We present the results of an experiment on measuring the gradient of the Casimir force between an Au-coated hollow glass microsphere and graphene-coated fused silica plate by means of a modified atomic force microscope cantilever based technique oper
ated in the dynamic regime. These measurements were performed in high vacuum at room temperature. The energy gap and the concentration of impurities in the graphene sample used have been measured utilizing scanning tunnelling spectroscopy and Raman spectroscopy, respectively. The measurement results for the gradients of the Casimir force are found to be in a very good agreement with theory using the polarization tensor of graphene at nonzero temperature depending on the energy gap and chemical potential with no fitting parameters. The theoretical predictions of the same theory at zero temperature are experimentally excluded over the measurement region from 250 to 517 nm. We have also investigated a dependence of the thermal correction to the Casimir force gradient on the values of the energy gap, chemical potential, and on the presence of a substrate supporting the graphene sheet. It is shown that the observed thermal effect is consistent in size with that arising for pristine graphene sheets if the impact of real conditions such as nonzero values of the energy gap, chemical potential, and the presence of a substrate is included. Implications of the obtained results to the resolution of the long-standing problems in Casimir physics are discussed. In addition to the paper published previously [M. Liu {it et al}., Phys. Rev. Lett. {bf 126}, 206802 (2021)], we present measurement results for the energy gap of the graphene sample, double the experimental data for the Casimir force, and perform a more complete theoretical analysis.
We quantify evolution in the cluster scale stellar mass - halo mass (SMHM) relations parameters using 2323 clusters and brightest central galaxies (BCGs) over the redshift range $0.03 le z le 0.60$. The precision on inferred SMHM parameters is improv
ed by including the magnitude gap ($rm m_{gap}$) between the BCG and fourth brightest cluster member (M14) as a third parameter in the SMHM relation. At fixed halo mass, accounting for $rm m_{gap}$, through a stretch parameter, reduces the SMHM relations intrinsic scatter. To explore this redshift range, we use clusters, BCGs, and cluster members identified using the Sloan Digital Sky Survey C4 and redMaPPer cluster catalogs and the Dark Energy Survey redMaPPer catalog. Through this joint analysis, we detect no systematic differences in BCG stellar mass, $rm m_{gap}$, and cluster mass (inferred from richness) between the datsets. We utilize the Pareto function to quantify each parameters evolution. We confirm prior findings of negative evolution in the SMHM relations slope (3.5$sigma$) and detect negative evolution in the stretch parameter (4.0$sigma$) and positive evolution in the offset parameter (5.8$sigma$). This observed evolution, combined with the absence of BCG growth, when stellar mass is measured within 50kpc, suggests that this evolution results from changes in the clusters $rm m_{gap}$. For this to occur, late-term growth must be in the intra-cluster light surrounding the BCG. We also compare the observed results to Illustris TNG 300-1 cosmological hydrodynamic simulations and find modest qualitative agreement. However, the simulations lack the evolutionary features detected in the real data.
To explore correlated electrons in the presence of local and non-local disorder, the Blackman-Esterling-Berk method for averaging over off-diagonal disorder is implemented into dynamical mean-field theory using tensor notation. The impurity model com
bining disorder and correlations is solved using the recently developed fork tensor-product state solver, which allows one to calculate the single particle spectral functions on the real-frequency axis. In the absence of off-diagonal hopping, we establish exact bounds of the spectral function of the non-interacting Bethe lattice with coordination number $Z$. In the presence of interaction, the Mott insulating paramagnetic phase of the one-band Hubbard model is computed at zero temperature in alloys with site- and off-diagonal disorder. When the Hubbard $U$ parameter is increased, transitions from an alloy band-insulator through a correlated metal into a Mott insulating phase are found to take place.
We prove that it is possible for nonconvex low-rank matrix recovery to contain no spurious local minima when the rank of the unknown ground truth $r^{star}<r$ is strictly less than the search rank $r$, and yet for the claim to be false when $r^{star}
=r$. Under the restricted isometry property (RIP), we prove, for the general overparameterized regime with $r^{star}le r$, that an RIP constant of $delta<1/(1+sqrt{r^{star}/r})$ is sufficient for the inexistence of spurious local minima, and that $delta<1/(1+1/sqrt{r-r^{star}+1})$ is necessary due to existence of counterexamples. Without an explicit control over $r^{star}le r$, an RIP constant of $delta<1/2$ is both necessary and sufficient for the exact recovery of a rank-$r$ ground truth. But if the ground truth is known a priori to have $r^{star}=1$, then the sharp RIP threshold for exact recovery is improved to $delta<1/(1+1/sqrt{r})$.
