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- W136199085 abstract "There are many instances when quantum systems have both light and heavy degrees of freedom, with masses m and M, respectively. Here, the case in which the dynamics is governed by a non-Hermitian Hamiltonian is considered. Since a small parameter µ = (m/M) 1/2 arises naturally, a rigorous procedure (based on the partial Wigner representation of quantum mechanics and the linear expansion of the equations of motion in µ) can be applied to the non-Hermitian quantum equation in order to obtain the classical limit over the heavy degrees of freedom. Such a procedure does not depend on the adoption on any particular basis set and provides an exact equation when the dependence in the heavy degrees of freedom is quadratic for the Hermitian part of the total non-Hermitian Hamiltonian and linear for the anti-Hermitian part. When only heavy degrees of freedom are present in the system, the formalism also provides a rigorous classical limit for non-Hermitian quantum dynamics. The result of such a complete classical limit is that the phase space dynamics acquires a natural compressibility, arising from the anticommutator in the non-Hermitian quantum equation. Once the non-Hermitian quantum-classical equations of motion are represented in the adiabatic basis selected from the Hermitian part of the total Hamiltonian, piecewise-deterministic algorithms can be developed and their adiabatic limit can be conveniently integrated in the case of weak coupling between light and heavy degrees of freedom. In order to illustrate the formalism, the quantum-classical non-Hermitian dynamics of a Heisenberg two-spin chain with spin independently coupled to a harmonic oscillator is studied. Two decays operator (one depending only on the quantum degrees of freedom and the other only on the classical coordinates) are explicitly considered. It is shown that the algorithms provided can propagate efficiently the quantum-classical non-Hermitian dynamics of t models, simulating the loss of probability and the damping that one would expect in an open quantum system." @default.
- W136199085 created "2016-06-24" @default.
- W136199085 creator A5035776559 @default.
- W136199085 date "2015-02-21" @default.
- W136199085 modified "2023-09-27" @default.
- W136199085 title "Non-Hermitian quantum-classical dynamics" @default.
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