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• W4382986568 startingPage "2079" @default.
• W4382986568 abstract "We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked controllability conditions, for non necessarily reversible models with possibly transient free particle diffusions, the ground state and the zero-point energy are explicitly computed in terms of the unique positive fixed point of a continuous time algebraic Riccati matrix equation. We also present an explicit solution of normalised and time dependent Feynman–Kac measures on path spaces in terms of a time varying linear dynamical system coupled with a differential Riccati matrix equation. A refined non asymptotic analysis of the stability of these models is developed based on a recently developed Floquet-type representation of time varying exponential semigroups of Riccati matrices. We provide explicit and non asymptotic estimates of the exponential decays to equilibrium of Feynman–Kac semigroups in terms of Wasserstein distances or Boltzmann-relative entropy. For reversible models we develop a series of functional inequalities including de Bruijn identity, Fisher’s information decays, log-Sobolev inequalities, and entropy contraction estimates. In this context, we also provide a complete and explicit description of all the spectrum and the excited states of the Hamiltonian, yielding what seems to be the first result of this type for this class of models. We illustrate these formulae with the traditional harmonic oscillator associated with real time Brownian particles and Mehler’s formula. The analysis developed in this article can also be extended to solve time dependent Schrodinger equations equipped with time varying linear diffusions and quadratic potential functions." @default.
• W4382986568 created "2023-07-04" @default.
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• W4382986568 date "2023-07-03" @default.
• W4382986568 modified "2023-10-18" @default.
• W4382986568 title "Coupled Quantum Harmonic Oscillators and Feynman–Kac path integrals for Linear Diffusive Particles" @default.
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• W4382986568 doi "https://doi.org/10.1007/s00220-023-04772-z" @default.
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