Hamiltonian formulation of the standard PT-symmetric nonlinear Schrodinger dimer

被引：35

作者：

Barashenkov, I. V. ^{[1
,2
]}

机构：

[1] Univ Cape Town, Ctr Theoret & Math Phys, ZA-7701 Rondebosch, South Africa

[2] Joint Inst Nucl Res, Dubna 141980, Russia

来源：

PHYSICAL REVIEW A | 2014年 / 90卷 / 04期

关键词：

NON-HERMITIAN HAMILTONIANS; SELF-TRAPPING DIMER; QUANTUM; EQUATION; REPRESENTATION; STABILITY; DYNAMICS; COUPLERS; SOLITONS; LATTICES;

D O I：

10.1103/PhysRevA.90.045802

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

The standard PT-symmetric dimer is a linearly coupled two-site discrete nonlinear Schrodinger equation with one site losing and the other one gaining energy at the same rate. We show that despite gain and loss, the standard PT dimer is a Hamiltonian system. We also produce a Lagrangian formulation for the dimer.

引用

页数：4

共 52 条

[1] Optical solitons in PT-symmetric nonlinear couplers with gain and loss [J].

Alexeeva, N. V. ;

Barashenkov, I. V. ;

Sukhorukov, Andrey A. ;

Kivshar, Yuri S. .

PHYSICAL REVIEW A, 2012, 85 (06)

[2] Gross-Pitaevskii equation for Bose particles in a double-well potential: Two-mode models and beyond [J].

Ananikian, D ;

Bergeman, T .

PHYSICAL REVIEW A, 2006, 73 (01)

[3]

[Anonymous], 2012, ADV TOPICS QUANTUM F, DOI DOI 10.1017/9781108885911

[4] An exactly solvable PT-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss [J].

Barashenkov, I. V. ;

Gianfreda, Mariagiovanna .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (28)

[5] Blow-up regimes in the PT-symmetric coupler and the actively coupled dimer [J].

Barashenkov, I. V. ;

Jackson, G. S. ;

Flach, S. .

PHYSICAL REVIEW A, 2013, 88 (05)

[6] Breathers in PT-symmetric optical couplers [J].

Barashenkov, I. V. ;

Suchkov, Sergey V. ;

Sukhorukov, Andrey A. ;

Dmitriev, Sergey V. ;

Kivshar, Yuri S. .

PHYSICAL REVIEW A, 2012, 86 (05)

[7] Making sense of non-Hermitian Hamiltonians [J].

Bender, Carl M. .

REPORTS ON PROGRESS IN PHYSICS, 2007, 70 (06) :947-1018

[8] Twofold transition in PT-symmetric coupled oscillators [J].

Bender, Carl M. ;

Gianfreda, Mariagiovanna ;

Oezdemir, Sahin K. ;

Peng, Bo ;

Yang, Lan .

PHYSICAL REVIEW A, 2013, 88 (06)

[9] Introduction to PT-symmetric quantum theory [J].

Bender, CM .

CONTEMPORARY PHYSICS, 2005, 46 (04) :277-292

[10] Real spectra in non-Hermitian Hamiltonians having PT symmetry [J].

Bender, CM ;

Boettcher, S .

PHYSICAL REVIEW LETTERS, 1998, 80 (24) :5243-5246

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