Functional integral formulations for classical fluids

A quantum Hamiltonian, defined on the half-line, will typically not lead to unitary time evolution unless the domain of the Hamiltonian is carefully specified. Different choices of the domain result in different Green’s functions. For a wide class of non-relativistic Hamiltonians we show how to define the functional integral on the half-line in a way which matches the various Green’s functions. To do so we analytically continue, in time, functional integrals constructed with real measures that give weight to paths on the half-line according to how much time they spend near the origin.

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Theory of simple classical fluids: Universality in the short-range structure

Physical Review A ◽

10.1103/physreva.20.1208 ◽

1979 ◽

Vol 20 (3) ◽

pp. 1208-1235 ◽

Cited By ~ 566

Author(s):

Yaakov Rosenfeld ◽

N. W. Ashcroft

Keyword(s):

Short Range ◽

Classical Fluids ◽

Short Range Structure

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An unified approach to inelastic light scattering in Keldysh–Schwinger functional integral formalism

International Journal of Modern Physics B ◽

10.1142/s021797921550040x ◽

2015 ◽

Vol 29 (07) ◽

pp. 1550040 ◽

Cited By ~ 1

Author(s):

Hyun Cheol Lee

Keyword(s):

Light Scattering ◽

Cross Sections ◽

Golden Rule ◽

Functional Integral ◽

Integral Formalism ◽

Inelastic Light Scattering ◽

Scattering Geometry ◽

The One ◽

Resonant Part ◽

Functional Integral Formalism

We propose a theoretical framework which can treat the nonresonant and the resonant inelastic light scattering on an equal footing in the form of correlation function, employing Keldysh–Schwinger functional integral formalism. The interference between the nonresonant and the resonant process can be also incorporated in this framework. This approach is applied to the magnetic Raman scattering of two-dimensional antiferromagnetic insulators. The entire set of the scattering cross-sections are obtained at finite temperature, the result for the resonant part agrees with the one obtained by the conventional Fermi golden rule at zero temperature. The interference contribution is shown to be very sensitive to the scattering geometry and the band structure.

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Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

International Journal of Analysis ◽

10.1155/2014/280709 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Mahmoud Bousselsal ◽

Sidi Hamidou Jah

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Existence Of Solutions ◽

Functional Integral ◽

Nonlinear Integral Equations ◽

Measure Of Weak Noncompactness ◽

Krasnoselskii’S Fixed Point Theorem ◽

Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

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