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The Spectrum of a Schrödinger Operator in a Wire-Like Domain with a Purely Imaginary Degenerate Potential in the Semiclassical Limit
 
Y. Almog Louisiana State University, Baton Rouge, LA
B. Helffer Université Paris-Sud, Orsay, France
A publication of the Société Mathématique de France
The Spectrum of a Schr\"odinger Operator in a Wire-Like Domain with a Purely Imaginary Degenerate Potential in the Semiclassical Limit
Softcover ISBN:  978-2-85629-928-9
Product Code:  SMFMEM/166
List Price: $52.00
AMS Member Price: $41.60
Please note AMS points can not be used for this product
The Spectrum of a Schr\"odinger Operator in a Wire-Like Domain with a Purely Imaginary Degenerate Potential in the Semiclassical Limit
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The Spectrum of a Schrödinger Operator in a Wire-Like Domain with a Purely Imaginary Degenerate Potential in the Semiclassical Limit
Y. Almog Louisiana State University, Baton Rouge, LA
B. Helffer Université Paris-Sud, Orsay, France
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-928-9
Product Code:  SMFMEM/166
List Price: $52.00
AMS Member Price: $41.60
Please note AMS points can not be used for this product
  • Book Details
     
     
    Mémoires de la Société Mathématique de France
    Volume: 1662020; 94 pp
    MSC: Primary 35; 82

    Consider a two-dimensional domain shaped like a wire, not necessarily of uniform cross section. Let \(V\) denote an electric potential driven by a voltage drop between the conducting surfaces of the wire. The authors consider the operator \(\mathcal{A}_{h}=-h^{2}\Delta+iV\) in the semi-classical limit \(h\to 0\) and obtain both the asymptotic behavior of the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. They extend here previous results obtained for potentials for which the set where the current (or \(\nabla V\)) is normal to the boundary is discrete, in contrast with the present case where \(V\) is constant along the conducting surfaces.

    A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

    Readership

    Graduate students and research mathematicians.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1662020; 94 pp
MSC: Primary 35; 82

Consider a two-dimensional domain shaped like a wire, not necessarily of uniform cross section. Let \(V\) denote an electric potential driven by a voltage drop between the conducting surfaces of the wire. The authors consider the operator \(\mathcal{A}_{h}=-h^{2}\Delta+iV\) in the semi-classical limit \(h\to 0\) and obtain both the asymptotic behavior of the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. They extend here previous results obtained for potentials for which the set where the current (or \(\nabla V\)) is normal to the boundary is discrete, in contrast with the present case where \(V\) is constant along the conducting surfaces.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.