Molecular mechanics decoherence

The first part of the chapter focuses on the derivation of a mixed quantum-classical theory for rationalizing chemical reactions involving two electronic states. The central piece of this mixed quantum-classical rate constant is the appearance of a characteristic decoherence time. The second part of the chapter deals with numerical approaches at the atomic level that can be carried out to decipher the molecular mechanisms governing decoherence in real systems of biological interest. 

The term decoherence describes the process by which the off-diagonal elements of the reduced density matrix tend to zero when evolving with time. Our objective is to reach an understanding of the molecular mechanisms governing decoherence with an atomic resolution. In addition we wish to be in a position to treat systems consisting of tens to thousands of atoms since the brute force simulation of the time evolution of p t) by the Liouville-von Neuman equation (p (i) = ih [H, p ]), the equivalent of the TDSE in the density matrix formalism, is out of question for such molecular systems. 

Before reviewing existing examples, a very brief explanation on the mechanisms of decoherence for molecular spin qubits is necessary more details are available elsewhere [67]. Broadly speaking, the three decoherence sources for these systems are spin bath decoherence, oscillator bath decoherence and pairwise dipolar decoherence, and can be regulated by a combination of temperature, magnetic field and chemical design of the system [70]. The spin bath mainly consists of nuclear spins, but in general it also includes any localized excitations that can couple to the... 

Section 4 is entitled Ideas (for mechanisms and models). It deals with how we can interpret/calculate the behavior of molecular transport junctions utilizing particular model approaches and chemical mechanisms. It also discusses time parameters, and coherence/decoherence as well as pathways and structure/function relationships. 

In a separate contribution [11], we have analysed within the present framework an assessment of the various arrows of time and the possible symmetry violations instigated by gravitation including the fundamental problem of molecular chirality [12]. Other related developments involve Penrose s concept of objective reduction (OR), i.e. gravity s role in quantum state reduction and decoherence as a fundamental concept that relates micro-macro domains including theories of human consciousness [13], see also Ref. [3] for more details. Note also efforts to derive quantum mechanics from general relativity [14]. 

Whereas coherence can persist up to the nanosecond range for atomic and molecular systems exposed to dilute gaseous environments, the situation is radically different in liquids and solids. Interactions with neighbouring atoms, with phonons in crystalline materials and with conduction electrons in metals, shift the coherence times down by several orders of magnitude, and local quantum superpositions are usually not observable. Intermediate cases are the electronic states used as qubits in the form of superconducting islands introduced by Y. Nakamura et al. [4]. The latest reports [5] show coherence times up to 10 s for these objects, which would allow time for operations of a quantum computer. The decoherence mechanisms in such circuits have been discussed theoretically by Burkhard et al. [6],... 

During my student days (pre-university, university, PhD), we learned quantum mechanics from the books authored by L. D. Landau and E. M. Lifshitz, A. S. Davydov, D. Bohm, Feynman s course of Lectures on Physics, and from P. A. M. Dirac s Principles . We were exeited with the theories of hidden variables, EPR paradox, decoherence, entanglement, and concerned for a life of immortal Schrodinger s cat - they were in the air at that time Did I understand it Yes - because, due to a conventional wisdom, I used it more than 24 hours a day and every day. I however doubt - doubt together with Feynman who once remarked that Nobody understands it - that I ve actually understood it. I touched and used it throughout the molecular world, which is nowadays inhabited by 21 million molecules, and which I studied as a quantum chemist - in fact, by education, I am a theoretical physicist. 

Then the recent notion of nonadiabaticity in electron d3mamics is introduced. To be consistent with the wavepacket bifurcation, we introduce the method of electron wavepacket d3mamics that undergoes bifurcation while being carried along the so-called non-Born-Oppenheimer paths, which also branch due to nonadiabatic interactions. We will further proceed to the discussion about the interaction of molecular nonadiabatic states with intense laser fields. In this way, we penetrate on one hand into unknown domains of molecular properties such as (1) electron-nuclear quantmn entanglement due to nonadiabatic transitions and its experimental observation, (2) coherence and decoherence of electron and nuclear wavepackets, which qualitatively dominate the quantmn mechanical probabiUties of quantum transition dynamics, (3) characteristic phenomena arising from the time-dependent fluctuation of molecular electronic states, (4) the physics of interference between the nonadiabatic djmamics and external fields, and so on. 

Spin relaxation phenomena are usually described by the semiclassical theory developed by Wangsness, Bloch and Redfield and known as the WBR theory or Redfield theory. The semiclassical nature of the theory implies that the spin system is treated quantum mechanically, while the remaining degrees of freedom (such as molecular rotations) are treated classically. Few years ago, Segnorile and Zamar studied the issue of quantum decoherence (loss of system phase memory) in proton NMR of nematic liquid crystals. The spin dynamics - and the decay of the free induction decay - was found to be governed by several different processes, partly of purely quantum nature. During the period under the present review, the same group reported a related work concerned with the Jeener-Broekaert experiment on liquid crystals. ... 

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