10 citations · 27 across the 12 of their papers we have counts for
11 papers · 1 filter
Solutions of Gross-Pitaevskii Equation with Periodic Potential in Dimension Three
Yulia Karpeshina, Seonguk Kim, Roman Shterenberg
Quasi-periodic solutions of the Gross-Pitaevskii equation with a periodic potential in dimension three are studied. It is proven that there is an extensive "non-resonant" set ${\ma…
Ballistic Transport for Schrödinger Operators with Quasi-periodic Potentials
Yulia Karpeshina, Leonid Parnovski, Roman Shterenberg
We prove the existence of ballistic transport for a Schrödinger operator with a generic quasi-periodic potential in any dimension .
Bethe-Sommerfeld Conjecture and Absolutely Continuous Spectrum of Multi-Dimensional Quasi-Periodic Schrödinger Operators
Yulia Karpeshina, Leonid Parnovski, Roman Shterenberg
We consider Schrödinger operators in , , with quasi-periodic potentials . We prove that the absolutely continuous spect…
Solutions of Gross-Pitaevskii Equation with Periodic Potential in Dimension Two
Yulia Karpeshina, Seonguk Kim, Roman Shterenberg
Quasi-periodic solutions of a nonlinear polyharmonic equation for the case in , , are studied. This includes Gross-Pitaevskii equation in dimension two ($l=1,n=…
Solutions of Nonlinear Polyharmonic Equation with Periodic Potential
Yulia Karpeshina, Seonguk Kim
Quasi-periodic solutions of a nonlinear periodic polyharmonic equation in , , are studied. It is proven that there is an extensive "non-resonant" set ${\mathcal G}\subse…
Ballistic Transport for the Schrödinger Operator with Limit-Periodic or Quasi-periodic Potential in Dimension Two
Yulia Karpeshina, Young-Ran Lee, Roman Shterenberg +1
We prove the existence of ballistic transport for the Schrödinger operator with limit-periodic or quasi-periodic potential in dimension two. This is done under certain regularity a…