Molecular thermodynamics of quantum square-well fluids using a path-integral perturbation theory

Singular repulsive barrier [Formula: see text] inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction [Formula: see text] in nonlinear Schrödinger equation. In the linearized case, Rayleigh–Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small [Formula: see text] or after an amendment of the unperturbed Hamiltonian. At any spike strength [Formula: see text], the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables [Formula: see text] which interchanges the roles of the asymptotic and central boundary conditions.

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Perturbation theory in the path-integral representation and its application to some simple quantum systems

International Journal of Quantum Chemistry ◽

10.1002/qua.560120202 ◽

1977 ◽

Vol 12 (2) ◽

pp. 233-246

Author(s):

Y. U. E. Perlin ◽

S. H. N. Gifeisman ◽

Pham Van Quyet

Keyword(s):

Perturbation Theory ◽

Integral Representation ◽

Path Integral ◽

Quantum Systems ◽

Path Integral Representation ◽

Simple Quantum

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Thermodynamic perturbation theory: Sticky chains and square-well chains

Physical Review E ◽

10.1103/physreve.48.3760 ◽

1993 ◽

Vol 48 (5) ◽

pp. 3760-3765 ◽

Cited By ~ 69

Author(s):

M. Banaszak ◽

Y. C. Chiew ◽

M. Radosz

Keyword(s):

Perturbation Theory ◽

Thermodynamic Perturbation Theory ◽

Square Well ◽

Thermodynamic Perturbation

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Perturbation Theory of Transformed Quantum Fields

Mathematical Physics Analysis and Geometry ◽

10.1007/s11040-020-09357-z ◽

2020 ◽

Vol 23 (3) ◽

Author(s):

Paul-Hermann Balduf

Keyword(s):

Perturbation Theory ◽

Path Integral ◽

Field Variable ◽

Quantum Field ◽

Arbitrary Polynomial ◽

Free Theory ◽

Scalar Quantum ◽

Additional Interaction ◽

The One ◽

Quadratic Order

Abstract We consider a scalar quantum field ϕ with arbitrary polynomial self-interaction in perturbation theory. If the field variable ϕ is repaced by a global diffeomorphism ϕ(x) = ρ(x) + a1ρ2(x) + …, this field ρ obtains infinitely many additional interaction vertices. We propose a systematic way to compute connected amplitudes for theories involving vertices which are able to cancel adjacent edges. Assuming tadpole graphs vanish, we show that the S-matrix of ρ coincides with the one of ϕ without using path-integral arguments. This result holds even if the underlying field has a propagator of higher than quadratic order in the momentum. The diffeomorphism can be tuned to cancel all contributions of an underlying ϕt-type self interaction at one fixed external offshell momentum, rendering ρ a free theory at this momentum. Finally, we mention one way to extend the diffeomorphism to a non-diffeomorphism transformation involving derivatives without spoiling the combinatoric structure of the global diffeomorphism.

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