Related papers: Partial Dynamical Symmetries
A symmetry-based approach for describing shape-coexistence, is presented in the framework of the interacting boson model of nuclei. It involves a construction of a number-conserving Hamiltonian which preserves the dynamical symmetry of…
Phase transitions are a fundamental concept in science describing diverse phenomena ranging from, e.g., the freezing of water to Bose-Einstein condensation. While the concept is well-established in equilibrium, similarly fundamental…
Non-Hermitian PT-symmetric quantum-mechanical Hamiltonians generally exhibit a phase transition that separates two parametric regions, (i) a region of unbroken PT symmetry in which the eigenvalues are all real, and (ii) a region of broken…
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new…
Symmetry is a guiding principle in physics that allows to generalize conclusions between many physical systems. In the ongoing search for new topological phases of matter, symmetry plays a crucial role because it protects topological…
In ${\cal PT}-$symmetric quantum mechanics one of the most characteristic mathematical features of the formalism is the explicit Hamiltonian-dependence of the physical Hilbert space of states ${\cal H}={\cal H}(H)$. Some of the most…
We describe the implications of permutation symmetry for the state space and dynamics of quantum mechanical systems of matrices of general size $N$. We solve the general 11- parameter permutation invariant quantum matrix harmonic oscillator…
We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian,…
The low-lying spectra of atomic nuclei display diverse behaviors, for example rotational bands, which can be described phenomenologically by simple symmetry groups such as spatial SU(3). This leads to the idea of dynamical symmetry, where…
A non-${\cal{PT}}$-symmetric Hamiltonian system of a Duffing oscillator coupled to an anti-damped oscillator with a variable angular frequency is shown to admit periodic solutions. The result implies that ${\cal{PT}}$-symmetry of a…
We consider scenarios where the dynamics of a quantum system are partially determined by prior local measurements of some interacting environmental degrees of freedom. The resulting effective system dynamics are described by a disordered…
Many manifestly non-Hermitian Hamiltonians (typically, PT-symmetric complex anharmonic oscillators) possess a strictly real, "physical" bound-state spectrum. This means that they are (quasi-)Hermitian with respect to a suitable non-standard…
Multi-dimensional complex optical potentials with partial parity-time (PT) symmetry are proposed. The usual PT symmetry requires that the potential is invariant under complex conjugation and simultaneous reflection in all spatial…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
PT-symmetric systems can have a real spectrum even when their Hamiltonian is non-hermitian, but develop a complex spectrum when the degree of non-hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous…
\noindent In our contribution to this volume we deal with \emph{discrete} symmetries: these are symmetries based upon groups with a discrete set of elements (generally a set of elements that can be enumerated by the positive integers). In…
Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of…
This paper investigates finite-dimensional representations of PT-symmetric Hamiltonians. In doing so, it clarifies some of the claims made in earlier papers on PT-symmetric quantum mechanics. In particular, it is shown here that there are…
We introduce the simplest model to describe parametric interactions in a quadratically nonlinear optical medium with the fundamental harmonic containing two components with (slightly) different carrier frequencies [which is a direct analog…
We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in…