January 2014
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Month January 2014

Bohmian quantum trajectories from coherent states

Sanjib Dey, Andreas Fring

We find that real and complex Bohmian quantum trajectories resulting from well-localized Klauder coherent states in the quasi-Poissonian regime possess qualitatively the same type of trajectories as those obtained from a purely classical analysis of the corresponding Hamilton-Jacobi equation. In the complex cases treated the quantum potential results to a constant, such that the agreement is exact. For the real cases we provide conjectures for analytical solutions for the trajectories as well as the corresponding quantum potentials. The overall qualitative behaviour is governed by the Mandel parameter determining the regime in which the wavefunctions evolve as soliton like structures. We demonstrate these features explicitly for the harmonic oscillator and the Poeschl-Teller potential.

Quantum Physics (quant-ph); Mathematical Physics (math-ph)

Tunneling of Obliquely-Incident Waves through PT-Symmetric Epsilon-Near-Zero Bi-Layers

Silvio Savoia, Giuseppe Castaldi, Vincenzo Galdi, Andrea Alú, Nader Engheta

We show that obliquely-incident, transversely-magnetic-polarized plane waves can be totally transmitted (with zero reflection) through epsilon-near-zero (ENZ) bi-layers characterized by balanced loss and gain with parity-time (PT) symmetry. This tunneling phenomenon is mediated by the excitation of a surface-wave localized at the interface separating the loss and gain regions. We determine the parameter configurations for which the phenomenon may occur and, in particular, the relationship between the incidence direction and the electrical thickness. We show that, below a critical threshold of gain and loss, there always exists a tunneling angle which, for moderately thick (wavelength-sized) structures, approaches a critical value dictated by the surface-wave phase-matching condition. We also investigate the unidirectional character of the tunneling phenomenon, as well as the possible onset of spontaneous symmetry breaking, typical of PT-symmetric systems. Our results constitute an interesting example of a PT-symmetry-induced tunneling phenomenon, and may open up intriguing venues in the applications of ENZ materials featuring loss and gain.

Optics (physics.optics); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

The large-g observability of the low-lying energies in the strongly singular potentials \(V(x)=x^2+g^2/x^6\) after their PT-symmetric regularization

Miloslav Znojil

The elementary quadratic plus inverse sextic interaction containing a strongly singular repulsive core in the origin is made regular by a complex shift of coordinate \(x=s−i\epsilon\). The shift \(\epsilon>0\) is fixed while the value of s is kept real and potentially observable, \(s∈(−\infty,\infty)\). The low-lying energies of bound states are found in closed form for the large couplings g. Within the asymptotically vanishing \(\mathcal{O}(g^{−1/4})\) error bars these energies are real so that the time-evolution of the system may be expected unitary in an {\em ad hoc} physical Hilbert space.

Quantum Physics (quant-ph)

PT-symmetric quantum mechanics is a Hermitian quantum mechanics

Sungwook Lee

The author introduces a different kind of Hermtian quantum mechanics, called J-Hermitian quantum mechanics. He shows that PT-symmetric quantum mechanics is indeed J-Hermitian quantum mechanics, and that temporal evolution is unitary if and only if Hamiltonian is PT-symmetric.

Quantum Physics (quant-ph); Mathematical Physics (math-ph)