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<jats:p>We propose a renormalization group (RG) theory of eigen microstates, which are introduced in the statistical ensemble composed of microstates obtained from experiments or computer simulations. A microstate in the ensemble can be considered as a linear superposition of eigen microstates with probability amplitudes equal to their eigenvalues. Under the renormalization of a factor <jats:italic>b</jats:italic>, the largest eigenvalue <jats:italic>σ</jats:italic> <jats:sub>1</jats:sub> has two trivial fixed points at low and high temperature limits and a critical fixed point with the RG relation <jats:inline-formula> <jats:tex-math> <?CDATA ${\sigma }_{1}^{b}={b}^{\beta /\nu }{\sigma }_{1}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>σ</mml:mi> <mml:mn>1</mml:mn> <mml:mi>b</mml:mi> </mml:msubsup> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>b</mml:mi> <mml:mrow> <mml:mi>β</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ν</mml:mi> </mml:mrow> </mml:msup> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpl_39_8_080503_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>, where <jats:italic>β</jats:italic> and <jats:italic>ν</jats:italic> are the critical exponents of order parameter and correlation length, respectively. With the Ising model in different dimensions, it has been demonstrated that the RG theory of eigen microstates is able to identify the critical point and to predict critical exponents and the universality class. Our theory can be used in research of critical phenomena both in equilibrium and non-equilibrium systems without considering the Hamiltonian, which is the foundation of Wilson’s RG theory and is absent for most complex systems.</jats:p>

<jats:p>NIM-Sr2 optical lattice clock has been developed on the Changping campus of National Institute of Metrology (NIM). Considering the limitations in NIM-Sr1, several improved parts have been designed including a differential pumping stage in the vacuum system, a permanent magnet Zeeman slower, water-cooled anti-Helmholtz coils, an extended viewport for Zeeman slower, etc. A clock laser with a short-time stability better than 3 × 10<jats:sup>−16</jats:sup> is realized based on a self-designed 30-cm-long ultra-low expansion cavity. The systematic frequency shift has been evaluated to an uncertainty of 7.2 × 10<jats:sup>−18</jats:sup>, with the uncertainty of BBR shift and the collisional frequency shift being an order of magnitude lower than the last evaluation of NIM-Sr1.</jats:p>

<jats:p>The atom-atom-anion three-body recombination (TBR) and collision induced dissociation (CID) processes of the <jats:sup>3</jats:sup>He–<jats:sup>3</jats:sup>He–T<jats:sup>−</jats:sup> system at ultracold temperatures are investigated by solving the Schrödinger equation in the adiabatic hyperspherical representation. The variations of the TBR and CID rates with the collision energies in the ultracold temperatures are obtained. It is found that the <jats:italic>J<jats:sup>Π</jats:sup> </jats:italic> = 1<jats:sup>−</jats:sup> symmetry dominates the TBR and CID processes in most of the considered collision energy range. The rate of TBR (CID) into (from) the <jats:italic>l</jats:italic> = 1 anion is larger than those for the <jats:italic>l</jats:italic> = 0 and <jats:italic>l</jats:italic> = 2 anions, with the <jats:italic>l</jats:italic> representing the rotational quantum number of <jats:sup>3</jats:sup>HeT<jats:sup>−</jats:sup>. This can be understood via the nonadiabatic couplings among the different channels.</jats:p>

<jats:p>Dual-species single-atom array in optical tweezers has several advantages over the single-species atom array as a platform for quantum computing and quantum simulation. Thus, creating the defect-free dual-species single-atom array with atom numbers over hundreds is essential. As recent experiments demonstrated, one of the main difficulties lies in designing an efficient algorithm to rearrange the stochastically loaded dual-species atoms arrays into arbitrary demanded configurations. We propose a heuristic connectivity optimization algorithm to provide the near-fewest number of atom moves. Our algorithm introduces the concept of using articulation points in an undirected graph to optimize connectivity as a critical consideration for arranging the atom moving paths. Tested in array size of hundreds atoms and various configurations, our algorithm shows a high success rate (&gt;97%), low extra atom moves ratio, good scalability, and flexibility. Furthermore, we propose a complementary step to solve the problem of atom loss during the rearrangement.</jats:p>

