相关论文: $Sp(4;\mathbb{R})$ Squeezing for Bloch Four-Hyperb…

Crane and Frenkel proposed a state sum invariant for triangulated 4-manifolds.They defined and used new algebraic structures called Hopf categories for their construction. Crane and Yetter studied Hopf categories and gave some examples…

We discuss twistor-like interpretation of the $Sp(8)$ invariant formulation of 4d massless fields in ten dimensional Lagrangian Grassmannian $Sp(8)/P$ which is the generalized space-time in this framework. The correspondence space…

We give alternative computations of the Schur multiplier of $Sp(2g,\mathbb Z/D\mathbb Z)$, when $D$ is divisible by 4 and $g\geq 4$: a first one using $K$-theory arguments based on the work of Barge and Lannes and a second one based on the…

Parallel to $\widetilde{\mathrm{SL}(2,\mathbb{R})}$-geometry fibering over the hyperbolic plane, we construct a geometry fibering over the Siegel upper half-space $\mathrm{Sp}(2n,\mathbb{R})\curvearrowright {\mathfrak{H}}_n$, and provide a…

We introduce a construction that simultaneously yields cusped spaces of relatively hyperbolic groups, and spaces quasi-isometric to Teichmueller metrics. We use this to study Dehn-filling-like quotients of various groups, among which…

The physical meaning of the particularly simple non-degenerate supermetric, introduced in the previous part by the authors, is elucidated and the possible connection with processes of topological origin in high energy physics is analyzed…

Given a triple $H$ of (possibly non-semisimple) Hopf algebras equipped with pairings satisfying a set of properties, we describe a construction of an associated smooth, scalar invariant $\tau_H(X,\pi)$ of a simply connected, compact,…

We develop a noncompact version of the Hopf maps based on the split algebras. The split algebras consist of three species: split-complex numbers, split quaternions, and split octonions. They correspond to three noncompact Hopf maps that…

We study $4n$-dimensional smooth manifolds admitting a $\mathsf{SO}^*(2n)$- or a $\mathsf{SO}^*(2n)\mathsf{Sp}(1)$-structure, where $\mathsf{SO}^*(2n)$ is the quaternionic real form of $\mathsf{SO}(2n, \mathbb{C})$. We show that such…

In this paper we treat coherent-squeezed states of Fock space once more and study some basic properties of them from a geometrical point of view. Since the set of coherent-squeezed states $\{\ket{\alpha, \beta}\ |\ \alpha, \beta \in…

Recently a $f$-deformed Fock space which is spanned by $|n>_{\lambda}$ has been introduced. These bases are indeed the eigen-states of a deformed non-Hermitian Hamiltonian. In this contribution, we will use a rather new non-orthogonal basis…

We study the spin squeezing in a spin-1/2 Bose-Einstein condensates (BEC) with Raman induced spin-orbit coupling (SOC). Under the condition of two-photon resonance and weak Raman coupling strength, the system possesses two degenerate ground…

Following an approach developed by Gieseker, Kn\"orrer and Trubowitz for discretized Schr\"odinger operators, we study the spectral theory of Harper operators in dimension two and one, as a discretized model of magnetic Laplacians, from the…

We investigate the quantum properties of superpositions of oppositely squeezed states, which can be regarded as Schrodinger cat states. Compared with conventional coherent-state cat states, these states exhibit distinct photon-number…

We introduce a new method for constructing squeezed states for the 2D isotropic harmonic oscillator. Based on the construction of coherent states in [1], we define a new set of ladder operators for the 2D system as a linear combination of…

We discuss a new pseudometric on the space of all norms on a finite-dimensional vector space (or free module) $\mathbb{F}^k$, with $\mathbb{F}$ the real, complex, or quaternion numbers. This metric arises from the Lipschitz-equivalence of…

It is shown that the SU(1,1)-like and SU(2)-like two-photon coherent states can be combined to form a O(3,2)-like two-photon states. Since the O(3,2) group has many subgroups, there are also many new interesting new coherent and squeezed…

The Bloch Sphere visualization of the possible states of a single qubit has proved a useful pedagogical and conceptual tool as a one-to-one map between qubit states and points in a 3-D space. However, understanding many important concepts…

Current definitions of both squeezing operator and squeezed vacuum state are critically examined on the grounds of consistency with the underlying su(1,1) algebraic structure. Accordingly, the generalized coherent states for su(1,1) in its…

Denote by $Sp(k,l)$ the quaternionic symplectic group of signature $(k,l)$. We study the deformation rigidity of the embedding $Sp(k,l) \times Sp(1) \hookrightarrow H$, where $H$ is either $Sp(k+1,l)$ or $Sp(k,l+1)$, this is done by…