Collective atomic recoil motion in short-pulse multi-matter-optical wave mixing

An analytical perturbation theory of short-pulse, matter-wave superradiant scatterings is presented. We show that Bragg resonant enhancement is incapacitated and both positive and negative order scatterings contribute equally. We further show that propagation gain is small and scattering events primarily occur at the end of the condensate where the generated field has maximum strength, thereby explaining the apparent ``asymmetry" in the scattered components with respect to the condensate center. In addition, the generated field travels near the speed of light in a vacuum, resulting in significant spontaneous emission when the one-photon detuning is not sufficiently large. Finally, we show that when the excitation rate increases, the generated-field front-edge-steepening and peak forward-shifting effects are due to depletion of the ground state matter wave.Comment: This manuscript was submitted for publication in Nov., 200

Single-cluster dynamics for the random-cluster model

We formulate a single-cluster Monte Carlo algorithm for the simulation of the random-cluster model. This algorithm is a generalization of the Wolff single-cluster method for the $q$-state Potts model to non-integer values $q>1$. Its results for static quantities are in a satisfactory agreement with those of the existing Swendsen-Wang-Chayes-Machta (SWCM) algorithm, which involves a full cluster decomposition of random-cluster configurations. We explore the critical dynamics of this algorithm for several two-dimensional Potts and random-cluster models. For integer $q$, the single-cluster algorithm can be reduced to the Wolff algorithm, for which case we find that the autocorrelation functions decay almost purely exponentially, with dynamic exponents $z_{\rm exp} =0.07 (1), 0.521 (7)$, and $1.007 (9)$ for $q=2, 3$, and 4 respectively. For non-integer $q$, the dynamical behavior of the single-cluster algorithm appears to be very dissimilar to that of the SWCM algorithm. For large critical systems, the autocorrelation function displays a range of power-law behavior as a function of time. The dynamic exponents are relatively large. We provide an explanation for this peculiar dynamic behavior.Comment: 7 figures, 4 table

Computing the Least-core and Nucleolus for Threshold Cardinality Matching Games

Cooperative games provide a framework for fair and stable profit allocation in multi-agent systems. \emph{Core}, \emph{least-core} and \emph{nucleolus} are such solution concepts that characterize stability of cooperation. In this paper, we study the algorithmic issues on the least-core and nucleolus of threshold cardinality matching games (TCMG). A TCMG is defined on a graph $G=(V,E)$ and a threshold $T$, in which the player set is $V$ and the profit of a coalition $S\subseteq V$ is 1 if the size of a maximum matching in $G[S]$ meets or exceeds $T$, and 0 otherwise. We first show that for a TCMG, the problems of computing least-core value, finding and verifying least-core payoff are all polynomial time solvable. We also provide a general characterization of the least core for a large class of TCMG. Next, based on Gallai-Edmonds Decomposition in matching theory, we give a concise formulation of the nucleolus for a typical case of TCMG which the threshold $T$ equals $1$. When the threshold $T$ is relevant to the input size, we prove that the nucleolus can be obtained in polynomial time in bipartite graphs and graphs with a perfect matching

Probing the Melting of a Two-dimensional Quantum Wigner Crystal via its Screening Efficiency

One of the most fundamental and yet elusive collective phases of an interacting electron system is the quantum Wigner crystal (WC), an ordered array of electrons expected to form when the electrons' Coulomb repulsion energy eclipses their kinetic (Fermi) energy. In low-disorder, two-dimensional (2D) electron systems, the quantum WC is known to be favored at very low temperatures ($T$) and small Landau level filling factors ($\nu$), near the termination of the fractional quantum Hall states. This WC phase exhibits an insulating behavior, reflecting its pinning by the small but finite disorder potential. An experimental determination of a $T$ vs $\nu$ phase diagram for the melting of the WC, however, has proved to be challenging. Here we use capacitance measurements to probe the 2D WC through its effective screening as a function of $T$ and $\nu$. We find that, as expected, the screening efficiency of the pinned WC is very poor at very low $T$ and improves at higher $T$ once the WC melts. Surprisingly, however, rather than monotonically changing with increasing $T$, the screening efficiency shows a well-defined maximum at a $T$ which is close to the previously-reported melting temperature of the WC. Our experimental results suggest a new method to map out a $T$ vs $\nu$ phase diagram of the magnetic-field-induced WC precisely.Comment: The formal version is published on Phys. Rev. Lett. 122, 116601 (2019