandro H.
2015-07-01
Path integrals are at the heart of quantum field theory. In spite of their covariance and seeming simplicity, they are hard to define and evaluate. In contrast, functional differentiation, as it is used, for example, in variational problems, is relatively straightforward. This has motivated the development of new techniques that allow one to express functional integration in terms of functional differentiation. In fact, the new techniques allow one to express integrals in general through differentiation. These techniques therefore add to the general toolbox for integration and for integral transforms such as the Fourier and Laplace transforms. Here, we review some of these results, we give simpler proofs and we add new results, for example, on expressing the Laplace transform and its inverse in terms of derivatives, results that may be of use in quantum field theory, e.g., in the context of heat traces.
Path-integral simulation of solids.
Herrero, C P; Ramírez, R
2014-06-11
The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practical techniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-IV materials (diamond and elemental semiconductors), and molecular solids (with emphasis on hydrogen and ice). Structural, vibrational, and thermodynamic properties of these materials are discussed. Applications also include point defects in solids (structure and diffusion), as well as nuclear quantum effects in solid surfaces and adsorbates. Different phenomena are discussed, as solid-to-solid and orientational phase transitions, rates of quantum processes, classical-to-quantum crossover, and various finite-temperature anharmonic effects (thermal expansion, isotopic effects, electron-phonon interactions). Nuclear quantum effects are most remarkable in the presence of light atoms, so that especial emphasis is laid on solids containing hydrogen as a constituent element or as an impurity. PMID:24810944
Path Integration: Effect of Curved Path Complexity and Sensory System on Blindfolded Walking
Koutakis, Panagiotis; Mukherjee, Mukul; Vallabhajosula, Srikant; Blanke, Daniel J.; Stergiou, Nicholas
2012-01-01
Path integration refers to the ability to integrate continuous information of the direction and distance travelled by the system relative to the origin. Previous studies have investigated path integration through blindfolded walking along simple paths such as straight line and triangles. However, limited knowledge exists regarding the role of path complexity in path integration. Moreover, little is known about how information from different sensory input systems (like vision and proprioception) contributes to accurate path integration. The purpose of the current study was to investigate how sensory information and curved path complexity affect path integration. Forty blindfolded participants had to accurately reproduce a curved path and return to the origin. They were divided into four groups that differed in the curved path, circle (simple) or figure-eight (complex), and received either visual (previously seen) or proprioceptive (previously guided) information about the path before they reproduced it. The dependent variables used were average trajectory error, walking speed, and distance travelled. The results indicated that (a) both groups that walked on a circular path and both groups that received visual information produced greater accuracy in reproducing the path. Moreover, the performance of the group that received proprioceptive information and later walked on a figure-eight path was less accurate than their corresponding circular group. The groups that had the visual information also walked faster compared to the group that had proprioceptive information. Results of the current study highlight the roles of different sensory inputs while performing blindfolded walking for path integration. PMID:22840893
Flexible integration of path-planning capabilities
NASA Astrophysics Data System (ADS)
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 for Dirac oscillator with generalized uncertainty principle
Benzair, H.; Boudjedaa, T.; Merad, M.
2012-12-15
The propagator for Dirac oscillator in (1+1) dimension, with deformed commutation relation of the Heisenberg principle, is calculated using path integral in quadri-momentum representation. As the mass is related to momentum, we then adapt the space-time transformation method to evaluate quantum corrections and this latter is dependent from the point discretization interval.
Transport path optimization algorithm based on fuzzy integrated weights
NASA Astrophysics Data System (ADS)
Hou, Yuan-Da; Xu, Xiao-Hao
2014-11-01
Natural disasters cause significant damage to roads, making route selection a complicated logistical problem. To overcome this complexity, we present a method of using a trapezoidal fuzzy number to select the optimal transport path. Using the given trapezoidal fuzzy edge coefficients, we calculate a fuzzy integrated matrix, and incorporate the fuzzy multi-weights into fuzzy integrated weights. The optimal path is determined by taking two sets of vertices and transforming undiscovered vertices into discoverable ones. Our experimental results show that the model is highly accurate, and requires only a few measurement data to confirm the optimal path. The model provides an effective, feasible, and convenient method to obtain weights for different road sections, and can be applied to road planning in intelligent transportation systems.
Path integral Monte Carlo and the electron gas
NASA Astrophysics Data System (ADS)
Brown, Ethan W.
Path integral Monte Carlo is a proven method for accurately simulating quantum mechanical systems at finite-temperature. By stochastically sampling Feynman's path integral representation of the quantum many-body density matrix, path integral Monte Carlo includes non-perturbative effects like thermal fluctuations and particle correlations in a natural way. Over the past 30 years, path integral Monte Carlo has been successfully employed to study the low density electron gas, high-pressure hydrogen, and superfluid helium. For systems where the role of Fermi statistics is important, however, traditional path integral Monte Carlo simulations have an exponentially decreasing efficiency with decreased temperature and increased system size. In this thesis, we work towards improving this efficiency, both through approximate and exact methods, as specifically applied to the homogeneous electron gas. We begin with a brief overview of the current state of atomic simulations at finite-temperature before we delve into a pedagogical review of the path integral Monte Carlo method. We then spend some time discussing the one major issue preventing exact simulation of Fermi systems, the sign problem. Afterwards, we introduce a way to circumvent the sign problem in PIMC simulations through a fixed-node constraint. We then apply this method to the homogeneous electron gas at a large swatch of densities and temperatures in order to map out the warm-dense matter regime. The electron gas can be a representative model for a host of real systems, from simple medals to stellar interiors. However, its most common use is as input into density functional theory. To this end, we aim to build an accurate representation of the electron gas from the ground state to the classical limit and examine its use in finite-temperature density functional formulations. The latter half of this thesis focuses on possible routes beyond the fixed-node approximation. As a first step, we utilize the variational
Quantum tunneling splittings from path-integral molecular dynamics.
Mátyus, Edit; Wales, David J; Althorpe, Stuart C
2016-03-21
We illustrate how path-integral molecular dynamics can be used to calculate ground-state tunnelling splittings in molecules or clusters. The method obtains the splittings from ratios of density matrix elements between the degenerate wells connected by the tunnelling. We propose a simple thermodynamic integration scheme for evaluating these elements. Numerical tests on fully dimensional malonaldehyde yield tunnelling splittings in good overall agreement with the results of diffusion Monte Carlo calculations. PMID:27004863
Song, Linze; Shi, Qiang
2015-11-21
Based on recent findings in the hierarchical equations of motion (HEOM) for correlated initial state [Y. Tanimura, J. Chem. Phys. 141, 044114 (2014)], we propose a new stochastic method to obtain the initial conditions for the real time HEOM propagation, which can be used further to calculate the equilibrium correlation functions and symmetrized correlation functions. The new method is derived through stochastic unraveling of the imaginary time influence functional, where a set of stochastic imaginary time HEOM are obtained. The validity of the new method is demonstrated using numerical examples including the spin-Boson model, and the Holstein model with undamped harmonic oscillator modes.
Song, Linze; Shi, Qiang
2015-11-21
Based on recent findings in the hierarchical equations of motion (HEOM) for correlated initial state [Y. Tanimura, J. Chem. Phys. 141, 044114 (2014)], we propose a new stochastic method to obtain the initial conditions for the real time HEOM propagation, which can be used further to calculate the equilibrium correlation functions and symmetrized correlation functions. The new method is derived through stochastic unraveling of the imaginary time influence functional, where a set of stochastic imaginary time HEOM are obtained. The validity of the new method is demonstrated using numerical examples including the spin-Boson model, and the Holstein model with undamped harmonic oscillator modes. PMID:26590526
QED spectra in the path integral formalism
NASA Astrophysics Data System (ADS)
Simonov, Yu. A.
2014-07-01
Relativistic Hamiltonians, derived from the path integrals, are known to provide a simple and useful formalism for hadron spectroscopy in QCD. The accuracy of this approach is tested using the QED systems, and the calculated spectrum is shown to reproduce exactly that of the Dirac hydrogen atom, while the Breit-Fermi nonrelativistic expansion is obtained using Foldy-Wouthuizen transformation. The calculated positronium spectrum, including spin-dependent terms, coincides with the standard QED perturbation theory to the considered order O(α4).
Path integral quantization of generalized quantum electrodynamics
Bufalo, R.; Pimentel, B. M.; Zambrano, G. E. R.
2011-02-15
In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the Hamiltonian structure of the system following Dirac's methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximations of all Green's functions and a discussion about the obtained results are presented.
Tackling higher derivative ghosts with the Euclidean path integral
Fontanini, Michele; Trodden, Mark
2011-05-15
An alternative to the effective field theory approach to treat ghosts in higher derivative theories is to attempt to integrate them out via the Euclidean path integral formalism. It has been suggested that this method could provide a consistent framework within which we might tolerate the ghost degrees of freedom that plague, among other theories, the higher derivative gravity models that have been proposed to explain cosmic acceleration. We consider the extension of this idea to treating a class of terms with order six derivatives, and find that for a general term the Euclidean path integral approach works in the most trivial background, Minkowski. Moreover we see that even in de Sitter background, despite some difficulties, it is possible to define a probability distribution for tensorial perturbations of the metric.
Building a cognitive map by assembling multiple path integration systems.
Wang, Ranxiao Frances
2016-06-01
Path integration and cognitive mapping are two of the most important mechanisms for navigation. Path integration is a primitive navigation system which computes a homing vector based on an animal's self-motion estimation, while cognitive map is an advanced spatial representation containing richer spatial information about the environment that is persistent and can be used to guide flexible navigation to multiple locations. Most theories of navigation conceptualize them as two distinctive, independent mechanisms, although the path integration system may provide useful information for the integration of cognitive maps. This paper demonstrates a fundamentally different scenario, where a cognitive map is constructed in three simple steps by assembling multiple path integrators and extending their basic features. The fact that a collection of path integration systems can be turned into a cognitive map suggests the possibility that cognitive maps may have evolved directly from the path integration system. PMID:26442503
Complexified Path Integrals, Exact Saddles, and Supersymmetry.
Behtash, Alireza; Dunne, Gerald V; Schäfer, Thomas; Sulejmanpasic, Tin; Ünsal, Mithat
2016-01-01
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semiclassical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real. We find new exact complex saddles, and show that without their contribution the semiclassical expansion is in conflict with basic properties such as the positive semidefiniteness of the spectrum, as well as constraints of supersymmetry. Generic saddles are not only complex, but also possibly multivalued and even singular. This is in contrast to instanton solutions, which are real, smooth, and single valued. The multivaluedness of the action can be interpreted as a hidden topological angle, quantized in units of π in supersymmetric theories. The general ideas also apply to nonsupersymmetric theories. PMID:26799010
Path integration and perturbation theory with complex Euclidean actions
NASA Astrophysics Data System (ADS)
Alexanian, Garnik; MacKenzie, R.; Paranjape, M. B.; Ruel, Jonathan
2008-05-01
The Euclidean path integral quite often involves an action that is not completely real, i.e. a complex action. This occurs when the Minkowski action contains t-odd CP-violating terms. This usually consists of topological terms, such as the Chern-Simons term in odd dimensions, the Wess-Zumino term, the θ term or Chern character in 4-dimensional gauge theories, or other topological densities. Analytic continuation to Euclidean time yields an imaginary term in the Euclidean action. It also occurs when the action contains fermions, the fermion path integral being in general a sum over positive and negative real numbers. Negative numbers correspond to the exponential of iπ and hence indicate the presence of an imaginary term in the action. In the presence of imaginary terms in the Euclidean action, the usual method of perturbative quantization can fail. Here the action is expanded about its critical points, the quadratic part serving to define the Gaussian free theory and the higher order terms defining the perturbative interactions. For a complex action, the critical points are generically obtained at complex field configurations. Hence the contour of path integration does not pass through the critical points and the perturbative paradigm cannot be directly implemented. The contour of path integration has to be deformed to pass through the complex critical point using a generalized method of steepest descent, in order to do so. Typically, this procedure is not followed. Rather, only the real part of the Euclidean action is considered, and its critical points are used to define the perturbation theory, a procedure that can lead to incorrect results. In this article we present a simple example to illustrate this point. The example consists of N scalar fields in 0+1 dimensions interacting with a U(1) gauge field in the presence of a Chern-Simons term. In this example the path integral can be done exactly, the procedure of deformation of the contour of path integration
Habershon, Scott
2013-09-14
We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency.
BOOK REVIEW: Path Integrals in Field Theory: An Introduction
NASA Astrophysics Data System (ADS)
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
On the Feynman Path Integral for Nonrelativistic Quantum Electrodynamics
NASA Astrophysics Data System (ADS)
Ichinose, Wataru
The Feynman path integral for regularized nonrelativistic quantum electrodynamics is studied rigorously. We begin with the Lagrangian function of the corresponding classical mechanics and construct the Feynman path integral. In the present paper, the electromagnetic potentials are assumed to be periodic with respect to a large box and quantized through their Fourier coefficients with large wave numbers cut off. Firstly, the Feynman path integral with respect to paths on the space of particles and vector potentials is defined rigorously by means of broken line paths under the constraints. Secondly, the Feynman path integral with respect to paths on the space of particles and electromagnetic potentials is also defined rigorously by means of broken line paths and piecewise constant paths without the constraints. This Feynman path integral is stated heuristically in Feynman and Hibbs' book. Thirdly, the vacuum and the state of photons of given momenta and polarizations are expressed concretely as functions of variables consisting of the Fourier coefficients of vector potentials. It is also proved rigorously in terms of distribution theory that the Coulomb potentials between charged particles naturally appear in the above Feynman path integral approach. This shows that the photons give rise to the Coulomb force.
Path integral quantization of the relativistic Hopfield model
NASA Astrophysics Data System (ADS)
Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.; Doronzo, M.
2016-03-01
The path-integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and dielectric quantum matter, with particular reference to the context of analogue gravity. In order to take into account the constraints occurring in the model, we adopt the Faddeev-Jackiw approach to constrained quantization in the path-integral formalism. In particular, we demonstrate that the propagator obtained with the Faddeev-Jackiw approach is equivalent to the one which, in the framework of Dirac canonical quantization for constrained systems, can be directly computed as the vacuum expectation value of the time-ordered product of the fields. Our analysis also provides an explicit example of quantization of the electromagnetic field in a covariant gauge and coupled with the polarization field, which is a novel contribution to the literature on the Faddeev-Jackiw procedure.
Hidden Topological Angles in Path Integrals
NASA Astrophysics Data System (ADS)
Behtash, Alireza; Sulejmanpasic, Tin; Schäfer, Thomas; Ünsal, Mithat
2015-07-01
We demonstrate the existence of hidden topological angles (HTAs) in a large class of quantum field theories and quantum mechanical systems. HTAs are distinct from theta parameters in the Lagrangian. They arise as invariant angles associated with saddle points of the complexified path integral and their descent manifolds (Lefschetz thimbles). Physical effects of HTAs become most transparent upon analytic continuation in nf to a noninteger number of flavors, reducing in the integer nf limit to a Z2 valued phase difference between dominant saddles. In N =1 super Yang-Mills theory we demonstrate the microscopic mechanism for the vanishing of the gluon condensate. The same effect leads to an anomalously small condensate in a QCD-like S U (N ) gauge theory with fermions in the two-index representation. The basic phenomenon is that, contrary to folklore, the gluon condensate can receive both positive and negative contributions in a semiclassical expansion. In quantum mechanics, a HTA leads to a difference in semiclassical expansion of integer and half-integer spin particles.
Hidden Topological Angles in Path Integrals.
Behtash, Alireza; Sulejmanpasic, Tin; Schäfer, Thomas; Ünsal, Mithat
2015-07-24
We demonstrate the existence of hidden topological angles (HTAs) in a large class of quantum field theories and quantum mechanical systems. HTAs are distinct from theta parameters in the Lagrangian. They arise as invariant angles associated with saddle points of the complexified path integral and their descent manifolds (Lefschetz thimbles). Physical effects of HTAs become most transparent upon analytic continuation in n_{f} to a noninteger number of flavors, reducing in the integer n_{f} limit to a Z_{2} valued phase difference between dominant saddles. In N=1 super Yang-Mills theory we demonstrate the microscopic mechanism for the vanishing of the gluon condensate. The same effect leads to an anomalously small condensate in a QCD-like SU(N) gauge theory with fermions in the two-index representation. The basic phenomenon is that, contrary to folklore, the gluon condensate can receive both positive and negative contributions in a semiclassical expansion. In quantum mechanics, a HTA leads to a difference in semiclassical expansion of integer and half-integer spin particles. PMID:26252675
Multi-Level Indoor Path Planning Method
NASA Astrophysics Data System (ADS)
Xiong, Q.; Zhu, Q.; Zlatanova, S.; Du, Z.; Zhang, Y.; Zeng, L.
