Derivation of quantum work equalities using a quantum Feynman-Kac formula

Quantum Feynman-Kac perturbations

The Feynman-Kac formula

where ∆ is the Laplace operator. Here σ > 0 is a constant (the diffusion constant). It has dimensions of distance squared over time, so H0 has dimensions of inverse time. The operator exp(−tH0) for t > 0 is an self-adjoint integral operator, which gives the solution of the heat or diffusion equation. Here t is the time parameter. It is easy to solve for this operator by Fourier transforms. Sinc...

First Order Feynman-Kac Formula

We study the parabolic integral kernel associated with the weighted Laplacian with a potential. For manifold with a pole we deduce formulas and estimates for the derivatives of the Feynman-Kac kernels and their logarithms, these are in terms of a ‘Gaussian’ term and the semi-classical bridge. Assumptions are on the Riemannian data. AMS Mathematics Subject Classification : 60Gxx, 60Hxx, 58J65, 5...

Wiener Integration for Quantum Systems: A Unified Approach to the Feynman-Kac formula

A generalized Feynman–Kac formula based on the Wiener measure is presented. Within the setting of a quantum particle in an electromagnetic field it yields the standard Feynman–Kac formula for the corresponding Schrödinger semigroup. In this case rigorous criteria for its validity are compiled. Finally, phase–space path–integral representations for more general quantum Hamiltonians are derived. ...

A Feynman-Kac Formula for Unbounded Semigroups

We prove a Feynman-Kac formula for Schrödinger operators with potentials V (x) that obey (for all ε > 0) V (x) ≥ −ε|x| − Cε. Even though e is an unbounded operator, any φ, ψ ∈ L with compact support lie in D(e) and 〈φ, eψ〉 is given by a Feynman-Kac formula.