On entropy of P-twists

We compute the categorical entropy of autoequivalences given by P-twists, and show that these autoequivalences satisfy a Gromov-Yomdin type conjecture.Comment: 6 pages. Comments are welcome

Quantum nondemolition measurements of a flux qubit coupled to a noisy detector

We theoretically study the measurement-induced dephasing caused by back action noise in quantum nondemolition measurements of a superconducting flux qubit which is coupled to a superconducting quantum interference device (SQUID). Our analytical results indicate that information on qubit flows from qubit to detector, while quantum fluctuations which may cause dephasing of the qubit also inject to qubit. Furthermore, the measurement probability is frequency dependent in a short time scale and has a close relationship with the measurement-induced dephasing. When the detuning between driven and bare resonator equals coupling strength, we will access the state of qubit more easily. In other words, we obtain the maximum measurement rate. Finally, we analyzed mixed effect caused by coupling between non-diagonal term and external variable. We found that the initial information of qubit is destroyed due to quantum tunneling between the qubit states.Comment: 6 pages, 3 figure

Swallowtail Structure in Fermi Superfluids with Periodically Modulated Interactions

We study the superfluid flow in a quasi-one-dimensional Fermi gas with spatially modulated interactions induced by an optical Feshbach resonance. Due to the competition between the periodicity of the modulated interaction and the nonlinearity of the background interaction, an interesting swallowtail structure emerges in the energy spectrum under appropriate parameters. As the interaction strengths are tuned, the swallowtail structure may disappear, giving rise to various different states on a rich phase diagram. We investigate the spatial distribution of the order parameter and the particle density under various parameters, which are useful for the experimental detection of the interesting phases in these systems.Comment: 7 pages, 5 figure

Multiobjective controller design by solving a multiobjective matrix inequality problem

In this study, linear matrix inequality (LMI) approaches and multiobjective (MO) evolutionary algorithms are integrated to design controllers. An MO matrix inequality problem (MOMIP) is first defined. A hybrid MO differential evolution (HMODE) algorithm is then developed to solve the MOMIP. The hybrid algorithm combines deterministic and stochastic searching schemes. In the solving process, the deterministic part aims to exploit the structures of matrix inequalities, and the stochastic part is used to fully explore the decision variable space. Simulation results show that the HMODE algorithm can produce an approximated Pareto front (APF) and Pareto-efficient controllers that stabilise the associated controlled system. In contrast with single-objective designs using LMI approaches, the proposed MO methodology can clearly illustrate how the objectives involved affect each other, that is, a broad perspective on optimality is provided. This facilitates the selecting process for a representative design, and particularly the design that corresponds to a non-dominated vector lying in the knee region of the APF. In addition, controller gains can be readily modified to incorporate the preference or need of a system designer.Comment: 22 pages, 5 figure

There are no 76 equiangular lines in R19R^{19}

Maximum size of equiangular lines in $\mathbb{R}^{19}$ has been known in the range between 72 to 76 since 1973. Acoording to the nonexistence of strongly regular graph $(75,32,10,16)$ \cite{aza15}, Larmen-Rogers-Seidel Theorem \cite{lar77} and Lemmen-Seidel bounds on equiangular lines with common angle $\frac 1 3$ \cite{lem73}, we can prove that there are no 76 equiangular lines in $\mathbb{R}^{19}$. As a corollary, there is no strongly regular graph $(76,35,18,14)$. Similar discussion can prove that there are no 96 equiangular lines in $\mathbb{R}^{20}$

Local Unitary Representation of Braids and N-Qubit Entanglements

In this paper, by utilizing the idea of stabilizer codes, we give some relationships between one local unitary representation of braid group in N-qubit tensor space and the corresponding entanglement properties of the N-qubit pure state $|\Psi\rangle$, where the N-qubit state $|\Psi\rangle$ is obtained by applying the braiding operation on the natural basis. Specifically, we show that the separability of $|\Psi\rangle=\mathcal{B}|0\rangle^{\otimes N}$ is closely related to the diagrammatic version of the braid operator $\mathcal{B}$. This may provide us more insights about the topological entanglement and quantum entanglement.Comment: 5 pages, Comments are welcom