2015-05-01
Indoor navigation is increasingly widespread in complex indoor environments, and indoor path planning is the most important part of indoor navigation. Path planning generally refers to finding the most suitable path connecting two locations, while avoiding collision with obstacles. However, it is a fundamental problem, especially for 3D complex building model. A common way to solve the issue in some applications has been approached in a number of relevant literature, which primarily operates on 2D drawings or building layouts, possibly with few attached attributes for obstacles. Although several digital building models in the format of 3D CAD have been used for path planning, they usually contain only geometric information while losing abundant semantic information of building components (e.g. types and attributes of building components and their simple relationships). Therefore, it becomes important to develop a reliable method that can enhance application of path planning by combining both geometric and semantic information of building components. This paper introduces a method that support 3D indoor path planning with semantic information.
Path integral approach to two-dimensional QCD in the light-front frame
NASA Astrophysics Data System (ADS)
Gaete, P.; Gamboa, J.; Schmidt, I.
1994-05-01
Two-dimensional quantum chromodynamics in the light-front frame is studied following Hamiltonian methods. The theory is quantized using the path integral formalism and an effective theory similar to the Nambu-Jona-Lasinio model is obtained. Confinement in two dimensions is derived by analyzing directly the constraints in the path integral.
Path integral Monte Carlo on a lattice: extended states.
O'Callaghan, Mark; Miller, Bruce N
2014-04-01
The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and atoms are restricted to the sites of a one-dimensional lattice. A path integral formalism is developed within the context of the canonical ensemble in which the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. For the case of a free particle, analytical expressions for the energy, its fluctuations, and the qp-qp correlation function are derived and compared with the Monte Carlo simulations. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp for a periodic interaction potential, forcing the qp to occupy extended states. We consider a striped potential in one dimension, where every other lattice site is occupied by an atom with potential ε, and every other lattice site is empty. This potential serves as a stress test for the path integral formalism because of its rapid site-to-site variation. An analytical solution was determined in this case by utilizing Bloch's theorem due to the periodicity of the potential. Comparisons of the potential energy, the total energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the analytical calculations. PMID:24827210
Yang-Mills Theory and Fermionic Path Integrals
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
The Yang-Mills gauge field theory, which was proposed 60 years ago, is extremely successful in describing the basic interactions of fundamental particles. The Yang-Mills theory in the course of its developments also stimulated many important field theoretical machinery. In my talk I discuss the path integral techniques, in particular, the fermionic path integrals which were developed together with the successful applications of quantized Yang-Mills field theory. I start with the Faddeev-Popov path integral formula with emphasis on the treatment of fermionic ghosts as an application of Grassmann numbers. I then discuss the ordinary fermionic path integrals and the general treatment of quantum anomalies. The contents of this talk are mostly pedagogical except for a recent analysis of path integral bosonization.
Yang-Mills theory and fermionic path integrals
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-01-01
The Yang-Mills gauge field theory, which was proposed 60 years ago, is extremely successful in describing the basic interactions of fundamental particles. The Yang-Mills theory in the course of its developments also stimulated many important field theoretical machinery. In this brief review I discuss the path integral techniques, in particular, the fermionic path integrals which were developed together with the successful applications of quantized Yang-Mills field theory. I start with the Faddeev-Popov path integral formula with emphasis on the treatment of fermionic ghosts as an application of Grassmann numbers. I then discuss the ordinary fermionic path integrals and the general treatment of quantum anomalies. The contents of this review are mostly pedagogical except for a recent analysis of path integral bosonization.
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.
New open-path remote optical sensing method to estimate methane emission from soil
Technology Transfer Automated Retrieval System (TEKTRAN)
The U.S. EPA recently developed an open-path remote sensing method to identify hot spots and estimate fugitive gas emissions from closed landfills. The method measures several path-integrated concentrations (PICs) of gases using open-path optical instruments. These PICs are then processed using a co...
Spin in the worldline path integral in 2 + 1 dimensions
Fosco, C.D.; Sanchez-Guillen, J.; Vazquez, R.A.
2008-02-15
We present a constructive derivation of a worldline path integral for the effective action and the propagator of a Dirac field in 2 + 1 dimensions, in terms of spacetime and SU(2) paths. After studying some general properties of this representation, we show that the auxiliary gauge-group variable can be integrated, deriving a worldline action depending only on x({tau}), the spacetime paths. We then show that the functional integral automatically imposes the constraint x{sup .2}({tau})=1, while there is a spin action, which agrees with the one one should expect for a spin-1/2 field.
Selecta from a Life-Long Obsession with Path Integrals
Klauder, John R.
2008-06-18
The definition and interpretation of canonical, phase space path integrals has evolved over many years to achieve a form that now admits a correct and rigorous formulation, which is also covariant under canonical coordinate transformations. Such formulations involve coherent state representations, which, in their modern version, were originally introduced as an alternative tool to construct phase space path integrals. Moreover, coherent state representations lead to physical interpretations that are more natural than those afforded by more traditional representations. Suitable continuous time regularization procedures lead to a covariant phase space path integral formulation that greatly clarifies the vague phrase that canonical quantization requires Cartesian coordinates.
Do-It-Yourself Critical Path Method.
ERIC Educational Resources Information Center
Morris, Edward P., Jr.
This report describes the critical path method (CPM), a system for planning and scheduling work to get the best time-cost combination for any particular job. With the use of diagrams, the report describes how CPM works on a step-by-step basis. CPM uses a network to show which parts of a job must be done and how they would eventually fit together…
Sensory feedback in a bump attractor model of path integration.
Poll, Daniel B; Nguyen, Khanh; Kilpatrick, Zachary P
2016-04-01
Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error. PMID:26754972
Path integral Monte Carlo on a lattice. II. Bound states.
O'Callaghan, Mark; Miller, Bruce N
2016-07-01
The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and the atoms are restricted to sites on a one-dimensional lattice. A path integral formalism developed within the context of the canonical ensemble is utilized, where the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp in the context of a square well potential, forcing the qp to occupy bound states. We consider a one-dimensional square well potential where all atoms on the lattice are occupied with one atom with an on-site potential except for a contiguous set of sites of various lengths centered at the middle of the lattice. Comparison of the potential energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the numerical calculations. PMID:27575090
Spinor path integral Quantum Monte Carlo for fermions
NASA Astrophysics Data System (ADS)
Shin, Daejin; Yousif, Hosam; Shumway, John
2007-03-01
We have developed a continuous-space path integral method for spin 1/2 fermions with fixed-phase approximation. The internal spin degrees of freedom of each particle is represented by four extra dimensions. This effectively maps each spinor onto two of the excited states of a four dimensional harmonic oscillator. The phases that appear in the problem can be treated within the fixed-phase approximation. This mapping preserves rotational invariance and allows us to treat spin interactions and fermionic exchange on equal footing, which may lead to new theoretical insights. The technique is illustrated for a few simple models, including a spin in a magnetic field and interacting electrons in a quantum dot in a magnetic field at finite temperature. We will discuss possible extensions of the method to molecules and solids using variational and diffusion Quantum Monte Carlo.
Canonical formulation and path integral for local vacuum energy sequestering
NASA Astrophysics Data System (ADS)
Bufalo, R.; KlusoÅ, J.; Oksanen, M.
2016-08-01
We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the Universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity. It is argued to imply a relation between the fraction of the most likely values of the gravitational and cosmological constants and the average values of the energy density and pressure of matter over spacetime. Finally, we construct and analyze a Becchi-Rouet-Stora-Tyutin-exact formulation of the theory, which can be considered as a topological field theory.
Path integral approach to electron scattering in classical electromagnetic potential
NASA Astrophysics Data System (ADS)
Chuang, Xu; Feng, Feng; Ying-Jun, Li
2016-05-01
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. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374360, 11405266, and 11505285) and the National Basic Research Program of China (Grant No. 2013CBA01504).
Quantum-classical interactions through the path integral
NASA Astrophysics Data System (ADS)
Metaxas, Dimitrios
2007-03-01
I consider the case of two interacting scalar fields, ϕ and ψ, and use the path integral formalism in order to treat the first classically and the second quantum-mechanically. I derive the Feynman rules and the resulting equation of motion for the classical field which should be an improvement of the usual semiclassical procedure. As an application I use this method in order to enforce Gauss’s law as a classical equation in a non-Abelian gauge theory. I argue that the theory is renormalizable and equivalent to the usual Yang-Mills theory as far as the gauge field terms are concerned. There are additional terms in the effective action that depend on the Lagrange multiplier field λ that is used to enforce the constraint. These terms and their relation to the confining properties of the theory are discussed.
Path Integrals, BRST Identities, and Regularization Schemes in Nonstandard Gauges
NASA Astrophysics Data System (ADS)
Ren, Hai-cang
2000-07-01
The path integral of a gauge theory is studied in Coulomb-like gauges. The Christ-Lee terms of operator ordering are reproduced within the path integration framework. In the presence of fermions, a new operator term, in addition to that of Christ and Lee, is discovered. Such terms are found to be instrumental in restoring the invariance of the effective Lagrangian under a field-dependent gauge transformation, which underlies the BRST symmetry. A unitary regularization scheme which maintains manifest BRST symmetry and is free from energy divergences is proposed for a nonabelian gauge field.
Action with Acceleration i: Euclidean Hamiltonian and Path Integral
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
2013-10-01
An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity — and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of the similarity transformation are explicitly evaluated.
Quantum Thermal Bath for Path Integral Molecular Dynamics Simulation.
Brieuc, Fabien; Dammak, Hichem; Hayoun, Marc
2016-03-01
The quantum thermal bath (QTB) method has been recently developed to account for the quantum nature of the nuclei by using standard molecular dynamics (MD) simulation. QTB-MD is an efficient but approximate method when dealing with strongly anharmonic systems, while path integral molecular dynamics (PIMD) gives exact results but in a huge amount of computation time. The QTB and PIMD methods have been combined in order to improve the PIMD convergence or correct the failures of the QTB-MD technique. Therefore, a new power spectral density of the random force within the QTB has been developed. A modified centroid-virial estimator of the kinetic energy, especially adapted to QTB-PIMD, has also been proposed. The method is applied to selected systems: a one-dimensional double-well system, a ferroelectric phase transition, and the position distribution of an hydrogen atom in a fuel cell material. The advantage of the QTB-PIMD method is its ability to give exact results with a more reasonable computation time for strongly anharmonic systems. PMID:26799437
Path Integral Understanding in the Context of the Electromagnetic Theory
NASA Astrophysics Data System (ADS)
Gonzalez, Maria D.
2006-12-01
Introductory electromagnetic courses at the University of Juarez are in general identified by the use of a traditional instruction. The path integral is a fundamental mathematical knowledge to understand the properties of conservative fields such that the electric field. Many students in these courses do not develop the necessary scientific skills and mathematical formalism to understand the fact that the potential difference does not depend on the path followed from one point to another one inside an electric field. It is fundamental to probe the student understanding difficulties to apply the concept of path integral in an electromagnetic context. The use of the software CABRI could become an important didactic choice during the development of the potential difference concept. It was necessary the recollection of data related to the student procedural difficulties in the use of the designed CABRI activities. Sponsor: member Sergio Flores
The functional measure for the in-in path integral
NASA Astrophysics Data System (ADS)
Kaya, Ali
2015-05-01
The in-in path integral of a scalar field propagating in a fixed background is formulated in a suitable function space. The free kinetic operator, whose inverse gives the propagators of the in-in perturbation theory, becomes essentially self adjoint after imposing appropriate boundary conditions. An explicit spectral representation is given for the scalar in the flat space, and the standard propagators are rederived using this representation. In this way the subtle boundary path integral over the field configurations at the return time is handled straightforwardly. It turns out that not only the values of the forward (+) and the backward (-) evolving fields but also their time derivatives must be matched at the return time, which is mainly overlooked in the literature. This formulation also determines the field configurations that are included in the path integral uniquely. We show that some of the recently suggested instanton-like solutions corresponding to the stationary phases of the cosmological in-in path integrals can be rigorously identified as limits of sequences in the function space.
Trouvé, Hélène; Couturier, Yves; Etheridge, Francis; Saint-Jean, Olivier; Somme, Dominique
2010-01-01
Background 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. Purpose 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. Methods 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. Results 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. Conclusion 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. PMID:20689740
Integral representation of the edge diffracted waves along the ray path of the transition region.
Umul, Yusuf Z
2008-09-01
The expression of the edge diffracted fields, in terms of the Fresnel integral, is transformed into a path integral. The obtained integral considers the integration of the incident field along the ray path of the transition region. The similarities of the path integral with Kirchhoff's theory of diffraction and the modified theory of physical optics are examined. PMID:18758538
Inter-Domain Redundancy Path Computation Methods Based on PCE
NASA Astrophysics Data System (ADS)
Hayashi, Rie; Oki, Eiji; Shiomoto, Kohei
This paper evaluates three inter-domain redundancy path computation methods based on PCE (Path Computation Element). Some inter-domain paths carry traffic that must be assured of high quality and high reliability transfer such as telephony over IP and premium virtual private networks (VPNs). It is, therefore, important to set inter-domain redundancy paths, i. e. primary and secondary paths. The first scheme utilizes an existing protocol and the basic PCE implementation. It does not need any extension or modification. In the second scheme, PCEs make a virtual shortest path tree (VSPT) considering the candidates of primary paths that have corresponding secondary paths. The goal is to reduce blocking probability; corresponding secondary paths may be found more often after a primary path is decided; no protocol extension is necessary. In the third scheme, PCEs make a VSPT considering all candidates of primary and secondary paths. Blocking probability is further decreased since all possible candidates are located, and the sum of primary and secondary path cost is reduced by choosing the pair with minimum cost among all path pairs. Numerical evaluations show that the second and third schemes offer only a few percent reduction in blocking probability and path pair total cost, while the overheads imposed by protocol revision and increase of the amount of calculation and information to be exchanged are large. This suggests that the first scheme, the most basic and simple one, is the best choice.
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. For participants who learned the objects in the large room, the testing position and the learning position were in the same room so that participants did not cross boundaries before testing; for participants who learned the objects in the small room, the testing position and the learning position were in 2 different rooms so that participants crossed boundaries before testing. Participants who learned the objects in the large room, during testing, either saw cues indicating the targets' locations (piloting group) or not (path integration group). Participants who learned the objects in the small room, during testing did not see any cues correctly indicating the targets' locations. The results showed that pointing accuracy was higher for those who learned the objects in the large room and in the piloting group than for those who learned the objects in the small room. However, this cross-boundary cost did not occur when we contrasted participants who learned objects in the large room and in the path integration group with participants who learned in a small room. These results suggested that navigation that relies on path integration only is not sensitive to boundary crossing, although navigation that relies on piloting is less efficient across boundaries than within boundaries. PMID:24933698
NASA Astrophysics Data System (ADS)
Kleinert, H.
1989-06-01
The Feynman formula, which expresses the time displacement amplitude > x b | exp (-t Ȟ) | x a< in terms of a path integral Π 1N (∫ dn) Π 1N+1 ( {∫ dp n}/{2π}) exp{Σ 1N [ ip n(x n-x n-1) - ɛH (p n, x n)]} with large N, does not exist for systems with Coulomb {-1}/{r} potential and gives incorrect threshold behaviours near centrifugal {1}/{r 2} or angular {1}/{sin2θ } barriers. We discuss the physical origin of this failure and propose an alternative well-defined path integral formula based on a family of amplitudes that is invariant under arbitrary local time reparametrizations. The time slicing with finite N breaks this invariance. For appropriate choices of the reparametrization function the fluctuations are stabilized and the new formula is applicable to all the above systems.
Path integral approach to Asian options in the Black-Scholes model
NASA Astrophysics Data System (ADS)
Devreese, J. P. A.; Lemmens, D.; Tempere, J.
2010-02-01
We derive a closed-form solution for the price of an average strike as well as an average price geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is approximate when the correlation increases.
