Environment-induced dephasing versus von Neumann measurements in proton tunneling

Abstract

In this work we compare two theoretical approaches to modeling the action of the environment on an open quantum system. It is often assumed that as the temperature of the environment surrounding a quantum system increases, so does the speed of environment-induced dephasing, or decoherence (dynamical noise), and so the efficacy of processes such as quantum tunneling drops. An alternative way of viewing the action of the environment is to consider it as carrying out von Neumann-type measurements that, in the limit of continuous observation, lead to the so-called quantum Zeno effect, whereby the system is never allowed to evolve because its wave function is collapsed to its initial state with overwhelming likelihood. However, it has been established in recent years that under certain conditions quantum processes such as tunneling can actually be enhanced (thermally assisted) when the system couples to its environment, as this allows transitions to higher-energy eigenstates closer to the top of the potential barrier. Here we show that, over a specific temperature range, increasing the temperature of the heat bath to encourage such thermally induced tunneling is equivalent to increasing the frequency of a von Neumann-type measurement on the system by the environment (an anti-Zeno effect). However, this correspondence between these two independent pictures of quantum measurement breaks down above a certain limit: Increasing the frequency of measurement above this limit leads to a reversal from an anti-Zeno to a Zeno effect and the tunneling rate decreases again, whereas raising the temperature further leads to a leveling off in the tunneling probability.

Quantum Biology: An Update and Perspective

“…Furthermore, increasing the temperature of the bath strengthens the coupling to the environment and enhances the rate of thermally assisted tunnelling. A similar enhancement can be observed in a simpler model by simulating successive von-Neumann measurements, where an increase in the frequency of observation/measurement leads to an anti-Zeno effect [329]. A transition state search using CASTEP at B3LYP level provided a description of the potential surface for the proton transfer.…”

“…Godbeer et al [328][329][330] combined DFT studies with the open quantum systems approach of using dissipative terms in the Lindblad equation and applied it to the A-T base pair. They demonstrated that the dissipative Lindblad term couples the eigenstates localised in the canonical well to the excited states in the tautomeric well, thus leading to thermally assisted tunnelling-whereby the environment couples to the system providing it with a thermal boost.…”

Quantum and classical effects in DNA point mutations: Watson–Crick tautomerism in AT and GC base pairs

“…Furthermore, increasing the temperature of the bath leads to stronger coupling to the environment and hence an enhanced rate of thermally assisted tunnelling. Quantum thermalisation can be correlated with a similar enhancement predicted by a simpler model in which it is produced by successive von-Neumann measurements, 30 whereby the frequency of observation/measurement is increased, and an anti-Zeno effect is observed. A transition state search using CASTEP at B3LYP level provided a description of the potential surface for the proton transfer.…”

“…[26][27][28] Intra-base tunnelling studies show that the reaction has a high forward barrier; however, when water is included near the donor site, the barrier is reduced. [26][27][28] Godbeer et al [29][30][31] combined density functional theory studies with an open quantum systems approach using dissipative terms in the Lindblad equation and applied it to the A-T base pair, to include thermal nuclear quantum effects (NQEs). The derivation of the model used was based on the work by Meyer and Ernst, 32,33 who studied Benzoic acid.…”

Analytic calculation of ground state splitting in symmetric double well potential

“…therein). Within the framework of proton transfer description this scheme is developed in [13], [14] and used in [4], [15], [16]. In it the Hamiltonian of a system under consideration includes the terms…”