Related papers: Experimentally-realizable $\mathcal{PT}$ phase tra…
The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks,…
If a Hamiltonian is PT symmetric, there are two possibilities: Either the eigenvalues are entirely real, in which case the Hamiltonian is said to be in an unbroken-PT-symmetric phase, or else the eigenvalues are partly real and partly…
Non-Hermitian parity-time ($\mathcal{PT}$) and anti-parity-time ($\mathcal{APT}$)-symmetric systems exhibit novel quantum properties and have attracted increasing interest. Although many counterintuitive phenomena in $\mathcal{PT}$- and…
Scattering experiments with microwave cavities were performed and the effects of broken time-reversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate…
Noninvertible symmetry generalizes traditional group symmetries, advancing our understanding of quantum matter, especially one-dimensional gapped quantum systems. In critical lattice models, it is usually realized as emergent symmetries in…
The Casimir-Polder (CP) effect -- the force between a neutral atom and an uncharged conducting plate in empty space -- is an intriguing consequence of quantum vacuum fluctuations. The typically attractive CP potential crosses over from a…
Spontaneous symmetry breaking is a universal concept throughout science. For instance, the Landau-Ginzburg paradigm of translational symmetry breaking underlies the classification of nearly all quantum phases of matter and explains the…
The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension $d$ and symmetry group $G$ so that the cohomology group, $H^{d+1}(G,U(1))$, contains at least one $Z_{2n}$…
We solve the problem of electron scattering at a potential temporal step discontinuity. We show that the Schrodinger equation cannot account for scattering in this problem, necessitating resort to the Dirac equation, and that breaking gauge…
Aubry-Andre Harper (AAH) lattice models, characterized by reflection-asymmetric, sinusoidally varying nearest-neighbor tunneling profile, are well-known for their topological properties. We consider the fate of such models in the presence…
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast,…
Symmetry underpins our understanding of physical law. Open systems, those in contact with their environment, can provide a platform to explore parity-time symmetry. While classical parity-time symmetric systems have received a lot of…
Photodetachment of H$^-$ near a potential barrier is studied. A new formula is presented for the cross sections induced by a barrier. The new formula describes two quantum effects near barrier tops. For energies near and above barrier tops,…
More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, $\mathcal{PT}$.…
Eigenspectra of a spinless quantum particle trapped inside a rigid, rectangular, two-dimensional (2D) box subject to diverse inner potential distributions are investigated under hermitian, as well as non-hermitian antiunitary $\mathcal{PT}$…
We are concerned with the justification of the statement, commonly (explicitly or implicitly) used in quantum scattering theory, that for a free non-relativistic quantum particle with initial wave function $\Psi_0(\boldsymbol{x})$,…
We propose a new type of quantum thermodynamic cycle whose efficiency is greater than the one of the classical Carnot cycle for the same conditions for a system when viewed as homogeneous. In our model this type of cycle only exists in the…
Some important rigorous results on phase transitions accompanied by the spontaneous breaking of symmetries in statistical mechanics and relativistic quantum field theory are reviewed. Basic ideas, mainly inspired by quantum field theory,…
We present a renewed wave-packet analysis based on the following ideas: if a quantum one-particle scattering process and the corresponding state are described by an indivisible wave packet to move as a whole at all stages of scattering,…
Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which…