Entropy of an autoequivalence on Calabi-Yau manifolds

We prove that the categorical entropy of the autoequivalence $T_{\mathcal{O}}\circ(-\otimes\mathcal{O}(-1))$ on a Calabi-Yau manifold is the unique positive real number $\lambda$ satisfying $$\sum_{k\geq 1}\frac{\chi(\mathcal{O}(k))}{e^{k\lambda}}=e^{(d-1)t}.$$ We then use this result to construct the first counterexamples of a conjecture on categorical entropy by Kikuta and Takahashi.Comment: 10 pages. Comments are welcome

The small and large D limit of Parikh-Wilczek tunneling model for Hawking radiation

In this note, we study both the small and large dimension $D$ limit of the tunneling model of Hwaking radiation proposed by Parikh and Wilczek\cite{Parikh:1999mf}. We confirm that the result $\Gamma \sim e^{\Delta S}$ is still valid for arbitrary $D>3$. The sensible large $D$ limit is given by $\sqrt{D} \ll r_0$ in order to have nonzero radiation. On the other hand, the sensible small $D$ limit is given by taking $D=3+\epsilon$ as a continuous parameter. We also explicitly show the leading order correction to the thermal radiation and discuss its connection to the two-dimensional dilaton gravity.Comment: 7 pages, updated version submitted to CQ

Determining the luminosity function of Swift long gamma-ray bursts with pseudo-redshifts

The determination of luminosity function (LF) of gamma-ray bursts (GRBs) is of an important role for the cosmological applications of the GRBs, which is however hindered seriously by some selection effects due to redshift measurements. In order to avoid these selection effects, we suggest to calculate pseudo-redshifts for Swift GRBs according to the empirical L-E_p relationship. Here, such a $L-E_p$ relationship is determined by reconciling the distributions of pseudo- and real redshifts of redshift-known GRBs. The values of E_p taken from Butler's GRB catalog are estimated with Bayesian statistics rather than observed. Using the GRB sample with pseudo-redshifts of a relatively large number, we fit the redshift-resolved luminosity distributions of the GRBs with a broken-power-law LF. The fitting results suggest that the LF could evolve with redshift by a redshift-dependent break luminosity, e.g., L_b=1.2\times10^{51}(1+z)^2\rm erg s^{-1}. The low- and high-luminosity indices are constrained to 0.8 and 2.0, respectively. It is found that the proportional coefficient between GRB event rate and star formation rate should correspondingly decrease with increasing redshifts.Comment: 5 pages, 5 figures, accepted for publication in ApJ

Uplink Multicell Processing with Limited Backhaul via Per-Base-Station Successive Interference Cancellation

This paper studies an uplink multicell joint processing model in which the base-stations are connected to a centralized processing server via rate-limited digital backhaul links. Unlike previous studies where the centralized processor jointly decodes all the source messages from all base-stations, this paper proposes a suboptimal achievability scheme in which the Wyner-Ziv compress-and-forward relaying technique is employed on a per-base-station basis, but successive interference cancellation (SIC) is used at the central processor to mitigate multicell interference. This results in an achievable rate region that is easily computable, in contrast to the joint processing schemes in which the rate regions can only be characterized by exponential number of rate constraints. Under the per-base-station SIC framework, this paper further studies the impact of the limited-capacity backhaul links on the achievable rates and establishes that in order to achieve to within constant number of bits to the maximal SIC rate with infinite-capacity backhaul, the backhaul capacity must scale logarithmically with the signal-to-interference-and-noise ratio (SINR) at each base-station. Finally, this paper studies the optimal backhaul rate allocation problem for an uplink multicell joint processing model with a total backhaul capacity constraint. The analysis reveals that the optimal strategy that maximizes the overall sum rate should also scale with the log of the SINR at each base-station.Comment: JSAC Oct 2013, special issue on VMIM