Two-Parameter Deformed Quantum Algebra SUq,s(4)

The commutation relations of thegenerators of the two-parameter deformed quantum algebra SU_q,s(4) are given and irreducible q,s-tensor operators of rank (1/2) of the quantum algebra SU_q,s(2) are constructed.     

Deformed quantum double realization of the toric code and beyond

Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase and destroying the exact solvability of the quantum double model. We modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase, thus nullifying the effect of the perturbation. The algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra. The Abelian cases are shown to be in the quantum double phase whereas the non-Abelian phases are shown to be in a modified phase of the corresponding quantum double phase. These are illustrated with the groups Z_n${\mathbb{Z}}_n$ and S₃$S_3$. The quantum phases are determined by studying the excitations of these systems namely their fusion rules and the statistics. We then go further to construct a transfer matrix which contains the other Z₂${\mathbb{Z}}_2$ phase namely the double semion phase. More generally for other discrete groups these transfer matrices contain the twisted quantum double models. These transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories. These parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice. As in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties.     

Majorana fermion realization and relevant transport processes in a triple-quantum dot system

Nonequilibrium electronic transports through a system hosting three quantum dots hybridized with superconductors are investigated. By tuning the relative positions of the dot levels, we illustrate the existence of Majorana fermions and show that the Majorana feimions will either survive separately on single dots or distribute themselves among different dots with tunable probabilities. As a result, different physical mechanisms appear, including local Andreev reflection(LAR),cross Andreev reflection(CAR), and cross resonant tunneling(CRT). The resulting characteristics may be used to reveal the unique properties of Majorana fermions. In addition, we discuss the spin-polarized transports and find a pure spin current and a spin filter effect due to the joint effect of CRT and CAR, which is important for designing spintronic devices.     

SO(18) unification of fermion generations

We discuss the mass spectrum of light fermions in a recently proposed SO(18) model for family unification. We find that an intermediate B-L violating scale in the range of 10³ TeV provides a proper understanding of light neutrino (v_e, v_μ, v_τ, …) masses as well as the masses of their mirror partners. In this scenario, we expect at most four mirror neutrinos in the 2–10 GeV range, which could contribute to the width of the Z boson.     

一种4阶RLL(2,12)调制码的CPLD的实现

现有的光存储系统采用二值的记录模式,普遍使用的是游程长度受限(Run-length limited,RLL)的调制编码,并将信息编码记录在信息符的长度中。新型多阶RLL光存储采用多阶RLL编码方案,将信息同时记录在信息符的长度和信号幅值中,从而大幅度地提高了光盘的容量。为了研究多阶RLL编码的逻辑正确性和电路复杂度,设计了基于可编程逻辑器件的硬件平台。多阶RLL编码可以用有限数量逻辑门实现编码,有望用于未来高密度多阶光存储系统。     

Hierarchical fermion masses in SU(5)

Rediative masses are generated for the first and the second fermion families by exploiting the idea that their chirality is a symmetry of the “low-energy” SU(3) × SU(2) × U(1) approximation of SU(5), broken only by including the effects of superheavy particles. With only 5's of Higgs coupled to fermions and getting a non-zero vacuum expectation value, we unavoidably get (i) $\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{=}\text{m}{}_{\mathrm{\mu }}\text{3}$ at the grand unification scale; (ii) the charm quark needing a direct mass as the third family; (iii) neutrino masses of size $\text{? (}\text{α}\text{π}\text{)}\text{M}{}_{\mathrm{W}}{}^2\text{M}$.     

Pairing in 4-component fermion systems: The bulk limit of SU(4)-symmetric Hamiltonians

Fermion systems with more than two components can exhibit pairing condensates of a much more complex structure than the well-known single BCS condensate of spin-up and spin-down fermions. In the framework of the exactly solvable SO(8) Richardson-Gaudin (RG) model with SU(4)-symmetric Hamiltonians, we show that the BCS approximation remains valid in the thermodynamic limit of large systems for describing the ground-state energy and the canonical and quasiparticle excitation gaps. Correlations beyond BCS pairing give rise to a spectrum of collective excitations, but these do not affect the bulk energy and quasiparticle gaps.     

Schwinger boson mapping of SO(8) fermion model

The Schwinger representation of the SO(8) fermion pair algebra in terms ofd and quasispin vector (u, s, v) bosons is used in deriving a microscopic boson coherent state having both particle-hole and pair excitations. The coherent state is the exact boson image of the HFB variational solution. We can study the shape phase transition and pairing behaviour of the nuclear ground states using the coherent states.     

A model for so(5) = sp(4) lie algebra

The paper is the continuation of a previous one [Physica Scripta22 (1980), 545–555] devoted to quadrupling in the shell model. We consider here a simple model of the ten- dimensional quasi-spin Lie algebra which is spectrum generating for the quadrupling Hamiltonian. The model allows us to investigate many concrete aspects of the theory of linear representations of the quasi-spin algebra. In particular, we present an explicit construction of the irreducible representation module for the finite dimensional representations, and we consider the direct product of the such irreducible modules.     

