The macroscopic zero-temperature behavior of weakly incommensurate systems in one dimension is described in terms of solitons. The soliton density n obeys equations displaying several types of singular interfacelike solutions: (i) equilibrium or moving boundary between the $n=0$ and finite n regions, and (ii) stationary or moving annihilation front separating solitons from antisolitons.The macroscopic zero-temperature behavior of weakly incommensurate systems in one dimension is described in terms of solitons. The soliton density n obeys equations displaying several types of singular interfacelike solutions: (i) equilibrium or moving boundary between the $n=0$ and finite n regions, and (ii) stationary or moving annihilation front separating solitons from antisolitons.

arXiv:cond-mat/9911003Physical review. B, Condensed matterAug 8, 20011 citation

Stationary states in 1-D

Benjamin W. Schumacher, Michael D. Westmoreland

Cambridge University Press eBooksMar 25, 20100 citations

Star-quantization of an infinite wall

S. V. Kryukov, Mark A. Walton

In deformation quantization (a.k.a. the WignerWeylMoyal formulation of quantum mechanics), we consider a single quantum particle moving freely in one dimension, except for the presence of one infinite potential wall. Dias and Prata pointed out that, surprisingly, its stationary-state Wigner function does not obey the naive equation of motion, i.e., the naive stargenvalue (*-genvalue) equation. We review our recent work on this problem that treats the infinite wall as the limit of a Liouville potential. Also included are some new results: (i) we show explicitly that the Wigner-Weyl transform of the usual density matrix is the physical solution, (ii) we prove that an effective-mass treatment of the problem is equivalent to the Liouville one, and (iii) we point out that self-adjointness of the operator Hamiltonian requires a boundary potential, but one apparently different from that proposed by Dias and Prata. PACS Nos.: 03.65.w, 03.65.Ca, 03.65.GeIn deformation quantization (a.k.a. the WignerWeylMoyal formulation of quantum mechanics), we consider a single quantum particle moving freely in one dimension, except for the presence of one infinite potential wall. Dias and Prata pointed out that, surprisingly, its stationary-state Wigner function does not obey the naive equation of motion, i.e., the naive stargenvalue (*-genvalue) equation. We review our recent work on this problem that treats the infinite wall as the limit of a Liouville potential. Also included are some new results: (i) we show explicitly that the Wigner-Weyl transform of the usual density matrix is the physical solution, (ii) we prove that an effective-mass treatment of the problem is equivalent to the Liouville one, and (iii) we point out that self-adjointness of the operator Hamiltonian requires a boundary potential, but one apparently different from that proposed by Dias and Prata. PACS Nos.: 03.65.w, 03.65.Ca, 03.65.Ge

arXiv:quant-ph/0508005Canadian Journal of PhysicsJan 15, 20067 citations

Bound States in One Dimension

S. Brandt, Hans Dieter Dahmen, Tilo Stroh

Springer eBooksNov 26, 20100 citations

n=0

and finite n regions, and (ii) stationary or moving annihilation front separating solitons from antisolitons.