From Davydov solitons to decoherence-free subspaces: Self-consistent propagation of coherent-product states

Abstract

The self-consistent propagation of generalized D1 [coherent-product] states and of a class of gaussian density matrix generalizations is examined, at both zero and finite-temperature, for arbitrary interactions between the localized lattice (electronic or vibronic) excitations and the phonon modes. It is shown that in all legitimate cases, the evolution of D1 states reduces to the disentangled evolution of the component D2 states. The self-consistency conditions for the latter amount to conditions for decoherence-free propagation, which complement the D2 Davydov soliton equations in such a way as to lift the nonlinearity of the evolution for the on-site degrees of freedom. Although it cannot support Davydov solitons, the coherent-product ansatz does provide a wide class of exact density-matrix solutions for the joint evolution of the lattice and phonon bath in compatible systems. Included are solutions for initial states given as a product of a [largely arbitrary] lattice state and a thermal equilibrium state of the phonons. It is also shown that external pumping can produce self-consistent Frohlich-like effects. A few sample cases of coherent, albeit not solitonic, propagation are briefly discussed.

Influence of structure disorders and temperatures of systems on the bio-energy transport in protein molecules (II)

“…In accordance with these three criteria and utilizing the above equations and the above initial conditions we can calculate the evolution of time and space for the probability by using MATLAB language and data-parallel programming, where the time step size is chosen as 0.01 ps. In this calculation the values of the physical parameters we use are as follows: The mass M = 5.73 × 10 −25 kg=114×3 amu (atomic mass units), 114 amu is the mass of myosine, W =39 N/m, ε 0 = 0.2035 eV, J = 9.68 × 10 −4 eV, χ 1 = 6.2 × 10 −11 N, χ 2 = (10 − 18) × 10 −12 N and L = 1.5 meV for the α-helix protein molecules with three channels [5,82]. We numerically calculate their solutions related to time and the probability of the soliton occurring at the nth amino acid molecule, |a j | 2 .…”

“…(4) and (5). According to Forner's method [18,19] the changes in parameters are represented by their fluctuations of average increments, ΔW = W − W , ΔJ = J − J, Δ(χ 1 + χ 2 ) = (χ 1 + χ 2 ) − (χ 1 + χ 2 ) and Δε 0 = ε 0 − ε 0 , respectively, where W, J, (χ 1 + χ 2 ) and ε 0 are the values of the parameters in the protein molecules without the structural disorders.…”

“…Although Eqs. (4) and (5) can become the dynamic equations in the Davydov model when χ 2 =0 and √ 2a n are replaced by A n , (in such a case, the normalization condition of the Davydov wavefunction then becomes…”

Quantum computation in triangular decoherence-free subdynamic space

“…Although many publications in the last several years have formulated a remarkable theory for decoherencefree (DF) subspaces and subsystems, in which quantum computing is performed in a DF subspace despite the total space being subject to decoherence [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], the DF subspaces cannot be exactly established without introducing an approximation. Many proposals [19][20][21][22][23][24][25][26] have used the Born-Markov approximation or restrictions on the type of decoherence (e.g., symmetric and collective decoherence), even though some papers also considered DF subspaces that do not invoke the Born-Markov approximation and seems to be general regarding the type of decoherence [19].…”

Dynamics of a One-Dimensional Holstein Polaron with the Hierarchical Equations of Motion Approach

“…Subsequently developed were two Ansätze with varying sophistication, specifically, the Davydov D 1 [15][16][17] and D 2 trial state, with the latter being a simplified version of the former. Following the Dirac-Frenkel time dependent variational principle, a time dependent Merrifield-type trial state [18] with zero crystal momentum was proposed to study ultrafast relaxation dynamics of a photoexcited one-dimensional polaron [19].…”