Recursive Schrödinger equation approach to faster converging path integrals

Balaž, Antun; Bogojević, A.; Vidanović, Ivana; Pelster, Axel

doi:10.1103/physreve.79.036701

Cited by 22 publications

(70 citation statements)

References 39 publications

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“…[48], we see that new terms appear which contain time derivatives of the potential. In particular, we observe the emergence of terms with odd powers of the discretized velocity δ, which was previously not the case.…”

Section: Path-integral Calculation Of the Propagatormentioning

confidence: 80%

Fast converging path integrals for time-dependent potentials: I. Recursive calculation of short-time expansion of the propagator

Balaž¹,

Vidanović²,

Bogojević³

et al. 2011

J. Stat. Mech.

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In this and subsequent paper [1] we develop a recursive approach for calculating the short-time expansion of the propagator for a general quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used to substantially speed up numerical Monte Carlo simulations for path integrals, or to set up various analytic approximation techniques to study properties of quantum systems in time-dependent potentials. The analytically derived results are numerically verified by treating several simple models.

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Section: Path-integral Calculation Of the Propagatormentioning

confidence: 80%

Fast converging path integrals for time-dependent potentials: I. Recursive calculation of short-time expansion of the propagator

Balaž¹,

Vidanović²,

Bogojević³

et al. 2011

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…(2.5), we obtain the recursion relation derived in Ref. [17], where the sum over r goes from max{0, k−m+l +2} to min{k, l}. This recursion can be used to calculate all coefficients c m,k to a given level p, starting from the known initial condition, c 0,0 = V. The diagonal coefficients can be calculated immediately, …”

Section: One Particle In One Dimensionmentioning

confidence: 99%

“…It was introduced first for single-particle 1D models [13][14][15] and later extended to general manybody systems in arbitrary number of spatial dimensions [5,17]. This approach allows systematic derivation of higher-order terms to a chosen order p in the short time of propagation.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…[17], is based on solving the underlying Schrödinger equation for the amplitude. It has proven to be the most efficient tool for treatment of higher-order expansion.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Recently introduced effective action approach [13][14][15][16][17] provides an ideal framework for exact numerical calculation of quantum mechanical amplitudes. It gives systematic short-time expansion of amplitudes for a general potential, thus allowing accurate calculation of short-time properties of quantum systems directly, as has been demonstrated in Refs.…”

Section: Introductionmentioning

confidence: 99%

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SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach

Balaž

Vidanović

Stojiljković

et al. 2012

Commun. comput. phys.

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Abstract. We present Path Integral Monte Carlo C code for calculation of quantum mechanical transition amplitudes for 1D models. The SPEEDUP C code is based on the use of higher-order short-time effective actions and implemented to the maximal order p=18 in the time of propagation (Monte Carlo time step), which substantially improves the convergence of discretized amplitudes to their exact continuum values. Symbolic derivation of higher-order effective actions is implemented in SPEEDUP Mathematica codes, using the recursive Schrödinger equation approach. In addition to the general 1D quantum theory, developed Mathematica codes are capable of calculating effective actions for specific models, for general 2D and 3D potentials, as well as for a general many-body theory in arbitrary number of spatial dimensions.

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Development of Grid e-Infrastructure in South-Eastern Europe

et al. 2011

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Over the period of 6 years and three phases, the SEE-GRID programme has established a strong regional human network in the area of distributed scientific computing and has set up a powerful regional Grid infrastructure. It attracted a number of user communities and applications from diverse fields from countries throughout the South-Eastern Europe. From the infrastructure point view, the first project phase has established a pilot Grid infrastructure with more than 20 resource centers in 11 countries. During the subsequent two phases of the project, the infrastructure has grown to currently 55 resource centers with more than 6600 CPUs and 750 TBs of disk storage, distributed in 16 participating countries. Inclusion of new resource centers to the existing infrastructure, as well as a support to new user communities, has demanded setup of regionally distributed core services, development of new monitoring and operational tools, and close collaboration of all partner institution in managing such a complex infrastructure. In this paper we give an overview of the development and current status of SEE-GRID regional infrastructure and describe its transition to the NGI-based Grid model in EGI, with the strong SEE regional collaboration.Comment: 22 pages, 12 figures, 4 table

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Recursive Schrödinger equation approach to faster converging path integrals

Cited by 22 publications

References 39 publications

Fast converging path integrals for time-dependent potentials: I. Recursive calculation of short-time expansion of the propagator

Fast converging path integrals for time-dependent potentials: I. Recursive calculation of short-time expansion of the propagator

SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach

Development of Grid e-Infrastructure in South-Eastern Europe

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