اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA Reciprocal-Space Formulation of Mixed Quantum-Classical Dynamics
69
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We derive a formulation of mixed quantum-classical dynamics for describing electronic carriers interacting with phonons in reciprocal space. For dispersionless phonons, we start by expressing the real-space classical coordinates in terms of complex variables. A Fourier series over these coordinates then yields the reciprocal-space coordinates. Evaluating the electron-phonon interaction term through Ehrenfests theorem, we arrive at a reciprocal-space formalism that is equivalent to mean-field mixed quantum-classical dynamics in real space. This equivalence is numerically verified for the Holstein and Peierls models, for which we find the reciprocal-space Hellmann-Feynman forces to involve momentum derivative contributions in addition to the position derivative terms commonly seen in real space. We close by presenting a proof of concept for the inexpensive modeling of low-momentum carriers interacting with phonons by means of a truncated basis in reciprocal space, which is not possible within a real space formulation.
قيم البحث
اقرأ أيضاً
We extend the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), a semiclassical method for computing real-time correlation functions, to electronically nonadiabatic systems using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian to treat
electronic and nuclear degrees of freedom (dofs) within a consistent dynamic framework. We introduce an efficient symplectic integration scheme, the MInt algorithm, for numerical time-evolution of the nuclear and electronic phase space variables as well as the Monodromy matrix, under the non-separable MMST Hamiltonian. We then calculate the probability of transmission through a curve-crossing in model two-level systems and show that in the quantum limit MQC-IVR is in good agreement with the exact quantum results, whereas in the classical limit the method yields results in keeping with mean-field approaches like the Linearized Semiclassical IVR. Finally, exploiting the ability of MQC-IVR to quantize different dofs to different extents, we present a detailed study of the extents to which quantizing the nuclear and electronic dofs improves numerical convergence properties without significant loss of accuracy.
We study how decoherence rules the quantum-classical transition of the Kicked Harmonic Oscillator (KHO). When the amplitude of the kick is changed the system presents a classical dynamics that range from regular to a strong chaotic behavior. We show
that for regular and mixed classical dynamics, and in the presence of noise, the distance between the classical and the quantum phase space distributions is proportional to a single parameter $chiequiv Khbar_{rm eff}^2/4D^{3/2}$ which relates the effective Planck constant $hbar_{rm eff}$, the kick amplitude $K$ and the diffusion constant $D$. This is valid when $chi < 1$, a case that is always attainable in the semiclassical regime independently of the value of the strength of noise given by $D$. Our results extend a recent study performed in the chaotic regime.
The mapping approach addresses the mismatch between the continuous nuclear phase space and discrete electronic states by creating an extended, fully continuous phase space using a set of harmonic oscillators to encode the populations and coherences o
f the electronic states. Existing quasiclassical dynamics methods based on mapping, such as the linearised semiclassical initial value representation (LSC-IVR) and Poisson bracket mapping equation (PBME) approaches, have been shown to fail in predicting the correct relaxation of electronic-state populations following an initial excitation. Here we generalise our recently published modification to the standard quasiclassical approximation for simulating quantum correlation functions. We show that the electronic-state population operator in any system can be exactly rewritten as a sum of a traceless operator and the identity operator. We show that by treating the latter at a quantum level instead of using the mapping approach, the accuracy of traditional quasiclassical dynamics methods can be drastically improved, without changes to their underlying equations of motion. We demonstrate this approach for the seven-state Frenkel-Exciton model of the Fenna-Matthews-Olson light harvesting complex, showing that our modification significantly improves the accuracy of traditional mapping approaches when compared to numerically exact quantum results.
We consider the application of the original Meyer-Miller (MM) Hamiltonian to mapping fermionic quantum dynamics to classical equations of motion. Non-interacting fermionic and bosonic systems share the same one-body density dynamics when evolving fro
m the same initial many-body state. The MM classical mapping is exact for non-interacting bosons, and therefore it yields the exact time-dependent one-body density for non-interacting fermions as well. Starting from this observation, the MM mapping is compared to different mappings specific for fermionic systems, namely the spin mapping (SM) with and without including a Jordan-Wigner transformation, and the Li-Miller mapping (LMM). For non-interacting systems, the inclusion of fermionic anti-symmetry through the Jordan-Wigner transform does not lead to any improvement in the performance of the mappings and instead it worsens the classical description. For an interacting impurity model and for models of excitonic energy transfer, the MM and LMM mappings perform similarly, and in some cases the former outperforms the latter when compared to a full quantum description. The classical mappings are able to capture interference effects, both constructive and destructive, that originate from equivalent energy transfer pathways in the models.
Nonadiabatic molecular dynamics occur in a wide range of chemical reactions and femtochemistry experiments involving electronically excited states. These dynamics are hard to treat numerically as the systems complexity increases and it is thus desira
ble to have accurate yet affordable methods for their simulation. Here, we introduce a linearized semiclassical method, the generalized discrete truncated Wigner approximation (GDTWA), which is well-established in the context of quantum spin lattice systems, into the arena of chemical nonadiabatic systems. In contrast to traditional continuous mapping approaches, e.g. the Meyer-Miller-Stock-Thoss and the spin mappings, GDTWA samples the electron degrees of freedom in a discrete phase space, and thus forbids an unphysical unbounded growth of electronic state populations. The discrete sampling also accounts for an effective reduced but non-vanishing zero-point energy without an explicit parameter, which makes it possible to treat the identity operator and other operators on an equal footing. As numerical benchmarks on two Linear Vibronic Coupling models show, GDTWA has a satisfactory accuracy in a wide parameter regime, independently of whether the dynamics is dominated by relaxation or by coherent interactions. Our results suggest that the method can be very adequate to treat challenging nonadiabatic dynamics problems in chemistry and related fields.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
