Accurate Calculation of Equilibrium Reduced Density Matrix for the System-Bath Model:a Multilayer Multiconfiguration Time-Dependent Hartree Approach and its Comparison to a Multi-Electronic-State Path Integral Molecular Dynamics Approach

An efficient and accurate method for computing the equilibriurn reduced density matrix is presented for treating open quantum systems characterized by the systern-bath model. The method employs the rnultilayer nmlticonfiguration tirne-dependent Hartree theory for imag- inary time propagation and an importance sampling procedure for calculating the quantum mechanical trace. The method is applied to the spin-boson Harniltonian, which leads to ac- curate results in agreement with those produced by the rnulti-electronic-state path integral molecular dynamics method.

Reduced one-body density matrix of Tonks-Girardeau gas at finite temperature

With thermal Bose–Fermi mapping method, we investigate the Tonks–Girardeau gas at finite temperature. It is shown that at low temperature, the Tonks gas displays the Fermi-like density profiles, and with the increase in temperature, the Tonks gas distributes in wider region. The reduced one-body density matrix is diagonal dominant in the whole temperature region, and the off-diagonal elements shall vanish rapidly with the deviation from the diagonal part at high temperature.

Generalized Quantum Master Equation:A Tutorial Review and Recent Advances

The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of open quantum systems is important in excitation energy,charge,and quantum coherence transfer as well as reactive photochemistry.The system is usually chosen to be the interested degrees of freedom such as the electronicstates in light-harvesting molecules or tagged vibrational modes in a condensed-phase system.The environment is also called the bath,whose influence on the system has to be considered,and for instance can be described by the GQME formalisms using the projection operator technique.In this review,we provide a heuristic description of the development of two canonical forms of GQME,namely the time-convoluted Nakajima-Zwanzig form(NZ-GQME)and the time-convolutionless form(TCL-GQME).In the more popular NZ-GQME form,the memory kernel serves as the essential part that reflects the non-Markovian and non-perturbative effects,which gives formally exact dynamics of the reduced density matrix.We summarize several schemes to express the projection-based memory kernel of NZ-GQME in terms of projection-free time correlation function inputs that contain molecular information.In particular,the recently proposed modified GQME approach based on NZ-GQME partitions the Hamiltonian into a more general diagonal and off-diagonal parts.The projection-free inputs in the above-mentioned schemes expressed in terms of different system-dependent time correlation functions can be calculated via numerically exact or approximate dynamical methods.We hope this contribution would help lower the barrier of understanding the theoretical pillars for GQME-based quantum dynamics methods and also envisage that their combination with the quantum computing techniques will pave the way for solving complex problems related to quantum dynamics and quantum information that are currently intractable even with today’s state-of-the-art classical supercomputers.

Wick’s theorem and reconstruction schemes for reduced density matrices

We first obtained a closed form of the Wick's theorem expressed in Grassmanwedge product, which is similar to a binomial expansion. With this new expansion, new reconstructionschemes for reduced density matrices are derived rigorously. The higher order reduced densitymatrices are systematically decomposed into a sum of the lower order reduced density matrices whichcould be used to solve the contracted Schroedinger equation.

Internal Conversion Process of Chlorophyll a in Solvents in Femtosecond Pump-Probe Laser Fields

The internal conversion （IC） processes of chlorophyll a （chl-a） in solvents are studied based on the reduced density matrix theory. The IC times can be obtained by simulating the experimental fluorescence depletion spectra （FDS）. The calculated IC times of chl-a in ethyl acetate, tetrahydrofuran and dimethyl formamide are 141, 147, and 241 fs, respectively. The oscillation feature of the FDS results from the forward and backward transfer of the population between coupled electronic states. The effects of diabatic coupling between two electronic states on the IC time and the FDS are described. The influence of molecule-reservoir coupling on the IC time is also investigated.

Construction of many-particle spin entangled states and signature

Using the collective rotational transformation, Rx(π), we construct two types of many-particle spin entangled states in terms of the bases of angular momentum uncoupling and coupling representations. The concept of signature is introduced. The entanglement properties of a four-particle system is investigated by analyzing various subsystem reduced density matrices.