<jats:p>Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments. Recently, with the discovery of various higher-order topological insulators, such spectral topological characteristics are extended from edge states to corner states. However, the chiral symmetry protecting the corner states is often broken in genuine materials, leading to vulnerable corner states even when the higher-order topological numbers remain quantized and invariant. Here, we show that a local artificial gauge flux can serve as a robust probe of the Wannier type higher-order topological insulators, which is effective even when the chiral symmetry is broken. The resultant observable signature is the emergence of the cyclic spectral flows traversing one or multiple band gaps. These spectral flows are associated with the local modes bound to the artificial gauge flux. This phenomenon is essentially due to the cyclic transformation of the Wannier orbitals when the local gauge flux acts on them. We extend topological Wannier cycles to systems with <jats:italic>C</jats:italic> <jats:sub>2</jats:sub> and <jats:italic>C</jats:italic> <jats:sub>3</jats:sub> symmetries and show that they can probe both the bulk and the edge Wannier centers, yielding rich topological phenomena.</jats:p>

<jats:p>Metal-pentazolate compounds as candidates for novel high-energy-density materials have attracted extensive attention in recent years. However, dehydrated pentazolate salts of transition metal iron are rarely reported. We predict two new iron pentazolate salts <jats:italic>Fdd</jats:italic>2-FeN<jats:sub>10</jats:sub> and <jats:inline-formula> <jats:tex-math> <?CDATA $P\bar{1}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mover accent="true"> <mml:mn>1</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpl_39_8_087101_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>(No.1)-FeN<jats:sub>10</jats:sub> using a constrained crystal search method based on first-principles calculations. We propose that the stable <jats:italic>Fdd</jats:italic>2-FeN<jats:sub>10</jats:sub> crystal may be synthesized from FeN and N<jats:sub>2</jats:sub> above 20 GPa, and its formation enthalpy is lower than the reported iron pentazolate salt (marked as <jats:inline-formula> <jats:tex-math> <?CDATA $P\bar{1}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mover accent="true"> <mml:mn>1</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpl_39_8_087101_ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>(No.2)-FeN<jats:sub>10</jats:sub>). Crystal <jats:inline-formula> <jats:tex-math> <?CDATA $P\bar{1}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mover accent="true"> <mml:mn>1</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpl_39_8_087101_ieqn3.gif" xlink:type="simple" /> </jats:inline-formula>(No.1)-FeN<jats:sub>10</jats:sub> is composed of iron bispentazole molecules. Formation enthalpy, phonon spectrum and <jats:italic>ab initio</jats:italic> molecular dynamics calculations are performed to show their thermodynamic, mechanical and dynamic properties. Moreover, the high energy density (3.709 kJ/g, 6.349 kJ/g) and good explosive performance indicate their potential applications as high-energy-density materials.</jats:p>

<jats:p>This work reveals the giant influence of spatial distribution of disordered surface roughness on electron tunneling, which is of immediate relevance to the magneto tunnel device and imaging technologies. We calculate the spin-dependent tunneling in Fe/vacuum/Fe junction with disordered surface roughness with the first-principles non-equilibrium dynamical cluster theory. It is found that, at high concentration of surface roughness, different spatial distributions, including the clustered, anti-clustered and completely random roughness characterized by Warren–Cowley parameters, present large deviations from each other in all spin channels. By changing from clustered to anti-clustered roughness, it is surprising that spin polarization of tunneling in parallel configuration (PC) can be drastically reversed from –0.52 to 0.93, while complete randomness almost eliminates the polarization. It is found that the anti-clustered roughness can dramatically quench the tunneling of minority spin in both PC and anti-PC by orders of magnitude, but significantly enhance the transmission of majority spin in PC (by as large as 40%) compared to the results of clustered roughness, presenting distinct influences of differently correlated surface roughness. The spatial correlation of disordered surface roughness can significantly modify the surface resonance of Fe minority spin.</jats:p>