An algorithm to find minimum free-energy paths using umbrella integration
NASA Astrophysics Data System (ADS)
Bohner, Matthias U.; Kästner, Johannes
2012-07-01
The calculation of free-energy barriers by umbrella sampling and many other methods is hampered by the necessity for an a priori choice of the reaction coordinate along which to sample. We avoid this problem by providing a method to search for saddle points on the free-energy surface in many coordinates. The necessary gradients and Hessians of the free energy are obtained by multidimensional umbrella integration. We construct the minimum free-energy path by following the gradient down to minima on the free-energy surface. The change of free energy along the path is obtained by integrating out all coordinates orthogonal to the path. While we expect the method to be applicable to large systems, we test it on the alanine dipeptide in vacuum. The minima, transition states, and free-energy barriers agree well with those obtained previously with other methods.
A path integral approach to the Langevin equation
NASA Astrophysics Data System (ADS)
Das, Ashok K.; Panda, Sudhakar; Santos, J. R. L.
2015-02-01
We study the Langevin equation with both a white noise and a colored noise. We construct the Lagrangian as well as the Hamiltonian for the generalized Langevin equation which leads naturally to a path integral description from first principles. This derivation clarifies the meaning of the additional fields introduced by Martin, Siggia and Rose in their functional formalism. We show that the transition amplitude, in this case, is the generating functional for correlation functions. We work out explicitly the correlation functions for the Markovian process of the Brownian motion of a free particle as well as for that of the non-Markovian process of the Brownian motion of a harmonic oscillator (Uhlenbeck-Ornstein model). The path integral description also leads to a simple derivation of the Fokker-Planck equation for the generalized Langevin equation.
Path integral pricing of outside barrier Asian options
NASA Astrophysics Data System (ADS)
Cassagnes, Aurelien; Chen, Yu; Ohashi, Hirotada
2014-01-01
Using the path-integral framework to cast the pricing problem of the outside barrier Asian option into a Wiener functional integral form, we show that, after the introduction of a law-equivalent process and transformation of the new system, the deviation from the Monte Carlo price is seen to be widely reduced. Bypassing the path-partitioning step, we show that our results behave nicely with respect to increasing correlation. After putting forward empirical evidence of this improvement, we extend the scope to a double knock-out outside barrier, and derive there an original formula. In the latter setting, we propose a simple scheme to reduce the relative error due to a nearby knock-out barrier.
Spin foam models for quantum gravity from lattice path integrals
Bonzom, Valentin
2009-09-15
Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and includes the Immirzi parameter. In addition, a measure is inserted to ensure a consistent gluing of simplices, so that the amplitude is dominated by configurations that satisfy the parallel transport relations. We explicitly compute the path integral as a sum over spin foams for a generic measure. The Freidel-Krasnov and Engle-Pereira-Rovelli models correspond to a special choice of gluing. In this case, the equations of motion describe genuine geometries, where the constraints of area-angle Regge calculus are satisfied. Furthermore, the Immirzi parameter drops out of the on-shell action, and stationarity with respect to area variations requires spacetime geometry to be flat.
Path integral Liouville dynamics for thermal equilibrium systems
NASA Astrophysics Data System (ADS)
Liu, Jian
2014-06-01
We show a new imaginary time path integral based method—path integral Liouville dynamics (PILD), which can be derived from the equilibrium Liouville dynamics [J. Liu and W. H. Miller, J. Chem. Phys. 134, 104101 (2011)] in the Wigner phase space. Numerical tests of PILD with the simple (white noise) Langevin thermostat have been made for two strongly anharmonic model problems. Since implementation of PILD does not request any specific form of the potential energy surface, the results suggest that PILD offers a potentially useful approach for general condensed phase molecular systems to have the two important properties: conserves the quantum canonical distribution and recovers exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits.
Path integral Liouville dynamics for thermal equilibrium systems
Liu, Jian
2014-06-14
We show a new imaginary time path integral based method—path integral Liouville dynamics (PILD), which can be derived from the equilibrium Liouville dynamics [J. Liu and W. H. Miller, J. Chem. Phys. 134, 104101 (2011)] in the Wigner phase space. Numerical tests of PILD with the simple (white noise) Langevin thermostat have been made for two strongly anharmonic model problems. Since implementation of PILD does not request any specific form of the potential energy surface, the results suggest that PILD offers a potentially useful approach for general condensed phase molecular systems to have the two important properties: conserves the quantum canonical distribution and recovers exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits.
Gauge Invariance of Parametrized Systems and Path Integral Quantization
NASA Astrophysics Data System (ADS)
de Cicco, Hernán; Simeone, Claudio
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action functional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The procedure is applied to the relativistic particle and toy universes, which are quantized by imposing canonical gauge conditions in the path integral; in the case of empty models, we first quantize the parametrized system called "ideal clock," and then we examine the possibility of obtaining the amplitude for the minisuperspaces by matching them with the ideal clock. The relation existing between the geometrical properties of the constraint surface and the variables identifying the quantum states in the path integral is discussed.
Birkholz, Adam B; Schlegel, H Bernhard
2015-12-28
The development of algorithms to optimize reaction pathways between reactants and products is an active area of study. Existing algorithms typically describe the path as a discrete series of images (chain of states) which are moved downhill toward the path, using various reparameterization schemes, constraints, or fictitious forces to maintain a uniform description of the reaction path. The Variational Reaction Coordinate (VRC) method is a novel approach that finds the reaction path by minimizing the variational reaction energy (VRE) of Quapp and Bofill. The VRE is the line integral of the gradient norm along a path between reactants and products and minimization of VRE has been shown to yield the steepest descent reaction path. In the VRC method, we represent the reaction path by a linear expansion in a set of continuous basis functions and find the optimized path by minimizing the VRE with respect to the linear expansion coefficients. Improved convergence is obtained by applying constraints to the spacing of the basis functions and coupling the minimization of the VRE to the minimization of one or more points along the path that correspond to intermediates and transition states. The VRC method is demonstrated by optimizing the reaction path for the Müller-Brown surface and by finding a reaction path passing through 5 transition states and 4 intermediates for a 10 atom Lennard-Jones cluster. PMID:26723645
Birkholz, Adam B.; Schlegel, H. Bernhard
2015-12-28
The development of algorithms to optimize reaction pathways between reactants and products is an active area of study. Existing algorithms typically describe the path as a discrete series of images (chain of states) which are moved downhill toward the path, using various reparameterization schemes, constraints, or fictitious forces to maintain a uniform description of the reaction path. The Variational Reaction Coordinate (VRC) method is a novel approach that finds the reaction path by minimizing the variational reaction energy (VRE) of Quapp and Bofill. The VRE is the line integral of the gradient norm along a path between reactants and products and minimization of VRE has been shown to yield the steepest descent reaction path. In the VRC method, we represent the reaction path by a linear expansion in a set of continuous basis functions and find the optimized path by minimizing the VRE with respect to the linear expansion coefficients. Improved convergence is obtained by applying constraints to the spacing of the basis functions and coupling the minimization of the VRE to the minimization of one or more points along the path that correspond to intermediates and transition states. The VRC method is demonstrated by optimizing the reaction path for the Müller-Brown surface and by finding a reaction path passing through 5 transition states and 4 intermediates for a 10 atom Lennard-Jones cluster.
NASA Astrophysics Data System (ADS)
Birkholz, Adam B.; Schlegel, H. Bernhard
2015-12-01
The development of algorithms to optimize reaction pathways between reactants and products is an active area of study. Existing algorithms typically describe the path as a discrete series of images (chain of states) which are moved downhill toward the path, using various reparameterization schemes, constraints, or fictitious forces to maintain a uniform description of the reaction path. The Variational Reaction Coordinate (VRC) method is a novel approach that finds the reaction path by minimizing the variational reaction energy (VRE) of Quapp and Bofill. The VRE is the line integral of the gradient norm along a path between reactants and products and minimization of VRE has been shown to yield the steepest descent reaction path. In the VRC method, we represent the reaction path by a linear expansion in a set of continuous basis functions and find the optimized path by minimizing the VRE with respect to the linear expansion coefficients. Improved convergence is obtained by applying constraints to the spacing of the basis functions and coupling the minimization of the VRE to the minimization of one or more points along the path that correspond to intermediates and transition states. The VRC method is demonstrated by optimizing the reaction path for the Müller-Brown surface and by finding a reaction path passing through 5 transition states and 4 intermediates for a 10 atom Lennard-Jones cluster.
Converged Nuclear Quantum Statistics from Semi-Classical Path Integrals
NASA Astrophysics Data System (ADS)
Poltavskyi, Igor; Tkatchenko, Alexandre
2015-03-01
The quantum nature of nuclear motions plays a vital role in the structure, stability, and thermodynamics of molecular systems. The standard approach to take nuclear quantum effects (NQE) into account is the Feynman-Kac imaginary-time path-integral molecular dynamics (PIMD). Conventional PIMD simulations require exceedingly large number of classical subsystems (beads) to accurately capture NQE, resulting in considerable computational cost even at room temperature due to the rather high internal vibrational frequencies of many molecules of interest. We propose a novel parameter-free form for the PI partition function and estimators to calculate converged thermodynamic averages. Our approach requires the same ingredients as the conventional PIMD simulations, but decreases the number of required beads by roughly an order of magnitude. This greatly extends the applicability of ab initio PIMD for realistic molecular systems. The developed method has been applied to study the thermodynamics of N2, H2O, CO2, and C6H6 molecules. For all of the considered systems at room temperature, 4 to 8 beads are enough to recover the NQE contribution to the total energy within 2% of the fully converged quantum result.
Path integral approach to the quantum fidelity amplitude
2016-01-01
The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called ‘dephasing representation,’ circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact. PMID:27140973
Path integral approach to the quantum fidelity amplitude.
Vaníček, Jiří; Cohen, Doron
2016-06-13
The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called 'dephasing representation,' circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact. PMID:27140973
A path-integral Langevin equation treatment of low-temperature doped helium clusters
NASA Astrophysics Data System (ADS)
Ing, Christopher; Hinsen, Konrad; Yang, Jing; Zeng, Toby; Li, Hui; Roy, Pierre-Nicholas
2012-06-01
We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)], 10.1063/1.3489925 sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of HeN-CO2 clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], 10.1002/(SICI)1096-987X(20000130)21:2<79::AID-JCC1>3.0.CO;2-B, an open-source molecular simulation package.
Method of path coefficients: a trademark of Sewall Wright.
Li, C C
1991-02-01
This address is a tribute to a pioneer of population genetics, including human population genetics. The unique methodology employed by Sewall Wright in many genetic problems is the method of path coefficients. This essay traces the historical landmarks in the development of the path method and then shows how some of the conventional statistical results can be converted into expressions involving path coefficients. The construction of a path diagram to represent such statistical results is explained in terms of examples. In the last section an example of applying the path method to the problem of genetic linkage in a random mating population is given. I hope that, despite the ending of the Sewall Wright era, the path method will continue to serve the scientific world. PMID:2004740
Integrable Systems on Flag Manifold and Coherent State Path-Integral
NASA Astrophysics Data System (ADS)
Kim, Myung-Ho; Oh, Phillial
We construct integrable models on flag manifold by using the symplectic structure explicitly given in the Bruhat coordinatization of flag manifold. They are noncommutative integrable and some of the conserved quantities are given by the Casimir invariants. We quantize the systems using the coherent state path-integral technique and find the exact expression for the propagator for some special cases.
NASA Astrophysics Data System (ADS)
Halliwell, J. J.; Yearsley, J. M.
2013-06-01
Path integrals appear to offer natural and intuitively appealing methods for defining quantum-mechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time interval is typically defined by summing over all paths between given initial and final points but restricting them to pass through the region at any time. We argue that there is, however, under very general conditions, a significant complication in such constructions. This is the fact that the concrete implementation of the restrictions on paths over an interval of time corresponds, in an operator language, to sharp monitoring at every moment of time in the given time interval. Such processes suffer from the quantum Zeno effect - the continual monitoring of a quantum system in a Hilbert subspace prevents its state from leaving that subspace. As a consequence, path integral amplitudes defined in this seemingly obvious way have physically and intuitively unreasonable properties and in particular, no sensible classical limit. In this paper we describe this frequently-occurring but little-appreciated phenomenon in some detail, showing clearly the connection with the quantum Zeno effect. We then show that it may be avoided by implementing the restriction on paths in the path integral in a "softer" way. The resulting amplitudes then involve a new coarse graining parameter, which may be taken to be a timescale epsilon, describing the softening of the restrictions on the paths. We argue that the complications arising from the Zeno effect are then negligible as long as epsilon >> 1/E, where E is the energy scale of the incoming state. Our criticisms of path integral constructions largely apply to approaches to quantum theory such as the decoherent histories approach or quantum measure theory, which do not specifically involve measurements. We address some criticisms of our approach by Sokolovksi, concerning the relevance of our results to
Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.
Gao, J
2016-01-01
Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects. PMID:27498645
Direct path integral estimators for isotope fractionation ratios
Cheng, Bingqing; Ceriotti, Michele
2014-12-28
Fractionation of isotopes among distinct molecules or phases is a quantum effect which is often exploited to obtain insights on reaction mechanisms, biochemical, geochemical, and atmospheric phenomena. Accurate evaluation of isotope ratios in atomistic simulations is challenging, because one needs to perform a thermodynamic integration with respect to the isotope mass, along with time-consuming path integral calculations. By re-formulating the problem as a particle exchange in the ring polymer partition function, we derive new estimators giving direct access to the differential partitioning of isotopes, which can simplify the calculations by avoiding thermodynamic integration. We demonstrate the efficiency of these estimators by applying them to investigate the isotope fractionation ratios in the gas-phase Zundel cation, and in a few simple hydrocarbons.
Neural dynamics for landmark orientation and angular path integration
Seelig, Johannes D.; Jayaraman, Vivek
2015-01-01
Summary Many animals navigate using a combination of visual landmarks and path integration. In mammalian brains, head direction cells integrate these two streams of information by representing an animal's heading relative to landmarks, yet maintaining their directional tuning in darkness based on self-motion cues. Here we use two-photon calcium imaging in head-fixed flies walking on a ball in a virtual reality arena to demonstrate that landmark-based orientation and angular path integration are combined in the population responses of neurons whose dendrites tile the ellipsoid body — a toroidal structure in the center of the fly brain. The population encodes the fly's azimuth relative to its environment, tracking visual landmarks when available and relying on self-motion cues in darkness. When both visual and self-motion cues are absent, a representation of the animal's orientation is maintained in this network through persistent activity — a potential substrate for short-term memory. Several features of the population dynamics of these neurons and their circular anatomical arrangement are suggestive of ring attractors — network structures proposed to support the function of navigational brain circuits. PMID:25971509
Neural dynamics for landmark orientation and angular path integration.
Seelig, Johannes D; Jayaraman, Vivek
2015-05-14
Many animals navigate using a combination of visual landmarks and path integration. In mammalian brains, head direction cells integrate these two streams of information by representing an animal's heading relative to landmarks, yet maintaining their directional tuning in darkness based on self-motion cues. Here we use two-photon calcium imaging in head-fixed Drosophila melanogaster walking on a ball in a virtual reality arena to demonstrate that landmark-based orientation and angular path integration are combined in the population responses of neurons whose dendrites tile the ellipsoid body, a toroidal structure in the centre of the fly brain. The neural population encodes the fly's azimuth relative to its environment, tracking visual landmarks when available and relying on self-motion cues in darkness. When both visual and self-motion cues are absent, a representation of the animal's orientation is maintained in this network through persistent activity, a potential substrate for short-term memory. Several features of the population dynamics of these neurons and their circular anatomical arrangement are suggestive of ring attractors, network structures that have been proposed to support the function of navigational brain circuits. PMID:25971509
Quantum corrections from a path integral over reparametrizations
Makeenko, Yuri; Olesen, Poul
2010-08-15
We study the path integral over reparametrizations that has been proposed as an ansatz for the Wilson loops in the large-N QCD and reproduces the area law in the classical limit of large loops. We show that a semiclassical expansion for a rectangular loop captures the Luescher term associated with d=26 dimensions and propose a modification of the ansatz that reproduces the Luescher term in other dimensions, which is observed in lattice QCD. We repeat the calculation for an outstretched ellipse advocating the emergence of an analog of the Luescher term and verify this result by a direct computation of the determinant of the Laplace operator and the conformal anomaly.
Path-integral approach to the Wigner-Kirkwood expansion.
