Fermi's golden rule rate expression for transitions due to nonadiabatic derivative couplings in the adiabatic basis
- URL: http://arxiv.org/abs/2405.02697v1
- Date: Sat, 4 May 2024 15:34:54 GMT
- Title: Fermi's golden rule rate expression for transitions due to nonadiabatic derivative couplings in the adiabatic basis
- Authors: Seogjoo J. Jang, Young Min Rhee,
- Abstract summary: We make careful consideration of nonadiabatic derivative coupling terms between adiabatic states.
We derive a well-defined FGR rate expression based on a quasi-adiabatic approximation.
The resulting rate expression includes terms due to quadratic contribution of NDC terms and also their couplings to Franck-Condon modes.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Starting from a compact but general molecular Hamiltonian expressed in the bases of adiabatic electronic states and position states of nuclei, we make careful consideration of nonadiabatic derivative coupling (NDC) terms between adiabatic states. It is clarified that the conventional use of NDC terms evaluated for an adiabatic electronic state in the textbook expression for the Fermi's golden rule (FGR) rate implicitly invokes an additional approximation that ignores non-orthogonality of adiabatic states at different geometries. Thus, we derive a well-defined FGR rate expression based on a quasi-adiabatic approximation that explicitly uses the adiabatic states and NDC terms evaluated at the minimum potential energy state of the initial adiabatic states. We then clarify conditions and approximations leading to the modeling of all the nuclear degrees of freedom as a set of harmonic oscillators, and then derive a closed form FGR rate expression while accounting for the non-Condon effects due to momenta in NDC terms explicitly. The resulting rate expression includes terms due to quadratic contribution of NDC terms and also their couplings to Franck-Condon modes. Model calculations for the case where nuclear vibrations consist of both a sharp high frequency mode and a broad Ohmic bath spectral density illustrate new features and implications of the rate expression.
Related papers
- Nonadiabatic Field on Quantum Phase Space: A Century after Ehrenfest [19.83226336051656]
Nonadiabatic field (NaF) is based on a generalized exact coordinate-momentum phase space formulation of quantum mechanics.
A few benchmark tests for gas phase and condensed phase systems indicate that NaF offers a practical tool to capture the correct correlation of electronic and nuclear dynamics.
arXiv Detail & Related papers (2024-04-07T08:19:47Z) - Exact counterdiabatic driving for finite topological lattice models [0.0]
Counterdiabatic driving is a technique to speed up adiabatic protocols by including additional terms calculated from the instantaneous eigenstates that counter diabatic excitations.
We formulate this approach for all states of lattice models, including bound and in-gap states which appear, e.g., in topological insulators.
The derived analytical counterdiabatic driving Hamiltonian can be utilised to inform control protocols in many-body lattice models or to probe the non-equilibrium properties of lattice models.
arXiv Detail & Related papers (2024-03-18T18:07:33Z) - Adiabatic amplification of the harmonic oscillator energy when the
frequency passes through zero [77.34726150561087]
After a single frequency passage through zero value, the famous adiabatic invariant ratio of energy to frequency is reestablished again.
The dependence on the initial state disappears after averaging over phases of initial states with the same energy.
The original Born-Fock theorem does not work after the frequency passes through zero.
arXiv Detail & Related papers (2023-03-15T01:18:55Z) - Role of boundary conditions in the full counting statistics of
topological defects after crossing a continuous phase transition [62.997667081978825]
We analyze the role of boundary conditions in the statistics of topological defects.
We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate.
arXiv Detail & Related papers (2022-07-08T09:55:05Z) - Photoinduced prethermal order parameter dynamics in the two-dimensional
large-$N$ Hubbard-Heisenberg model [77.34726150561087]
We study the microscopic dynamics of competing ordered phases in a two-dimensional correlated electron model.
We simulate the light-induced transition between two competing phases.
arXiv Detail & Related papers (2022-05-13T13:13:31Z) - The moving crude adiabatic alternative to the adiabatic representation
in excited state dynamics [0.0]
Moving crude adiabatic (MCA) representation is proposed and successfully tested in low energy dynamics.
We show that MCA is indeed able to properly model non-adiabatic transitions.
Tests are done on linear vibronic coupling models for the bis(methylene) adamantyl cation and the butatriene cation.
arXiv Detail & Related papers (2022-04-29T23:33:29Z) - Rotating Majorana Zero Modes in a disk geometry [75.34254292381189]
We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor.
We analyze the second-order topological corner modes that arise when an in-plane magnetic field is applied.
We show that oscillations persist even in the adiabatic phase because of a frequency independent coupling between zero modes and excited states.
arXiv Detail & Related papers (2021-09-08T11:18:50Z) - Energy Transport in Sachdev-Ye-Kitaev Networks Coupled to Thermal Baths [0.0]
We develop a framework for studying the equilibrium and non-equilibrium properties of arbitrary networks of Sachdev-Ye-Kitaev clusters coupled to thermal baths.
We study the emerging non-equilibrium steady state using the Schwinger-Keldysh formalism.
We establish a relationship between energy transport and quantum chaos by showing that the diffusion constant is upper bounded by the chaos propagation rate at all temperatures.
arXiv Detail & Related papers (2021-09-07T18:06:02Z) - Probing eigenstate thermalization in quantum simulators via
fluctuation-dissipation relations [77.34726150561087]
The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems.
Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations.
Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
arXiv Detail & Related papers (2020-07-20T18:00:02Z) - New Perspectives on the so-called Fermi's Golden Rule in Quantum
Mechanics including Adiabatic Following [0.0]
derivation of the Golden Rule of time dependent perturbation theory is presented.
derivation is based on adiabatic turning on of the perturbation as used in some formal developments of scattering theory.
arXiv Detail & Related papers (2020-06-23T17:30:13Z) - The critical transition of Coulomb impurities in gapped graphene [77.34726150561087]
graphene can be considered as a natural testing ground for the analysis of quantum field theory vacuum instabilities.
We analyze the quantum transition from subcritical to supercritical charge regimes in gapped graphene in a common framework.
We show that for subcritical charges there are also non-trivial boundary conditions which are similar to those that appear in QED for nuclei in the intermediate regime 118Z137.
arXiv Detail & Related papers (2020-05-08T17:16:09Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.