Related papers: Complex WKB Analysis of a PT Symmetric Eigenvalue …
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. In…
For a general complex scattering potential defined on a real line, we show that the equations governing invisibility of the potential are invariant under the combined action of parity and time-reversal (PT) transformation. We determine the…
It is well known in classical mechanics that, the frequencies of a periodic system can be obtained rather easily through the action variable, without completely solving the equation of motion. The equivalent quantum action variable…
Paraxial linear propagation of light in an optical waveguide with material gain and loss is governed by a Schr\"odinger equation with a complex potential. Properties of parity-time-symmetric complex potentials have been heavily studied…
We consider Witten Laplacians associated to some non-Morse potentials. We prove Eyring-Kramers formulas for the bottom of the spectrum of these operators in the semiclassical regime and quantify the spectral gap separating these eigenvalues…
Spectra of the second derivative operators corresponding to the special PT-symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT-symmetric point interactions causing…
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…
We briefly explain some simple arguments based on pseudo Hermiticity, supersymmetry and PT-symmetry which explain the reality of the spectrum of some non-Hermitian Hamiltonians. Subsequently we employ PT-symmetry as a guiding principle to…
The one-dimensional Schrodinger equation for the potential $x^6+\alpha x^2 +l(l+1)/x^2$ has many interesting properties. For certain values of the parameters l and alpha the equation is in turn supersymmetric (Witten), quasi-exactly…
Entanglement is central to our understanding of many-body quantum matter. In particular, the entanglement spectrum, as eigenvalues of the reduced density matrix of a subsystem, provides a unique footprint of properties of strongly…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
The properties of coherence and polarization of light has been the subject of intense investigations and form the basis of many technological applications. These concepts which historically have been treated independently can now be…
The WKB approximation for deformed space with minimal length is considered. The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in presence of deformation is that the WKB approximation is valid for intermediate…
An approach, based on the Smith Normal Form, is introduced to study the spectra of symmetric matrices with a given graph. The approach serves well to explain how the path cover number (resp. diameter of a tree T) is related to the maximum…
Static properties of an anharmonic potential model for planar two-electron quantum dots are investigated using a method which allows for the exact representation of the matrix elements, including the full Coulombic electron - electron…
We present an implementation of the three-neutron quantization condition (QC) derived in previous work. We construct the matrices appearing in the QC and determine solutions numerically. The symmetries of the QC allow the projection onto…
Generalized PT symmetry provides crucial insight into the sign problem for two classes of models. In the case of quantum statistical models at non-zero chemical potential, the free energy density is directly related to the ground state…
Semiclassical methods provide important tools for approximating solutions in quantum mechanics. In several cases these methods are intriguingly exact rather than approximate, as has been shown by direct calculations on particular systems.…
We study the spectra of quantum graphs with the method of trace identities (sum rules), which are used to derive inequalities of Lieb-Thirring, Payne-P\'olya-Weinberger, and Yang types, among others. We show that the sharp constants of…
We study theoretically a PT-symmetric saturable balanced gain-loss system in a ring cavity configuration. The saturable gain and loss are modeled by two-level medium with or without population inversion. We show that the specifics of the…