arXiv subjects
Publications and source records attributed to Vivek M Vyas.
It is shown that in (2+1)-dimensional condensed matter systems, induced gravitational Chern-Simons (CS) action can play a crucial role for coherent spin transport in a finite geometry, provided zero-curvature condition is satisfied on the boundary. The role of the resultant KdV solitons is explicated. The fact that KdV solitons can pass through each other without interference, represent 'resistanceless' spin transport.
The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an $SO(2,1)$ symmetry in two dimensions. This facilitates an exact map from the interacting to the non-interacting system, both with and without a harmonic trap, and explains the short-distance scaling behavior of the wave-function. Taking advantage of the phenomenological Calogero-Sutherland-type interaction, motivated by the density functional approach, we connect the ground-state energy shift, to many-body correlation effect. For the excited states, modes at integral values of the harmonic frequency $ω$, are predicted in one dimension, in contrast to the breathing modes with frequency $2ω$ in two dimensions.
We analyse the structure of the exact, dark and bright soliton solutions of the driven non-linear Schrödinger equation. It is found that, a wide class of solutions of the higher order non-linear Schrödinger equation with a source can also be obtained through the above procedure. Distinct parameter ranges, allowing the existence of these solutions, phase locked with their respective sources, are delineated. Conditions for obtaining non-propagating solutions are found to be quite different for both the equations. A special case, where the scale of the soliton emerges as a free parameter, is obtained and the condition under which solitons can develop singularity is pointed out. We also study the highly restrictive structure of the localised solutions, when the phase and amplitude get coupled.