Feynman propagator for the δ-function potential

Lawande, S. V.; Bhagwat, K.V.

doi:10.1016/0375-9601(88)90622-6

Cited by 40 publications

(30 citation statements)

References 2 publications

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“…The performance and implementation details will be discussed. While the free-space zero-range propagators have been reported in the literature [25][26][27][28], the zero-range propagators for the harmonically trapped system with infinite coupling constant are, to the best of our knowledge, new. Finally, Sec.…”

Section: Introductionmentioning

confidence: 90%

Incorporating exact two-body propagators for zero-range interactions intoN-body Monte Carlo simulations

Yan¹,

Blume²

2015

Phys. Rev. A

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Ultracold atomic gases are, to a very good approximation, described by pairwise zero-range interactions. This paper demonstrates that N -body systems with two-body zero-range interactions can be treated reliably and efficiently by the finite temperature and ground state path integral Monte Carlo approaches, using the exact two-body propagator for zero-range interactions in the pair product approximation. Harmonically trapped one-and three-dimensional systems are considered. A new propagator for the harmonically trapped two-body system with infinitely strong zero-range interaction, which may also have applications in real time evolution schemes, is presented.

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Section: Introductionmentioning

confidence: 90%

Incorporating exact two-body propagators for zero-range interactions intoN-body Monte Carlo simulations

Yan¹,

Blume²

2015

Phys. Rev. A

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“…[15,25]. The objective of this combined procedure is to extract "nonperturbative" results, including the emergence of bound states (whenever appropriate), from a manifestly perturbative scheme.…”

Section: Infinite Summation Of Perturbation Theorymentioning

confidence: 99%

Path Integral Treatment of Singular Problems and Bound States

Camblong

Ordóñez

2004

Int. J. Mod. Phys. A

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A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the inverse square potential-possibly combined with a delta-function interaction. The emergence of these singular potentials as low-energy nonrelativistic limits of quantum field theory is highlighted. Not surprisingly, the analogue of ultraviolet regularization is required for the interpretation of these singular problems.

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“…The reduced (or normalized) relative propagator corresponding to the Hamiltonian given in Eq. (39) reads [61,63] …”

Section: Propagator For Two-body Zero-range Interactionsmentioning

confidence: 99%

“…This shows explicitly that the kinetic energy operator is non-local in position space. IfV andK are both non-zero, then the propagator at finite τ is known only for a few selected problems such as non-interacting particles in a harmonic trap [59] and two particles with zero-range interactions [45,60,61,62,63]. In general, the N -particle imaginary time evolution operator or propagator is unknown.…”

Section: Basic Conceptsmentioning

confidence: 99%

Path integral Monte Carlo ground state approach: formalism, implementation, and applications

Yan

Blume

2017

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. Monte Carlo techniques have played an important role in understanding strongly-correlated systems across many areas of physics, covering a wide range of energy and length scales. Among the many Monte Carlo methods applicable to quantum mechanical systems, the path integral Monte Carlo approach with its variants has been employed widely. Since semi-classical or classical approaches will not be discussed in this review, path integral based approaches can for our purposes be divided into two categories: approaches applicable to quantum mechanical systems at zero temperature and approaches applicable to quantum mechanical systems at finite temperature. While these two approaches are related to each other, the underlying formulation and aspects of the algorithm differ. This paper reviews the path integral Monte Carlo ground state (PIGS) approach, which solves the time-independent Schrödinger equation. Specifically, the PIGS approach allows for the determination of expectation values with respect to eigen states of the few-or many-body Schrödinger equation provided the system Hamiltonian is known. The theoretical framework behind the PIGS algorithm, implementation details, and sample applications for fermionic systems are presented. : Formalism, implementation, and applications2 Path integral Monte Carlo ground state approach

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Feynman propagator for the δ-function potential

Cited by 40 publications

References 2 publications

Incorporating exact two-body propagators for zero-range interactions intoN-body Monte Carlo simulations

Incorporating exact two-body propagators for zero-range interactions intoN-body Monte Carlo simulations

Path Integral Treatment of Singular Problems and Bound States

Path integral Monte Carlo ground state approach: formalism, implementation, and applications

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