The visualization of an exceptional point in a PT-symmetric directional coupler (DC) is demonstrated. In such a system the exceptional point can be probed by varying only a single parameter. Using ...the Rayleigh-Schrödinger perturbation theory we prove that the spectrum of a PT-symmetric Hamiltonian is real as long as the radius of convergence has not been reached. We also show how one can use a PT-symmetric directional coupler to measure the radius of convergence for non-PT-symmetric structures. For such systems the physical meaning of the rather mathematical term radius of convergence is exemplified.
The quantum mechanical brachistochrone system with a PT-symmetric Hamiltonian is Naimark-dilated and reinterpreted as a subsystem of a Hermitian system in a higher-dimensional Hilbert space. This ...opens a way to a direct experimental implementation of the recently hypothesized PT-symmetric ultrafast brachistochrone regime of Bender et al. Phys. Rev. Lett. 98, 040403 (2007) in an entangled two-spin system.
PT-symmetric quantum state discrimination Bender, Carl M.; Brody, Dorje C.; Caldeira, João ...
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences,
04/2013, Letnik:
371, Številka:
1989
Journal Article
Recenzirano
Odprti dostop
The objective of this paper is to explain and elucidate the formalism of quantum mechanics by applying it to a well-known problem in conventional Hermitian quantum mechanics, namely the problem of ...state discrimination. Suppose that a system is known to be in one of two quantum states, |ψ1〉 or |ψ2〉. If these states are not orthogonal, then the requirement of unitarity forbids the possibility of discriminating between these two states with one measurement; that is, determining with one measurement what state the system is in. In conventional quantum mechanics, there is a strategy in which successful state discrimination can be achieved with a single measurement but only with a success probability p that is less than unity. In this paper, the state-discrimination problem is examined in the context of quantum mechanics and the approach is based on the fact that a non-Hermitian -symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states. It is shown that it is always possible to choose this inner product so that the two states |ψ1〉 and |ψ2〉 are orthogonal. Using quantum mechanics, one cannot achieve a better state discrimination than in ordinary quantum mechanics, but one can instead perform a simulated quantum state discrimination, in which with a single measurement a perfect state discrimination is realized with probability p.
Bypassing the bandwidth theorem with PT symmetry Ramezani, Hamidreza; Schindler, J.; Ellis, F. M. ...
Physical review. A, Atomic, molecular, and optical physics,
06/2012, Letnik:
85, Številka:
6
Journal Article
The existence of magnetohydrodynamic mean-field ...-dynamos with spherically symmetric, isotropic helical turbulence function ... is related to a non-self-adjoint spectral problem for a coupled ...system of two singular second order ordinary differential equations. The authors establish global estimates for the eigenvalues of this system in terms of the turbulence function ... and its derivative ... They allow them to formulate an antidynamo theorem and a nonoscillation theorem. The conditions of these theorems, which again involve ... and ..., must be violated in order to reach supercritical or oscillatory regimes.
The $\mathcal{PT}-$symmetric quantum mechanical $V=ix^3$ model over the real
line, $x\in\mathbb{R}$, is infrared (IR) truncated and considered as
Sturm-Liouville problem over a finite interval
...$x\in\left-L,L\right\subset\mathbb{R}$. Via WKB and Stokes graph analysis,
the location of the complex spectral branches of the $V=ix^3$ model and those
of more general $V=-(ix)^{2n+1}$ models over
$x\in\left-L,L\right\subset\mathbb{R}$ are obtained. The corresponding
eigenvalues are mapped onto $L-$invariant asymptotic spectral scaling graphs
$\mathcal{R}\subset \mathbb{C}$. These scaling graphs are geometrically
invariant and cutoff-independent so that the IR limit $L\to \infty $ can be
formally taken. Moreover, an increasing $L$ can be associated with an
$\mathcal{R}-$constrained spectral UV$\to$IR renormalization group flow on
$\mathcal{R}$. The existence of a scale-invariant $\mathcal{PT}$ symmetry
breaking region on each of these graphs allows to conclude that the unbounded
eigenvalue sequence of the $ix^3$ Hamiltonian over $x\in\mathbb{R}$ can be
considered as tending toward a mapped version of such a $\mathcal{PT}$ symmetry
breaking region at spectral infinity. This provides a simple heuristic
explanation for the specific eigenfunction properties described in the
literature so far and clear complementary evidence that the
$\mathcal{PT}-$symmetric $V=-(ix)^{2n+1}$ models over the real line
$x\in\mathbb{R}$ are not equivalent to Hermitian models, but that they rather
form a separate model class with purely real spectra. Our findings allow us to
hypothesize a possible physical interpretation of the non-Rieszian mode
behavior as a related mode condensation process.
Polystyrene sulfonate (PSS) of different molecular weight M w is adsorbed to oppositely charged DODAB monolayers from dilute solutions (0.01 mmol/L). PSS adsorbs flatly in a lamellar manner, as is ...shown by X-ray reflectivity and grazing incidence diffraction (exception: PSS with M w below 7 kDa adsorbs flatly disordered to the liquid expanded phase). The surface coverage and the separation of the PSS chains are independent of PSS M w. On monolayer compression, the surface charge density increases by a factor of 2, and the separation of the PSS chains decreases by the same factor. Isotherms show that on increase of PSS M w the transition pressure of the LE/LC (liquid expanded/liquid condensed) phase transition decreases. When the contour length exceeds the persistence length (21 nm), the transition pressure is low and constant. For low-M w PSS (<7 kDa) the LE/LC transition of the lipids and the disordered/ordered transition of adsorbed PSS occur simultaneously, leading to a maximum in the contour length dependence of the transition enthalpy. These findings show that lipid monolayers at the air/water interface are a suitable model substrate with adjustable surface charge density to study the equilibrium conformation of adsorbed polyelectrolytes as well as their interactions with a model membrane.
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