Jizba, Petr; Zatloukal, Václav
2014-01-01
We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As shown by its applications to different potentials, the presented expansion turns out to be quite efficient in generating analytic form of the higher-order expansion coefficients. To put some flesh on the bare bones, we apply the expansion to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator. Further salient issues, such as generalization to the Bloch density matrix and comparison with the more customary world-line formulation, are discussed. PMID:24580200
Path-integral approach to the Wigner-Kirkwood expansion
NASA Astrophysics Data System (ADS)
Jizba, Petr; Zatloukal, Václav
2014-01-01
We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As shown by its applications to different potentials, the presented expansion turns out to be quite efficient in generating analytic form of the higher-order expansion coefficients. To put some flesh on the bare bones, we apply the expansion to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator. Further salient issues, such as generalization to the Bloch density matrix and comparison with the more customary world-line formulation, are discussed.
A note on the path integral representation for Majorana fermions
NASA Astrophysics Data System (ADS)
Greco, Andrés
2016-04-01
Majorana fermions are currently of huge interest in the context of nanoscience and condensed matter physics. Different to usual fermions, Majorana fermions have the property that the particle is its own anti-particle thus, they must be described by real fields. Mathematically, this property makes nontrivial the quantization of the problem due, for instance, to the absence of a Wick-like theorem. In view of the present interest on the subject, it is important to develop different theoretical approaches in order to study problems where Majorana fermions are involved. In this note we show that Majorana fermions can be studied in the context of field theories for constrained systems. Using the Faddeev-Jackiw formalism for quantum field theories with constraints, we derived the path integral representation for Majorana fermions. In order to show the validity of the path integral we apply it to an exactly solvable problem. This application also shows that it is rather simple to perform systematic calculations on the basis of the present framework.
Investigation of the spinfoam path integral with quantum cuboid intertwiners
NASA Astrophysics Data System (ADS)
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.
Regularized path integrals and anomalies: U(1) chiral gauge theory
NASA Astrophysics Data System (ADS)
Kopper, Christoph; Lévêque, Benjamin
2012-02-01
We analyze the origin of the Adler-Bell-Jackiw anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [Kopper, C. and Müller, V. F., "Renormalization of spontaneously broken SU(2) Yang-Mills theory with flow equations," Rev. Math. Phys. 21, 781 (2009)], 10.1142/S0129055X0900375X. Here we analyze U(1) chiral gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-photon amplitude leads to a violation of the Slavnov-Taylor identities which cannot be restored on taking the UV limit in the renormalized theory. We point out that this fact is related to the nonanalyticity of this amplitude in the infrared region.
Path Following in the Exact Penalty Method of Convex Programming
Zhou, Hua; Lange, Kenneth
2015-01-01
Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value. PMID:26366044
Efficient algorithms for semiclassical instanton calculations based on discretized path integrals
Kawatsu, Tsutomu E-mail: smiura@mail.kanazawa-u.ac.jp; Miura, Shinichi E-mail: smiura@mail.kanazawa-u.ac.jp
2014-07-14
Path integral instanton method is a promising way to calculate the tunneling splitting of energies for degenerated two state systems. In order to calculate the tunneling splitting, we need to take the zero temperature limit, or the limit of infinite imaginary time duration. In the method developed by Richardson and Althorpe [J. Chem. Phys. 134, 054109 (2011)], the limit is simply replaced by the sufficiently long imaginary time. In the present study, we have developed a new formula of the tunneling splitting based on the discretized path integrals to take the limit analytically. We have applied our new formula to model systems, and found that this approach can significantly reduce the computational cost and gain the numerical accuracy. We then developed the method combined with the electronic structure calculations to obtain the accurate interatomic potential on the fly. We present an application of our ab initio instanton method to the ammonia umbrella flip motion.
NLOS UV channel modeling using numerical integration and an approximate closed-form path loss model
NASA Astrophysics Data System (ADS)
Gupta, Ankit; Noshad, Mohammad; Brandt-Pearce, Maïté
2012-10-01
In this paper we propose a simulation method using numerical integration, and develop a closed-form link loss model for physical layer channel characterization for non-line of sight (NLOS) ultraviolet (UV) communication systems. The impulse response of the channel is calculated by assuming both uniform and Gaussian profiles for transmitted beams and different geometries. The results are compared with previously published results. The accuracy of the integration approach is compared to the Monte Carlo simulation. Then the path loss using the simulation method and the suggested closed-form expression are presented for different link geometries. The accuracies are evaluated and compared to the results obtained using other methods.
Potential theory, path integrals and the Laplacian of the indicator
NASA Astrophysics Data System (ADS)
Lange, Rutger-Jan
2012-11-01
This 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 following seemingly ill-defined potential: V(x):=∓ {{σ^2}}/2nabla_x^2{1_{{xin D}}} where the volatility is the reciprocal of the mass (i.e. m = 1/ σ 2) and ħ = 1. The Laplacian of the indicator can be interpreted using the theory of distributions: it is the d-dimensional analogue of the Dirac δ'-function, which can formally be defined as partial_x^2{1_{x>0 }} . We show, first, that the path integral's perturbation series (or Born series) matches the classical single and double boundary layer series of potential theory, thereby connecting two hitherto unrelated fields. Second, we show that the perturbation series is valid for all domains D that allow Green's theorem (i.e. with a finite number of corners, edges and cusps), thereby expanding the classical applicability of boundary layers. Third, we show that the minus (plus) in the potential holds for the Dirichlet (Neumann) boundary condition; showing for the first time a particularly close connection between these two classical problems. Fourth, we demonstrate that the perturbation series of the path integral converges as follows:
Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations
Weinstein, Marvin; /SLAC
2009-02-12
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for the behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will
PhytoPath: an integrative resource for plant pathogen genomics.
Pedro, Helder; Maheswari, Uma; Urban, Martin; Irvine, Alistair George; Cuzick, Alayne; McDowall, Mark D; Staines, Daniel M; Kulesha, Eugene; Hammond-Kosack, Kim Elizabeth; Kersey, Paul Julian
2016-01-01
PhytoPath (www.phytopathdb.org) is a resource for genomic and phenotypic data from plant pathogen species, that integrates phenotypic data for genes from PHI-base, an expertly curated catalog of genes with experimentally verified pathogenicity, with the Ensembl tools for data visualization and analysis. The resource is focused on fungi, protists (oomycetes) and bacterial plant pathogens that have genomes that have been sequenced and annotated. Genes with associated PHI-base data can be easily identified across all plant pathogen species using a BioMart-based query tool and visualized in their genomic context on the Ensembl genome browser. The PhytoPath resource contains data for 135 genomic sequences from 87 plant pathogen species, and 1364 genes curated for their role in pathogenicity and as targets for chemical intervention. Support for community annotation of gene models is provided using the WebApollo online gene editor, and we are working with interested communities to improve reference annotation for selected species. PMID:26476449
PhytoPath: an integrative resource for plant pathogen genomics
Pedro, Helder; Maheswari, Uma; Urban, Martin; Irvine, Alistair George; Cuzick, Alayne; McDowall, Mark D.; Staines, Daniel M.; Kulesha, Eugene; Hammond-Kosack, Kim Elizabeth; Kersey, Paul Julian
2016-01-01
PhytoPath (www.phytopathdb.org) is a resource for genomic and phenotypic data from plant pathogen species, that integrates phenotypic data for genes from PHI-base, an expertly curated catalog of genes with experimentally verified pathogenicity, with the Ensembl tools for data visualization and analysis. The resource is focused on fungi, protists (oomycetes) and bacterial plant pathogens that have genomes that have been sequenced and annotated. Genes with associated PHI-base data can be easily identified across all plant pathogen species using a BioMart-based query tool and visualized in their genomic context on the Ensembl genome browser. The PhytoPath resource contains data for 135 genomic sequences from 87 plant pathogen species, and 1364 genes curated for their role in pathogenicity and as targets for chemical intervention. Support for community annotation of gene models is provided using the WebApollo online gene editor, and we are working with interested communities to improve reference annotation for selected species. PMID:26476449
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
path integral approach to closed form pricing formulas in the Heston framework.
NASA Astrophysics Data System (ADS)
Lemmens, Damiaan; Wouters, Michiel; Tempere, Jacques; Foulon, Sven
2008-03-01
We present a path integral approach for finding closed form formulas for option prices in the framework of the Heston model. The first model for determining option prices was the Black-Scholes model, which assumed that the logreturn followed a Wiener process with a given drift and constant volatility. To provide a realistic description of the market, the Black-Scholes results must be extended to include stochastic volatility. This is achieved by the Heston model, which assumes that the volatility follows a mean reverting square root process. Current applications of the Heston model are hampered by the unavailability of fast numerical methods, due to a lack of closed-form formulae. Therefore the search for closed form solutions is an essential step before the qualitatively better stochastic volatility models will be used in practice. To attain this goal we outline a simplified path integral approach yielding straightforward results for vanilla Heston options with correlation. Extensions to barrier options and other path-dependent option are discussed, and the new derivation is compared to existing results obtained from alternative path-integral approaches (Dragulescu, Kleinert).
NASA Technical Reports Server (NTRS)
Yu, Jirong; Petros, Mulugeta; Reithmaier, Karl; Bai, Yingxin; Trieu, Bo C.; Refaat, Tamer F.; Kavaya, Michael J.; Singh, Upendra N.
2012-01-01
A 2-micron pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This instrument will provide an alternate approach to measure atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement.
Federal Register 2010, 2011, 2012, 2013, 2014
2012-07-05
... COMMISSION Certain Integrated Circuit Packages Provided With Multiple Heat- Conducting Paths and Products... the sale within the United States after importation of certain integrated circuit packages provided... integrated circuit packages provided with multiple heat-conducting paths and products containing same...
Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways
Seyler, Sean L.; Kumar, Avishek; Thorpe, M. F.; Beckstein, Oliver
2015-01-01
Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example, showed that
Looping probabilities of elastic chains: a path integral approach.
Cotta-Ramusino, Ludovica; Maddocks, John H
2010-11-01
We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e.g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end
A path integral approach to fractional quantum Hall effect
Kvale, M.N.
1989-01-01
In this paper the author reformulates and further develops the cooperative-ring-exchange (CRE) theory of the fractional quantum Hall effect. Initially, a classical two-dimensional electron gas is considered and a guiding-center approximation is made for strong magnetic fields. The resulting Lagrangian is quantized via path integration and the integral is evaluated using the semiclassical approximation. By considering the CRE processes and a time discretization procedure, the 2DEG is mapped to two different lattice models that bracket the behavior of the system. Analysis of the behavior of the system shows an underlying modular symmetry and allows one to made some new experimental predictions. By interpreting the CRE processes as a loop-space formulation of a lattice gauge field theory, a Landau-Ginzburg action is derived that contains most of the important physics associated with the FQHE and chose ground state can be identified with the Laughlin wave function. Finally, the Laughlin wave function is derived directly from the partition function in the FQHE regime.
The core of the research effort in the Regional Vulnerability Assessment Program (ReVA) is a set of data integration methods ranging from simple overlays to complex multivariate statistics. These methods are described in the EPA publication titled, "Regional Vulnerability Assess...
Federal Register 2010, 2011, 2012, 2013, 2014
2012-06-06
... COMMISSION Certain Integrated Circuit Packages Provided With Multiple Heat- Conducting Paths and Products... With Multiple Heat-Conducting Paths and Products Containing Same, DN 2899; the Commission is soliciting... multiple heat-conducting paths and products containing same. The complaint names as respondents...
Path integral formulation of scattering theory with application to scattering by black holes
Zhang, T.R.
1985-01-01
The computational power of Feynman path integrals was exploited. Path-integration formalism for the quantum mechanics scattering and classical wave scattering was generalized. Firstly, the standard WKB approximation was generalized to the cases where the critical points of the action functional are degenerate. Three typical semiclassical scattering features served as examples for a classification of degenerate critical points: conservation laws, rainbows, glories. Secondly, the method developed for non-relativistic quantum mechanics scattering was used in the case of classical wave scattering. Scattering by Schwarzschild black holes was chosen as an example, and WKB cross sections for scalar, vector, and tensor fields were worked out. Finally, 2s-th Bessel function behavior of WKB cross section for helicity-s polarized glory scattering in curved space time was proved.
Dornheim, Tobias; Schoof, Tim; Groth, Simon; Filinov, Alexey; Bonitz, Michael
2015-11-28
The uniform electron gas (UEG) at finite temperature is of high current interest due to its key relevance for many applications including dense plasmas and laser excited solids. In particular, density functional theory heavily relies on accurate thermodynamic data for the UEG. Until recently, the only existing first-principle results had been obtained for N = 33 electrons with restricted path integral Monte Carlo (RPIMC), for low to moderate density, rs=r¯/aB≳1. These data have been complemented by configuration path integral Monte Carlo (CPIMC) simulations for rs ≤ 1 that substantially deviate from RPIMC towards smaller rs and low temperature. In this work, we present results from an independent third method-the recently developed permutation blocking path integral Monte Carlo (PB-PIMC) approach [T. Dornheim et al., New J. Phys. 17, 073017 (2015)] which we extend to the UEG. Interestingly, PB-PIMC allows us to perform simulations over the entire density range down to half the Fermi temperature (θ = kBT/EF = 0.5) and, therefore, to compare our results to both aforementioned methods. While we find excellent agreement with CPIMC, where results are available, we observe deviations from RPIMC that are beyond the statistical errors and increase with density. PMID:26627944
Bias annealing: A method for obtaining transition paths de novo
NASA Astrophysics Data System (ADS)
Hu, Jie; Ma, Ao; Dinner, Aaron R.
2006-09-01
Computational studies of dynamics in complex systems require means for generating reactive trajectories with minimum knowledge about the processes of interest. Here, we introduce a method for generating transition paths when an existing one is not already available. Starting from biased paths obtained from steered molecular dynamics, we use a Monte Carlo procedure in the space of whole trajectories to shift gradually to sampling an ensemble of unbiased paths. Application to basin-to-basin hopping in a two-dimensional model system and nucleotide-flipping by a DNA repair protein demonstrates that the method can efficiently yield unbiased reactive trajectories even when the initial steered dynamics differ significantly. The relation of the method to others and the physical basis for its success are discussed.
Automatic Tool Path Generation for Robot Integrated Surface Sculpturing System
NASA Astrophysics Data System (ADS)
Zhu, Jiang; Suzuki, Ryo; Tanaka, Tomohisa; Saito, Yoshio
In this paper, a surface sculpturing system based on 8-axis robot is proposed, the CAD/CAM software and tool path generation algorithm for this sculpturing system are presented. The 8-axis robot is composed of a 6-axis manipulator and a 2-axis worktable, it carves block of polystyrene foams by heated cutting tools. Multi-DOF (Degree of Freedom) robot benefits from the faster fashion than traditional RP (Rapid Prototyping) methods and more flexibility than CNC machining. With its flexibility driven from an 8-axis configuration, as well as efficient custom-developed software for rough cutting and finish cutting, this surface sculpturing system can carve sculptured surface accurately and efficiently.
NASA Astrophysics Data System (ADS)
Wang, Jin; Zhang, Kun; Wang, Erkwang
2010-09-01
We developed a general framework to quantify three key ingredients for dynamics of nonequilibrium systems through path integrals in length space. First, we identify dominant kinetic paths as the ones with optimal weights, leading to effective reduction of dimensionality or degrees of freedom from exponential to polynomial so large systems can be treated. Second, we uncover the underlying nonequilibrium potential landscapes from the explorations of the state space through kinetic paths. We apply our framework to a specific example of nonequilibrium network system: lambda phage genetic switch. Two distinct basins of attractions emerge. The dominant kinetic paths from one basin to another are irreversible and do not follow the usual steepest descent or gradient path along the landscape. It reflects the fact that the dynamics of nonequilibrium systems is not just determined by potential gradient but also the residual curl flux force, suggesting experiments to test theoretical predictions. Third, we have calculated dynamic transition time scales from one basin to another critical for stability of the system through instantons. Theoretical predictions are in good agreements with wild type and mutant experiments. We further uncover the correlations between the kinetic transition time scales and the underlying landscape topography: the barrier heights along the dominant paths. We found that both the dominant paths and the landscape are relatively robust against the influences of external environmental perturbations and the system tends to dissipate less with less fluctuations. Our general framework can be applied to other nonequilibrium systems.
