Investigation of the dynamics of two-quantum states within Davydov mod D 2 ) dynamics reveals remarkable differences from one-quantum dynamics. Soliton formation and pinning starts from smaller values of the non-linearity parameter X. From X=30 pN propagating solitons from X=62 pN pinned solitons are observed if both quanta are on the same end of the chain in the initial state. In the case of soliton collisions, the solitons penetrate each other unperturbed for small X, but fuse to a pinned two-quantum soliton for large X. Both one- and two-quantum states are very sensitive to diagonal disorder in the Hamiltonian. In mod D 1 ) ansatz states, the soliton is found to appear for larger non-linearity but its sensitivity to diagonal disorder is essentially unchanged.Investigation of the dynamics of two-quantum states within Davydov mod D 2 ) dynamics reveals remarkable differences from one-quantum dynamics. Soliton formation and pinning starts from smaller values of the non-linearity parameter X. From X=30 pN propagating solitons from X=62 pN pinned solitons are observed if both quanta are on the same end of the chain in the initial state. In the case of soliton collisions, the solitons penetrate each other unperturbed for small X, but fuse to a pinned two-quantum soliton for large X. Both one- and two-quantum states are very sensitive to diagonal disorder in the Hamiltonian. In mod D 1 ) ansatz states, the soliton is found to appear for larger non-linearity but its sensitivity to diagonal disorder is essentially unchanged.

Journal of Physics Condensed MatterMay 13, 199129 citations

Quantum solitons: experimental progress and perspectives

Andreas Sizmann

Applied Physics BDec 1, 199718 citations

Simulation of solitons in an Ising-like S=(1/2 antiferromagnet on a linear chain

Fumitaka Matsubara, Sakari Inawashiro

The dynamics of quantum solitons in an Ising-like S=(1/2 antiferromagnet on finite linear chains with spins N (\ensuremath{\le}15) is studied by integrating the Schr\"odinger equation of motion. Space-time correlation functions ${S}^{\mathrm{zz}}$ (r,t) and their Fourier transforms, i.e., dynamical structure factor ${S}^{\mathrm{zz}}$ (q,\ensuremath{\omega}), are calculated for both even and odd N. A slow but large oscillation of ${S}^{\mathrm{zz}}$ (r,t) is seen, which gives a direct evidence of the occurrence of propagating domain walls, i.e., solitons. The oscillation leads to a low-energy component of ${S}^{\mathrm{zz}}$ (q,\ensuremath{\omega}) whose line shape greatly depends on whether N is even or odd and on the temperature. We analyze in detail the dependence of soliton number in the line shape and give a plausible conjecture that ${S}^{\mathrm{zz}}$ (q,\ensuremath{\omega}) for N=\ensuremath{\infty} should exhibit a very broad double maximum at low temperatures. We estimate ${S}^{\mathrm{zz}}$ (q,\ensuremath{\omega}) at various temperatures. Our results reproduce experimental observations of ${S}^{\mathrm{zz}}$ (q,\ensuremath{\omega}) on ${\mathrm{CsCoCl}}_{3}$ and ${\mathrm{CsCoBr}}_{3}$ very well over a wide temperature range.The dynamics of quantum solitons in an Ising-like S=(1/2 antiferromagnet on finite linear chains with spins N (\ensuremath{\le}15) is studied by integrating the Schr\"odinger equation of motion. Space-time correlation functions ${S}^{\mathrm{zz}}$(r,t) and their Fourier transforms, i.e., dynamical structure factor ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}), are calculated for both even and odd N. A slow but large oscillation of ${S}^{\mathrm{zz}}$(r,t) is seen, which gives a direct evidence of the occurrence of propagating domain walls, i.e., solitons. The oscillation leads to a low-energy component of ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}) whose line shape greatly depends on whether N is even or odd and on the temperature. We analyze in detail the dependence of soliton number in the line shape and give a plausible conjecture that ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}) for N=\ensuremath{\infty} should exhibit a very broad double maximum at low temperatures. We estimate ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}) at various temperatures. Our results reproduce experimental observations of ${S}^{\mathrm{zz}}$(q,\ensuremath{\omega}) on ${\mathrm{CsCoCl}}_{3}$ and ${\mathrm{CsCoBr}}_{3}$ very well over a wide temperature range.

Physical review. B, Condensed matterFeb 1, 19909 citations

Solitary excitations in one-dimensional spin chains

Anton Wöllert, A. Honecker

We study the real-time evolution of solitary excitations in one-dimensional quantum spin chains using exact diagonalization and the density-matrix renormalization group. The underlying question of this work is the correspondence between classical solitons and solitons in quantum mechanics. While classical solitons as eigensolutions of nonlinear wave equations are localized and have a sharp momentum, this is not possible in the corresponding quantum case due to the linearity of the Schr\"odinger equation or, seen in a more pictorial way, because of the uncertainty relation. For the case of the XXZ model it is shown that the real-time evolution of quantum wave packets accompanied by spreading is in qualitative accordance with that predicted by classical solitons.We study the real-time evolution of solitary excitations in one-dimensional quantum spin chains using exact diagonalization and the density-matrix renormalization group. The underlying question of this work is the correspondence between classical solitons and solitons in quantum mechanics. While classical solitons as eigensolutions of nonlinear wave equations are localized and have a sharp momentum, this is not possible in the corresponding quantum case due to the linearity of the Schr\"odinger equation or, seen in a more pictorial way, because of the uncertainty relation. For the case of the XXZ model it is shown that the real-time evolution of quantum wave packets accompanied by spreading is in qualitative accordance with that predicted by classical solitons.

arXiv:1202.4634Physical Review BMay 30, 201214 citations

Quantum Optical Solitons

F. Kh. Abdullaev, Sergei Darmanyan, Pulat K. Khabibullaev

Springer series in nonlinear dynamicsJan 1, 19933 citations

{S}^{\mathrm{zz}}

(r,t) and their Fourier transforms, i.e., dynamical structure factor

{S}^{\mathrm{zz}}

(q,\ensuremath{\omega}), are calculated for both even and odd N. A slow but large oscillation of

{S}^{\mathrm{zz}}

(r,t) is seen, which gives a direct evidence of the occurrence of propagating domain walls, i.e., solitons. The oscillation leads to a low-energy component of

{S}^{\mathrm{zz}}

(q,\ensuremath{\omega}) whose line shape greatly depends on whether N is even or odd and on the temperature. We analyze in detail the dependence of soliton number in the line shape and give a plausible conjecture that

{S}^{\mathrm{zz}}

(q,\ensuremath{\omega}) for N=\ensuremath{\infty} should exhibit a very broad double maximum at low temperatures. We estimate

{S}^{\mathrm{zz}}

(q,\ensuremath{\omega}) at various temperatures. Our results reproduce experimental observations of

{S}^{\mathrm{zz}}

(q,\ensuremath{\omega}) on

{\mathrm{CsCoCl}}_{3}

and

{\mathrm{CsCoBr}}_{3}

very well over a wide temperature range.