arXiv subjects

Dong Ruan

Publications and source records attributed to Dong Ruan.

27 records · Page 2Linked to original sources

arXiv2017

Single phonon source based on a giant acoustic nonlinear effect

We propose a single phonon source based on nitrogen-vacancy (NV) centers, which are located in a diamond phononic crystal resonator. The strain in the lattice would induce the coupling between the NV centers and the phonon mode. The strong coupling between the excited state of the NV centers and the phonon is realized by adding an optical laser driving. This four level NV centers system exhibits the coherent population trapping (CPT), and yields giant resonantly enhanced acoustic nonlinearities, with zero linear susceptibility. Based on this nonlinearity, the single phonon source can be realized. We numerically calculate $g^{(2)}(0)$ of the single phonon source. We discuss the effects of the thermal noise and the external driving strength.

quant-ph↗

arXiv2017

Random Invariant Tensors

Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon of `concentration of measure', saying that for any bipartition, the expected value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimension goes to infinity. This is also true even when the average is over the invariant subspace instead of the whole space for $4-$valent tensors, although its entropy deficit is divergent. One might expect that for $n\geq 5$, $n-$valent random invariant tensor would behavior similarly. However, we show that, the expected entropy deficit of reduced density matrix of such $n-$valent random invariant tensor from maximum, is not divergent but a finite number. Under some special situation, the number could be even smaller than half a bit, which is the deficit of random pure state over the whole Hilbert space from maximum.

quant-ph↗

arXiv2012

Indecomposable representations and oscillator realizations of the exceptional Lie algebra G_2

In this paper various representations of the exceptional Lie algebra G_2 are investigated in a purely algebraic manner, and multi-boson/multi-fermion realizations are obtained. Matrix elements of the master representation, which is defined on the space of the universal enveloping algebra of G_2, are explicitly determined. From this master representation, different indecomposable representations defined on invariant subspaces or quotient spaces with respect to these invariant subspaces are discussed. Especially, the elementary representations of G_2 are investigated in detail, and the corresponding six-boson realization is given. After obtaining explicit forms of all twelve extremal vectors of the elementary representation with the highest weight Λ, all representations with their respective highest weights related to Λ are systematically discussed. For one of these representations the corresponding five-boson realization is constructed. Moreover, a new three-fermion realization from the fundamental representation (0,1) of G_2 is constructed also.

math-ph↗

arXiv2008

An Experiment of Research-Oriented Teaching/Learning

We introduce our experiment of research-oriented teaching mainly in Nanjing University and Tsinghua University, China. The great population and enrollment in China makes it worth to concern. It lasts 20 years and involves thousands of students and hundreds of instructors, consultant experts. We tried many characteristic styles such as integrated teaching and case analysis, open resources, interactive mode, course paper program, elite solutions and so on. The research on the contents is also placed on the agenda. Many students joined research works that lead to PRL, APL, Nature, Science, and Cell papers. To impart colleagues the essence we offered some examples in every session. We declare the accomplishment of the experiment through this paper and new project is programming.

physics.ed-ph↗

arXiv2003

Two-boson realizations of the Higgs algebra and some applications

In this paper two kinds of two-boson realizations of the Higgs algebra are obtained by generalizing the well known Jordan-Schwinger realizations of the SU(2) and SU(1,1) algebras. In each kind, an unitary realization and two nonunitary realizations, together with the properties of their respective acting spaces are discussed in detail. Furthermore, similarity transformations, which connect the nonunitary realizations with the unitary ones, are gained by solving the corresponding unitarization equations. As applications, the dynamical symmetry of the Kepler system in a two-dimensional curved space is studied and the phase operators of the Higgs algebra is constructed.

math-ph↗

arXiv2002

General realization of N=4 supersymmetric quantum mechanics and its applications

Based upon the general supercharges which involve not only generators C_j of the Clifford algebra C(4,0) with positive metric, but also operators of third order, C_j C_k C_l, the general form of N=4 supersymmetric quantum mechanics (SSQM), which brings out the richer structures, is realized. Then from them, an one-dimensional physical realization and a new multi-dimensional physical realization of N=4 SSQM are respectively obtained by solving the constraint conditions. As applications, N=4 dynamical superconformal symmetries, which possess both the N=4 supersymmetries and the usual dynamical conformal symmetries, are studied in detail by considering two simple superpotentials k/x and ωx, and their corresponding superalgebraic structures, which are spanned by eight fermionic generators and six bosonic generators, are established as well.

quant-ph↗

arXiv2001

Single mode realizations of the Higgs algebra

In this paper we obtained for the Higgs algebra three kinds of single-mode realizations such as the unitary Holstein-Primakoff-like realization, the non-unitary Dyson-like realization and the unitary realization based upon Villain-like realization. The corresponding similarity transformations between the Holstein-Primakoff-like realizations and the Dyson-like realizations are revealed.

quant-ph↗

arXiv2001

The Irreducible Tensor Bases of Exceptional Lie Algebras 1. G2, F_4 and E_6

The irreducible tensor bases of exceptional Lie algebras G2, F4 and E6 are built by grouping their Cartan-Weyl bases according to the respective chains G2> SO(3) * SO(3), F4 > SO(3)*SO(3)*SO(3)*SO(3) and E6> SO(3)*SO(3)*SO(3)*SO(3). The explicit commutation relations of the irreducible tensor bases of these algebras are given also respectively.

math-ph↗

arXiv2001

Inhomogeneous boson realizations of the polynomial angular momentum algebra of arbitrary power

The inhomogeneous single-, two- and three-boson realizations of the more general polynomial angular momentum algebra SU_n(2) are obtained from the Fock representations of SU_n(2) that corresponds to the indecomposable representation on the space of universal enveloping algebra U(SU_n(2)) and to the induced representations on the quotient spaces U(SU_n(2))/I_i, with I_i being some left ideals of U(SU_n(2)).

quant-ph↗