The exact fundamental solution for the Benes filter: a Feynman path integral derivation
NASA Astrophysics Data System (ADS)
Balaji, Bhashyam
2011-06-01
The Benes filtering problem has been shown to be related to the quantum mechanical simple harmonic oscillator. In a previous paper, the exact fundamental solution for the filtering problem was derived. The methods employed included the method of separation of variables for solving PDEs, results from Strum-Liouville theory, and properties of the Hermite special function. In this paper, the results are rederived more simply and directly using Feynman path integral methods. Numerical examples are included that demonstrate the correctness of formulas and their utility in solving continuous-discrete filtering problems with Benes drift and nonlinear measurement model.
Path integral duality modified propagators in spacetimes with constant curvature
Kothawala, Dawood; Padmanabhan, T.; Sriramkumar, L.; Shankaranarayanan, S.
2009-08-15
The hypothesis of path integral duality provides a prescription to evaluate the propagator of a free, quantum scalar field in a given classical background, taking into account the existence of a fundamental length, say, the Planck length L{sub P} in a locally Lorentz invariant manner. We use this prescription to evaluate the duality modified propagators in spacetimes with constant curvature (exactly in the case of one spacetime, and in the Gaussian approximation for another two), and show that (i) the modified propagators are ultraviolet finite, (ii) the modifications are nonperturbative in L{sub P}, and (iii) L{sub P} seems to behave like a 'zero point length' of spacetime intervals such that <{sigma}{sup 2}(x,x{sup '})>=[{sigma}{sup 2}(x,x{sup '})+O(1)L{sub P}{sup 2}], where {sigma}(x,x{sup '}) is the geodesic distance between the two spacetime points x and x{sup '}, and the angular brackets denote (a suitable) average over the quantum gravitational fluctuations. We briefly discuss the implications of our results.
Path integral regularization of pure Yang-Mills theory
Jacquot, J. L.
2009-07-15
In enlarging the field content of pure Yang-Mills theory to a cutoff dependent matrix valued complex scalar field, we construct a vectorial operator, which is by definition invariant with respect to the gauge transformation of the Yang-Mills field and with respect to a Stueckelberg type gauge transformation of the scalar field. This invariant operator converges to the original Yang-Mills field as the cutoff goes to infinity. With the help of cutoff functions, we construct with this invariant a regularized action for the pure Yang-Mills theory. In order to be able to define both the gauge and scalar fields kinetic terms, other invariant terms are added to the action. Since the scalar fields flat measure is invariant under the Stueckelberg type gauge transformation, we obtain a regularized gauge-invariant path integral for pure Yang-Mills theory that is mathematically well defined. Moreover, the regularized Ward-Takahashi identities describing the dynamics of the gauge fields are exactly the same as the formal Ward-Takahashi identities of the unregularized theory.
A parallel multiple path tracing method based on OptiX for infrared image generation
NASA Astrophysics Data System (ADS)
Wang, Hao; Wang, Xia; Liu, Li; Long, Teng; Wu, Zimu
2015-12-01
Infrared image generation technology is being widely used in infrared imaging system performance evaluation, battlefield environment simulation and military personnel training, which require a more physically accurate and efficient method for infrared scene simulation. A parallel multiple path tracing method based on OptiX was proposed to solve the problem, which can not only increase computational efficiency compared to serial ray tracing using CPU, but also produce relatively accurate results. First, the flaws of current ray tracing methods in infrared simulation were analyzed and thus a multiple path tracing method based on OptiX was developed. Furthermore, the Monte Carlo integration was employed to solve the radiation transfer equation, in which the importance sampling method was applied to accelerate the integral convergent rate. After that, the framework of the simulation platform and its sensor effects simulation diagram were given. Finally, the results showed that the method could generate relatively accurate radiation images if a precise importance sampling method was available.
Song, Linze; Shi, Qiang
2015-05-07
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.
NASA Astrophysics Data System (ADS)
Song, Linze; Shi, Qiang
2015-05-01
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.
Sequential quadratic programming method for determining the minimum energy path.
Burger, Steven K; Yang, Weitao
2007-10-28
A new method, referred to as the sequential quadratic programming method, is presented for determining minimum energy paths. The method is based on minimizing the points representing the path in the subspace perpendicular to the tangent of the path while using a penalty term to prevent kinks from forming. Rather than taking one full step, the minimization is divided into a number of sequential steps on an approximate quadratic surface. The resulting method can efficiently determine the reaction mechanism, from which transition state can be easily identified and refined with other methods. To improve the resolution of the path close to the transition state, points are clustered close to this region with a reparametrization scheme. The usefulness of the algorithm is demonstrated for the Muller-Brown potential, amide hydrolysis, and an 89 atom cluster taken from the active site of 4-oxalocrotonate tautomerase for the reaction which catalyzes 2-oxo-4-hexenedioate to the intermediate 2-hydroxy-2,4-hexadienedioate. PMID:17979319
Path-integral approach to 't Hooft's derivation of quantum physics from classical physics
Blasone, Massimo; Jizba, Petr; Kleinert, Hagen
2005-05-15
We present a path-integral formulation of 't Hooft's derivation of quantum physics from classical physics. The crucial ingredient of this formulation is Gozzi et al.'s supersymmetric path integral of classical mechanics. We quantize explicitly two simple classical systems: the planar mathematical pendulum and the Roessler dynamical system.
An Abelian Model of Gravity and Canonical Quantization by Means of Path Integrals
NASA Astrophysics Data System (ADS)
Bracken, Paul
An Abelian model of gravity is introduced and its constraint structure is obtained. The main task is to show that the model with constraints can be canonically quantized by means of the canonical path integral formalism using the Faddeev-Popov approach. It is shown how the path integral can be simplified by carrying out the integrals over those variables for which the integrals can be computed.
THE CRITICAL-PATH METHOD OF CONSTRUCTION CONTROL.
ERIC Educational Resources Information Center
DOMBROW, RODGER T.; MAUCHLY, JOHN
THIS DISCUSSION PRESENTS A DEFINITION AND BRIEF DESCRIPTION OF THE CRITICAL-PATH METHOD AS APPLIED TO BUILDING CONSTRUCTION. INTRODUCING REMARKS CONSIDER THE MOST PERTINENT QUESTIONS PERTAINING TO CPM AND THE NEEDS ASSOCIATED WITH MINIMIZING TIME AND COST ON CONSTRUCTION PROJECTS. SPECIFIC DISCUSSION INCLUDES--(1) ADVANTAGES OF NETWORK TECHNIQUES,…
i-PI: A Python interface for ab initio path integral molecular dynamics simulations
NASA Astrophysics Data System (ADS)
Ceriotti, Michele; More, Joshua; Manolopoulos, David E.
2014-03-01
Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these developments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first principles calculations and path integral molecular dynamics, i-PI can also be used to perform classical molecular dynamics simulations, and can just as easily be interfaced with an empirical forcefield code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum effects in high-pressure water. Catalogue identifier: AERN_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AERN_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 138626 No. of bytes in distributed program, including test data, etc.: 3128618 Distribution format: tar.gz Programming language: Python. Computer: Multiple architectures. Operating system: Linux, Mac OSX, Windows. RAM: Less than 256 Mb Classification: 7.7. External routines: NumPy Nature of problem: Bringing the latest developments in the modelling of nuclear quantum effects with path integral molecular dynamics to ab initio electronic structure programs with minimal implementational effort. Solution method: State-of-the-art path integral molecular dynamics techniques are implemented in a Python interface. Any electronic structure code can be patched to receive the atomic
Geng, Hua Y.
2015-02-15
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model—the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of r{sub s}=0.912.
NASA Astrophysics Data System (ADS)
Geng, Hua Y.
2015-02-01
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model-the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of rs = 0.912.
NASA Astrophysics Data System (ADS)
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.
Birkholz, Adam B; Schlegel, H Bernhard
2016-05-14
Reaction path optimization is being used more frequently as an alternative to the standard practice of locating a transition state and following the path downhill. The Variational Reaction Coordinate (VRC) method was proposed as an alternative to chain-of-states methods like nudged elastic band and string method. The VRC method represents the path using a linear expansion of continuous basis functions, allowing the path to be optimized variationally by updating the expansion coefficients to minimize the line integral of the potential energy gradient norm, referred to as the Variational Reaction Energy (VRE) of the path. When constraints are used to control the spacing of basis functions and to couple the minimization of the VRE with the optimization of one or more individual points along the path (representing transition states and intermediates), an approximate path as well as the converged geometries of transition states and intermediates along the path are determined in only a few iterations. This algorithmic efficiency comes at a high per-iteration cost due to numerical integration of the VRE derivatives. In the present work, methods for incorporating redundant internal coordinates and potential energy surface interpolation into the VRC method are described. With these methods, the per-iteration cost, in terms of the number of potential energy surface evaluations, of the VRC method is reduced while the high algorithmic efficiency is maintained. PMID:27179465
NASA Astrophysics Data System (ADS)
Birkholz, Adam B.; Schlegel, H. Bernhard
2016-05-01
Reaction path optimization is being used more frequently as an alternative to the standard practice of locating a transition state and following the path downhill. The Variational Reaction Coordinate (VRC) method was proposed as an alternative to chain-of-states methods like nudged elastic band and string method. The VRC method represents the path using a linear expansion of continuous basis functions, allowing the path to be optimized variationally by updating the expansion coefficients to minimize the line integral of the potential energy gradient norm, referred to as the Variational Reaction Energy (VRE) of the path. When constraints are used to control the spacing of basis functions and to couple the minimization of the VRE with the optimization of one or more individual points along the path (representing transition states and intermediates), an approximate path as well as the converged geometries of transition states and intermediates along the path are determined in only a few iterations. This algorithmic efficiency comes at a high per-iteration cost due to numerical integration of the VRE derivatives. In the present work, methods for incorporating redundant internal coordinates and potential energy surface interpolation into the VRC method are described. With these methods, the per-iteration cost, in terms of the number of potential energy surface evaluations, of the VRC method is reduced while the high algorithmic efficiency is maintained.
Theory of extreme correlations using canonical Fermions and path integrals
NASA Astrophysics Data System (ADS)
Shastry, B. Sriram
2014-04-01
The t-J model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson-Maleev transformation relating spin operators to canonical Bosons. This representation gives rise to a non Hermitian quantum theory, characterized by minimal redundancies. A path integral representation of the canonical theory is given. Using it, the salient results of the extremely correlated Fermi liquid (ECFL) theory, including the previously found Schwinger equations of motion, are easily rederived. Further, a transparent physical interpretation of the previously introduced auxiliary Greens function and the ‘caparison factor’, is obtained. The low energy electron spectral function in this theory, with a strong intrinsic asymmetry, is summarized in terms of a few expansion coefficients. These include an important emergent energy scale Δ0 that shrinks to zero on approaching the insulating state, thereby making it difficult to access the underlying very low energy Fermi liquid behavior. The scaled low frequency ECFL spectral function, related simply to the Fano line shape, has a peculiar energy dependence unlike that of a Lorentzian. The resulting energy dispersion obtained by maximization is a hybrid of a massive and a massless Dirac spectrum EQ∗˜γ Q-√{Γ02+Q2}, where the vanishing of Q, a momentum type variable, locates the kink minimum. Therefore the quasiparticle velocity interpolates between (γ∓1) over a width Γ0 on the two sides of Q=0, implying a kink there that strongly resembles a prominent low energy feature seen in angle resolved photoemission spectra (ARPES) of cuprate materials. We also propose novel ways of analyzing the ARPES data to isolate the predicted asymmetry between particle and hole excitations.
Aircraft Engine Gas Path Diagnostic Methods: Public Benchmarking Results
NASA Technical Reports Server (NTRS)
Simon, Donald L.; Borguet, Sebastien; Leonard, Olivier; Zhang, Xiaodong (Frank)
2013-01-01
Recent technology reviews have identified the need for objective assessments of aircraft engine health management (EHM) technologies. To help address this issue, a gas path diagnostic benchmark problem has been created and made publicly available. This software tool, referred to as the Propulsion Diagnostic Method Evaluation Strategy (ProDiMES), has been constructed based on feedback provided by the aircraft EHM community. It provides a standard benchmark problem enabling users to develop, evaluate and compare diagnostic methods. This paper will present an overview of ProDiMES along with a description of four gas path diagnostic methods developed and applied to the problem. These methods, which include analytical and empirical diagnostic techniques, will be described and associated blind-test-case metric results will be presented and compared. Lessons learned along with recommendations for improving the public benchmarking processes will also be presented and discussed.
CPM (Critical Path Method) as a Curriculum Tool.
ERIC Educational Resources Information Center
Mongerson, M. Duane
This document discusses and illustrates the use of the Critical Path Method (CPM) as a tool for developing curriculum. In so doing a brief review of the evolution of CPM as a management tool developed by E. I. duPont de Nemours Company is presented. It is also noted that CPM is only a method of sequencing learning activities and not an end unto…
2014-01-01
Background Saccharomyces cerevisiae is able to adapt to a wide range of external oxygen conditions. Previously, oxygen-dependent phenotypes have been studied individually at the transcriptional, metabolite, and flux level. However, the regulation of cell phenotype occurs across the different levels of cell function. Integrative analysis of data from multiple levels of cell function in the context of a network of several known biochemical interaction types could enable identification of active regulatory paths not limited to a single level of cell function. Results The graph theoretical method called Enriched Molecular Path detection (EMPath) was extended to enable integrative utilization of transcription and flux data. The utility of the method was demonstrated by detecting paths associated with phenotype differences of S. cerevisiae under three different conditions of oxygen provision: 20.9%, 2.8% and 0.5%. The detection of molecular paths was performed in an integrated genome-scale metabolic and protein-protein interaction network. Conclusions The molecular paths associated with the phenotype differences of S. cerevisiae under conditions of different oxygen provisions revealed paths of molecular interactions that could potentially mediate information transfer between processes that respond to the particular oxygen availabilities. PMID:24528924
Israël, I; Grasso, R; Georges-Francois, P; Tsuzuku, T; Berthoz, A
1997-06-01
According to path integration, the brain is able to compute the distance of a traveled path. In this research we applied our previously reported method for studying memory of linear distance, a crucial mechanism in path integration; our method is based on the overt reconstruction of a passive transport. Passive transport is a special case of navigation in which no active control is performed. Blindfolded subjects were first asked to travel 2 m forward, in darkness, by driving with a joystick the robot on which they were seated. The results show that all subjects but two undershot this distance, i.e., overestimated their own displacement. Then, subjects were submitted to a passive linear forward displacement along 2, 4, 6, 8, or 10 m, and had to reproduce the same distance, still blindfolded. The results show that the distance of the stimulus was accurately reproduced, as well as stimulus duration, peak velocity, and velocity profile. In this first condition, the imposed velocity profile was triangular and therefore stimulus distance and duration were correlated. In a second condition, it was shown that distance was correctly reproduced also when the information about stimulus duration was kept constant. Here, different velocity profiles were used as stimuli, and most subjects also reproduced the velocity profile. Statistical analyses indicated that distance was not reproduced as a consequence of duration, peak velocity, or velocity profile reproduction, but was uniquely correlated to stimulus distance. The previous hypothesis of a double integration of the otolith signal to provide a distance estimate can explain our results. There was a large discrepancy between the accuracy with which the subjects matched the velocity profiles and that of distance reproduction. It follows that, whereas the dynamics of passive motion are stored and available to further use, distance is independently estimated. It is concluded that vestibular and somatosensory signals excited by
Yang, Sandy; Yamamoto, Takeshi; Miller, William H.
2005-11-28
The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial(-type) estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.
A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates
Shiga, Motoyuki; Fujisaki, Hiroshi
2012-05-14
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{sub 3} molecule and N{sub 2}H{sub 5}{sup -} 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{sub 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{sub 2}H{sub 5}{sup -}, the centroid IRC is largely deviated from the ''classical'' IRC, and the free energy barrier is reduced by the quantum effects even more drastically.
A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates
NASA Astrophysics Data System (ADS)
Shiga, Motoyuki; Fujisaki, Hiroshi
2012-05-01
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 NH3 molecule and N2H_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 NH3, 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 N2H_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.
Tanizaki, Yuya; Koike, Takayuki
2014-12-15
Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integrals on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem. - Highlights: • Real-time path integral is studied based on Picard–Lefschetz theory. • Lucid demonstration is given through simple examples of quantum mechanics. • This technique is applied to quantum mechanics of the double-well potential. • Difficulty for practical applications is revealed, and we discuss its generality. • Quantum tunneling is shown to be closely related to complex classical solutions.
