Is space-time symmetry a suitable generalization of parity-time symmetry?

Amore, Paolo; Garcia, Javier

doi:10.1016/J.AOP.2014.07.026

Title: Is space-time symmetry a suitable generalization of parity-time symmetry?

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Abstract

We discuss space-time symmetric Hamiltonian operators of the form H=H{sub 0}+igH{sup ′}, where H{sub 0} is Hermitian and g real. H{sub 0} is invariant under the unitary operations of a point group G while H{sup ′} is invariant under transformation by elements of a subgroup G{sup ′} of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 00. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries. - Highlights: • Space-time symmetry is a generalization of PT symmetry. • The eigenvalues of a space-time Hamiltonian are either real or appear as pairs of complex conjugate numbers. • In some cases all the eigenvalues are real for some values of a potential-strength parameter g. • At some value of g space-time symmetry is broken and complex eigenvalues appear. • Some multidimensional oscillators exhibit broken space-time symmetry for all values of g.

Authors:

Amore, Paolo ^[1]; Garcia, Javier ^[2]

Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima (Mexico)
INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)

Publication Date:: Sat Nov 15 00:00:00 EST 2014

OSTI Identifier:: 22403449

Resource Type:: Journal Article

Journal Name:: Annals of Physics (New York)

Additional Journal Information:: Journal Volume: 350; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENVALUES; HAMILTONIANS; IRREDUCIBLE REPRESENTATIONS; OSCILLATORS; PARITY; PERTURBATION THEORY; SPACE-TIME; SYMMETRY BREAKING; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats


                    Amore, Paolo, Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar, and Garcia, Javier. Is space-time symmetry a suitable generalization of parity-time symmetry?.  United States: N. p., 2014. 
        Web.  doi:10.1016/J.AOP.2014.07.026.

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                    Amore, Paolo, Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar, & Garcia, Javier. Is space-time symmetry a suitable generalization of parity-time symmetry?.  United States.  https://doi.org/10.1016/J.AOP.2014.07.026

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                    Amore, Paolo, Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar, and Garcia, Javier. 2014.  
        "Is space-time symmetry a suitable generalization of parity-time symmetry?".  United States.  https://doi.org/10.1016/J.AOP.2014.07.026.

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@article{osti_22403449,

  title        = {Is space-time symmetry a suitable generalization of parity-time symmetry?},

  author       = {Amore, Paolo and Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar and Garcia, Javier},

  abstractNote = {We discuss space-time symmetric Hamiltonian operators of the form H=H{sub 0}+igH{sup ′}, where H{sub 0} is Hermitian and g real. H{sub 0} is invariant under the unitary operations of a point group G while H{sup ′} is invariant under transformation by elements of a subgroup G{sup ′} of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 00. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries. - Highlights: • Space-time symmetry is a generalization of PT symmetry. • The eigenvalues of a space-time Hamiltonian are either real or appear as pairs of complex conjugate numbers. • In some cases all the eigenvalues are real for some values of a potential-strength parameter g. • At some value of g space-time symmetry is broken and complex eigenvalues appear. • Some multidimensional oscillators exhibit broken space-time symmetry for all values of g.},

  doi          = {10.1016/J.AOP.2014.07.026},

  url          = {https://www.osti.gov/biblio/22403449},
  journal      = {Annals of Physics (New York)},

  issn         = {0003-4916},

  number       = ,

  volume       = 350,

  place        = {United States},

  year         = {Sat Nov 15 00:00:00 EST 2014},

  month        = {Sat Nov 15 00:00:00 EST 2014}

}

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