# Lower bound on the spectrum of the two-dimensional Schrï¿½dinger operator with a d-perturbation on a curve

## Related Articles

- Infinitesimal form boundedness and Trudingerï¿½s subordination for the Schrï¿½dinger operator. Maz�ya, V. G.; Verbitsky, I. E. // Inventiones Mathematicae;Oct2005, Vol. 162 Issue 1, p81
We give explicit analytic criteria for two problems associated with the Schrï¿½dinger operator H=-?+ Q on L2(R n) where Q? Dï¿½(R n) is an arbitrary real- or complex-valued potential. First, we obtain necessary and sufficient conditions on Q so that the quadratic form $\langle{Q}\cdot,\...

- Variational Estimates for Discrete Schrï¿½dinger Operators with Potentials of Indefinite Sign. Damanik, D.; Hundertmark, D.; Killip, R.; Simon, B. // Communications in Mathematical Physics;Jul2003, Vol. 238 Issue 3, p545
Let H be a one-dimensional discrete Schrï¿½dinger operator. We prove that if sess ? [-2, 2], then H - H0 is compact and sess (H) = [-2, 2].We also prove that if H0 + ï¿½Vï¿½ has at least one bound state, then the same is true for H0 + V . Further, if H0+ ï¿½Vï¿½ has infinitely...

- SchrÃ¶dinger Operator Levels for a Crystal Film with a Nonlocal Potential. Smetanina, M. S.; Chuburin, Yu. P. // Theoretical & Mathematical Physics;Aug2004, Vol. 140 Issue 2, p1146
For a crystal film, we consider the SchrÃ¶dinger operator defined on Bloch functions (with respect to two variables) in a cell. The potential is the sum of two small terms: a function decreasing with respect to the third variable and an operator of rank one. We prove the existence of two...

- OPTIMAL CONTROL OF SYSTEMS INVOLVING SCHRÃ–DINGER OPERATORS. Serag, H. M. // Control & Intelligent Systems;2004, Vol. 32 Issue 3, p154
The existence and uniqueness of solutions for cooperative systems involving Schrodinger operators are proved under conditions on the coefficients stated by the principal eigenvalue of Schrodinger eigenvalue problem with weight function; then the necessary and sufficient conditions of optimality...

- On the absolutely continuous and negative discrete spectra of SchrÃ¶dinger operators on the line with locally integrable globally square summable potentials. Rybkin, Alexei // Journal of Mathematical Physics;Apr2004, Vol. 45 Issue 4, p1418
For one-dimensional SchrÃ¶dinger operators with potentials q subject to âˆ‘[sub n=-âˆž][sup âˆž](âˆ«[sub n][sup n+1]|q(x)|dx)[sup 2]<âˆž, we prove that the absolutely continuous spectrum is [0,âˆž), extending the 1999 result due to Dieftâ€“Killip. As a by-product we...

- Conditional Wegner Estimate for the Standard Random Breather Potential. Täufer, Matthias; Veselić, Ivan // Journal of Statistical Physics;Nov2015, Vol. 161 Issue 4, p902
We prove a conditional Wegner estimate for SchrÃ¶dinger operators with random potentials of breather type. More precisely, we reduce the proof of the Wegner estimate to a scale free unique continuation principle. The relevance of such unique continuation principles has been emphasized in...

- Power-Law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension. Damanik, David; Tcheremchantsev, Serguei // Communications in Mathematical Physics;Jun2003, Vol. 236 Issue 3, p513
: We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schrï¿½dinger operators which is based on power-law bounds on transfer matrices. It suffices to have such bounds for a nonempty set of energies. We apply this result to various models, including the...

- Some Improvements in the Method of the Weakly Conjugate Operator. Richard, Serge // Letters in Mathematical Physics;Apr2006, Vol. 76 Issue 1, p27
We present some improvements in the method of the weakly conjugate operator, one variant of the Mourre theory. When applied to certain two-body SchrÃ¶dinger operators, this leads to a limiting absorption principle that is uniform on the positive real axis.

- Dynamical Analysis of Schrï¿½dinger Operators with Growing Sparse Potentials. Tcheremchantsev, Serguei // Communications in Mathematical Physics;Jan2005, Vol. 253 Issue 1, p221
We consider discrete half-line Schrï¿½dinger operatorsHwith potentials of the formV(n)=S(n)+Q(n). HereQis any compactly supported real function,ifn=L N andS(n)=0 otherwise, where?? (0,1) andL N is a very fast growing sequence. We study in a rather detailed manner the time-averaged dynamics...