Stimulation of the Fluctuation Superconductivity by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:math>Symmetry

Chtchelkatchev, N. M.; Golubov, A. A.; Baturina, T. I.; Vinokur, V. M.

doi:10.1103/physrevlett.109.150405

Cited by 109 publications

(89 citation statements)

References 37 publications

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“…The boundary between these two regions is a phase transition, and this phase transition has recently been observed in several different laboratory experiments [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Extending $\mathcal{P}\mathcal{T}$ Symmetry from Heisenberg Algebra to E2 Algebra

Bender

Kalveks

2010

Int J Theor Phys

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The E2 algebra has three elements, J, u, and v, which satisfy the commutation relations [u, J] = iv, [v, J] = −iu, [u, v] = 0. We can construct the Hamiltonian H = J 2 + gu, where g is a real parameter, from these elements. This Hamiltonian is Hermitian and consequently it has real eigenvalues. However, we can also construct the PT symmetric and non-Hermitian Hamiltonian H = J 2 + igu, where again g is real. As in the case of PT -symmetric Hamiltonians constructed from the elements x and p of the Heisenberg algebra, there are two regions in parameter space for this PT -symmetric Hamiltonian, a region of unbroken PT symmetry in which all the eigenvalues are real and a region of broken PT symmetry in which some of the eigenvalues are complex. The two regions are separated by a critical value of g.

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“…The boundary between these two regions is a phase transition, and this phase transition has recently been observed in several different laboratory experiments [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Extending $\mathcal{P}\mathcal{T}$ Symmetry from Heisenberg Algebra to E2 Algebra

Bender

Kalveks

2010

Int J Theor Phys

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“…The predicted properties of PT -symmetric Hamiltonians [1,2] have been observed at the classical level in a wide variety of laboratory experiments involving superconductivity [3,4], optics [5][6][7][8], microwave cavities [9], atomic diffusion [10], nuclear magnetic resonance [11], and coupled electronic and mechanical oscillators [12,13]. Although PT -symmetric systems were originally explored at a highly mathematical level, it is now understood that one can interpret PT -symmetric systems simply as nonisolated physical systems having a balanced loss and gain.…”

Section: Introductionmentioning

confidence: 99%

Twofold transition inPT-symmetric coupled oscillators

et al. 2013

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The inspiration for this theoretical paper comes from recent experiments on a PT -symmetric system of two coupled optical whispering galleries (optical resonators). The optical system can be modeled as a pair of coupled linear oscillators, one with gain and the other with loss. If the coupled oscillators have a balanced loss and gain, the system is described by a Hamiltonian and the energy is conserved. This theoretical model exhibits two PT transitions depending on the size of the coupling parameter . For small the PT symmetry is broken and the system is not in equilibrium, but when becomes sufficiently large, the system undergoes a transition to an equilibrium phase in which the PT symmetry is unbroken. For very large the system undergoes a second transition and is no longer in equilibrium. The classical and the quantized versions of the system exhibit transitions at exactly the same values of .

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“…The PT transition occurs in both the classical and the quantized versions of a PT -symmetric Hamiltonian [5] and this transition has been observed in numerous laboratory experiments [9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 92%

Behavior of eigenvalues in a region of broken PT symmetry

et al. 2017

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PT -symmetric quantum mechanics began with a study of the Hamiltonian H = p 2 + x 2 (ix) ε . When ε ≥ 0, the eigenvalues of this non-Hermitian Hamiltonian are discrete, real, and positive. This portion of parameter space is known as the region of unbroken PT symmetry. In the region of broken PT symmetry ε < 0 only a finite number of eigenvalues are real and the remaining eigenvalues appear as complex-conjugate pairs. The region of unbroken PT symmetry has been studied but the region of broken PT symmetry has thus far been unexplored. This paper presents a detailed numerical and analytical examination of the behavior of the eigenvalues for −4 < ε < 0. In particular, it reports the discovery of an infinite-order exceptional point at ε = −1, a transition from a discrete spectrum to a partially continuous spectrum at ε = −2, a transition at the Coulomb value ε = −3, and the behavior of the eigenvalues as ε approaches the conformal limit ε = −4.

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Stimulation of the Fluctuation Superconductivity byPTSymmetry

Cited by 109 publications

References 37 publications

Extending $\mathcal{P}\mathcal{T}$ Symmetry from Heisenberg Algebra to E2 Algebra

Extending $\mathcal{P}\mathcal{T}$ Symmetry from Heisenberg Algebra to E2 Algebra

Twofold transition inPT-symmetric coupled oscillators

Behavior of eigenvalues in a region of broken PT symmetry

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