CONCENTRATION OF BLOCH EIGENSTATES IN THE PRESENCE OF GAUGE AT THE SEMI-CLASSICAL LIMIT

doi:10.1016/S0252-9602(11)60399-8

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (6): 2278-2284.doi: 10.1016/S0252-9602(11)60399-8

CONCENTRATION OF BLOCH EIGENSTATES IN THE PRESENCE OF GAUGE AT THE SEMI-CLASSICAL LIMIT

Gershon Wolansky

Department of Mathematics, Technion, Haifa 32000, Israel

收稿日期:2011-10-08 出版日期:2011-11-20 发布日期:2011-11-20
基金资助:
This research was supported by the Israel Science Foundation.

CONCENTRATION OF BLOCH EIGENSTATES IN THE PRESENCE OF GAUGE AT THE SEMI-CLASSICAL LIMIT

Gershon Wolansky

Department of Mathematics, Technion, Haifa 32000, Israel

Received:2011-10-08 Online:2011-11-20 Published:2011-11-20
Supported by:
This research was supported by the Israel Science Foundation.

摘要/Abstract

摘要：

We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge. In the semi-classical limit h ! 0 these eigenstates concentrate near a maximizer of the scalar potential of the associated Schr¨odinger operator, provided the constant gauge converges to a critical value from above. This is in contrast with the ground states which concentrate for any gauge in this limit near a minimizer of the scalar potential.

关键词: Schr¨odinger equation, gauge, semi classical limit, Bloch eigenstate

Abstract:

Key words: Schr¨odinger equation, gauge, semi classical limit, Bloch eigenstate

中图分类号:

35J15

Gershon Wolansky. CONCENTRATION OF BLOCH EIGENSTATES IN THE PRESENCE OF GAUGE AT THE SEMI-CLASSICAL LIMIT[J]. 数学物理学报(英文版), 2011, 31(6): 2278-2284.

Gershon Wolansky. CONCENTRATION OF BLOCH EIGENSTATES IN THE PRESENCE OF GAUGE AT THE SEMI-CLASSICAL LIMIT[J]. Acta mathematica scientia,Series B, 2011, 31(6): 2278-2284.

[1]	程级鹏, 贺劲松. THE INTEGRAL TYPE GAUGE TRANSFORMATION AND THE ADDITIONAL SYMMETRY FOR THE CONSTRAINED KP HIERARCHY[J]. 数学物理学报(英文版), 2015, 35(5): 1111-1121.
[2]	代晋军, 何其汉, 李必文. NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRÖDINGER EQUATIONS[J]. 数学物理学报(英文版), 2014, 34(6): 1892-1906.
[3]	刘朝霞. ON A CLASS OF INHOMOGENEOUS, ENERGY-CRITICAL, FOCUSING, NONLINEAR SCHRÖDINGER EQUATIONS[J]. 数学物理学报(英文版), 2013, 33(6): 1522-1530.
[4]	B. Muatjetjeja, C. M. Khalique. EMDEN-FOWLER TYPE SYSTEM: NOETHER SYMMETRIES AND FIRST INTEGRALS[J]. 数学物理学报(英文版), 2012, 32(5): 1959-1966.
[5]	万莉莉, 唐春雷. EXISTENCE OF SOLUTIONS FOR NON-PERIODIC SUPERLINEAR SCHRÖDINGER EQUATIONS WITHOUT (AR) CONDITION[J]. 数学物理学报(英文版), 2012, 32(4): 1559-1570.
[6]	朱世辉, 张健. LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL[J]. 数学物理学报(英文版), 2012, 32(3): 1181-1192.
[7]	Jeffery C.DiFranco, Peter D.Miller, Benson K.Muite. ON THE MODIFIED NONLINEAR SCHRÖDINGER EQUATION IN THE SEMICLASSICAL LIMIT: SUPERSONIC, SUBSONIC, AND TRANSSONIC BEHAVIOR[J]. 数学物理学报(英文版), 2011, 31(6): 2343-2377.
[8]	朱世辉, 张健. ON THE CONCENTRATION PROPERTIES FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH A STARK POTENTIAL[J]. 数学物理学报(英文版), 2011, 31(5): 1923-1938.
[9]	杨亦松. ELECTRICALLY CHARGED SOLITONS IN GAUGE FIELD THEORY[J]. 数学物理学报(英文版), 2010, 30(6): 1975-2005.
[10]	井思聪, 阮图南, 范洪义. INFINITESIMAL GAUGE OPERATORS FOR PSEUDOSCALAR FIELDS[J]. 数学物理学报(英文版), 1995, 15(2): 121-125.
[11]	李子平. SYMMETRY IN FIELD THEORY FOR SINGULAR LAGRANGIAN WITH DERIVATIVES OF HIGHER ORDER[J]. 数学物理学报(英文版), 1994, 14(S1): 30-39.

CONCENTRATION OF BLOCH EIGENSTATES IN THE PRESENCE OF GAUGE AT THE SEMI-CLASSICAL LIMIT

CONCENTRATION OF BLOCH EIGENSTATES IN THE PRESENCE OF GAUGE AT THE SEMI-CLASSICAL LIMIT

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 11

Metrics

本文评价

推荐阅读 10