Finite-mode regularization of the fermion functional integral (II)

Using the finite-mode regularization introduced in a previous paper, we define the functional integral for a theory of Weyl fermions. We check this definition by making sure the resulting triangle anomaly satisfies the Wess-Zumino consistency conditions. We compare our result with others found in the literature. We apply the finite-mode regularization to compute the axial anomaly in any space-time dimension and to find the explicit expression of anomalous currents in terms of the gauge fields. We illustrate the phenomenon of the infrared compensation of the chiral anomaly.     

Deformed Algebras from Elliptic sl(N) Algebras

We extend to the sl(N)sl(N) case the results that we previously obtained on the construction of W_q,p{\cal W}_{q,p} algebras from the elliptic algebra A_q,p([^(sl)](2)_c){\cal A}_{q,p}(\widehat{sl}(2)_{c}). The elliptic algebra \elp\elp at the critical level c= m N has an extended center containing trace-like operators t(z). Families of Poisson structures indexed by N(Nу)/2 integers, defining q-deformations of the W_N{\cal W}_{N} algebra, are constructed. The operators t(z) also close an exchange algebra when (-p^\sfrac12)^NM = q^-c-N(-p^\sfrac{1}{2})^{NM} = q^{-c-N} for M ? \ZZM\in\ZZ. It becomes Abelian when in addition p= q^Nh, where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed W_N{\cal W}_{N} algebras depending on the parity of h, characterizing the exchange structures at p p q^Nh as new W_q,p(sl(N)){\cal W}_{q,p}(sl(N)) algebras.     

Source Identities and Kernel Functions for Deformed (Quantum) Ruijsenaars Models

We consider the relativistic generalization of the quantum A _N-1 Calogero–Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic cases. For each of these cases, we find an exact common eigenfunction for a generalization of Ruijsenaars analytic difference operators that gives, as special cases, many different kernel functions; in particular, we find kernel functions for Chalykh–Feigin–Veselov–Sergeev-type deformations of such difference operators which generalize known kernel functions for the Ruijsenaars models. We also discuss possible applications of our results.     

Strong coupled and doubly decoupled bands in the SU BF (3) ⊗ U F (2j + 1) limit of interacting boson — fermion — fermion model

The quantum numbers labelling the basis states and the corresponding strong coupled wavefunctions in the SU ^BF (3) ? U ^F (2j + 1) limit of interacting boson — fermion — fermion model are given. This dynamical symmetry limit is appropriate for heavy deformed odd — odd nuclei for configurations with one of the odd particle (proton or neutron) occupying all the natural parity orbits in the corresponding valence shell and the other particle occupying a single j — orbit. A boson — fermion — fermion interaction that can change the positions of the strong coupled bands without admixing and generate degenerate quadruplet of bands is constructed. A simple spin — spin and spin — orbital interaction that splits and changes the positions of the members of the quadruplet of bands is given. Adding a coriolis term to the hamiltonian generates doubly decoupled bands such as those seen in ¹⁷⁶Re nucleus.     

SU (4) × SU (4) symmetry breaking and its implications for SU (3) × SU (3) breaking

We investigate models where the SU (4) × SU (4) symmetry breaking Hamiltonian, $\text{H}$_SB, belongs to the (15, 15) and $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ representations, and show how they are equivalent to models of SU (3) × SU (3) breaking where $\text{H}$_SB belongs to a mixture of different representations. The results for the ππ scattering lengths in the (15, 15) model are outside the experimental limits, but the $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ model yields solutions with a wide range of values for the scattering lengths within the experimental bounds.     

Dynamical electroweak symmetry breaking via fermion condensates inSU(5) model

TheSU(4) symmetry scheme, used in a previous paper for the study of the 2v double decay, is applied to the study of the 0v double decay. Differences and similarities between the 2 processes are emphasized. The sensitivity to short-range correlations is discussed.     

Acoustic superscatterer and its multilayer realization

Picosecond (40 ps) pulsed Nd:YAG laser irradiation of a WTi thin film on silicon with a wavelength of 532 nm and a fluence 2.1 J/cm² was performed in air. This led to significant changes of the chemical composition and morphology on the surface of the WTi thin film. The results show an increase in surface roughness, due to formation of conical structures, about 50 nm wide in the base, and a very thin oxide layer composed of WO₃ and TiO₂, with a dominant TiO₂ phase at the top, within the depth of about 20 nm. The thickness of the oxide layer was dependent on the number of laser pulses. The samples were analyzed by scanning electron microscopy, atomic force microscopy, and X-ray photoelectron spectroscopy.