Possible bound nuclei beyond the two-neutron drip line in the $50leqslant Z leqslant 70$ region are investigated by using the deformed relativistic Hartree-Bogoliubov theory in continuum with density functional PC-PK1. Bound nuclei beyond the drip li
nes of $_{56}$Ba, $_{58}$Ce, $_{62}$Sm, $_{64}$Gd and $_{66}$Dy are predicted, forming peninsulas of stability in nuclear landscape. Near these peninsulas, several multi-neutron emitters are predicted. The underlying mechanism of the peninsulas of stability is investigated by studying the total energy, Fermi surface, quadrupole deformation and the single-neutron spectrum in the canonical basis. It is found that the deformation effect is crucial for forming the peninsulas of stability, and pairing correlations are also essential in specific cases. The dependence on the deformation evolution is also discussed. The decay rates of multi-neutron radioactivity in Ba and Sm isotopic chains are estimated by using the direct decay model.
Non-negative matrix and tensor factorisations are a classical tool for finding low-dimensional representations of high-dimensional datasets. In applications such as imaging, datasets can be regarded as distributions supported on a space with metric s
tructure. In such a setting, a loss function based on the Wasserstein distance of optimal transportation theory is a natural choice since it incorporates the underlying geometry of the data. We introduce a general mathematical framework for computing non-negative factorisations of both matrices and tensors with respect to an optimal transport loss. We derive an efficient computational method for its solution using a convex dual formulation, and demonstrate the applicability of this approach with several numerical illustrations with both matrix and tensor-valued data.
Motivated by its potential use in constraining the structure of 6D renormalization group flows, we determine the low energy dilaton-axion effective field theory of conformal and global symmetry breaking in 6D conformal field theories (CFTs). While ou
r analysis is largely independent of supersymmetry, we also investigate the case of 6D superconformal field theories (SCFTs), where we use the effective action to present a streamlined proof of the 6D a-theorem for tensor branch flows, as well as to constrain properties of Higgs branch and mixed branch flows. An analysis of Higgs branch flows in some examples leads us to conjecture that in 6D SCFTs, an interacting dilaton effective theory may be possible even when certain 4-dilaton 4-derivative interaction terms vanish, because of large momentum modifications to 4-point dilaton scattering amplitudes. This possibility is due to the fact that in all known $D > 4$ CFTs, the approach to a conformal fixed point involves effective strings which are becoming tensionless.
Above-threshold ionization spectra from cesium are measured as a function of the carrier-envelope phase (CEP) using laser pulses centered at 3.1 $mu$m wavelength. The directional asymmetry in the energy spectra of backscattered electrons oscillates t
hree times, rather than once, as the CEP is changed from $0$ to $2pi$. Using the improved strong-field approximation, we show that the unusual behavior arises from the interference of few quantum orbits. We discuss the conditions for observing the high-order CEP dependence, and draw an analogy with time-domain holography with electron wave packets.
We consider the problem of ranking $n$ players from partial pairwise comparison data under the Bradley-Terry-Luce model. For the first time in the literature, the minimax rate of this ranking problem is derived with respect to the Kendalls tau distan
ce that measures the difference between two rank vectors by counting the number of
A new $alpha$-emitting isotope $^{214}$U, produced by fusion-evaporation reaction $^{182}$W($^{36}$Ar, 4n)$^{214}$U, was identified by employing the gas-filled recoil separator SHANS and recoil-$alpha$ correlation technique. More precise $alpha$-deca
y properties of even-even nuclei $^{216,218}$U were also measured in reactions of $^{40}$Ar, $^{40}$Ca with $^{180, 182, 184}$W targets. By combining the experimental data, improved $alpha$-decay reduced widths $delta^2$ for the even-even Po--Pu nuclei in the vicinity of magic neutron number $N=126$ were deduced. Their systematic trends are discussed in terms of $N_{p}N_{n}$ scheme in order to study the influence of proton-neutron interaction on $alpha$ decay in this region of nuclei. It is strikingly found that the reduced widths of $^{214,216}$U are significantly enhanced by a factor of two as compared with the $N_{p}N_{n}$ systematics for the $84 leq Z leq 90$ and $N<126$ even-even nuclei. The abnormal enhancement is interpreted by the strong monopole interaction between the valence protons and neutrons occupying the $pi 1f_{7/2}$ and $ u 1f_{5/2}$ spin-orbit partner orbits, which is supported by a large-scale shell model calculation.
