arXiv subjects

David M. Wilkins

Publications and source records attributed to David M. Wilkins.

21 records · Page 2Linked to original sources

arXiv2014

Why quantum coherence is not important in the Fenna-Matthews-Olsen Complex

We develop and present an improvement to the conventional technique for solving the Hierarchical Equations of Motion which reduces the memory cost by more than 75% while retaining the same convergence rate and accuracy. This allows for a full calculation of the population dynamics of the 24-site FMO trimer for long timescales with very little effort, and we present the first fully converged, exact results for the 7-site subsystem of the monomer, and for the full 24-site trimer. Owing to this new approach, our numerically exact 24-site, 2-exponential results are the most demanding HEOM calculations performed to date, surpassing the 50-site, 1-exponential results of Strumpfer and Schulten [2012, J. Chem. Thy. & Comp., 8, 2808]. We then show where our exact 7-site results deviate from the approximation of Ishizaki and Fleming [2009, Proc. Natl. Acad. Sci. USA, 106, 17255]. Our exact results are then compared to calculations using the incoherent Forster theory, and it is found that the energy transfer from the antenna to the reaction center occurs more than 50 times faster than the fluorescence lifetime of the excitation, whether or not coherence is considered. This means that coherence is not likely to improve the efficiency of the photosynthesis. In fact, the incoherent theory often tends to over-predict the rates of energy transfer, suggesting that in some cases electronic coherence may actually slow down the photosynthetic process.

physics.chem-ph↗

arXiv2012

Optimal representation of the bath response function & fast calculation of influence functional coefficients in open quantum systems with BATHFIT 1

Today's most popular techniques for accurately calculating the dynamics of the reduced density operator in an open quantum system, either require, or gain great computational benefits, from representing the bath response function a(t) in the form a(t)=Σ_k^K p_k e^{O_k t} . For some of these techniques, the number of terms in the series K plays the lead role in the computational cost of the calculation, and is therefore often a limiting factor in simulating open quantum system dynamics. We present an open source MATLAB program called BATHFIT 1, whose input is any spectral distribution functions J(w) or bath response function, and whose output attempts to be the set of parameters {p_k,w_k}_k=1^K such that for a given value of K, the series Σ_k^k p_k e^{O_k t} is as close as possible to a(t). This should allow the user to represent a(t) as accurately as possible with as few parameters as possible. The program executes non-linear least squares fitting, and for a very wide variety of spectral distribution functions, competent starting parameters are used for these fits. For most forms of J(w), these starting parameters, and the exact a(t) corresponding to the given J(w), are calculated using the recent Pade decomposition technique - therefore this program can also be used to merely implement the Pade decomposition for these spectral distribution functions; and it can also be used just to efficiently and accurately calculate a(t) for any given J(w) . The program also gives the J(w) corresponding to a given a(t), which may allow one to assess the quality (in the w-domain) of a representation of a(t) being used. Finally, the program can calculate the discretized influence functional coefficients for any J(w), and this is computed very efficiently for most forms of J(w) by implementing the recent technique published in [Quantum Physics Letters (2012) 1 (1) pg. 35].

quant-ph↗

arXiv2012

Analytic influence functionals for numerical Feynman integrals in most open quantum systems

Fully analytic formulas, which do not involve any numerical integration, are derived for the discretized influence functionals of a very extensive assortment of spectral distributions. For Feynman integrals derived using the Trotter splitting and Strang splitting, we present general formulas for the discretized influence functionals in terms of proper integrals of the bath response function. When an analytic expression exists for the bath response function, these integrals can almost always be evaluated analytically. In cases where these proper integrals cannot be integrated analytically, numerically computing them is much faster and less error-prone than calculating the discretized influence functionals in the traditional way, which involves numerically calculating integrals whose bounds are both infinite. As an example, we present the analytic discretized influence functional for a bath response function of the form α(t)=\sum_{j}^{K}p_{j}e^{Ω_{j}t}, which is a natural form for many spectral distribution functions (including the very popular Lorentz-Drude/Debye function), and for other spectral distribution functions it is a form that is easily obtainable by a least-squares fit . Evaluating our analytic formulas for this example case is much faster and easier to implement than numerically calculating the discretized influence funcitonal in the traditional way. In the appendix we provide analytic expressions for p_{j} and Ω_{j} for a variety of spectral distribution forms, and as a second example we provide the analytic bath response function and analytic influence functionals for spectral distributions of the form J(ω)\proptoω^{s}e^{-(ω/ω_{c})^{q}}. The value of the analytic expression for this bath response function extends beyond its use for calculating Feynman integrals.

quant-ph↗