dorsal/arxiv
View SchemaReal Description of Classical Hamiltonian Dynamics Generated by a Complex Potential
| Authors | Ali Mostafazadeh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603091 |
| URL | https://arxiv.org/abs/quant-ph/0603091 |
| DOI | 10.1016/j.physleta.2006.04.045 |
| Journal | Phys.Lett. A357 (2006) 177-180 |
Abstract
Analytic continuation of the classical dynamics generated by a standard Hamiltonian, H = p^2/2m + v(x), into the complex plane yields a particular complex classical dynamical system. For an analytic potential v, we show that the resulting complex system admits a description in terms of the phase space R^4 equipped with an unconventional symplectic structure. This in turn allows for the construction of an equivalent real description that is based on the conventional symplectic structure on R^4, and establishes the equivalence of the complex extension of classical mechanics that is based on the above-mentioned analytic continuation with the conventional classical mechanics. The equivalent real Hamiltonian turns out to be twice the real part of H, while the imaginary part of H plays the role of an independent integral of motion ensuring the integrability of the system. The equivalent real description proposed here is the classical analog of the equivalent Hermitian description of unitary quantum systems defined by complex, typically PT-symmetric, potentials.
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"abstract": "Analytic continuation of the classical dynamics generated by a standard\nHamiltonian, H = p^2/2m + v(x), into the complex plane yields a particular\ncomplex classical dynamical system. For an analytic potential v, we show that\nthe resulting complex system admits a description in terms of the phase space\nR^4 equipped with an unconventional symplectic structure. This in turn allows\nfor the construction of an equivalent real description that is based on the\nconventional symplectic structure on R^4, and establishes the equivalence of\nthe complex extension of classical mechanics that is based on the\nabove-mentioned analytic continuation with the conventional classical\nmechanics. The equivalent real Hamiltonian turns out to be twice the real part\nof H, while the imaginary part of H plays the role of an independent integral\nof motion ensuring the integrability of the system. The equivalent real\ndescription proposed here is the classical analog of the equivalent Hermitian\ndescription of unitary quantum systems defined by complex, typically\nPT-symmetric, potentials.",
"arxiv_id": "quant-ph/0603091",
"authors": [
"Ali Mostafazadeh"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP",
"physics.class-ph"
],
"doi": "10.1016/j.physleta.2006.04.045",
"journal_ref": "Phys.Lett. A357 (2006) 177-180",
"title": "Real Description of Classical Hamiltonian Dynamics Generated by a Complex Potential",
"url": "https://arxiv.org/abs/quant-ph/0603091"
},
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