Benchmarking Gas Path Diagnostic Methods: A Public Approach
NASA Technical Reports Server (NTRS)
Simon, Donald L.; Bird, Jeff; Davison, Craig; Volponi, Al; Iverson, R. Eugene
2008-01-01
Recent technology reviews have identified the need for objective assessments of engine health management (EHM) technology. The need is two-fold: technology developers require relevant data and problems to design and validate new algorithms and techniques while engine system integrators and operators need practical tools to direct development and then evaluate the effectiveness of proposed solutions. This paper presents a publicly available gas path diagnostic benchmark problem that has been developed by the Propulsion and Power Systems Panel of The Technical Cooperation Program (TTCP) to help address these needs. The problem is coded in MATLAB (The MathWorks, Inc.) and coupled with a non-linear turbofan engine simulation to produce "snap-shot" measurements, with relevant noise levels, as if collected from a fleet of engines over their lifetime of use. Each engine within the fleet will experience unique operating and deterioration profiles, and may encounter randomly occurring relevant gas path faults including sensor, actuator and component faults. The challenge to the EHM community is to develop gas path diagnostic algorithms to reliably perform fault detection and isolation. An example solution to the benchmark problem is provided along with associated evaluation metrics. A plan is presented to disseminate this benchmark problem to the engine health management technical community and invite technology solutions.
Navigational path integration by cortical neurons: origins in higher-order direction selectivity
Page, William K.; Sato, Nobuya; Froehler, Michael T.; Vaughn, William
2015-01-01
Navigation relies on the neural processing of sensory cues about observer self-movement and spatial location. Neurons in macaque dorsal medial superior temporal cortex (MSTd) respond to visual and vestibular self-movement cues, potentially contributing to navigation and orientation. We moved monkeys on circular paths around a room while recording the activity of MSTd neurons. MSTd neurons show a variety of sensitivities to the monkey's heading direction, circular path through the room, and place in the room. Changing visual cues alters the relative prevalence of those response properties. Disrupting the continuity of self-movement paths through the environment disrupts path selectivity in a manner linked to the time course of single neuron responses. We hypothesize that sensory cues interact with the spatial and temporal integrative properties of MSTd neurons to derive path selectivity for navigational path integration supporting spatial orientation. PMID:25589586
An introduction to stochastic control theory, path integrals and reinforcement learning
NASA Astrophysics Data System (ADS)
Kappen, Hilbert J.
2007-02-01
Control theory is a mathematical description of how to act optimally to gain future rewards. In this paper I give an introduction to deterministic and stochastic control theory and I give an overview of the possible application of control theory to the modeling of animal behavior and learning. I discuss a class of non-linear stochastic control problems that can be efficiently solved using a path integral or by MC sampling. In this control formalism the central concept of cost-to-go becomes a free energy and methods and concepts from statistical physics can be readily applied.
Garberoglio, Giovanni; Jankowski, Piotr; Szalewicz, Krzysztof; Harvey, Allan H.
2014-07-28
We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H{sub 2}) and deuterium (D{sub 2}) in the temperature range 15–2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H{sub 2} between 100 and 200 K.
Path Integral Solution for the Coulomb Potential in a Curved Space of Constant Positive Curvature
NASA Astrophysics Data System (ADS)
Aggoun, L.; Bounouioua, N.; Benamira, F.; Guechi, L.
2016-05-01
A new path integral treatment of a hydrogen-like atom in a uniformly curved space with a constant positive curvature is presented. By converting the radial path integral into a path integral for the modified Pöschl-Teller potential with the help of the space-time transformation technique, the radial Green's function is expressed in closed form, from which the energy spectrum and the corresponding normalized wave functions of the bound states are extracted. In the limit of vanishing curvature, the Green's function, the energy spectra and the correctly normalized wave functions of bound and scattering states for a standard hydrogen-like atom are found.
Inequivalent Quantizations and Holonomy Factor from the Path-Integral Approach
NASA Astrophysics Data System (ADS)
Tanimura, Shogo; Tsutsui, Izumi
1997-08-01
A path-integral quantization on a homogeneous spaceG/His proposed, based on the guiding principle "first lift toGand then project toG/H". It is then shown that this principle gives a simple procedure to obtain the inequivalent quantizations (superselection sectors), along with the holonomy factor (induced gauge field) found earlier by algebraic approaches. We also prove that the resulting matrix-valued path-integral is physically equivalent to the scalar-valued path-integral derived in the Dirac approach, and thereby we present a unified viewpoint to discuss the basic features of quantizing onG/Hobtained in various approaches so far.
Botelho, L.C.L.
1985-03-15
We study a two-dimensional quantum field model with axial-vector-current--pseudoscalar derivative interaction using path-integral methods. We construct an effective Lagrangian by performing a chiral change in the fermionic variables leading to an exact solution of the model.
Piloting and Path Integration within and across Boundaries
ERIC Educational Resources Information Center
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.…
On path-following methods for structural failure problems
NASA Astrophysics Data System (ADS)
Stanić, Andjelka; Brank, Boštjan; Korelc, Jože
2016-08-01
We revisit the consistently linearized path-following method that can be applied in the nonlinear finite element analysis of solids and structures in order to compute a solution path. Within this framework, two constraint equations are considered: a quadratic one (that includes as special cases popular spherical and cylindrical forms of constraint equation), and another one that constrains only one degree-of-freedom (DOF), the critical DOF. In both cases, the constrained DOFs may vary from one solution increment to another. The former constraint equation is successful in analysing geometrically nonlinear and/or standard inelastic problems with snap-throughs, snap-backs and bifurcation points. However, it cannot handle problems with the material softening that are computed e.g. by the embedded-discontinuity finite elements. This kind of problems can be solved by using the latter constraint equation. The plusses and minuses of the both presented constraint equations are discussed and illustrated on a set of numerical examples. Some of the examples also include direct computation of critical points and branch switching. The direct computation of the critical points is performed in the framework of the path-following method by using yet another constraint function, which is eigenvector-free and suited to detect critical points.
Dynamic response characteristics of dual flow-path integrally bladed rotors
NASA Astrophysics Data System (ADS)
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.
PathCase-SB: integrating data sources and providing tools for systems biology research
2012-01-01
Background Integration of metabolic pathways resources and metabolic network models, and deploying new tools on the integrated platform can help perform more effective and more efficient systems biology research on understanding the regulation of metabolic networks. Therefore, the tasks of (a) integrating under a single database environment regulatory metabolic networks and existing models, and (b) building tools to help with modeling and analysis are desirable and intellectually challenging computational tasks. Results PathCase Systems Biology (PathCase-SB) is built and released. This paper describes PathCase-SB user interfaces developed to date. The current PathCase-SB system provides a database-enabled framework and web-based computational tools towards facilitating the development of kinetic models for biological systems. PathCase-SB aims to integrate systems biology models data and metabolic network data of selected biological data sources on the web (currently, BioModels Database and KEGG, respectively), and to provide more powerful and/or new capabilities via the new web-based integrative framework. Conclusions Each of the current four PathCase-SB interfaces, namely, Browser, Visualization, Querying, and Simulation interfaces, have expanded and new capabilities as compared with the original data sources. PathCase-SB is already available on the web and being used by researchers across the globe. PMID:22697505
New methods for calculating short-wave radio paths
NASA Astrophysics Data System (ADS)
Popov, A. V.; Tsedilina, E. E.; Cherkashin, Iu. N.
Recent research on the calculation of short-wave paths at IZMIRAN (the Soviet Institute for the Study of Terrestrial Magnetism, the Ionosphere, and the Propagation of Radio Waves) is reviewed. Particular attention is given to: (1) the development of approximate analytical methods for ray-tracing calculations and for determining the geometrical-optics characteristics of a radio signal in a horizontally irregular ionosphere; (2) investigations of the long-range and short-wave propagation of decametric waves; and (3) the development of a parabolic-equation method for considering diffraction and scattering in a medium with regular and random irregularities.
Path Integral Quantization of the Chiral Schwinger Model in Bosonized Form
NASA Astrophysics Data System (ADS)
Bracken, Paul
The development of the Wess-Zumino action or one-cycle is reviewed from the path integral approach. This is related to the occurrence of anomalies in the theory, and generally signifies a breakdown of gauge invariance. The Jackiw-Rajaraman version of the chiral Schwinger model is studied by means of path integrals. It is shown how the model can be made gauge invariant by using a Wess-Zumino term to write a gauge invariant Lagrangian. The model is considered only in bosonized form without any reference to fermions. The constraints are determined. These components are then used to write a path integral quantization for the bosonized form of the model. Some physical quantities and information, in particular, propagators are derived from the path integral.
A brief view of known landmarks reorientates path integration in hamsters
NASA Astrophysics Data System (ADS)
Etienne, A. S.; Boulens, V.; Maurer, R.; Rowe, T.; Siegrist, C.
In darkness, hamsters commute between their nest and a feeding site through path integration only, and therefore show cumulative errors in the return direction to the nest. We examined whether a brief presentation of familiar room cues could reset the path integrator. The hamsters could see the room cues either during, or at the end of, the outward journey to the food place, in a conflict situation where motion cues and visual information were set at variance. In both conditions, the animals used mainly visual information to return home. Thus, hamsters can determine their azimuth, and possibly their location, through a visual fix, and can reset their path integrator through the fix. This allows them to update their position during further locomotion in the dark and thus to compute a correct homing vector with respect to a visually induced reference frame. Taking episodic positional fixes may greatly enhance the functional value of path integration.
Path Integral Calculation of GREEN’S Function for SCHRÖDINGER Equation in Unitary Gauge
NASA Astrophysics Data System (ADS)
Rozansky, L.
Green’s function of Schrödinger equation is represented as a time-reparametrization invariant path integral. Unitary gauge fixing enables us to get the WKB preexponential factor without calculating determinants of operators containing derivatives.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat.
Liu, Jian; Li, Dezhang; Liu, Xinzijian
2016-07-14
We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used. PMID:27421393
Deciphering the hippocampal polyglot: the hippocampus as a path integration system.
McNaughton, B L; Barnes, C A; Gerrard, J L; Gothard, K; Jung, M W; Knierim, J J; Kudrimoti, H; Qin, Y; Skaggs, W E; Suster, M; Weaver, K L
1996-01-01
Hippocampal 'place' cells and the head-direction cells of the dorsal presubiculum and related neocortical and thalamic areas appear to be part of a preconfigured network that generates an abstract internal representation of two-dimensional space whose metric is self-motion. It appears that viewpoint-specific visual information (e.g. landmarks) becomes secondarily bound to this structure by associative learning. These associations between landmarks and the preconfigured path integrator serve to set the origin for path integration and to correct for cumulative error. In the absence of familiar landmarks, or in darkness without a prior spatial reference, the system appears to adopt an initial reference for path integration independently of external cues. A hypothesis of how the path integration system may operate at the neuronal level is proposed. PMID:8576689
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat
NASA Astrophysics Data System (ADS)
Liu, Jian; Li, Dezhang; Liu, Xinzijian
2016-07-01
We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.
Path Integral Approach to a Single Polymer Chain with Random Media
NASA Astrophysics Data System (ADS)
Kunsombat, Ch.; Sa-Yakanit, V.
In this paper we consider the problem of a polymer chain in random media with finite correlation. We show that the mean square end-to-end distance of a polymer chain can be obtained using the Feynman path integral developed by Feynman for treating the polaron problem and successfuly applied to the theory of heavily doped semiconductor. We show that for short-range correlation or the white Gaussian model we derive the results obtained by Edwards and Muthukumar using the replica method and for long-range correlation we obtain the result of Yohannes Shiferaw and Yadin Y. Goldschimidt. The main idea of this paper is to generalize the model proposed by Edwards and Muthukumar for short-range correlation to finite correlation. Instead of using a replica method, we employ the Feynman path integral by modeling the polymer Hamiltonian as a model of non-local quadratic trial Hamiltonian. This non-local trial Hamiltonian is essential as it will reflect the translation invariant of the original Hamiltonian. The calculation is proceeded by considering the differences between the polymer propagator and the trial propagator as the first cumulant approximation. The variational principle is used to find the optimal values of the variational parameters and the mean square end-to-end distance is obtained. Several asymptotic limits are considered and a comparison between this approaches and replica approach will be discussed.
Equivalence of the Path Integral for Fermions in Cartesian and Spherical Coordinates
NASA Astrophysics Data System (ADS)
Briggs, Andrew; Camblong, Horacio E.; Ordóñez, Carlos R.
2013-06-01
The path integral calculation for the free energy of a spin-1/2 Dirac-fermion gas is performed in spherical polar coordinates for a flat space-time geometry. Its equivalence with the Cartesian-coordinate representation is explicitly established. This evaluation involves a relevant limiting case of the fermionic path integral in a Schwarzschild background, whose near-horizon limit has been shown to be related to black hole thermodynamics.
Accelerated adaptive integration method.
Kaus, Joseph W; Arrar, Mehrnoosh; McCammon, J Andrew
2014-05-15
Conformational changes that occur upon ligand binding may be too slow to observe on the time scales routinely accessible using molecular dynamics simulations. The adaptive integration method (AIM) leverages the notion that when a ligand is either fully coupled or decoupled, according to λ, barrier heights may change, making some conformational transitions more accessible at certain λ values. AIM adaptively changes the value of λ in a single simulation so that conformations sampled at one value of λ seed the conformational space sampled at another λ value. Adapting the value of λ throughout a simulation, however, does not resolve issues in sampling when barriers remain high regardless of the λ value. In this work, we introduce a new method, called Accelerated AIM (AcclAIM), in which the potential energy function is flattened at intermediate values of λ, promoting the exploration of conformational space as the ligand is decoupled from its receptor. We show, with both a simple model system (Bromocyclohexane) and the more complex biomolecule Thrombin, that AcclAIM is a promising approach to overcome high barriers in the calculation of free energies, without the need for any statistical reweighting or additional processors. PMID:24780083
Accelerated Adaptive Integration Method
2015-01-01
Conformational changes that occur upon ligand binding may be too slow to observe on the time scales routinely accessible using molecular dynamics simulations. The adaptive integration method (AIM) leverages the notion that when a ligand is either fully coupled or decoupled, according to λ, barrier heights may change, making some conformational transitions more accessible at certain λ values. AIM adaptively changes the value of λ in a single simulation so that conformations sampled at one value of λ seed the conformational space sampled at another λ value. Adapting the value of λ throughout a simulation, however, does not resolve issues in sampling when barriers remain high regardless of the λ value. In this work, we introduce a new method, called Accelerated AIM (AcclAIM), in which the potential energy function is flattened at intermediate values of λ, promoting the exploration of conformational space as the ligand is decoupled from its receptor. We show, with both a simple model system (Bromocyclohexane) and the more complex biomolecule Thrombin, that AcclAIM is a promising approach to overcome high barriers in the calculation of free energies, without the need for any statistical reweighting or additional processors. PMID:24780083
Development of a Pulsed 2-Micron Integrated Path Differential Absorption Lidar for CO2 Measurement
NASA Technical Reports Server (NTRS)
Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer; Refaat, Tamer
2013-01-01
Atmospheric carbon dioxide (CO2) is an important greenhouse gas that significantly contributes to the carbon cycle and global radiation budget on Earth. Active remote sensing of CO2 is important to address several limitations that contend with passive sensors. A 2-micron double-pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This active remote sensing instrument will provide an alternate approach of measuring atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise ratio level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement. Commercial, on the shelf, components are implemented for the detection system. Instrument integration will be presented in this paper as well as a background for CO2 measurement at NASA Langley research Center
Quantum mechanical single molecule partition function from path integral Monte Carlo simulations.
Chempath, Shaji; Predescu, Cristian; Bell, Alexis T
2006-06-21
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. PMID:16821901
Quantum Mechanical Single Molecule Partition Function from PathIntegral Monte Carlo Simulations
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.
An adaptation of Krylov subspace methods to path following
Walker, H.F.
