Path integral approach to the quantum fidelity amplitude
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This thesis is focused on classical and semiclassical approximations of a specific quantum time correlation function, the “quantum fidelity.” Namely, we rigorously study the efficiency of a continuous class of algorithms for the evaluation of its classical ...
In quantum theory, any Hamiltonian describing a physical system is mathematically represented by a self-adjoint linear operator to ensure the reality of the associated observables. In an attempt to extend quantum mechanics into the complex domain, it was r ...
Dephasing representation of fidelity, also known as the phase averaging method, can be considered as a special case of Miller's linearized semiclassical initial value representation and belongs among the most efficient approximate semiclassical approaches ...
We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which in a certain way generalize the notion of dessins d'enfant. Furthermore, we give a proof of the quantum spectral curv ...
We consider the canonical quantization of an ordinary fluid. The resulting long-distance effective field theory is derivatively coupled, and therefore strongly coupled in the UV. The system however exhibits a number of peculiarities, associated with the vo ...
This is an overview of a program of stochastic deformation of the mathematical tools of classical mechanics, in the Lagrangian and Hamiltonian approaches. It can also be regarded as a stochastic version of Geometric Mechanics.The main idea is to construct ...
Initial value representations are constructed to avoid the search for trajectories that are only defined in semiclassical approximations by their boundary conditions. We show how to incorporate these procedures within the full Weyl representation, so that ...
We propose to measure nonadiabaticity of molecular quantum dynamics rigorously with the quantum fidelity between the Born-Oppenheimer and fully nonadiabatic dynamics. It is shown that this measure of nonadiabaticity applies in situations where other criter ...
In this paper a detailed mathematical procedure is described to evaluate modal scattering parameters conventionally defined in planar multilayered structures excited by wave ports. Combined Field Integral Equation technique is implemented and solved using ...
A review. Manipulation of the quantum properties of matter can influence the course of biochem. reactions. Can biol. functions, such as vision or photosynthesis, that are driven by incoherent phenomena have anything to do with quantum mechanics, where the ...