Market-based Control of Air-Conditioning Loads with Switching Constraints for Providing Ancillary Services

Air-conditioning loads (ACLs) are among the most promising demand side resources for their thermal storage capacity and fast response potential. This paper adopts the principle of market-based control (MBC) for the ACLs to participate in the ancillary services. The MBC method is suitable for the control of distributed ACLs because it can satisfy diversified requirements, reduce the communication bandwidth and protect users' privacy. The modified bidding and clearing strategies proposed in this paper makes it possible to adjust the switching frequency and strictly satisfy the lockout time constraint for mechanical wear reduction and device protection, without increasing the communication traffic and computational cost of the control center. The performance of the ACL cluster in two typical ancillary services is studied to demonstrate the effect of the proposed method. The case studies also investigate how the control parameters affect the response performance, comfort level and switching frequency.Comment: 5 pages, conferenc

On the 2-mode and kk-photon quantum Rabi models

By mapping the Hamiltonians of the two-mode and 2-photon Rabi models to differential operators in suitable Hilbert spaces of entire functions, we prove that the two models possess entire and normalizable wavefunctions in the Bargmann-Hilbert spaces only if the frequency $\omega$ and coupling strength $g$ satisfy certain constraints. This is in sharp contrast to the quantum Rabi model for which entire wavefunctions always exist. For model parameters fulfilling the aforesaid constraints we determine transcendental equations whose roots give the regular energy eigenvalues of the models. Furthermore, we show that for $k\geq 3$ the $k$-photon Rabi model does not possess wavefunctions which are elements of the Bargmann-Hilbert space for all non-trivial model parameters. This implies that the $k\geq 3$ case is not diagonalizable, unlike its RWA cousin, the $k$-photon Jaynes-Cummings model which can be completely diagonalized for all $k$.Comment: LaTex 15 pages. Version to appear in Reviews in Mathematical Physic

Exact polynomial solutions of second order differential equations and their applications

We find all polynomials $Z(z)$ such that the differential equation $${X(z)\frac{d^2}{dz^2}+Y(z)\frac{d}{dz}+Z(z)}S(z)=0,$$ where $X(z), Y(z), Z(z)$ are polynomials of degree at most 4, 3, 2 respectively, has polynomial solutions $S(z)=\prod_{i=1}^n(z-z_i)$ of degree $n$ with distinct roots $z_i$. We derive a set of $n$ algebraic equations which determine these roots. We also find all polynomials $Z(z)$ which give polynomial solutions to the differential equation when the coefficients of X(z) and Y(z) are algebraically dependent. As applications to our general results, we obtain the exact (closed-form) solutions of the Schr\"odinger type differential equations describing: 1) Two Coulombically repelling electrons on a sphere; 2) Schr\"odinger equation from kink stability analysis of $\phi^6$-type field theory; 3) Static perturbations for the non-extremal Reissner-Nordstr\"om solution; 4) Planar Dirac electron in Coulomb and magnetic fields; and 5) O(N) invariant decatic anharmonic oscillator.Comment: LaTex 25 page

Hidden sl(2)sl(2)-algebraic structure in Rabi model and its 2-photon and two-mode generalizations

It is shown that the (driven) quantum Rabi model and its 2-photon and 2-mode generalizations possess a hidden $sl(2)$-algebraic structure which explains the origin of the quasi-exact solvability of these models. It manifests the first appearance of a hidden algebraic structure in quantum spin-boson systems without $U(1)$ symmetry.Comment: LaTex 14 pages. Version to appear in Annals of Physic

Super Coherent States, Boson-Fermion Realizations and Representations of Superalgebras

Super coherent states are useful in the explicit construction of representations of superalgebras and quantum superalgebras. In this contribution, we describe how they are used to construct (quantum) boson-fermion realizations and representations of (quantum) superalgebras. We work through a few examples: $osp(1|2)$ and its quantum version $U_t[osp(1|2)]$, $osp(2|2)$ in the non-standard and standard bases and $gl(2|2)$ in the non-standard basis. We obtain free boson-fermion realizations of these superalgebras. Applying the boson-fermion realizations, we explicitly construct their finite-dimensional representations. Our results are expected to be useful in the study of current superalgebras and their corresponding conformal field theories.Comment: LaTex 20 pages. Invited contribution for the volume "Trends in Field Theory Research" by Nova Science Publishers Inc., New York, 2004. Accepted for publication in the volum

Quantum Phases and Collective Excitations in Bose-Hubbard Models with Staggered Magnetic Flux

We study the quantum phases of a Bose-Hubbard model with staggered magnetic flux in two dimensions, as has been realized recently [Aidelsburger {\it et al.}, PRL, {\bf 107}, 255301 (2011)]. Within mean field theory, we show how the structure of the condensates evolves from weak to strong coupling limit, exhibiting a tricritical point at the Mott-superfluid transition. Non-trivial topological structures (Dirac points) in the quasi-particle (hole) excitations in the Mott state are found within random phase approximation and we discuss how interaction modifies their structures. Excitation gap in the Mott state closes at different ${\bf k}$ points when approaching the superfluid states, which is consistent with the findings of mean field theory.Comment: 5 pages, 3 figure