Quantum and disorder effects in Davydov soliton theory

Abstract

Within the simple displaced oscillator state ansatz of Davydov [Phys. Scr. 20, 387 (1979)], called the D2 ansatz state, the soliton remains stable against strong disorder in the sequences of masses, spring constants, and coupling constants. However, weak diagonal disorder or disorder in the dipole coupling constants destroys the solitons. Within the D& ansatz, in which the quantum nature of the lattice plays a greater role than in the classical D2 state, the soliton appears only from nonlinearities roughly 3 to 4 times larger than those in D2 models. The sensitivity of such solitons to disorder is practically opposite that for the D2 state. Within the partial dressing model we find only dispersing solitary waves, no real traveling solitons. The sensitivity of such waves to disorder is similar to the D& case.

Theory of bio-energy transport in protein molecules and its experimental evidences as well as applications (I)

“…The wave function of Eq (40). does not only exhibit coherent properties, but agrees with the fact that the energy released in the ATP hydrolysis (about 0.43 eV) excites only two amide-I vibrational quanta, instead of multi-quanta (n > 2).…”

“…Meanwhile, the new wave function has another advantage, i.e., the equation of motion of the soliton can also be obtained from the Heisenberg equations of the creation and annihilation operators in quantum mechanics by using Eqs. (9) and (10), but the wave function of the states of the system in other models could not, including the one-quantum state [4][5][6][7][8][9][10][11][12] and the two-quantum state [35][36][37][38][39][40][41][42][43][44][45][46][47]. Therefore, the above Hamitonian and wave function, Eqs.…”

“…However, the standard coherent state [19][20][21][22][23] and the large-`n excitation state are not appropriate to protein molecules due to the above-mentioned reasons. Similarly, Förner's and Cruzeiro-Hansson's two-quantum states [35][36][37][38][39][40][41][42][43][44][45] do not fulfill the above criteria. For the convenience of calculation, the wave function of the system in Eq.…”

“…This indicates clearly that the Davydov solution is not a true wave function of the systems. A thorough study in terms of parameter values, different types of disorder, different thermalization schemes, different wave functions, and different associated dynamics leads to a very complicated picture for Davydov's model [35][36][37][38][39][40][41][42][43][44][45][46][47]. These results do not completely rule out the Davydov theory; however, they do not eliminate the possibility of another wave function and a more sophisticated Hamiltonian of the system having a soliton with longer lifetime and better thermal stability.…”

“…Therefore, the Hamitonian and wave function of the systems, Eqs. (9), (10), or(40) are reasonable and appropriate to protein molecules. Using the standard transformation in Eq.…”