1996-12-31
Krylov subspace methods at present constitute a very well known and highly developed class of iterative linear algebra methods. These have been effectively applied to nonlinear system solving through Newton-Krylov methods, in which Krylov subspace methods are used to solve the linear systems that characterize steps of Newton`s method (the Newton equations). Here, we will discuss the application of Krylov subspace methods to path following problems, in which the object is to track a solution curve as a parameter varies. Path following methods are typically of predictor-corrector form, in which a point near the solution curve is {open_quotes}predicted{close_quotes} by some easy but relatively inaccurate means, and then a series of Newton-like corrector iterations is used to return approximately to the curve. The analogue of the Newton equation is underdetermined, and an additional linear condition must be specified to determine corrector steps uniquely. This is typically done by requiring that the steps be orthogonal to an approximate tangent direction. Augmenting the under-determined system with this orthogonality condition in a straightforward way typically works well if direct linear algebra methods are used, but Krylov subspace methods are often ineffective with this approach. We will discuss recent work in which this orthogonality condition is imposed directly as a constraint on the corrector steps in a certain way. The means of doing this preserves problem conditioning, allows the use of preconditioners constructed for the fixed-parameter case, and has certain other advantages. Experiments on standard PDE continuation test problems indicate that this approach is effective.
Kamibayashi, Yuki; Miura, Shinichi
2016-08-21
In the present study, variational path integral molecular dynamics and associated hybrid Monte Carlo (HMC) methods have been developed on the basis of a fourth order approximation of a density operator. To reveal various parameter dependence of physical quantities, we analytically solve one dimensional harmonic oscillators by the variational path integral; as a byproduct, we obtain the analytical expression of the discretized density matrix using the fourth order approximation for the oscillators. Then, we apply our methods to realistic systems like a water molecule and a para-hydrogen cluster. In the HMC, we adopt two level description to avoid the time consuming Hessian evaluation. For the systems examined in this paper, the HMC method is found to be about three times more efficient than the molecular dynamics method if appropriate HMC parameters are adopted; the advantage of the HMC method is suggested to be more evident for systems described by many body interaction. PMID:27544094
Accelerating Ab Initio Path Integral Simulations via Imaginary Multiple-Timestepping.
Cheng, Xiaolu; Herr, Jonathan D; Steele, Ryan P
2016-04-12
This work investigates the use of multiple-timestep schemes in imaginary time for computationally efficient ab initio equilibrium path integral simulations of quantum molecular motion. In the simplest formulation, only every n(th) path integral replica is computed at the target level of electronic structure theory, whereas the remaining low-level replicas still account for nuclear motion quantum effects with a more computationally economical theory. Motivated by recent developments for multiple-timestep techniques in real-time classical molecular dynamics, both 1-electron (atomic-orbital basis set) and 2-electron (electron correlation) truncations are shown to be effective. Structural distributions and thermodynamic averages are tested for representative analytic potentials and ab initio molecular examples. Target quantum chemistry methods include density functional theory and second-order Møller-Plesset perturbation theory, although any level of theory is formally amenable to this framework. For a standard two-level splitting, computational speedups of 1.6-4.0x are observed when using a 4-fold reduction in time slices; an 8-fold reduction is feasible in some cases. Multitiered options further reduce computational requirements and suggest that quantum mechanical motion could potentially be obtained at a cost not significantly different from the cost of classical simulations. PMID:26966920
NASA Astrophysics Data System (ADS)
Voronov, Aleksandr V.; Tret'yakov, Evgeniy V.; Shuvalov, Vladimir V.
2004-06-01
Based on the path-integration technique and the Metropolis method, the original calculation scheme is developed for solving the problem of light propagation through highly scattering objects. The elimination of calculations of 'unnecessary' realisations and the phenomenological description of processes of multiple small-angle scattering provided a drastic increase (by nine and more orders of magnitude) in the calculation rate, retaining the specific features of the problem (consideration of spatial inhomogeneities, boundary conditions, etc.). The scheme allows one to verify other fast calculation algorithms and to obtain information required to reconstruct the internal structure of highly scattering objects (of size ~1000 scattered lengths and more) by the method of diffusion optical tomography.
Perturbative path-integral study of active- and passive-tracer diffusion in fluctuating fields
NASA Astrophysics Data System (ADS)
Démery, Vincent; Dean, David S.
2011-07-01
We study the effective diffusion constant of a Brownian particle linearly coupled to a thermally fluctuating scalar field. We use a path-integral method to compute the effective diffusion coefficient perturbatively to lowest order in the coupling constant. This method can be applied to cases where the field is affected by the particle (an active tracer) and cases where the tracer is passive. Our results are applicable to a wide range of physical problems, from a protein diffusing in a membrane to the dispersion of a passive tracer in a random potential. In the case of passive diffusion in a scalar field, we show that the coupling to the field can, in some cases, speed up the diffusion corresponding to a form of stochastic resonance. Our results on passive diffusion are also confirmed via a perturbative calculation of the probability density function of the particle in a Fokker-Planck formulation of the problem. Numerical simulations on simplified systems corroborate our results.
Bias in Human Path Integration Is Predicted by Properties of Grid Cells.
Chen, Xiaoli; He, Qiliang; Kelly, Jonathan W; Fiete, Ila R; McNamara, Timothy P
2015-06-29
Accurate wayfinding is essential to the survival of many animal species and requires the ability to maintain spatial orientation during locomotion. One of the ways that humans and other animals stay spatially oriented is through path integration, which operates by integrating self-motion cues over time, providing information about total displacement from a starting point. The neural substrate of path integration in mammals may exist in grid cells, which are found in dorsomedial entorhinal cortex and presubiculum and parasubiculum in rats. Grid cells have also been found in mice, bats, and monkeys, and signatures of grid cell activity have been observed in humans. We demonstrate that distance estimation by humans during path integration is sensitive to geometric deformations of a familiar environment and show that patterns of path integration error are predicted qualitatively by a model in which locations in the environment are represented in the brain as phases of arrays of grid cells with unique periods and decoded by the inverse mapping from phases to locations. The periods of these grid networks are assumed to expand and contract in response to expansions and contractions of a familiar environment. Biases in distance estimation occur when the periods of the encoding and decoding grids differ. Our findings explicate the way in which grid cells could function in human path integration. PMID:26073138
On the orthogonalised reverse path method for nonlinear system identification
NASA Astrophysics Data System (ADS)
Muhamad, P.; Sims, N. D.; Worden, K.
2012-09-01
The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi-degree-of-freedom (MDOF) system can be solved using the conditioned reverse path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): pp. 673-708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach - the orthogonalised reverse path (ORP) method - is illustrated here using data from simulated single-degree-of-freedom (SDOF) and MDOF systems.
Wong, Kim F.; Sonnenberg, Jason L.; Paesani, Francesco; Yamamoto, Takeshi; Vaníček, Jiří; Zhang, Wei; Schlegel, H. Bernhard; Case, David A.; Cheatham, Thomas E.; Miller, William H.; Voth, Gregory A.
2010-01-01
The rates of intramolecular proton transfer are calculated on a full-dimensional reactive electronic potential energy surface that incorporates high level ab initio calculations along the reaction path and by using classical Transition State theory, Path-Integral Quantum Transition State Theory, and the Quantum Instanton approach. The specific example problem studied is malonaldehyde. Estimates of the kinetic isotope effect using the latter two methods are found to be in reasonable agreement with each other. Improvements and extensions of this practical, yet chemically accurate framework for the calculations of quantized, reactive dynamics are also discussed. PMID:21116485
NASA Astrophysics Data System (ADS)
Douglas, Jack
2014-03-01
One of the things that puzzled me when I was a PhD student working under Karl Freed was the curious unity between the theoretical descriptions of excluded volume interactions in polymers, the hydrodynamic properties of polymers in solution, and the critical properties of fluid mixtures, gases and diverse other materials (magnets, superfluids,etc.) when these problems were formally expressed in terms of Wiener path integration and the interactions treated through a combination of epsilon expansion and renormalization group (RG) theory. It seemed that only the interaction labels changed from one problem to the other. What do these problems have in common? Essential clues to these interrelations became apparent when Karl Freed, myself and Shi-Qing Wang together began to study polymers interacting with hyper-surfaces of continuously variable dimension where the Feynman perturbation expansions could be performed through infinite order so that we could really understand what the RG theory was doing. It is evidently simply a particular method for resuming perturbation theory, and former ambiguities no longer existed. An integral equation extension of this type of exact calculation to ``surfaces'' of arbitrary fixed shape finally revealed the central mathematical object that links these diverse physical models- the capacity of polymer chains, whose value vanishes at the critical dimension of 4 and whose magnitude is linked to the friction coefficient of polymer chains, the virial coefficient of polymers and the 4-point function of the phi-4 field theory,...Once this central object was recognized, it then became possible solve diverse problems in material science through the calculation of capacity, and related ``virials'' properties, through Monte Carlo sampling of random walk paths. The essential ideas of this computational method are discussed and some applications given to non-trivial problems: nanotubes treated as either rigid rods or ensembles worm-like chains having
NASA Astrophysics Data System (ADS)
Simeone, Emilio; Donati, Alessandro
1998-12-01
The increment of the exploitable optical path represents one of the most important efforts in the differential optical absorption spectroscopy (DOAS) instruments improvement. The methods that allow long path measurements in the UV region are presented and discussed in this paper. These methods have been experimented in the new Italian DOAS instrument - SPOT - developed and manufactured by Kayser Italia. The system was equipped with a tele-controlled optical shuttle on the light source unit, allowing background radiation measurement. Wavelength absolute calibration of spectra by means of a collimated UV beam from a mercury lamp integrated in the telescope has been exploited. Besides, possible thermal effects on the dispersion coefficients of the holographic grating have been automatically compensated by means of a general non-linear fit during the spectral analysis session. Measurements in bistatic configuration have been performed in urban areas at 1300 m and 2200 m in three spectral windows from 245 to 380 nm. Measurements with these features are expected in the other spectral windows on path lengths ranging from about 5 to 10 km in urban areas. The DOAS technique can be used in field for very fast measurements in the 245-275 nm spectral range, on path lengths up to about 2500 m.
Song, Linze; Shi, Qiang
2015-05-01
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. PMID:25956086
Path Integrals, Fourier Transforms, and Feynman's Operational Calculus
Ahn, Byung Moo; Johnson, G. W.
1998-03-15
The disentangling process is the key to Feynman's operational calculus for noncommuting operators. The main result of his heuristic calculations deals with disentangling an exponential factor. We use the Wiener and Feynman integrals to make this disentangling (or time-ordering) mathematically rigorous in the case where the analytic functions from earlier work are replaced by Fourier transforms of complex-valued measures.
PathPPI: an integrated dataset of human pathways and protein-protein interactions.
Tang, HaiLin; Zhong, Fan; Liu, Wei; He, FuChu; Xie, HongWei
2015-06-01
Integration of pathway and protein-protein interaction (PPI) data can provide more information that could lead to new biological insights. PPIs are usually represented by a simple binary model, whereas pathways are represented by more complicated models. We developed a series of rules for transforming protein interactions from pathway to binary model, and the protein interactions from seven pathway databases, including PID, BioCarta, Reactome, NetPath, INOH, SPIKE and KEGG, were transformed based on these rules. These pathway-derived binary protein interactions were integrated with PPIs from other five PPI databases including HPRD, IntAct, BioGRID, MINT and DIP, to develop integrated dataset (named PathPPI). More detailed interaction type and modification information on protein interactions can be preserved in PathPPI than other existing datasets. Comparison analysis results indicate that most of the interaction overlaps values (O AB) among these pathway databases were less than 5%, and these databases must be used conjunctively. The PathPPI data was provided at http://proteomeview.hupo.org.cn/PathPPI/PathPPI.html. PMID:25591449
Huo, Pengfei; Miller, Thomas F. III; Coker, David F.
2013-10-21
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.
NASA Astrophysics Data System (ADS)
Park, Sungjin; Shin, Hyeondeok; Kwon, Yongkyung
2012-08-01
The recently-proposed fourth-order propagator based on the multi-product expansion has been applied to path-integral Monte Carlo calculations for asymmetric quantum quadruploar rotors fixed at face-centered cubic lattice sites. The rotors are observed to undergo an orientational orderdisorder phase transition at a low temperature when the electric quadrupole-quadrupole interaction is strong enough. At intermediate interaction strength, a further decrease of temperature after the first transition to the ordered phase results in a reentrant transition back to the disordered phase. The theoretical phase diagram of these asymmetric rotors determined by using fourth-order path-integral Monte Carlo calculations is found to be in good quantitative agreement with the experimental one for solid hydrogen deuteride. This leads us to conclude that the fourth-order propagator can be effectively implemented for an accurate path-integral Monte Carlo calculation of a quantum many-body system with rotational degrees of freedom.
NASA Astrophysics Data System (ADS)
Wang, Zhongyi; Gao, Qi; Wang, Chengyue; Wei, Runjie; Wang, Jinjun
2016-06-01
Particle image velocimetry (PIV)-based pressure reconstruction has become a popular technique in experimental fluid mechanics. Noise or errors in raw velocity field would significantly affect the quality of pressure reconstruction in PIV measurement. To reduce experimental errors in pressure gradient and improve the precision of reconstructed pressure field, a minimal 2-norm criteria-based new technique called irrotation correction (IC) with orthogonal decomposition is developed. The pressure reconstruction is therefore composed of three steps: calculation of pressure gradient from time-resolved velocity fields of PIV, an irrotation correction on the pressure gradient field, and finally a simple orthogonal-path integration (OPI) for pressure. Systematic assessments of IC algorithm are performed on synthetic solid-body rotation flow, direct numerical simulations of a channel flow and an isotropic turbulent flow. The results show that IC is a robust algorithm which can significantly improve the accuracy of pressure reconstruction primarily in the low wave number domain. After irrotation correction, noisy pressure gradient field ideally becomes an irrotational field on which the pressure integration is independent of integrating paths. Therefore, an OPI algorithm is proposed to perform the pressure integration in an efficient way with very few integration paths. This makes the new technique to be a doable method on three-dimensional pressure reconstruction with acceptable computational cost.
Robust path integration in the entorhinal grid cell system with hippocampal feed-back.
Samu, Dávid; Eros, Péter; Ujfalussy, Balázs; Kiss, Tamás
2009-07-01
Animals are able to update their knowledge about their current position solely by integrating the speed and the direction of their movement, which is known as path integration. Recent discoveries suggest that grid cells in the medial entorhinal cortex might perform some of the essential underlying computations of path integration. However, a major concern over path integration is that as the measurement of speed and direction is inaccurate, the representation of the position will become increasingly unreliable. In this paper, we study how allothetic inputs can be used to continually correct the accumulating error in the path integrator system. We set up the model of a mobile agent equipped with the entorhinal representation of idiothetic (grid cell) and allothetic (visual cells) information and simulated its place learning in a virtual environment. Due to competitive learning, a robust hippocampal place code emerges rapidly in the model. At the same time, the hippocampo-entorhinal feed-back connections are modified via Hebbian learning in order to allow hippocampal place cells to influence the attractor dynamics in the entorhinal cortex. We show that the continuous feed-back from the integrated hippocampal place representation is able to stabilize the grid cell code. PMID:19381679
Path integral calculation of free energies: quantum effects on the melting temperature of neon.
Ramírez, R; Herrero, C P; Antonelli, A; Hernández, E R
2008-08-14
The path integral formulation has been combined with several methods to determine free energies of quantum many-body systems, such as adiabatic switching and reversible scaling. These techniques are alternatives to the standard thermodynamic integration method. A quantum Einstein crystal is used as a model to demonstrate the accuracy and reliability of these free energy methods in quantum simulations. Our main interest focuses on the calculation of the melting temperature of Ne at ambient pressure, taking into account quantum effects in the atomic dynamics. The free energy of the solid was calculated by considering a quantum Einstein crystal as reference state, while for the liquid, the reference state was defined by the classical limit of the fluid. Our findings indicate that, while quantum effects in the melting temperature of this system are small, they still amount to about 6% of the melting temperature, and are therefore not negligible. The particle density as well as the melting enthalpy and entropy of the solid and liquid phases at coexistence is compared to results obtained in the classical limit and also to available experimental data. PMID:18715054
Ab initio path-integral molecular dynamics and the quantum nature of hydrogen bonds
NASA Astrophysics Data System (ADS)
Yexin, Feng; Ji, Chen; Xin-Zheng, Li; Enge, Wang
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. Project supported by the National Natural Science Foundation of China (Grant Nos. 11275008, 91021007, and 10974012) and the China Postdoctoral Science Foundation (Grant No. 2014M550005).
Path integral measure, constraints and ghosts for massive gravitons with a cosmological constant
Metaxas, Dimitrios
2009-12-15
For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on the graviton mass.
Path integral measure, constraints and ghosts for massive gravitons with a cosmological constant
NASA Astrophysics Data System (ADS)
Metaxas, Dimitrios
2009-12-01
For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on the graviton mass.
