Enhanced magnetic resonance signal of spin-polarized Rb atoms near surfaces of coated cells

Zhao, K.; Schaden, Martin; Wu, Zhen

doi:10.1103/physreva.81.042903

Cited by 75 publications

(72 citation statements)

References 56 publications

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“…this is nothing but the Hamilton function (12). The existence of two integrals of motion establishes the complete integrability of the system (13) and the dimer (10).…”

Section: Exact Linearisation Of the Dimermentioning

confidence: 90%

An exactly solvable $\mathcal {PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss

Barashenkov

Gianfreda

2014

J. Phys. A: Math. Theor.

102

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We show that a pair of coupled nonlinear oscillators, of which one oscillator has positive and the other one negative damping of equal rate, can form a Hamiltonian system. Small-amplitude oscillations in this system are governed by a PT -symmetric nonlinear Schrödinger dimer with linear and cubic coupling. The dimer also represents a Hamiltonian system and is found to be exactly solvable in elementary functions. We show that the nonlinearity softens the PT -symmetry breaking transition in the nonlinearly-coupled dimer: stable periodic and quasiperiodic states with large enough amplitudes persist for an arbitrarily large value of the gain-loss coefficient.

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“…this is nothing but the Hamilton function (12). The existence of two integrals of motion establishes the complete integrability of the system (13) and the dimer (10).…”

Section: Exact Linearisation Of the Dimermentioning

confidence: 90%

An exactly solvable $\mathcal {PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss

Barashenkov

Gianfreda

2014

J. Phys. A: Math. Theor.

102

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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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“…[3]. There are infinitely many solutions to the turning-point equation (12). The angular distance between successive turning points is 2 2+ε π.…”

Section: Stokes Wedgesmentioning

confidence: 99%

“…When the eigenvalues of a PT -symmetric Hamiltonian are real, the Hamiltonian is said to have an unbroken PT symmetry. A Hamiltonian with unbroken PT symmetry represents a physically viable and realistic quantum system, and such systems have been repeatedly observed and studied in laboratory experiments [9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Negative-energy $\mathcal {P}\mathcal {T}$-symmetric Hamiltonians

Bender

Hook

Klevansky

2012

J. Phys. A: Math. Theor.

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The non-Hermitian PT -symmetric quantum-mechanical Hamiltonian H = p 2 + x 2 (ix) ε has real, positive, and discrete eigenvalues for all ε ≥ 0. These eigenvalues are analytic continuations of the harmonic-oscillator eigenvalues E n = 2n + 1 (n = 0, 1, 2, 3, . . .) at ε = 0. However, the harmonic oscillator also has negative eigenvalues E n = −2n − 1 (n = 0, 1, 2, 3, . . .), and one may ask whether it is equally possible to continue analytically from these eigenvalues. It is shown in this paper that for appropriate PT -symmetric boundary conditions the Hamiltonian H = p 2 + x 2 (ix) ε also has real and negative discrete eigenvalues. The negative eigenvalues fall into classes labeled by the integer N (N = 1, 2, 3, . . .). For the N th class of eigenvalues, ε lies in the range (4N −6)/3 < ε < 4N −2. At the low and high ends of this range, the eigenvalues are all infinite. At the special intermediate value ε = 2N − 2 the eigenvalues are the negatives of those of the conventional Hermitian Hamiltonian H = p 2 + x 2N . However, when ε = 2N − 2, there are infinitely many complex eigenvalues. Thus, while the positive-spectrum sector of the Hamiltonian H = p 2 + x 2 (ix) ε has an unbroken PT symmetry (the eigenvalues are all real), the negative-spectrum sector of H = p 2 +x 2 (ix) ε has a broken PT symmetry (only some of the eigenvalues are real).

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Enhanced magnetic resonance signal of spin-polarized Rb atoms near surfaces of coated cells

Cited by 75 publications

References 56 publications

An exactly solvable $\mathcal {PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss

An exactly solvable $\mathcal {PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss

Twofold transition inPT-symmetric coupled oscillators

Negative-energy $\mathcal {P}\mathcal {T}$-symmetric Hamiltonians

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