Path Integrals and Transition Amplitudes

1984 ◽  
pp. 53-78
Author(s):  
Masud Chaichian ◽  
Nikolai F. Nelipa
Keyword(s):  
Path Integrals ◽  
Transition Amplitudes

scholarly journals Extended SUSY quantum mechanics: transition amplitudes and path integrals

2011 ◽  
Vol 2011 (6) ◽  
Author(s):  
Fiorenzo Bastianelli ◽  
Roberto Bonezzi ◽  
Olindo Corradini ◽  
Emanuele Latini
Keyword(s):  
Quantum Mechanics ◽  
Path Integrals ◽  
Transition Amplitudes

Path integrals and the solution of the Schwinger model in curved space-time

1986 ◽  
Vol 33 (8) ◽  
pp. 2262-2266 ◽  
Author(s):  
J. Barcelos-Neto ◽  
Ashok Das
Keyword(s):  
Path Integrals ◽  
Space Time ◽  
Curved Space ◽  
Schwinger Model

Unbiased Simulation Estimators for Path Integrals of Diffusions

2020 ◽  
Author(s):  
Guanting Chen ◽  
Alex Shkolnik ◽  
Kay Giesecke
Keyword(s):  
Path Integrals

scholarly journals Reducing a Class of Two-Dimensional Integrals to One-Dimension with an Application to Gaussian Transforms

Atoms ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 53
Author(s):  
Jack C. Straton
Keyword(s):  
Quantum Theory ◽  
Arbitrary Function ◽  
Plane Waves ◽  
Wave Functions ◽  
One Dimension ◽  
Two Dimensional ◽  
Transition Amplitudes ◽  
Multidimensional Integrals ◽  
Coulomb Potentials

Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers multiplied by an arbitrary function of xy/(x+y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, and Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.

On bimolecular kinetics, the Bloch equation and Wigner path integrals

1985 ◽  
Vol 83 (10) ◽  
pp. 5046-5051
Author(s):  
Frank McLafferty
Keyword(s):  
Path Integrals ◽  
Bloch Equation

scholarly journals Quantum channels in quantum gravity

2014 ◽  
Vol 23 (12) ◽  
pp. 1442009 ◽  
Author(s):  
Mukund Rangamani ◽  
Massimilliano Rota
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Quantum Gravity ◽  
Path Integrals ◽  
Quantum Channels ◽  
Hole Formation ◽  
Integral Formalism ◽  
Final State ◽  
State Boundary ◽  
Gauge Gravity

The black hole final state proposal implements manifest unitarity in the process of black hole formation and evaporation in quantum gravity, by postulating a unique final state boundary condition at the singularity. We argue that this proposal can be embedded in the gauge/gravity context by invoking a path integral formalism inspired by the Schwinger–Keldysh like thermo-field double construction in the dual field theory. This allows us to realize the gravitational quantum channels for information retrieval to specific deformations of the field theory path integrals and opens up new connections between geometry and information theory.

scholarly journals Computational Methods for Ab Initio Molecular Dynamics

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Eric Paquet ◽  
Herna L. Viktor
Keyword(s):  
Molecular Dynamics ◽  
Quantum Mechanics ◽  
Ab Initio ◽  
First Principles ◽  
Density Functional ◽  
Path Integrals ◽  
Ab Initio Molecular Dynamics ◽  
Molecular Systems ◽  
Hartree Fock ◽  
Computational Perspective

Ab initio molecular dynamics is an irreplaceable technique for the realistic simulation of complex molecular systems and processes from first principles. This paper proposes a comprehensive and self-contained review of ab initio molecular dynamics from a computational perspective and from first principles. Quantum mechanics is presented from a molecular dynamics perspective. Various approximations and formulations are proposed, including the Ehrenfest, Born–Oppenheimer, and Hartree–Fock molecular dynamics. Subsequently, the Kohn–Sham formulation of molecular dynamics is introduced as well as the afferent concept of density functional. As a result, Car–Parrinello molecular dynamics is discussed, together with its extension to isothermal and isobaric processes. Car–Parrinello molecular dynamics is then reformulated in terms of path integrals. Finally, some implementation issues are analysed, namely, the pseudopotential, the orbital functional basis, and hybrid molecular dynamics.

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