Making the gravitational path integral more Lorentzian or Life beyond Liouville gravity
NASA Astrophysics Data System (ADS)
Loll, R.; Ambjørn, J.; Anagnostopoulos, K. N.
2000-06-01
In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigorous, non-perturbative path integral and is inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity. It has a number of appealing features: i) its quantum geometry is non-fractal, ii) it remains consistent when coupled to matter, even beyond the c=1 barrier, iii) it is closer to canonical quantization approaches than previous path-integral formulations, and iv) its construction generalizes to higher dimensions.
NASA Astrophysics Data System (ADS)
Wagner, Gerd; Maxwell, Stephen; Plusquellic, David
2016-06-01
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.
NASA Astrophysics Data System (ADS)
Zamirian, M.; Kamyad, A. V.; Farahi, M. H.
2009-09-01
In this Letter a new approach for solving optimal path planning problems for a single rigid and free moving object in a two and three dimensional space in the presence of stationary or moving obstacles is presented. In this approach the path planning problems have some incompatible objectives such as the length of path that must be minimized, the distance between the path and obstacles that must be maximized and etc., then a multi-objective dynamic optimization problem (MODOP) is achieved. Considering the imprecise nature of decision maker's (DM) judgment, these multiple objectives are viewed as fuzzy variables. By determining intervals for the values of these fuzzy variables, flexible monotonic decreasing or increasing membership functions are determined as the degrees of satisfaction of these fuzzy variables on their intervals. Then, the optimal path planning policy is searched by maximizing the aggregated fuzzy decision values, resulting in a fuzzy multi-objective dynamic optimization problem (FMODOP). Using a suitable t-norm, the FMODOP is converted into a non-linear dynamic optimization problem (NLDOP). By using parametrization method and some calculations, the NLDOP is converted into the sequence of conventional non-linear programming problems (NLPP). It is proved that the solution of this sequence of the NLPPs tends to a Pareto optimal solution which, among other Pareto optimal solutions, has the best satisfaction of DM for the MODOP. Finally, the above procedure as a novel algorithm integrating parametrization method and fuzzy aggregation to solve the MODOP is proposed. Efficiency of our approach is confirmed by some numerical examples.
Numerical evaluation of the Feynman integral-over-paths in real and imaginary-time
NASA Astrophysics Data System (ADS)
Register, L. F.; Stroscio, M. A.; Littlejohn, M. A.
New techniques are described for Monte Carlo evaluation of the propagation of quantum mechanical systems in both real and imaginary-time using the Feynman integral-over-paths formulation of quantum mechanics. For imaginary-time calculations path translation is used to augment the technique of Lawande et. al. This simple-yet-powerful technique allows the equilibrium probability density to be accurately evaluated in the presence of multiple potential wells. It is shown that path translation permits the calculation of the unknown ground-state energy of one confining potential by comparison with the known ground-state energy of another. A double finite-square-well potential and a finite-square-well/parabolic-well pair are presented as examples. For real-time calculations, a weighted analytical averaging of the exponential in the classical action is performed over a region of paths. This "windowed action" has both real and imaginary components. The imaginary component yields an exponentially decaying probability for selecting paths, thereby providing a basis for the Monte Carlo evaluation of the real-time integral-over-paths. Examples of a wave-packet in a parabolic well and a wave-packet impinging upon a potential barrier are considered.
NASA Astrophysics Data System (ADS)
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.
A review of path-independent integrals in elastic-plastic fracture mechanics, task 4
NASA Technical Reports Server (NTRS)
Kim, K. S.
1985-01-01
The path independent (P-I) integrals in elastic plastic fracture mechanics which have been proposed in recent years to overcome the limitations imposed on the J integral are reviewed. The P-I integrals considered herein are the J integral by Rice, the thermoelastic P-I integrals by Wilson and Yu and by Gurtin, the J* integral by Blackburn, the J sub theta integral by Ainsworth et al., the J integral by Kishimoto et al., and the delta T sub p and delta T* sub p integrals by Atluri et al. The theoretical foundation of these P-I integrals is examined with emphasis on whether or not path independence is maintained in the presence of nonproportional loading and unloading in the plastic regime, thermal gradients, and material inhomogeneities. The similarities, differences, salient features, and limitations of these P-I integrals are discussed. Comments are also made with regard to the physical meaning, the possibility of experimental measurement, and computational aspects.
ERIC Educational Resources Information Center
Fraser, J. Scott; Solovey, Andrew D.; Grove, David; Lee, Mo Yee; Greene, Gilbert J.
2012-01-01
A moderate common factors approach is proposed as a synthesis or middle path to integrate common and specific factors in evidence-based approaches to high-risk youth and families. The debate in family therapy between common and specific factors camps is reviewed and followed by suggestions from the literature for synthesis and creative flexibility…
Singular path-independent energy integrals for elastic bodies with thin elastic inclusions
NASA Astrophysics Data System (ADS)
Shcherbakov, V. V.
2016-06-01
An equilibrium problem for a two-dimensional homogeneous linear elastic body containing a thin elastic inclusion and an interfacial crack is considered. The thin inclusion is modeled within the framework of Euler-Bernoulli beam theory. An explicit formula for the first derivative of the energy functional with respect to the crack perturbation along the interface is presented. It is shown that the formulas for the derivative associated with translation and self-similar expansion of the crack are represented as path-independent integrals along smooth contour surrounding one or both crack tips. These path-independent integrals consist of regular and singular terms and are analogs of the well-known Eshelby-Cherepanov-Rice J-integral and Knowles-Sternberg M-integral.
Walters, Peter L; Makri, Nancy
2015-12-17
We employ the quantum-classical path integral methodology to simulate the outer sphere charge-transfer process of the ferrocene-ferrocenium pair in liquid hexane with unprecedented accuracy. Comparison of the simulation results to those obtained by mapping the solvent on an effective harmonic bath demonstrates the accuracy of linear response theory in this system. PMID:26673195
Path-dependent J-integral evaluations around an elliptical hole for large deformation theory
NASA Astrophysics Data System (ADS)
Unger, David J.
2016-08-01
An exact expression is obtained for a path-dependent J-integral for finite strains of an elliptical hole subject to remote tensile tractions under the Tresca deformation theory for a thin plate composed of non-work hardening material. Possible applications include an analytical resistance curve for the initial stage of crack propagation due to crack tip blunting.
Coherent-state path integrals in the continuum: The SU(2) case
NASA Astrophysics Data System (ADS)
Kordas, G.; Kalantzis, D.; Karanikas, A. I.
2016-09-01
We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.
a Path-Integration Approach to the Correlators of XY Heisenberg Magnet and Random Walks
NASA Astrophysics Data System (ADS)
Bogoliubov, N. M.; Malyshev, C.
2008-11-01
The path integral approach is used for the calculation of the correlation functions of the XY Heisenberg chain. The obtained answers for the two-point correlators of the XX magnet are of the determinantal form and are interpreted in terms of the generating functions for the random turns vicious walkers.
Route-segment odometry and its interactions with global path-integration.
Collett, Thomas S; Collett, Matthew
2015-06-01
Insects such as desert ants and honeybees use visual memories to travel along familiar routes between their nest and a food-site. We trained Cataglyphis fortis foragers along a two-segment route to investigate whether they encode the lengths of route segments over which visual cues remain approximately constant. Our results support earlier studies suggesting that such route-segment odometry exists, and allows an individual to stop using a visual route memory at an appropriate point, even in the absence of any change in the visual surroundings. But we find that the behavioural effects of route-segment odometry are often complicated by interactions with guidance from the global path-integration system. If route-segment odometry and path-integration agree, they act together to produce a precise signal for search. If the endpoint of route-segment odometry arrives first, it does not trigger search but its effect can persist and cause guidance by path-integration to end early. Conversely, if ants start with their path-integration state at zero, they follow a route memory for no more than 3 m, irrespective of the route-segment length. A possible explanation for these results is that if one guidance system is made to overshoot its endpoint, it can cause the other to be cut short. PMID:25904159
Factors Affecting Technology Integration in K-12 Classrooms: A Path Model
ERIC Educational Resources Information Center
Inan, Fethi A.; Lowther, Deborah L.
2010-01-01
The purpose of this study was to examine the direct and indirect effects of teachers' individual characteristics and perceptions of environmental factors that influence their technology integration in the classroom. A research-based path model was developed to explain causal relationships between these factors and was tested based on data gathered…
Analyzing methods for path mining with applications in metabolomics.
Tagore, Somnath; Chowdhury, Nirmalya; De, Rajat K
2014-01-25
Metabolomics is one of the key approaches of systems biology that consists of studying biochemical networks having a set of metabolites, enzymes, reactions and their interactions. As biological networks are very complex in nature, proper techniques and models need to be chosen for their better understanding and interpretation. One of the useful strategies in this regard is using path mining strategies and graph-theoretical approaches that help in building hypothetical models and perform quantitative analysis. Furthermore, they also contribute to analyzing topological parameters in metabolome networks. Path mining techniques can be based on grammars, keys, patterns and indexing. Moreover, they can also be used for modeling metabolome networks, finding structural similarities between metabolites, in-silico metabolic engineering, shortest path estimation and for various graph-based analysis. In this manuscript, we have highlighted some core and applied areas of path-mining for modeling and analysis of metabolic networks. PMID:24230973
Nonlinear multi-agent path search method based on OFDM communication
NASA Astrophysics Data System (ADS)
Sato, Masatoshi; Igarashi, Yusuke; Tanaka, Mamoru
This paper presents novel shortest paths searching system based on analog circuit analysis which is called sequential local current comparison method on alternating-current (AC) circuit (AC-SLCC). Local current comparison (LCC) method is a path searching method where path is selected in the direction of the maximum current in a direct-current (DC) resistive circuit. Since a plurality of shortest paths searching by LCC method can be done by solving the current distribution on the resistive circuit analysis, the shortest path problem can be solved at supersonic speed. AC-SLCC method is a novel LCC method with orthogonal frequency division multiplexing (OFDM) communication on AC circuit. It is able to send data with the shortest path and without major data loss, and this suggest the possibility of application to various things (especially OFDM communication techniques).
Shim, Sangwoo; Aspuru-Guzik, Alán
2012-12-14
The reduced density matrix of excitons coupled to a phonon bath at a finite temperature is studied using the path integral Monte Carlo method. Appropriate choices of estimators and importance sampling schemes are crucial to the performance of the Monte Carlo simulation. We show that by choosing the population-normalized estimator for the reduced density matrix, an efficient and physically-meaningful sampling function can be obtained. In addition, the nonadiabatic phonon probability density is obtained as a byproduct during the sampling procedure. For importance sampling, we adopted the Metropolis-adjusted Langevin algorithm. The analytic expression for the gradient of the target probability density function associated with the population-normalized estimator cannot be obtained in closed form without a matrix power series. An approximated gradient that can be efficiently calculated is explored to achieve better computational scaling and efficiency. Application to a simple one-dimensional model system from the previous literature confirms the correctness of the method developed in this manuscript. The displaced harmonic model system within the single exciton manifold shows the numerically exact temperature dependence of the coherence and population of the excitonic system. The sampling scheme can be applied to an arbitrary anharmonic environment, such as multichromophoric systems embedded in the protein complex. The result of this study is expected to stimulate further development of real time propagation methods that satisfy the detailed balance condition for exciton populations. PMID:23249075
Path integral pricing of Wasabi option in the Black-Scholes model
NASA Astrophysics Data System (ADS)
Cassagnes, Aurelien; Chen, Yu; Ohashi, Hirotada
2014-11-01
In this paper, using path integral techniques, we derive a formula for a propagator arising in the study of occupation time derivatives. Using this result we derive a fair price for the case of the cumulative Parisian option. After confirming the validity of the derived result using Monte Carlo simulation, a new type of heavily path dependent derivative product is investigated. We derive an approximation for our so-called Wasabi option fair price and check the accuracy of our result with a Monte Carlo simulation.
PRELIMINARY PROJECT PLAN FOR LANSCE INTEGRATED FLIGHT PATHS 11A, 11B, 12, and 13
D. H. BULTMAN; D. WEINACHT - AIRES CORP.
2000-08-01
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).
Tcheang, Lili; Bülthoff, Heinrich H.; Burgess, Neil
2011-01-01
Our ability to return to the start of a route recently performed in darkness is thought to reflect path integration of motion-related information. Here we provide evidence that motion-related interoceptive representations (proprioceptive, vestibular, and motor efference copy) combine with visual representations to form a single multimodal representation guiding navigation. We used immersive virtual reality to decouple visual input from motion-related interoception by manipulating the rotation or translation gain of the visual projection. First, participants walked an outbound path with both visual and interoceptive input, and returned to the start in darkness, demonstrating the influences of both visual and interoceptive information in a virtual reality environment. Next, participants adapted to visual rotation gains in the virtual environment, and then performed the path integration task entirely in darkness. Our findings were accurately predicted by a quantitative model in which visual and interoceptive inputs combine into a single multimodal representation guiding navigation, and are incompatible with a model of separate visual and interoceptive influences on action (in which path integration in darkness must rely solely on interoceptive representations). Overall, our findings suggest that a combined multimodal representation guides large-scale navigation, consistent with a role for visual imagery or a cognitive map. PMID:21199934
Putz, Mihai V.
2009-01-01
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. PMID:20087467
NASA Astrophysics Data System (ADS)
Agarwal, Animesh; Delle Site, Luigi
2015-09-01
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.
Agarwal, Animesh Delle Site, Luigi
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.
Zhang, Sijie; Schönfeld, Fabian; Wiskott, Laurenz; Manahan-Vaughan, Denise
2014-01-01
Effective spatial navigation is enabled by reliable reference cues that derive from sensory information from the external environment, as well as from internal sources such as the vestibular system. The integration of information from these sources enables dead reckoning in the form of path integration. Navigation in the dark is associated with the accumulation of errors in terms of perception of allocentric position and this may relate to error accumulation in path integration. We assessed this by recording from place cells in the dark under circumstances where spatial sensory cues were suppressed. Spatial information content, spatial coherence, place field size, and peak and infield firing rates decreased whereas sparsity increased following exploration in the dark compared to the light. Nonetheless it was observed that place field stability in darkness was sustained by border information in a subset of place cells. To examine the impact of encountering the environment’s border on navigation, we analyzed the trajectory and spiking data gathered during navigation in the dark. Our data suggest that although error accumulation in path integration drives place field drift in darkness, under circumstances where border contact is possible, this information is integrated to enable retention of spatial representations. PMID:25009477
Contrasting effects on path integration after hippocampal damage in humans and rats
Kim, Soyun; Sapiurka, Maya; Clark, Robert E.; Squire, Larry R.
2013-01-01
The hippocampus and other medial temporal lobe structures have been linked to both memory and spatial cognition, but it has been unclear how these ideas are connected. We carried out parallel studies of path integration in patients with medial temporal lobe lesions and rats with hippocampal lesions. Subjects entered a circular arena without vision, searched for a target, and then attempted to return to the start location. Patients performed accurately, and as well as controls, so long as the outward path was relatively direct and the target was found within 20 s. In sharp contrast, rats with hippocampal lesions were impaired, even when the outward path was shorter than 1 m, involved no turns, and the target was found within 3 s. We suggest that patients succeeded because performance could be supported by working memory and that patients and rats differ after hippocampal lesions in their ability to construct a coherent working memory of spatial environments. PMID:23404706
Stochastic path integral approach to continuous quadrature measurement of a single fluorescing qubit
NASA Astrophysics Data System (ADS)
Jordan, Andrew N.; Chantasri, Areeya; Huard, Benjamin
I will present a theory of continuous quantum measurement for a superconducting qubit undergoing fluorescent energy relaxation. The fluorescence of the qubit is detected via a phase-preserving heterodyne measurement, giving the cavity mode quadrature signals as two continuous qubit readout results. By using the stochastic path integral approach to the measurement physics, we obtain the most likely fluorescence paths between chosen boundary conditions on the state, and compute approximate correlation functions between all stochastic variables via diagrammatic perturbation theory. Of particular interest are most-likely paths describing increasing energy during the florescence. Comparison to Monte Carlo numerical simulation and experiment will be discussed. This work was supported by US Army Research Office Grants No. W911NF-09-0-01417 and No. W911NF-15-1-0496, by NSF Grant DMR-1506081, by John Templeton Foundation Grant ID 58558, and by the DPSTT Project Thailand.