Ali Mostafazadeh
We extend the formulation of pseudo-Hermitian quantum mechanics to eta-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta. In particular, we give the details of the construction of the physical Hilbert space, observables, and equivalent Hermitian Hamiltonian for the case that H has a real and discrete spectrum and its eigenvectors belong to the domain of eta and its positive square root.
http://arxiv.org/abs/1203.6241
Mathematical Physics (math-ph); Quantum Physics (quant-ph)
Ali Mostafazadeh, Mustafa Sarisaman
The mathematical notion of a spectral singularity admits a physical interpretation as a zero-width resonance. It finds an optical realization as a certain type of lasing effect that occurs at the threshold gain. We explore spectral singularities of a complex spherical barrier potential and study their realization as transverse spherical electromagnetic waves emitted by a gain medium with a spherical geometry. In particular, for a typical dye laser material, we obtain a lower bound on the size of the gain medium for the occurence of this kind of spectral singularities.
http://arxiv.org/abs/1107.1873
Mathematical Physics (math-ph); Optics (physics.optics); Quantum Physics (quant-ph)
Ali Mostafazadeh
Using the Pais-Uhlenbeck Oscillator as a toy model, we outline a consistent alternative to the indefinite-metric quantization scheme that does not violate unitarity. We describe the basic mathematical structure of this method by giving an explicit construction of the Hilbert space of state vectors and the corresponding creation and annihilation operators. The latter satisfy the usual bosonic commutation relation and differ from those of the indefinite-metric theories by a sign in the definition of the creation operator. This change of sign achieves a definitization of the indefinite-metric that gives life to the ghost states without changing their contribution to the energy spectrum.
http://arxiv.org/abs/1107.1874
High Energy Physics – Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
Ali Mostafazadeh
We study the problem of locating spectral singularities of a general complex point interaction with a support at a single point. We also determine the bound states, examine the special cases where the point interaction is P-, T-, and PT-symmetric, and explore the issue of the coalescence of spectral singularities and bound states.
http://arxiv.org/abs/1107.1875
Mathematical Physics (math-ph); Quantum Physics (quant-ph)
Ali Mostafazadeh
Spectral singularities are among generic mathematical features of complex scattering potentials. Physically they correspond to scattering states that behave like zero-width resonances. For a simple optical system, we show that a spectral singularity appears whenever the gain coefficient coincides with its threshold value and other parameters of the system are selected properly. We explore a concrete realization of spectral singularities for a typical semiconductor gain medium and propose a method of constructing a tunable laser that operates at threshold gain.
http://arxiv.org/abs/1102.4695
Optics (physics.optics); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)