<jats:p>We report the detailed physical properties of YRu<jats:sub>3</jats:sub>Si<jats:sub>2</jats:sub> with the Ru kagome lattice at normal and superconducting states. The results of resistivity and magnetization show that YRu<jats:sub>3</jats:sub>Si<jats:sub>2</jats:sub> is a type-II bulk superconductor with <jats:italic>T</jats:italic> <jats:sub>c</jats:sub> ∼ 3.0 K. The specific heat measurement further suggests that this superconductivity could originate from the weak or moderate electron-phonon coupling. On the other hand, both large Kadawaki–Woods ratio and Wilson ratio indicate that there is a strong electron correlation effect in this system, which may have a connection with the featured flat band of kagome lattice.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Strontium titanate (SrTiO<jats:sub>3</jats:sub>) is a typical perovskite-type ceramic oxide and studying its high-pressure phases are critical to understand the ferroelastic phase transition. SrTiO<jats:sub>3</jats:sub> also can be used as an important analog of davemaoite (CaSiO<jats:sub>3</jats:sub>) to understand the compositional and velocity structure of the Earth’s interior. However, the high-pressure studies on the phase transition pressure and elastic properties from cubic to tetragonal remains unclear for SrTiO<jats:sub>3</jats:sub>. Here, we investigated the phase transition and elasticity of single-crystal SrTiO<jats:sub>3</jats:sub> by Raman and Brillouin scattering combined with diamond anvil cell (DAC). The acoustic velocities of single-crystal SrTiO<jats:sub>3</jats:sub> and the independent elastic constants of cubic and tetragonal SrTiO<jats:sub>3</jats:sub> are determined up to 27.5 GPa at room temperature. This study indicates that <jats:italic>C</jats:italic> <jats:sub>11</jats:sub>, <jats:italic>C</jats:italic> <jats:sub>12</jats:sub> and <jats:italic>C</jats:italic> <jats:sub>44</jats:sub> exhibit abnormal changes at 10.3 GPa which is related to the phase transition from cubic to tetragonal. Interestingly, a significant softening on shear modulus and a large anisotropy of shear wave splitting (<jats:italic>A</jats:italic> <jats:sub>S</jats:sub> <jats:sup>PO</jats:sup>) jump are observed at 10.3 GPa. Using obtained elastic constants, the coefficients of the Landau potential are calculated to understand the phase transition between cubic and tetragonal. The calculated coefficients of the Landau potential are, <jats:italic>λ</jats:italic> <jats:sub>2</jats:sub> = 3.12×10<jats:sup>-2</jats:sup> GPa, <jats:italic>λ</jats:italic> <jats:sub>4</jats:sub> = -2.02×10<jats:sup>-2</jats:sup> GPa, <jats:italic>B</jats:italic>* = 1.34×10<jats:sup>-4</jats:sup> GPa and <jats:italic>B</jats:italic> = 1.66×10<jats:sup>-4</jats:sup> GPa. The elastic results have profound implications in understanding the structure of the Earth’s interior and indicate that the presence of tetragonal Ti-bearing CaSiO<jats:sub>3</jats:sub> helps to explain the large <jats:italic>A</jats:italic> <jats:sub>S</jats:sub> <jats:sup>PO</jats:sup> of the Earth’s mid-mantle.</jats:p>

<jats:p>We predict a new physical phenomenon, induced fission-like process and chain reaction of hadronic molecular states. As a molecular state, if induced by a <jats:italic>D</jats:italic> meson, the <jats:italic>X</jats:italic>(3872) can split into <jats:inline-formula> <jats:tex-math> <?CDATA $D\bar{D}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mover accent="true"> <mml:mi>D</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpl_39_9_091401_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> final state which is forbidden due to the spin-parity conservation. The breeding of the <jats:italic>D</jats:italic> meson of the reaction, such as <jats:inline-formula> <jats:tex-math> <?CDATA ${D}^{0}X(3872)\to {D}^{0}{\bar{D}}^{0}{D}^{0}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mi>X</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>3872</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:msup> <mml:mover accent="true"> <mml:mi>D</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> <mml:mn>0</mml:mn> </mml:msup> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpl_39_9_091401_ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>, makes the chain reaction of <jats:italic>X</jats:italic>(3872) matter possible. We estimate the cross section of the <jats:italic>D</jats:italic> meson induced fission-like process of <jats:italic>X</jats:italic>(3872) into two <jats:italic>D</jats:italic> mesons. With very small <jats:italic>D</jats:italic> <jats:sup>0</jats:sup> beam momentum of 1 eV, the total cross section reaches an order of 1000 b, and decreases rapidly with the increasing beam momentum. With the transition of <jats:italic>D</jats:italic>* meson in molecular states to a <jats:italic>D</jats:italic> meson, the <jats:italic>X</jats:italic>(3872) can release large energy, which is acquired by the final mesons. The momentum distributions of the final <jats:italic>D</jats:italic> mesons are analyzed. In the laboratory frame, the spectator <jats:italic>D</jats:italic> meson in molecular state concentrates in the low momentum area. The energy from the transition from <jats:italic>D</jats:italic>* to <jats:italic>D</jats:italic> meson is mainly acquired by two scattered <jats:italic>D</jats:italic> mesons. The results suggest that the <jats:italic>D</jats:italic> meson environment will lead to the induced fission-like process and chain reaction of the <jats:italic>X</jats:italic>(3827). Such a phenomenon can be extended to other hadronic molecular states.</jats:p>